PFC/RR-81-24
DOE/ET/51013-21
UC 20 b, d, f
Conceptual Design of a Bitter Magnet
Toroidal Field System for the
ZEPHYR Ignition Test Reactor
J.E.C. Williams
H.D. Becker
E.S. Bobrov
L. Bromberg
D.R. Cohn
J.M. Davin
E. Erez
May 1981
TABLE OF CONTENTS
Page
1.0
Introduction
2.0
Parametric Study
3.0
5.0
10
2.1
Basic Relationships
10
2.2
Results
19
Configuration of the Bitter Plate Toroidal Field Coil
23
3.1
General Arrangement
3.2
Standard Turns
32
3.3
Flanges
35
3.4
4.0
1
3.3.1
Diagnostic Flange
35
3.3.2
Closure Flange
38
41
Structural Integrity
3.4.1
In-Plane Forces
41
3.4.2
Overturning Forces
42
3.4.3
Assembly
42
3.4.4
Girth Rings
43
46
Toroidal Field Ripple
4.1
Ripple Due to the Magnet Flanges
46
4.2
Neutral Beam Port Ripple
47
Effects of Magnetic and Thermal Diffusion and Neutron Heating
57
in the TF Coil
6.0
5.1
Heating Effects
57
5.2
Cooling
68
Structural Analysis of the Bitter Plate TF Magnet
74
6.1
Introduction
74
6.2
Single-Plate Axisymmetric Model of the TF Magnet
76
6.2.1
General Characteristics of the Model
76
6.2.2
Stress and Displacements Due to the TF Field
82
1
TABLE OF CONTENTS (Cont.)
Page
6.2.3
6.3
Stresses and Displacements Due to Precompression
97
A 22.5* Wedge FE Model of the TF Magnet With the Neutral
102
Beam Ports
6.4
6.3.1
Description of the Model
102
6.3.2
Discussion of the Results of the Analysis
113
6.3.3
Conclusions
156
Finite Difference Analysis of Torsional Stresses Due
160
to Poloidal Field
7.0
6.4.1
Differential Equation
160
6.4.2
Finite Difference Solution
163
167
Structures Engineering
7.1
Summary
167
7.2
Introduction
167
7.3
7.4
7.5
7.2.1
Basic Design Philosophy
167
7.2.2
Scope of Structures Engineering Activity
168
7.2.3
General Structural Requirements of Magnet
169
Structural Design Requirements
170
7.3.1
Purpose of Structural Components
170
7.3.2
Specific Structural Requirements
171
7.3.3
Design Constraints
172
7.3.4
Structural Function of TF Coil
173
7.3.5
Shear Load Transfer in Plates
173
Material Strength Requirements
174
7.4.1
Basic Considerations
174
7.4.2
Steel/Copper Composite
175
7.4.3
Insulator
178
Toroidal-Field Induced Stresses in TF Coil
7.5.1
178
178
Introduction
ii
TABLE OF CONTENTS (Cont.)
Page
7.5.2
General Character of Stresses
180
7.5.3
Lorentz Plus Precompression
182
7.5.4
Effect of Thinned Insulation
182
7.5.5
Thermal Stresses
186
7.5.5.1
Introduction
186
7.5.5.2
Slow Cooling From RT
188
7.5.5.3
Differential Expansion From PulsEed
188
Heating
7.5.6
7.6
7.7
7.5.5.4
Pulsed-Induced Toyroidal Gradient
189
7.5.5.5
Normal Gradient
192
7.5.5.6
Total Thermal Str(esses
192
194
Total Stresses
Torsional Stresses in TF Coil
195
7.6.1
Introduction
195
7.6.2
Analysis
195
7.6.3
Results
197
7.6.4
Shear Between Ports
198
7.6.5
Throat Lateral Bending
202
203
Poloidal Field.Coil
7.7.1
203
Introduction
203
7.7.2 Analysis
7.8
Materials Investigations
204
7.8.1
Introduction
204
7.8.2
Literature Survey
205
7.8.3
Insulator Testing Program
211
7.8.3.1
Introduction
211
7.8.3.2
Rationale
213
7.8.3.3
Failure Criterion
214
7.8.3.4
Initial Tests
215
iii
TABLE OF CONTENTS (Cont.)
Page
7.8.4
7.8.3.5
INEL Tests on Irradiated Specimens
219
7.8.3.6
MIT Tests
222
7.8.3.7
Friction Tests
227
7.8.3.8
Conclusions
227
7.8.3.9
Future Testing
227
Metal Composites Program
7.8.4.1
Introduction
228
7.8.4.2
Bare Copper
228
7.8.4.3
Copper/Steel Composite Tests
228
7.8.4.4. Selection of Joining Method
7.9
8.0
228
234
235
Areas for Further Study
238
Component Fabrication
8.1
General
238
8.2
Component Fabrication
238
8.2.1
Throat Composite
238
8.2.2
Copper Plate
240
8.2.3
Wedge Reinforcement
241
8.2.4
Insulators
'242
iv
LIST OF FIGURES
page
Figure 2.1
Value of n T
at ignition as a function of
Central pi9sm9 temperature To. Parabolic
density and temperature profiles are assumed.
Complete alpha particle confinement is
assumed.
11
Figure 2.2
Beam energy
for sharply
peaked (X/a
compression
the neutral
Figure 2.3
Number of cycles to failure for cold worked oxygen
free high conductivity at room temperature.
17
Figure 2.4
Tensile strength normalized to tensile strength at
room temperature, as a function of temperature, for
18
required to heat a plasma to ignition
peaked (X/a = 0.33) and moderately
= 0.25) profiles as a function of
ratio. A is the mean free path of
beam. To = 15 KeV, Zeff = 1.
14
60% cold worked oxygen free copper. (Taken from:
A. Reed and B. Mikesell, Designation B 170, Annual
Book of ASTM Standards, Part 6).
Figure 3-1
Magnet system assembly plan view
24
Figure 3-2
Magnet system assembly vertical section
25
Figure 3-3
TF magnet module plan view
26
Figure 3-4
TF magnet module end view development
28
Figure 3-5
Diagnostic flange
29
Figure 3-6
TF magnet diagnostic viewing areas
30
Figure 3-7
Closure flange and adjacent conductor
31
Figure 3-8
Turn dimensions
33
Figure 3-9
Standard turn
34
Figure 3-10
Diagnostic flange plate dimensions
36
Figure 3-11
Modified turn
37
Figure 3-12
Transition turn
39
Figure 3-13
Closure flange plate dimensions
40
Figure 3-14
TF magnet module horizontal midplane section
44
Figure 4.1
Contours of constant toroidal field percent ripple
48
in a cross-section of the precompressed plasma due
to the flanges. It is calculated in the plane of a
diagnostic flange.
v
LIST OF FIGURES
(continued)
page
Figure 4.2
Contours of constant toroidal field percent
ripple in the cross-section of the compressed
plasma due to the flanges. It is calculated.in
the plane of a diagnostic flange.
49.
Figure 4.3
Contours of constant flange-induced ripple on
the equatorial midplane. $ = 0 corresponds to a
diagnostic flange. R _ .7 corresponds to the inner
edge of the compressed plasma, and R , 2.6
corresponds to the outer edge of the precompressed
plasma.
50
Figure 4.4
Contours of maximum constant toroidal field ripple
in the precompressed plasma due to the port.
52
Figure 4.5
Contours of constant toroidal field ripple at the
midplane of the precompressed plasma.
53
Figure 4.6
Equatorial midplane ripple at $ = 0 (Diagnostic
Flange) as a function of major radius
54
Figure 5.1
Toroidal geometry approximation for the throat
of TF coil.
58
Figure 5.2
Temperature profile in 0K at t = 7 s
62
Figure 5.3
Temperature profile in OK at t = 13.5 s with
nuclear heating.
63
Figure 5.4
Temperature profile in OK at t = 20.5 s with
nuclear heating.
64
Figure 5.5
Temperature profile in 0 K at t = 13.5 s with
65
nuclear heating
Figure 5.6
Temperature profile in 0K at t = 13.5 s without
nuclear heating.
66
Figure 5.7
Temperature profile in 0K at t = 20.5 s without
67
nuclear heating.
Figure 5.8
ContoM rs of constant current density, in 10 7
amp/me for t = 13.5 s with nuclear heating.
69
Figure 5.9
Contours of constant magnetic field in Tesla for
the case of Figure 5.8.
70
Figure 5.10
Heat transfer rate from copper to liquid nitrogen
71
as a function of temperature difference taken from
NBS Technical Note 317
vi
LIST OF FIGURES
(continued)
page
Figure 5.11
Average temperature in throat of the TF magnet as
a function of time during cooling.
72
Figure 6.1
General view of a laminated Bitter plate considered
in the single-plate analysis.
75
Figure 6.2
Schematic of the 22.50 wedge model with port
77
Figure 6.3
Wedge conductor plate geometry
79
Figure 6.4
Finite element mesh used in the analysis of the
single plate model.
81
Figure 6.5
Distribution of vertical stress az (in MPa) incomplete
83
Figure 6.6
Single-plate FE model. a, stress distribution in
copper due to inplane Lorintz forces.
84
Figure 6.7
Single-plate FE model. Distribution of vertical
stress a7 (in MPa) in steel due to inplane
Lorentz forces.
85
Figure 6.8
Single-plate FE model. Distribution of radial stress
aR (in MPa) in copper due to inplane Lorentz forces.
86
Figure 6.9
Single-plate FE model. aR-stress distribution in
copper due to inplane Lorentz forces.
87
Figure 6.10
Single-plate FE model. Distribution of radial stress
aR (in MPa) in steel due to inplane Lorentz forces.
Figure 6.11
Single-plate FE model. Distribution of circumferential
stress a, (in MPa) due to inplane Lorentz forces.
89
Figure 6.12
Single-plate FE model. a -stress distribution due
to inplane Lorentz forceR.
90
Figure 6.13
Single-plate FE model. Distribution of von Mises
equivalent stress a (in MPa) in copper due to
inplane Lorentz fords (stresses are presented in
91
88
Mpa).
Figure 6.14
Single-plate FE model. a - stress distribution in
copper due to inplane LoY~ntz forces.
92
Figure 6.15
Single-plate FE model. Distribution of von Mises
equivalent stress (in MPa) in steel due to inplane
Lorentz forces.
93
Figure 6.16
Single-plate FE model. Radial displacements (.in mm)
due to inplane Lorentz forces.
94
vii
LIST OF FIGURES
(continued)
page
Figure 6.17
Single-plate FE model. Vertical displacements
(in mm) due to inplane Lorentz forces.
95
Figure 6.18
Single-plate FE model. Distribution of circumferential
stress a, (in MPa) due to precompression.
98
Figure 6.19
Single-plate FE model. Distribution of vertical stress
az (in MPa) in copper due to precompression.
99
Figure 6.20
Single-plate FE model. Distribution of vertical stress
Tz (in MPa) in steel due to precompression.
100
Figure 6.21
Single-plate FE model. Coil nondeformed and
deformed shapes due to precompression from poloidal
coils and Lorentz forces.
101
Figure 6.22
General view of the 22.50 wedge model with dimensions
used in this analysis.
103
Figure 6.23
Three-dimensional Finite Element Model (Isometric View)
With Numeration of Nodal Points
104
Figure 6.24
Three-dimensional Finite Element Model (Isometric View)
with indication of Material Types
105
Figure 6.25
Angular Division of the 22.50 Wedge Model into Finite
Element Sectors (Plan View)
106
Figure 6.26
22.50 wedge FE model.
108
Figure 6.27
Unsymmetric plate cross-section dimensions.
109
Figure 6.28
22.50 wedge FE model. Classification of elements on
the basis of compound material properties.
110
Figure 6.29
22.50 wedge FE model. az stress distribution in compound
material.
114
22.50 wedge model. az stress distribution in compound
115
Figure 6.30
FE mesh in RZ planes.
material.
Figure 6.31
22.50 wedge FE model. az stress distribution in compound
material.
116
Figure 6.32
22.50 wedge FE model. az stress distribution in compound
material.
117
Figure 6.33
22.50 wedge FE model. az stress distribution in compound
material.
118
22.50 wedge FE model. az stress distribution in compound
119
Figure 6.34
material.
viii
LIST OF FIGURES
(continued)
page
Figure 6.35
22.50 wedge FE model.
compound material.
Figure 6.36
22.5P wedge FE model.
compound material.
Figure 6.37
22.50 wedge FE model.
compound material.
Figure 6.38
a
stress distribution in
120
z0stress distribution in
122
0G
stress distribution in
123
22.5 wedge FE model.
compound material.
00
stress distribution in
124
Figure 6.39
22.50 wedge FE model.
compound material.
Ge stress distribution in
125
Figure 6.40
22.50 wedge FE model.
compound material.
a0 stress distribution in
126
Figure 6.41
22.50 wedge FE model.
compound material.
00 stress distribution in
127
Figure 6.42
22.50 wedge FE model. a stress distribution in
compound material.
128
Figure 6.43
22.50 wedge FE model.
compound material.
G
stress distribution in
129
Figure 6.44
22.50 wedge FE model.
compound material.
GR stress distribution in
130
Figure 6.45
22.50 wedge FE model.
compound material.
aR stress distribution in
131
Figure 6.46
22.50 wedge FE model.
compound material.
GR stress distribution in
132
Figure 6.47
22.50 wedge FE model.
compound material.
GR stress distribution i n
133
Figure 6.48
22.50 wedge FE model.
compound material.
T ez
stress distribution in
134
Figure 6.49
22.50 wedge FE model.
compound material.
T Oz
stress distribution in
135
Figure 6.50
22.50 wedge FE model.
compound material.
T ez
stress distribution in
136
Figure 6.51
22.50 wedge FE model.
compound material.
Tez stress distribution in
137
Figure 6.52
22.50 wedge FE model.
compound material.
T8z
stress distribution in
138
ix
LIST OF FIGURES
(continued)
page
Figure 6.53
22.50 wedge FE model. T ez stress distribution
the compound material.
139
Figure 6.54
22.50 wedge FE model.
the compound material.
Tez
stress distribution
141
Figure 6.55
22.50 wedge FE model.
TRe stress distribution
142
the compound material.
Figure 6.56
22.50 wedge FE model. TRe stress distribution
the compound material.
143
Figure 6.57
22.50 wedge FE model. TRe stress distribution
the compound material.
144
Figure 6.58
22.50 wedge FE model. TRe stress distribution
the compound material.
145
22.50 wedge FE model.
TRe stress distribution
146
Figure 6.60
22.50 wedge FE model. TRZ stress distribution
the compound material.
147
Figure 6.61
22.50 wedge FE model. TRZ stress distribution
the compound material.
148
Figure 6.62
22.50 wedge FE model. TRZ stress distribution
the compound material.
149
Figure 6.63
22.50 wedge FE model. TRZ stress distribution
the compound material.
150
Figure 6.64
22.50 wedge FE model. TRZ stress distribution
the compound material.
151
Figure 6.65
22.50 wedge FE model.
152
Figure 6.59
the compound material.
TRZ stress distribution
the compound material.
Figure 6.66
22.50 wedge FE model. Inplane displacements due to
the precompression.
153
Figure 6.67
22.50 wedge FE model. Inplane displacements due to
154
the precompression.
Figure 6.68
22.50 wedge FE model. Inplane displacements due to
Lorentz forces and precompression.
155
Figure 6.69
22.50 wedge FE model.
displacements.
157
x
Superposition in inplane
LIST OF FIGURES
(continued)
page
Figure 6.70
22.50 wedge FE model. Superposition of inplane
displacements of both planes of symmetry of the
model.
158
Figure 7.1
Representative RT fatigue data on unirradiated metals
for ITR.
177
Figure 7.2
Irradiated G-10 compression fatigue test data
179
Figure 7.3
2D and 3D stresses at selected locations
183
Figure 7.4
Couple action induced by thinning of insulation in
184
throat region.
Figure 7.5
Thermal expansion curves for structural materials
187
Figure 7.6
Decomposition of temperature field at end of flat top
190
Figure 7.7
Models used for thermal stress analysis
191
Figure 7.8
Normal gradient in the throat region
193
Figure 7.9
Forces perpendicular to magnet plate carrying current,
I, in vertical field,
Bz
196
Figure 7.10
Shear between ports
199
Figure 7.11
Survivability of irradiated nonmetallics
210
Figure 7.12
Epoxy strength loss as a function of dose level
212
Figure 7.13
Compressive degradation curve from cyclic loading
216
Figure 7.14
Test fixture schematic and loading cycle
217
Figure 7.15
Irradiated G-10 compression fatigue test data
221
Figure 7.16
Copper RT fatigue data, R = 0
229
Figure 7.17
Representative stress-strain curves for rollbonded
copper/stainless composite.
231
xi
List of Tables
Page
Table 1.1
The Principal Parameters of the Toroidal Field System
Table 2.1
Variation of Machine Parameters as a Function of Magnetic
7
22
Field Strength at the Axis of the Compressed Plasma for
the Following Constant Parameters
Table 7.1
Typical Properties of Unirradiated Materials for ITR
176
Table 7.2
Torsional Shears Between Neutral Beam Ports
200
Table 7.3
Fusion Reactor - Insulator Environment
206
Table 7.4
Results of Survey on Irradiated Insulator Data
207
Table 7.5
Results of Compression Fatigue Tests of Unirradiated
Samples at RT
218
Table 7.6
Results of INEL Compression Fatigue Tests on
220
Irradiated Insulators
Table 7.7
Common Resins, Hardeners and Reinforcements
Used in Insulators.
224
Table 7.8
Specimens Irradiated in M.IT. Reactor
225
Table 7.9
Results of M.I.T. Compression Tests on Insulators
226
Fatigue Test Results on Rollbonded Copper-Steel
232
Table 7.10
Composites
Table 7.11
Static and Fatigue Strengths of Explosively Bonded
and Cemented Composites
xii
233
CONCEPTUAL DESIGN OF A BITTER TOROIDAL FIELD SYSTEM
FOR THE ZEPHYR IGNITION TEST REACTOR
1.0
INTRODUCTION
The present studies have been carried out in support of the work
by the Max Planck Institute fi~r Plasma Physik, Garching, on the design of
ZEPHYR, Zund Experiment PHYsiken Reactor.
This Ignition Test Reactor (ITR) is a tokamak device designed to
generate an ignited deuterium-tritium plasma and to maintain the burning
phase for at least 3 seconds.
In the version of the machine considered
here plasma heating is by neutral beams together with adiabatic compression
of the plasma.
The present study examines the conceptual design of a toroidal field
magnet based on the Bitter plate principle.
The concept is an extrapola-
tion of the system used in Alcator A and C but with significant differences
in detail necessitated
by the scale of the machine.
Liquid nitrogen cool-
ing of the TF coil is used to allow a longer pulse than could otherwise
be obtained.
The use of adiabatic compression of the plasma demands a vacuum vessel
extended in the radial direction.
The magnet consequently has an extended
radial span, unlike Alcator, and it is this extended span that gives rise
to particular problems in the structural design, the chief of which is
the large vertical force in the throat of the magnet causing high stress.
-1-
In Alcator A and C the centripetal Lorentz force provides sufficient
lateral (circumferential) pressure over the whole plate for friction to
overcome both the vertical force across conductor discontinuities and the
overturning moment.
In the ITR by contrast the lateral pressure in the
outer regions of the plates generated by the centripetal Lorentz forces
is insufficient to develop the necessary frictional resistance between
plates.
This problem is compounded by the large apertures needed at the
outer periphery of the toroidal field magnet for neutral beam injection,
diagnostic ports and pumping.
The solution chosen for the non-uniform and low lateral pressure is
the use of the main vertical field coils as girth rings.
This provides
the required lateral pressure in the outer regions of the TF plates
throughout the vertical field cycle.
The unit turn of the toroidal field coil is composed of copper,
stainless-steel (high strength and low strength) and G-10.
In the throat,
full hard copper is bonded to high strength stainless-steel and the copper
is tapered.
At the outside the copper turn is split horizontally to pro-
vide the turn-to-turn electrical path, but the vertical force is carried
by the low strength steel.
The insulation between turns is G-10.
All com-
ponents in a turn and all the turns in a sector (450) are bonded by epoxy
during assembly and keys are used to provide additional positive restraint
of the overturning moment.
-2-
The turns of the Bitter toroidal field coil are distorted at the
neutral beam ports.
These distorted plates cause a ripple in the toroi-
dal field which is reduced to acceptable levels by two devices:
(a) The number of neutral beam ports is maximized.
This
induces periodicity in the source of the field dis-
tortion and so reduces the ripple. The maximum practical periodicity is 450 so that eight beam ports are
incorporated into the system, each port being located
at the mid-point of each octant of the magnet. This
periodicity also reduces ripple caused by the vertical diagnostic ports, which are housed in flanges
penetrating to the inside radius of the magnet. However, there are 16 of these flanges, eight for beams
and eight for vessel closure, so that the effect of
periodicity on reducing flange ripple is greater than
on~port ripple.
(b)
The copper conducting paths of the distorted turns are
located close to the walls of the neutral beam lines
so as to compensate for the absence of copper in the
normal positions.
The use of G-10 as interturn insulation is demanded by the need for
adequate shear strength between plates, both for assembly purposes and
overturning resistance.
Because G-10 is substantially organic it has a
limited resistance to irradiation.
Accordingly a program was initiated to
assess the degradation of mechanical and electrical properties of G-10
under irradiation, the neutron and gamma fluence of which matches the
condition prevailing in the throat of the magnet.
The program-includes static
and fatigue testing of samples at room temperature and 77 K before and
after neutron irradiation.
Static and fatigue tests have been performed on copper and coppersteel combinations to determine the life of the magnet, particularly as
dictated by conditions in the throat.
-3-
The vacuum vessel has to be supported against the forces induced
in it by plasma disruption currents.
These far exceed the vacuum forces.
The vessel consists of straight bellows sections interconnected by rigid
sections.
22 1/20.
The rigid sections are supported by the toroidal magnet every
Eight of the rigid sections are joined to the neutral beam
ports and eight are supported by the flanges between magnet octants. The
flow of disruption current in the rigid sections of the vacuum vessel
is
such as to produce torques as well as radial forces.
they must be supported at a number of points.
Consequently,
This support is provided
by the toroidal field magnet through the low strength stainless-steel
wedges in the outer regions of the plates.
These wedges are fully in-
sulated from the copper conducting components of the plates and can thus
support the rigid vessel sections by direct metallic links.
Detailed
consideration of the vacuum vessel is not a part of this study.
The temperature distribution in the toroidal field magnet varies
spatially and in time during the pulse.
Furthermore, the toroidal field
and current penetrates the radial depth of the copper plates with a time
constant of about 1 second.
in the magnet.
These combined effects influence the stresses
Accordingly, codes have been written with which the cur-
rent distribution and stresses can be computed.
A two dimensional finite
element code (ANSYS) is used to calculate stresses in the undistorted
regions of the plates away from the beam ports; the field and current
penetration effects are computed by an integrating code;
a three dimensional FE code is used to compute the stresses in the
whole of an octant with particular attention to concentration around
the neutral beam ports.
-4-
These problems are described and discussed in the following sections,
consisting of:
ii)
Parametric Studies.
These studies examine among other things the interdependence of throat stresses, plasma parameters
(margins of ignition) and stored energy. The latter
is a measure of cost and is minimized in the present
design.
iii)
Magnet Configuration.
The shape of the plates are considered in detail
including standard turns, turns located at beam
ports, diagnostic and closure flanges.
iv)
Ripple Computation.
This section describes the codes by which ripple
is computed.
v) Field Diffusion and Nuclear Heating.
The effect of magnetic field diffusion on heating
is considered along with neutron heating.
Current,
field'and temperature profiles are computed.
Vi)
Finite Element Analysis.
The two and three dimensional finite element codes
are described and the results discussed in detail.
vii)
Structures Engineering.
This considers the calculation of critical stresses
due to toroidal and overturning forces and discusses
the method of constraint of these forces. The Materials Testing Program is also discussed.
viii)
Fabrication.
The methods available for the manufacture of the
constituents parts of the Bitter plates, the method
of assembly and remote maintenance are summarized.
-5-
Table 1.1 below summarizes the characteristics of the system considered
in this report.
During the course of this conceptual design study the machine para-
meters were modified to accommodate changes in the plasma physics assumptions or exigencies of engineering.
these modifications.
Generally the design has incorporated
However, some aspects of analysis reported in this
study are based on original assumptions and have not been updated.
In
particular the finite element analysis is based on a field of 9.33 T
instead of the final modified value of 9.11 T. Other minor discrepancy
exist between the assumptions on which the various sections are based.
Nevertheless, the design is a conceptual entity for a toroidal field coil
for an ignition test reactor and is an appropriate base for a detailed
design study.
-6-
TABLE 1.1
THE PRINCIPLE PARAMETERS OF THE TOROIDAL FIELD SYSTEM
Major radius uncompressed plasma
2.04 m
Major radius compressed plasma
1.36 m
Minor radius compressed plasma
0.5
Field on the compressed plasma axis
9.11 T
Plasma-plate distance compressed plasma
10.5 cm
Plasma-plate distance uncompressed plasma
15
Overall plate dimensions - height
2.43 m
- radial
2.90 m
Plate edge radial position - inside
- outside
m
cm
0.40 m
3.30 m
Throat radial width
0.36 m
Outer limb radial width (standard)
0.49 m
Number of turns
256
Current per turn
242 kA
Diagnostic flange angle
2.630
Closure flange angle
2.630
Neutral beam aperture in TF coil
-7-
0.448 m x 0.80 m
Section 2
List of Symbols
A
-
aspect ratio
a
-
plasma minor radius
Bf
-
value of BT at R = R
BT
-
toroidal magnetic field on axis
C
-
compression ratio
F
cu
-
fraction of C
Ip
-
plasma current
jTF
-
current density in throat of magnet
KT
-
total vertical force from Lorentz-forces
K
-
margin in 3
-
margin of ignition from beam penetration
Mt
-
moment due to toroidal field
Ne
-
central ion density
-
resistive power of magnet at 770 K
q
-
safety factor
R
-
major radius
R
a
-
inner major radius of plasma bore at midplane
Rb
-
outer major radius of plasma bore at midplane
Rf
-
major radius of compressed plasma
R.
-
major radius of precompressed plasma
R
-
outer major radius of magnet
RI
-
inner major radius of magnet
MIbeam
Ptf
in throat
-8-
Section 2
List of Symbols
(continued)
T
-
initial magnet temperature at throat
T
-
post pulse magnet temperature at throat
to
-
central ion temperature
Vol
-
volume of conductor and structure of magnet
Wb
-
beam energy
Wb,eff
-
effective beam energy
Wme
-
stored energy in TF coil
af
-
distance between compressed plasma and TF magnet
a
-
distance between precompressed plasma and magnet
ST
-
ratio of plasma pressure to toroidal field pressure
Cic
-
compressional stresses in throat of TF coil
Goh
-
stresses in 0 - H central solenoid
aTF
-
vertical stress in throat of TF coil
Te
-
electron energy confinement time
Tflat
-
flat-top of TF magnet
Trise
-
rise time and ramp-down time
-9-
2.0
PARAMETRIC STUDY
The parametric study was performed to determine the effect on
various machine parameters of variation in field strength for constant
plasma conditions and constant stress in the magnet.
2.1
Basic Relationships
The plasma performance of an ignition experiment can be expressed in
terms of two margins of safety: the margin of safety for beams and the
margin of safety of beta.
The first margin is defined as
4.6 10 9W
(n T)
MI
beams
=
o e emp,beam pen
(-7n
-(n
.oT e) ign
beff
2.1
(oteT )ig
ign
where Wb,eff is the effective energy of the Do beam
in keV and (no T)
is the particle dens'ity-confinement time product and is shown in Figure 2.1
for parabolic temperature and density profiles.
It has been assumed that
Wb,eff = 9.0 10-15 (n aP)2 C3/ 2 keV
This effective energy level is necessary in order to-obtain peaked
deposition profiles with neutral beams injected in the near perpendicular
direction.
If compression is used, then,
-10-
2.2
~
0.
4.)
SS
0.
'
4-J
S-
-
+j
0
0
4-
4
to
4o
C
0
0
U-
cC
U
4J
4-)
CK)
4-
o
S
toC
CCL
(0
I
t
I
I
I
I
to
0
s
tSEW)
w
I
qtr()
u~i9 0
II2 U)
-11-
N~ -o
to
Wbeff = WbC 3 /2
2.3
where Wb is the actual beam energy and C is the compression ratio.
The margin of safety of beta for constant plasma temperature is defined as
emp, max beta .,22
e(no
(not )ign
~T,crit
beta
T
p
B a2
(I A)4
A2 K
R2 K
where BT is the field on the plasma axis, A is the aspect ratio, a
2.4
is
the plasma minor radius, R is the plasma major radius, K is the margin
in
and (noT demp, max beta is the value of n
t
at the beta limit, as-
sumed to be given by
0.09
A
1
T, crit
for q = 2.5.
MIbeta
g-
2.5
From Equations 2.4 and 2.5, IA ~ 9.106 A in order that
1
I when R
1.3 m at To = 15 keV.
The parameter (IpA) has been
shown to determine the confinement properties of the alpha particles in
the absence of toroidal ripple.
It has been estimated that in order to
confine -'90% of the alpha particles I A ~ 7.5 106 A. This is calculated assuming peaked temperature, density and current profiles in the
absence of toroidal field ripple.
Although somewhat higher values of
MIbeta can be achieved at lower temperatures, MIbeams is substantially
decreased at these temperatures.
-12-
The outer radius of the coil, R0 is determined to first order by
the compression ratio required for MIbeams ~
1. It is shown in Figure
2.2 that for 160 keV beams and moderately peaked beam penetration
C ~ 1.5 for MIbeams
1.
The main stresses in the TF coil are the tensile stresses in the
throat of the TF coil aTF, and the bending stresses in the horizontal
legs of the coil, abend'
Assuming that the tensile stresses in the throat of the TF magnet
are uniform (this is approximately true for the Alcator C tokamak and agrees
with Finite Element calculations (see Sec. 6)) the average (copper and reinforcing) tensile stresses in this region are given approximately by
R3
M
27 T
aTF
-
o
i(R2
3
b
- 2
0
b
-
F
T
2.6
3
Ra
R
R - R3
- R - R2
3 -
(R
- R )
Rb
where FT and MT are respectively the total upward force and the moment
due to the magnetic field and are given by
B R2
FT ~
T
L
OR
R
zn
(-)
a
R
+A
4a
-u-)
R
2 + (1
R
2.7
-))
a
3Ra)
and
rB2 R2 (R
(R
+ (Ra
Ta
+ }()
-
RR)
R
5 (
-
R
R
R
(1
)5 +
a
a
2.8
R
-13-
(D*
Ci
('j
0
Q
S.)
0
0
-
0
0
0
04-J
s
-
o
cj
4-3
c1
.
s-
0 0
0
r
CL
0a)J
0
4-2
a)
0
0
0
0
('1
(ASIt) 'M
-14-
0n
as
r)o.
40
c
0
0
0
ro'
-
0)
0'
I
a
E-~
-
4-
4 D
0- = G
4J
=J
-.
f-
We have assumed that the magnetic field increases linearly in the throat
of the magnet and that the forces generated in the outer limb
of the
magnet are small (the results change by ~ 1% when they are included).
Ra and Rb are given by
Ra = Rf - a
- 6 f,
2.9
Rb = R. + a. + 6.,
2.10
where R. and R are the initial and final major radii of the plasma,
a.
and af are their corresponding minor radii, and 6. and a are the distances
between the plasma edge and the TF coil of the precompressed plasma and
of the compressed plasma.
R0 and R1 are the maximum and minimum radii of
the TF coil,respectively.
The centering forces on the TF coil result in face forces on the individual plates.
The face pressure ac is calculated assuming that the throat
of the magnet behaves as a thick cylinder.
Results from this simple cal-
culation agree roughly with finite element method computation done for
Alcator C.
The maximum bending stresses are determined by calculating the bending moments in the horizontal legs of the magnet and then calculating the
corresponding bending stress using elementary theory of beams.
It is
found that the bending stresses are relatively flat in the region
Rf < R < R .
The height of the magnet that results in a maximum bending
stress of 0.7
x
108 Pa (10
x
10
psi) is then determined.
-15-
The cycling lifetime of the copper in the throat of the magnet is
assumed to depend simply on the tensile stress, aTF.
Thermal and
lateral compressive stresses are ignored.
The temperature dependence of the cycling lifetime has been.estimated by extrapolating data from room temperature, shown in Figure 2.3.
The tensile strength normalized to the tensile strength at room temperature is shown in Figure 2.4 as a function of the temperature of
the copper.
The stored magnetic energy is calculated in two parts; the energy
inside the TF bore and the energy in the TF conductor.
The energy in
the TF bore can be calculated analytically. The energy in the TF conductor is calculated numerically.
This energy contribution depends
on the current distribution in the TF coil, but changes by only 5% as
the current distribution goes from uniform everywhere to ~ r~
throat and uniform elsewhere.
at the
In typical Bitter type magnets, the
energy stored in the conductor region of the TF magnet is ~ 20-30% of
the energy in the bore.
The maximum pulse length is calculated assuming that the limiting
factor is the temperature rise of the TF coil.
rise occurs in the throat of the magnet.
The largest temperature
Assuming that the maximum
allowable temperature before shut-off is 330 0 K then the allowed pulse
length is given approximately by:
flat
< J2 C >
2
TF
8. 108 (A cm 2) 2 s
2
Cu
3Trise
-16-
2
TF
2
Cu - T 'rise
0
0
x
0
0
3
u
(U
o40
C
4-
4- 2
i. )4-
(DdW)S.
SS9S
-17-
'
-~
'
0
0
10
E
-0
,0
o
0
I
I
r.U -~ 4-
-&j)
0
0
en
S0
U)
ra)
S.
4-
C/)
w)
=
<
~ .4-
0
0
0
.-
4-)
to
0
S-.
4-
W)
4C
0
.0
c s +J
0 E
c4J 0
41
-'d
00C
4-
~
~
.)
S0
C-
o
L.
0
0U
4-
t
0
SN0
0
4)*
*,-,-
0
En
4-
-'
4-)
0
c
V)
.
CL
E-=
S-
S
0
0
>
I
I-
0
446UGJIS Oljsuj. pezOIDWJoN
-18-
a)
CU
F)-
C)
41
-
o )
3 .m
where JTF is the current density in the copper and FCu is the percentage
of the volume that is occupied by copper.
In the absence of neutron
heating, the temperature excussion is determined by the parameter
<2>
2
(A/cm2 )2
dt.
For
Tinitial =
770
K, Tf ; 3300 K, <32%>
-
8 x 101
rise is the time necessary for the TF current to reach the
flat top value.
When the plasma achieves ignited operation, the neutrons
contribute to heating of the TF coil.
It has been estimated that this
effect will reduce the flat top of the pulse by 20-40%.
density reduces the pulse length by another -20%.
Nonuniform current
The percentage of copper
in the inboard of the TF coil, FCu, is partially determined by the stresses
in this region, and has been assumed to be 66%.
The resistive power in the TF coil, Ptf' is also calculated.
This is
only an approximate result, and assumes that the TF coil is at 770 K. More
precise calculations are shown in Section 5.
Finally, the volume V
of the conductor and structural material in
the TF coil is calculated.
This is indicative of the cost of the magnet.
2.2
Results
In Table 2.1 the results of the parametric study are shown for plasma-
magnet distance
6
= 0.105 m. In the table, R0 is the outer radius of the
TF coil, Bf is in tesla, Rf and a are in cm, Ip is the plasma current of the
compressed plasma, Wme is the stored energy in the TF coil, Ptf and Pbeams
are the power requirements of the TF coil and neutral beams respectively,
and Vol cu is the volume of the copper.
top, Wb is the beam energy.
consumes 1.5 resistive V-s.
Tflat is the length of the flat
It has been assumed that the initial plasma
The average stress in the TF magnet
-19-
(copper and steel) in Table 2.1 are 275.8 MPa.
copper in the throat of the magnet is 66%.
The percentage of
This number determines
both the maximum stresses in the throat of the magnet and the pulse length.
The inner radius of the TF coil, R,, is chosen so that the stresses in
the OH coil are aoh ~ 200 106 Pa (_30
kpsi).
6s = 0.15 m and q(a ) = 2.5.
The numbers in Table 2.1 are obtained by choosing values of R
and IpA.
The minor radius of the plasma in the compressed state is then varied,
and the value of the toroidal field on axis of the compressed plasma is
found from
2Tr
f
B=
q(a ) I A
-~-2.12
io
ap
The major radius that results in GTF = 275.8 MPa is found.
The height of
the magnet is determined by the constraint abend = 275.8 MPa.
The pro-
duct of IpA is varied so that MIbeta = 1 when MIbeams = 1 with Kb = 1.5.
The process is repeated, and the lowest value of R
that satifies the
requirements is obtained.
From Table 2.1, R = 3.27 results from a compromise in the process of
minimizing Ptf'
me'
cu
and Pbeams'
As the magnetic field on
axis decreases, the stored magnetic field in the TF coil decreases
rapidly for Bf
>
10 T and slower for lower fields.
As B
decreases,
the volume of copper and hence the weight of the TF coil decreases with
decreasing field for Bf > 11 T and increases thereafter.
current I
The plasma
increases due to a decrease in aspect ratio (note that Ip A. con-
stant in Table ".I). The resistive power in the TF coil, Ptf, also decreases
as Bf is lowered.
For bf < 10 T, however, Wme' VOl,
-20-
Ptf vary slowly as the
fiel- is decreased further.
Lowering the field even further than the
value shown in Table 2.1 results in large plate size.
The results of the parametric study reveal that for Bf in the range
8 - 10.5 T, the TF coil parameters are only slowly varying.
-21-
4-)
U
r-%
C\j
In
C*j
Co
C6
LO
rl_
00~
r.:
CC)
r-
N-
4-
uc~
as
(3)
C4
2r-C
0:
4-J
(A
WU
Co
Co
(a
:d*
1-t
(a
L.1
LA
C"
_:
ml
(a
LO
Lii
co
(a
wi
CD 0
'N
(a
LO
r-4-)
'
S
u0
.f-
4-)
0)
20
4-
r_40 a)
0..
C\J 4-45Z(
F-
j
wi Li
U)
C"
m0
r,
'
IlC)
N
(a
(a
(a
(a
L.1
Co
.4
to0
Co
U~
UD)
C kA-0aL
-I&1
110C\I:00
LO r.4-
It
wi
00 Co
m~
Li
0
D
-1"
<71
U'N
Co
m'
w"
i
'
1
as
I'D
U.1
w
C
C"
C
(a
a%
.
14
a%
(a
U.1
II
Lii
M"
1
Lii
Lii
i
00
'
(a
(a
(0
0.
4-
-LJ
,
-:T
(a
(a
L.]
0o
C0l
Ln
(a
(
Li
LA
"r
Olt
r-UL-
'N
'ALA
LO
LO
C" co
M'
Co
CD
Lii
wi
(a0
C"
LAI
n cn
c
M'
w
m
(n
0 C's C T o Co Co Co asl
0 0
.-
U)
.0-0 It
U0U L. :mn /)U cmM:
: a
ca -4. .0
4-) -o
a) (A
U.1
E-=
CL~
Lii
(a
(ao
%a
Lii
LA)
(n1
wi
to,
d,
(Vn
Co
U.1
01
CV,
LA
Cl
(V ;
(a
wi
a%
wi
al
mU
C *
.
4-
~0
4-2
0
w
m
CD~
Co
C"
F-
0
o CV
0
4-2
LO
LO
CJ
m
-o
=0
4-)
0
4-J
S..
-
-
4-
aso
coj
-4j)
C
CV
9~
to
LI
(r) 0.
4.)
CO
w a)
S.-
c
(1 ) S. '4- C
S.- 4.) 0 tm
a)4c
V)
C) Lii 4-)
F-
(
r-
-
a)
C)
C)~
mV
CVY)
oD
C0
CoD
Ca
(0
Co
4-3 E20 -0 U 'A
C)'
0 CU = CU S.-n F-- co Li. a-
c6
o
C)
r-
C)
(=
C)
ro
0Y
-22-
o~
LA
m-
m
LO
m
(a0
3.0
CONFIGURATION OF ThE BITTER PLATE TOROIDAL FIELD COIL
3.1
General Arrangement
The Bitter plate principle of construction has been chosen for the TF
coil because of its great inplane strength, its simple modularity and its
ease of cooling.
and flanges.
The TF coil is composed of standard and nonstandard turns,
The turns are composed of copper, stainless steel and in-
sulating plates combined in ways that provide all the necessary characteristics and functions.
The flanges are extensions of the plasma
vessel, insulated electrically from the TF coil but locked into it mechanically.
The turns are held together by the combination of epoxy bonding and
a high radial clamping force provided by the use of the equilibrium field
dipole coils as girth bands.
Figure 3.1 shows the top of the magnet in
plan view with the nitrogen dewar removed.
Figure 3.2 shows a vertical
section of the major components of the magnet.
The turns are planar, having no helical "lead".
They consist of a
throat region, where the turn is thinnest and for the most part where
the stresses are greatest, radial arms above and below the plasma vessel
and an outer limb where the turn is at its thickest and where the copper
is split to allow inter-turn electrical connection.
Altogether there are 256 turns of both a standard type and of a
modified type, the latter to accommodate flanges.
The turns are grouped
into modules of 8 each centered about a diagnostic flange and bonded at
each end by one half of a closure flange.
-23-
Figure 3.3 shows the plan view
NEUTRAL
VERTICAL
DIAGNOSTIC
INTERSECTION
HORIZONTAL
DIAGNOSTIC
ENTRANCE
BEAM ENTRANCE
HORIZONTAL DIAGNOSTIC EXIT
-VERTICAL
0
Figure 3-1
Magnet system assembly plan view
a
,
DIAGNOSTIC
1.0 METERS
-LJ
0.
wn
in
I0]-
0,
u
w
0j
-
(D
w
=
0
0
a-
07
w
0
(D
z
LL
0
z
4-3
ULi
4-)
(D
0J
Q
EE
(%J
0
CV)
0
z
Q)
S..
CU
4-)
UA-
I~I
4-3
0
0
ww
U)
\
w
0
CL
i
4)
0
040
-j
w
CLr
Dr
(r0
U)
I4
W-J
w
-25-
wi
CD
z
U)
CDJ
j 4
U. Mj M
<
4i
-J
Uf)
0 U
U)
LLI
0
U)
z
M
I.-
z
ILi
0!
w
I-
t
z
<
a)
x
-
0 0r
:
irL
<
c=
0
0y)
E
CL
~
4-J
0-
0)
0-
rLL.
-26-
and Figure 3.4 a developed elevation of a module.
The diagnostic flange is shown in Figure 3.5.
It forms a rigid
sector of the plasma vacuum vessel and includes the port for the neutral
beam injection, horizontally oriented viewing ports and vertically oriented diagnostic ports.
The diagnostic
ports and horizontal ports are
located as shown in Figure 3.6.
The closure flange also forms part of a rigid sector in the vacuum
vessel and is shown in Figure 3.7.
Both types of flange represent a discontinuity in the otherwise
This discontinuity must be kept to a minimum
uniform pitch of the turns.
if toroidal field ripple is to be small.
The asymmetric nature of the
turns can be exploited for this purpose.
In effect, all turns have steel
reinforcement on one face and copper conductor on the other.
As the
closure flange subtends a smaller angle at the axis of the machine than
the diagnostic flange, it contritubes less to the field ripple.
The
turns are therefore arranged so that the copper component of a turn is
adjacent to each side of a diagnostic flange, while the steel component
faces the closure flange.
This arrangement is shown in Figures 3.3, 3.4
and 3.7.
A further method of ripple control is the choice of the path of the
current in the copper plate.
In order to reduce port ripple the path of
the current is deviated outwards by means of slits cut in the copper and
terminated by a hole for stress reduction.
The copper between the slits
is thus available for the transmission of lateral pressure but carries
-27-
4
w
06
Wo
Uc0
ZW
crZ
z
z
E
WW
U.
z
z
U.
00
flU
4J
r=
0-
22
2
4-J
__
I
I-_
aU
4
z 0
z
z
w
A
L
lt28 -
-j
a).
DIAGNOSTIC FLANGE PLATE
VERTICAL DIAGNOSTIC PORT
EXPANSION JOINT
BEAM
PORT CHANNEL
INSULATION
Figure 3-5
Diagnostic flange
-29-
CRANKED
INTER( CONNECTOR
o
z
o
z
CD W CD9h
44u
0
z
xU
M
. 9
Q_
00
0c0
00
f.0
C3
-30-
CLOSURE FLANGE PLATES
CONDUCTOR PLATE
INTERCONNECTOR
INSULATION
\CLOSURE
FLANGE KEYS
Figure 3-7
Closure flange and adjacent conductor
-31-
little current.
3.2
This is shown in Figure 3.8.
Standard Turns
The standard turn is shown in Figure 3.9.
It consists of a two re-
gion copper plate, a stainless-steel wedge plate and two insulators.
The two regions of the copper plate have characteristics broadly
matching the local stress conditions.
The throat is a composite of
copper and high strength stainless-steel.
hard condition and is appropriately
316LN type.
The copper is in the full
bonded to a stainless-steel of the
This throat region is electron beam welded (EBW) to
the top and bottom horizontal arms along contours of low stress.
faces of the outer part of the copper plate are parallel.
The
This eases
fabrication and minimizes the distorting effect of a large volume of
copper on the equilibrium field during the compressional phase.
The
wedge section left between turns by the copper is filled by stainlesssteel of type 304L or 304LN.
Because the faces of all the main components of a turn are planar
the connection between turns must be cranked.
The stainless-steel wedge
is recessed to accommodate the interconnectors within the outline of the
plates, thus eliminating any projections beyond the normal outer edge of
the plates, except at the closure flanges.
Although recessed for the in-
terconnector -he stainless-steel wedge is vertically continuous in the
outer limb and of cross-section at the equator sufficient to support
the vertical load easily in the outer limb.
In order to maintain both the copper and the steel wedge planar it
is necessary to insulate the steel wedge fully from the copper.
-32-
This
INSULATION
ELECTRON BEAM WELD JOINT
2.452
.051
2900
4.90
'
.051iT
-
290.0
TURN,TOP VIEW
89.6
COPPER
3.0
0.5
STEEL--
853
-.
--
90.0
THROAT, COMPOSITE MATERIAL
RELIEF HOLES
SAW CUTS AND STRESS
I
.
61.3R
'
8.OR\
25.4
CONDUCTO R PLATE
\
/
50.R
[96.4---
68.2
136.4
rUNCOMPRESSED PLASMA
COMPRESSED
PLASMA
121.5
REINFORCE MENT PLATE
155.0
-
76._R
K
3
[7
DIMENSIONS-Cm.
Figure 3-8
Turn dimensions
,-33-
INSULATION
CONDUCTOR
PLATE
REINFORCEMENT PLATE
INTERCONNECTOR
Figure 3-9
Standard turn
-34-
incidentally allows the wedges to be used as passive supports for the
vacuum vessel rigid sectors.
3.3
3.3.1
Flanges
Diagnostic Flange
This is shown in Figures 3.5 and 3.10.
The neutral beam port breaks
the continuity of the outer limbs of the turns so that both the stainlesssteel wedge plate and the copper plate must be modified.
The steel plate is truncated above and below the beam duct.
Friction
and bonding between the flange plate and modified turns transmit the vertical
load to steel plates of adjacent standard turns.
truncated.
The copper plates are also
However, copper conducting cross-over plates are brazed to
form a cranked interconnector to carry the coil current around the beam
duct.
See Figure 3.11.
The cranked interconnector around the diagnostic
flange is a special case.
It carries current from the modified turn on
one side of the diagnostic flange to the modified turn on the other side.
It is shown in Figure 3.5.
These cranked interconnectors are about as thick as the copper in
the throat so that they can be nested in a space requiring the truncation
of the least number of standard turns.
sides of the duct, see Figure 3.4.
This number is in fact 4 on both
No steel reinforcement is needed for
the interconnectors.
-35-
.051
A
7.625
1.'760
15.251
2.90.0
.051
INSULATION
289.9
121.5
76.2R
'55.0R
I
10.0
i1.0
234 .0
+-
73.7
-
1-
90.9 -
DIMENSIONS-Cm
Figure 3-10
Diagnostic flange plate dimensions
-36-
INSULATION
CRANKED
INTERCONNECTOR
REINFORCEMENT PLATES
CONDUCTOR PLATE
Figure 3-11
Modified turn
-37-
A transition turn, Figure 3.12 links these turns to standard turns.
Except for its conductor plate, which accepts a cranked interconnector
at one
end and a standard interconnector at the other, it is a standard
turn.
The diagnostic flange is a part of the rigid sector of the vacuum
vessel.
During a plasma disruption, forces on the rigid sector must be
transmitted to the magnet through both the diagnostic flange and directly
to the inside surfaces of the steel wedges.
In order to do the latter
through structure of sufficient modulus, strength and resistance to radiation, the steel wedges must be electrically insulated from the active conductors.
This insulation level must be compatible with only 0.20 cm of
epoxy laminate and is dictated largely by tracking.
may be appropriate.
A maximum of 50 volt
At a TF coil current of 240 kA the voltage is ± 292
V with respect to ground.
In order to reduce this to the required values,
the coil must be divided electrically into 8 modules, each energized by
a separate power unit.
The peak voltage between wedge and plate then be-
comes 36.5 V. Current control and balance problems have not yet been
addressed.
3.3.2
Closure Flange
This is shown in Figure 3.7 and 3.13.
It is used to provide the
high vacuum close out weld for the plasma vessel.
The current terminals
are attached to the copper plates on either side of the closure flange so
that no current connector has to pass through that flange.
INSULATION
REINFORCEMENT
PLATE
INTERCONNECTOR
CONDUCTOR PLATE
Figure 3-12
Transition turn
75
~.318
7 0
70.7
1.
Ocac2
121.5
76.3
55.OR
R
10.0
24i.O
73.7
90.9
OIMENSIONS-cm
Figure 3-13
Closure flange plate dimensions
-40-
3.4
Structural Integrity
Forces in the TF magnet arise from two distinct sources.
In-plane
forces are generated by the Lorentz interaction between toroidal field
and current and out of plane or overturning forces are generated by the
Lorentz interation between equilibrium field and toroidal current.
Dis-
tinct features are incorporated in the TF magnet to provide restraint
against those forces.
In-Plane Forces
3.4.1
In the throat, the vertical tensile load and the relatively small
bending moment are carried by the combination of high strength steel and
copper.
The forces are mostly generated in the top and bottom arms and
transmitted to the throat by tension and shears in the electron beam weld.
Uniform load sharing between the copper and steel in the throat is assured
by the bond.
The vertical load in the outer limb is carried by the steel wedge.
Forces generated in the copper of the top and bottom arms are transferred
to the steel wedge by shear.
The shear strength is provided by epoxy
bonding by friction (depending on the high lateral compression produced
by the girth rings), or by keys between the copper and steel plates.
The centripetal load generated by the Lorentz forces in the throat
is supported by wedging.
Because the insulation in the throat is thin
close to the equatorial mid-plane, the wedging occurs at the top and
bottom of the throat region.
The centrifugal force generated by Lorentz
forces in the outer limb are supported by the combination of tension in
the top and bottom arms and radial force provided by the girth rings.
-41-
3.4.2
Overturning Forces
The out-of-plane force is reacted by the torsional stiffness of
the TF magnet. This stiffness arises from the epoxy bonding of all the
components in the coil or from shear restraint provided by keys between
the copper plates and steel wedges.
These keys are shown in Figures 3.7,
3.9, 3.11 and 3.12.
Because the shear restraint must be placed across the potential
difference of adjacent turns any keys must be insulated with high strength
fiber reinforced plastic. The keys are an integral part of the copper
conductor.
In order to maintain low stresses and low current density in
this copper the keys are tapered to allow self jigging during assembly.
The only exception to this construction occurs within the closure
flange.
No potential difference exists between the two halves of the
closure flange.
The keys are not insulated and are fabricated as separate
pieces from the same steel as the flanges.
Keying between the two halves
of the closure flange is necessary because the close out weld is intended
only as a demountable vacuum seal and cannot support the overturning load.
3.4.3
Assembly
The components of all turns are bonded under high pressure with
a B-stage epoxy resin.
This achieves two goals: uneveness in the plates
is filled -thus reducing the initial low modulus when the complete system is compressed by the girth rings; high shear strength is obtainedindependent of local variations in lateral pressure.
All the components of a 450 module are assembled in this way,
with a diagnostic flange in the center, 16 turns on either side and a
half closure flange at each end.
The vacuum vessel is inside this module
welded to the diagnostic flange in the middle and to the inside edge of
-42-
the half closure flanges at the ends.
3.4.4
See Figure 3.14.
Girth Rings
An essential feature of the present Bitter type TF coil is the
use of girth rings to preload the magnet so as to generate a high lateral
pressure.
Because the girth rings magnetically link the equilibrium field
which is pulsed to compress the plasma, they must be an electrically open
circuit.
Two forms of construction are possible; FRP rings; wound metallic
rings with insulated turns.
FRP rings have the advantage of low modulus
of elasticity which allows ample "follow-up" to maintain radial pressure
on the TF plates.
However, the size, thermal contraction and required
force disqualify FRP in the present case so that wound steel rings must
be used.
Because the outward Lorentz force generated in the equilibrium
dipole coils is small compared with the required radial inward force on
the TF coil it was decided to combine the function of equilibrium coil
and girth ring.
-43-
CL
0
L-o
OjE
LL.
--.1....
-44-
Section 4
List of Symbols
a
-
plasma minor radius
B
-
toroidal field value
Bave
-
average value of toroidal field
R
-
major radius
r
-
minor radius (toroidal coordinate)
&
-
toroidal field ripple
-
toroidal angle
-45-
4.0
TOROIDAL FIELD RIPPLE
Ripple in the toroidal field arises from three sources; (1) the
finite pitch of the copper plates; (2) the periodic change in that pitch
caused by the flanges; (3) the distortion of current flow in the outer
limb caused by the neutral beam injection ports.
Of these only the latter
two have a significant effect.
The latter two types of ripple can be treated separately in the Bitter
design. The resulting ripple is a linear superposition of the two types.
4.1
Ripple Due to the Magnet Flanges
As discussed previously, there is one type of standard plate, but
having left-hand and right-hand versions, mirrored about the flanges.
In the calculation of flange ripple each Bitter plate is modelled as a
set of nonconcentric, noncircular current elements.
up of a number of straight current filaments.
Each element is made
The current and position of
these elements is chosen so that the current density in the copper plate
is approximately reproduced.
A study of the number of elements per plate
required to give acceptable accuracy showed that four elements per plate
are sufficient.
Because the current density distribution changes with time, the
ripple also varies.
The closer the equivalent line of the current is to
the plasma, the larger will be the ripple.
-46-
Because of a skin effect, the
equivalent line of the current is closest to the plasma at the beginning
of the pulse.
The ripple calculations are performed for such a non-
uniform current density.
The ripple decreases from then on as the equiv-
alent line of the current recedes from the regions of the plates closest
to the plasma.
Contours of constant ripple in the precompressed and compressed
plasmas are shown in Figures 4.1 and 4.2.
The ripple is defined as:
B - Bave
S= B
ave
Figures 4.1 and 4.2 show the ripple in the plasma cross-section in the
plane of the diagnostic flange.
Figure 4.3 shows the contours of constant ripple on the equatorial
mid-plane of the machine.
*
corresponds to the toroidal angle (t
= 0 is
at the location of a diagnostic flange, q = 2r/16 is at the location of
a closure flange).
The major radius R varies from
the inside edge of the
compressed plasma to the outside edge of the precompressed plasma.
At the edge of the precompressed plasma, the peak-to-peak ripple is
1.6% (near the top and bottom of the plasma).
The peak-to-peak ripple
of the compressed plasma is 1.2% at the plasma inner edge.
of the plasma, the peak-to-peak ripple is
4.2
<
Over the bulk
0.3%.
Neutral Beam Port Ripple
The geometry of the conductors around the neutral beam ports is
shown in Figure 3.11.
Ripple is introduced into the toroidal field by the displacement
of part of the outer limb to one side or other of the beam line.
-47-
The
1.0
0.9
0.8
0.1
0.7
-0.7
-0.7
Figure 4.1
Contours of constant toroidal field percent
ripple in
a cross-section of the precompressed plasma due .to the
flanges. It is calculated in the plane of a diagnostic
flange.
0.7
0.7
-7i?
~.
0.0.20.3-
0.8
0.4/
Q5
0.6
0.7
-0.7
Figure 4.2
Contours of constant toroidal field percent ripple in
the cross-section of the compressed plasma due to the
flanges.
It is calculated in the plane of a diagnostic
flange.
-4?
-
00
\ 0
Qo
0
II
0
c0
0)t~
-
cu
2
0
S-
S.-
0
C\J
roC
L.r-
0
CO
0
9
00
*-
d
d~C
C
d
Od
0
0
0
0~
0
ddd00000
-0
m
4--l
O D Cd I t
4
5
00000
w
Cdi
Cd
3
CL
0-
0-
r
E-
(A
.9-
9
-a
A)
C
c -o
oo
0.
Cl
0
0I
. .
(CL
0u
Cl.
4 - 4-3
01
Cd 5
Cn
C
S-Cd
0
M0 0
0.
*0
u
0
ro
3
C
C~-e0
0
08
N~~
C
00
C5 ()fiPdOD
C5
-50-
4-1
-a
) .
4.)
0
effect of this displacement is to introduce a dipole current, of rectangular
In all, nine outer limbs are
vertical-section and extended radial depth.
nine dipoles, each consisting of
interrupted, thus being equivalent to
four loops to simulate the radial depth of the outer limbs.
As the undistorted field in the absence of beam ports
has a pure
/R variation and no other, only the distorting component need be calculated as a fraction of the undistorted field.
Figure 4.4 shows contours of constant ripple of the precompressed
plasma due to the neutral beam port.
The ripple is plotted in the plane
that contains the largest local ripple.
The ripple due to the neutral
beam port at the compressed plasma is negligible.
Figure 4.5 shows the ripple contours on the mid-plane of the pre-
compressed plasma:
p
is the toroidal angle (again,
= 0 occurs at the
location of the diagnostic flange) and R varies from the inner edge to
the outer edge of the precompressed plasma.
The peak-to-peak ripple at
the outer edge is - 2.4%, but away from the port it decreases rapidly.
At r = 3/4a (a is the plasma minor radius), the peak to peak ripple is
down to 0.6%.
Finally, Figure 4.6 shows the ripple magnitude at the toroidal location of the diagnostic port as a function of the major radius, R. The ripple
contributions from both the flanges and the neutral beam port are shown.
The ripple calculated in this section results in relatively small
enhancement of the ion thermal conductivity.
-51-
Furthermore, the ripple in
C
6s
C
CL
-0W
g
4,-
oCL)
o
w
S-S
S-
a
0
I
0..
.
ou
0
0
O
r
C
0
o
-o
4)<
(n
O~
oEE 5-
U-)o
CL
0
I
-52-
V:J
C-i
0
0
0
cid
0
'00
5900
it.
oII
0
5
~d6
-
0
60.
.o
000
00
E
1
d
0
:
I-
I
I
0
o
CO CP
40r
0
.0
a)0
0*0
-
6666
ood
o
'o
g
..
4*-(W) snipDU JOUIHN
-53-
C5
(0L
*0--
4-3
CU
-0
0)
U-
-54-4
o
the precompressed plasma is small enough to prevent large losses of fast
injected neutrals (for coinjection sufficiently away from perpendicular
direction).
However, the effect of ripple on the suprathermal alpha
particles has not yet been determined.
-55-
List of Symbols
Section 5
a
-
inner minor radius of magnet
B
-
toroidal magnetic field
b
-
outer minor radius of magnet
f
-
fraction of copper
j
-
magnet current density
jr
-
current in r - direction
j@_
-
current in 4-* direction
R
-
major radius
r
-
minor radius (toroidal coordinate)
T
-
copper temperature
t
-
time
wn
-
nuclear heating
-4-
-
poloidal angle (toroidal coordinate)
x
-
l/e folding distance of neutron heating
y1
-
permeability of free space
a
-
conductivity
Smag
-
magneto - conductivity
-
toroidal angle (toroidal coordinate)
-56-
5.0
EFFECTS OF MAGNETIC AND THERMAL DIFFUSION AND NEUTRON
HEATING IN THE-TF COIL
5.1
Heating Effects
The joule and nuclear heating in the throat of the TF magnet has
been studied using a two dimensional model.
shown in Figure 5.1
-The geometry considered is
The simple toroidal model exaggerates the temperature
gradients by omitting conducting material from the top and bottom inner
corner and by placing the outer current paths closer to the compressed
plasma than they actually are.
The outline of the actual magnet is shown
dotted for comparison.
The penetration of the field in a conductor with non-uniform conductivity is given by
=-
V x
v x B
5.1
is the permeability of free space and
where B is the magnetic field, p
a is the non-uniform conductivity.
In toroidal coordinates (shown in
Figure 5.1), this equation reduces to
aB
-
= 1
1,0r
at
+
where B
3
1
r(a
r
(R + r cos e)
r(R +
is the magnetic field in the
a ( R + r c s O
r((R + r cos
e)acos
((R + r cos e)B,))
(toroidal) direction.
R is the
major radius of the torus, r is the minor radius coordinate, e is poloidal
angle and
*
is the toroidal angle (see Figure 5.1).
The zero of e is on.
the horizontal mid-plane in the direction of the uncompressed plasma.
-57-
5.2
41
/
.4
0
4-
0
L-
L1
S0
-o
-58-
a is defined by
a = f(r,e)
(
\
) +
5.3
cu
mag
where f(r,e) is the copper filling factor of the coil and T is the copper
temperature at the same radial location.
acu is the conductivity of copper.
amag represents the magneto-conductivity and is given by
amag = 2.2 1010 /B(r,e)
5.4
where B(r,e) is in tesla.
The copper filling fraction is given by
f(r,e) = 1- R +0.20cs e5.5
for R + r cos e < 1.36 and by,
f(r,
for R + r cos e
>
) = R +
R+r cos e
1.36.
The boundary conditions are
B (r = b,e) = 0, B (r = a,e) =R +Bt5.7
R+r cos e
where a and b are the inner and outer minor radii of the torus (see Figure
5.1).
In the case considered here, a = 0.7 m, b = 1.06 m and R = 1.46 m.
It is assumed that B(t) (the field at the minor axis of the bore) is
increased linearly in 7 sec. then remains constant for 6.5 sec. and finally
-59-
5.6
is decreased linearly in 7 sec.
The value of the field B after 7 sec.
is assumed to be 9.1 T at a radius of 1.35 m.
The temperature of the conductor is solved using
c
aT =
(j(r,e))2 + W
5.8
where Wn is the nuclear heating, cp is the heat capacity and p is the
density.
j(r,e) is the average current density at position r, e and is
given by
j(r,e) =(j(re))2 +
r
2
5.9
where j r and j e represent the current in the radial and poloidal directions respectively,
-
(R+ rcos o) a(R + r cos e)B
5.10
and
-
r
110
~
1~(R
r(r + r cos e)
(s
+r cos e)B
It is assumed that the copper and the reinforcing structure are at
the same temperature.
It is also assumed that the heat capacities and
the densities of the reinforcing structure and the copper conductor are
equal.
-60-
51
5.11
The neutron heating is included in the calculations.
It is assumed
that
1
1
ea
(2v)2 r(R + r cos e)
W=
W
X
5.12
T
where X is the l/e folding distance for the neutron heating and WT is the
total neutron power.
It is assumed that X = .11 m and WT = 100 MW.
The
neutron power is on for 4s during the flat top.
Figures 5.2 to 5.4 show contours of constant temperature in the magnet.
Figure 5.2 shows the temperature profile at the beginning of the
flat top, Figure 5.3 at the end of the flat top and Figure 5.4 at the
end of the pulse.
Figure 5.5 shows the same result as Figure 5.3 but in
expanded coordinates; the abscissa
is the poloidal angle and the ordinate
is the minor radius.
Figures 5.6 and 5.7 show the temperature profiles at the end of the
flat top and at the end of the pulse in the case that neutron heating is
not present.
The neutron heating does not have a very significant effect
on the final temperature or on the final temperature profile; the final
temperature in the case without neutron heating is - 25* lower than with
neutron heating.
Significant temperature differentials exist in the throat of the magnet at the beginning of the flat top.
The temperature differentials at
the end of the flat top are reduced in the case without neutron heating,
and remain approximately the same in the case with neutron heating.
-61-
N'l
(D
4-3
4-)
a))
40
0
0
00
a)
CL.
-62-
N~
/8
L
/
/
I
C
00-%
U-)
E
%..0
0
um
5L-
0
64-
0
0.-
0 0
'U
CL-
N
U
-63-
I
I
Ns
/
LO
-)
c
'
00-ft
_
__
0
E
%me
4c
S-f
O)
OD
-o
4-)
4-
N
0
OD
0
C'j
-64-
0
Ij-
N\
tl
CQC
4-.)
OD~
.9r.
1)
+to
le
0
CT0
'4-
0
S.-
4.)
S-
E
I-
Oo
0
snipoN jouiV4
05
(W) J
-65-
N
OD
Q')
LO
OD
r11
N
|
[
i
S
E
I
a3-
0
II
0
CL
0
4-)
-(o
100
E-
0
N
I
-66-
/
t
00
00
4-)
0
-
0)I
0~~
00
C~Co
-67-
Figure 5.8 shows the current profile at the end of the flat top in
the case with neutron heating.
Finally, Figure 5.9 shows the magnetic
field for the same conditions as Figure 5.8.
Finally, it should be stated that the scenario studied here has not
been optimized.
The ramp-up and ramp-down times for example,could be in-
creased without significantly affecting the final temperature of the magnet,
because the current would be distributed more uniformly throughout the
magnet.
5.2
This would also result in smaller temperature differentials.
Cooling
Between pulses the magnet is cooled by liquid nitrogen boiling at
The time for this recooling has been
available surfaces of the TF coil.
calculated for an initial temperature of 300*K and for two cases.
(a)
Cooldown is a function of conduction only, (b) both conduction and surThe surface heat transfer function
face heat transfer impede heat flow.
is assumed to be the curves shown in Figure 5.10.
The cooldown curves
are shown in Figure 5.11 in which average throat temperature is plotted
as a function of time.
The enhanced cooling curve is obtained when per-
fect surface heat transfer occurs.
Although this is a limiting case
never reached in practice, it can be approached by enhancement of the
surface heat transfer, by, for instance, the use of copper fins in the
throat, where the highest temperatures are reached and where good cooling will have the greatest effect.
The total cooldown time is between 3,400 seconds and 5,000 seconds
depending on surface heat transfer conditions.
-68-
co
N~
7-
/
/
7-
.-
/
/
4-)
000
/
(31
.-
N
#*W"W*
1.
.1
.
.
0
~4-)
E
--
Lo
4-
a) S..
S.-
coo
OD N
IN
42
4-
L
o
I
I
ca~
CQC
77
/
7
NC6
4-3
L-
/
Cj
-70-
0
0
0
0
0
0
- ;'C
4-U
oo
*1)
cr
CL
c
0-
C
0
*-
W
4-
o
oco
-7
0
4i
(0
V.)
4-
Q
0
~
-4-
LO
0
4-
-71-
--)
L* a
*r
I
I
5001300
IOO*K
(Conduction +
Transfer
Limi ted)
50
30
10*K
(Conduction
Limited)
5
3
1'*KI
1K0
I
I
t
I
4
8
12 16
I
I
I
I
I
I
I
I
I A
.
18 20 24 28 32 36 40 44 48 52 x 10 sec
Time (sec)
Figure 5.11
Average temperature in throat of the TF magnet as
a function of time during cooling.
-72-
List of Symbols
Section 6
Bz -
vertical component of the flux density
-
inner toroidal radius of the TF magnet
D
D2 -
radius of centroid of the compressed plasma
D3 -
radius of centroid of the precompressed plasma
D4 -
outer toroidal radius of the TF magnet
D5 -
half of TF magnet height
D6 -
offset of the compressed plasma centroid
D7 -
offset of the precompressed plasma centroid
E
-
Young's modulus
G
-
shear modulus
j
-
current density
m
-
torque angle
R -
radial coordinate
R. -
radius of the compressed plasma wall
R2 -
radius of the precompressed plasma wall
T -
insulation thickness
T2 -
steel thickness
T3 - copper thickness
V
-
circumferential displacement
Z
-
vertical coordinate
o
T
-
Laplace's operator in polar coordinate system
-
circumferential coordinate
-
axial stress
-
shear stress
-73-
I
6.0
STRUCTURAL ANALYSIS OF THE BITTER PLATE TF MAGNET
6.1
Introduction
Methods and results of the computer structural analyses of the Bitter
plate ITR TF magnet are discussed in this section.
Several discrete
models were generated for the purpose of these analyses.
Three major loads acting on the TF magnet were considered in this
study:
1. Inplane Lorentz forces induced by the toroidal field
2. Radial surface pressure produced by the girth rings
3. Out-of-plane Lorentz forces induced by the Vertical
field.
The analysis of the structural behavior of the TF magnet subject to
the first two loads was performed on the basis of the finite element method, for which two computer models have been generated.
The first model
did not take into account the geometric singularities caused by the presence of the neutral beam and diagnostic ports, and treated the magnet
as consisting of 256 identical laminated (copper-steel-insulation) wedged
plates.
Each of these plates was considered to have two planes of sym-
metry, RZ and Re, which are shown in Figure 6.1.
This persuits the
modelling of just one quadrant of the plate.
A special interactive computer code which incorporates the ANSYS (6.1)
finite element analysis program has been developed at MIT.
The code
generates a sequence of solutions which include a steady-state or a transient electrical conductivity analysis
-74-
(but excluding magnetic diffusion),
I
z
INSULA"TION
STAINLESS STEEL
COPPER
R
General view of a laminated6i'tter plate
considered in the single-plate analysis.
-75-
I
magnetic field analysis, generation of Lorentz body forces, and finally,
stress and displacement analysis.
The second finite element model developed on the basis of the former
was closer to the 3-dimensional reality.
The major goal pursued and
achieved by this model was to find the variation of stresses and displacements with respect to the circumferential coordinate and to account for
the presence of the neutral beam ports.
The model represented the upper
half of a 22.5* wedge (Figure-6.2) bounded by two radial toroidal Planes
of symmetry and one- central plane norwal to the vertical axis; thus only
half of the coil extending 22 1/2' from the
iagnostic port mid-plane
was considered.
A finite difference model is being used to analyze the torsional
stresses and displacements generated in the TF magnet by the out-of-plane
Lorentz forces.
The torque problem is represented by a second order dif-
ferential equation with respect to the torque angle which allows stresses
and circumferential displacements as well as the boundary conditions to
be expressed simply.
The following describes the three models and the results of the
structural analysis in greater detail.
6.2
6.2.1
Single-Plate Axisymmetric Model of the TF Magnet
General Characteristics of the Model
This model represents one quadrant of a laminated Bitter plate.
Its analysis gives a detailed picture of the TF magnet structural behavior
-76-
I
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U-
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81
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II
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I!
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-77-
i
if
the singularities caused by the neutral beam ports are neglected.
will be demonstrated later this model generates an
accurate
of stresses and displacements away from the NB ports.
As
picture
This especially
relates to the throat region where the vertical, radial, and circumferential stresses seem to be least affected by the presence of
the ports.
The plate is defined in cylindrical coordinates with a radial coordinate R measured from the central axis of the magnet system, a vertical
coordinate Z measured from the horizontal plane of symmetry, and an angle
e measured from the vertical plane of symmetry of the thickness of the
laminated plate.
The coordinate axes and the principle dimensions which
serve as input data for the FEM model generation are shown in Figure 6.3.
The wedge plate is composed of a copper current-carrying central
section (a symmetric turn is considered), a steel load carrying plate
bonded to copper, and a layer of insulation separating the plate from an
adjacent wedge.
Because of
symmetry ,
the insulation thickness T. in
the model equals half of the actual insulation thickness.
In accordance with the data describing the geometry of the coil
and with the precision of the finite element grid in each specified region of the plate the program automatically generates the grid point
mesh.
Each of the three materials is represented by one layer of finite
elements in the circumferential direction.
the fineness of the mesh in the RZ plane.
No constraint is imposed on
An example of a computer gen-
erated FEM mesh with a set of dimensions used in this analysis is shown
-78-
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CD
+
\ -
I'O
-D
C
Cl)
w
z
(1)
C/)
-j
w
w
0
w
0
z
0
z
0
4-.
V)
00
0
U')
z
C~*)
'.0
4,
q~Cj-
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S.o
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U..
0
u
C')
w
z
III
y
CH
~-40
IJ
w
w
H-
(\o
0
N
sixv -ivalo~iol
-79-
W0
I
in Figure 6.4.
After the mesh generation is completed a steady-state or a transient
current density distribution analysis is performed.
For this purpose
3-dimensional isoparametric solid electrical finite elements with 8 nodal
points (one degree of freedom in each - the potentials) are used.
Geo-
metrically they are identical with the finite elements used in the stress
and displacement analysis.
The output of this part of the code includes
voltages and current components in the nodal points as well as the current densities at the centroids of the elements.
On the basis of this current distribution the magnetic field analysis
is conducted.
The next step is generation of the Lorentz forces which are later
converted into the surface pressures acting on the sides of the finite
elements.
These pressures along with the pressures applied to the
boundaries of the coil (for example, the radial compression from the
girth-rings) are the input data for the FEM stress analysis.
Three-dimensional isoparametric solid elements with eight nodal
points and 24 degrees of freedom (nodal linear displacements) represent
copper and steel.
The insulation is modeled with 3-diriensional interface
elements which are capable of supporting only compressive stresses in
the circumferential direction and limited shear stresses in the RZ plane.
This means that when the shear exceeds the friction, slip occurs.
-80-
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Z.
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z
0
z
w
CMC
0
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ccri
-81
-
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As can be seen in Figure 6.4 a single-plate model used in this analysis had 520 nodal points and 1,260 degrees of freedom.
The following elastic moduli of the structural materials were used
in this analysis:
1. Copper
-
137.9 GPa in all directions
2. Stainless Steel
-
206.8 GPa in all directions
3. G-10 Insulation
-
27.6 GPa in all directions
A Poisson's ratio of 0.3 was used for all three materials.
The coeffi-
cient of friction between G-10 insulation and stainless steel to account
for the possible slippage was assumed to be 0.3.
6.2.2
Stress and Displacements Due to the TF Field
Stresses and displacements generated by this model under the
action of inplane Lorentz forces at an operating current of 246 kA are
presented in Figures 6.5 through 6.17.
Stresses are given in MPa, and
displacements are in mm.
Figures 6.5 and 6.6 show the distribution of the vertical axial
stress aZ in copper.
The distribution of this stress in the steel plate
is presented in Figure 6.7.
Both in copper and steel the maximum tensile
stresses take place in the throat region and are 298 MPa and 466 MPa, respectively.
The distribution of the radial stress a R in each of the materials
is demonstrated in Figures 6.8 through 6.10.
The maximum radial tensions
occur approximately in the middle of the upper and lower arms, at the
-82-
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edges.
They are 79.2 MPa and 119 MPa, in the copper and steel plates,
respectively.
As can be seen in Figure 6.9, the arms of the coil ex-
perience substantial bending.
The maximum horizontal shear stress TRe
(2 MPa) between copper and steel takes place in the throat region, at the
mid-plane.
Figures 6.11 and 6.12 illustrate the pattern of the circumferential
stress distribution due to the Lorentz forces.
This is important from
the point of view of the contribution of the Lorentz force to the frictional shear necessary to withstand the overturning forces induced by
the poloidal field.
The maximum compression of 151 MPa takes place at
the inner edge of the throat near the horizontal mid-plane.
In the
outer corner region the ae compressive stresses induced by toroidal field
Lorentz forces are negligible.
of girth-rings is used
For this reason precompression by means
to assist the resistance to torsion.
The distribution of the von Mises stresses in copper and steel is
presented in Figures 6.13 through 6.15 for the case where the insulation
is not thinned in the throat region.
The maximum values of this stress are 388 MPa and 551 MPa, in the
copper and steel respectively.
They occur in the throat region, where
substantial circumferential compression enhances the equivalent stresses
relative to the vertical tension.
Figures 6.16 and 6.17 illustrate the radial and vertical displacements of TF coil contours due to the inplane Lorentz forces.
The maximum
inward radial displacement of .96 mm is experienced by the throat region
at the horizontal mid-plane.
The maximum vertical displacements ofl.67mm
-96-
I
takes place at the inner boundaries of upper and lower arms of the coil.
6.2.3
Stresses and Displacements Due to Precompression
In order to compensate for the lack of circumferential compression
in the outer limb region which is needed to provide frictional shear
against the overturning force, the TF magnet is precompressed after assembly by means of girth-rings (PF coils).
The radial clamping pressure
exerted on the toroidal magnet over a height of 0.5 m at the outer upper
and lower corners of the plates is 37.9 MPa.
The additional circumferential compression generated by the precompression load in the outer limb region varies from 14.6 MPa at the
mid-plane to 37.3 MPa at the upper and lower outer corners of the coil.
(Figure 6.18).
Figures 6.19 and 6.20 show the distribution of the vertical (aZ)
precompression stresses in copper and steel, respectively.
In the throat
region these stresses are compressive which leads to the reduction of
the aZ stresses generated in the region by inplane Lorentz forces.
The comparison of the displacement profiles caused by each of the
inplane loads is illustrated in Figure 6.21.
It leads to the conclusion
that when the operating current achieves its nominal value the vertical
field coils will follow the TF coil without separation, and that the precompression which provides additional frictional shear in the vulnerable outer
limb region will be maintained.
-97-
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6.3
A 22.50 Wedge FE Model of the TF Magnet With the
Neutral Beam Ports
6.3.1
Description of the Model
As has been emphasized earlier in this section, the single-plate
model of the TF magnet introduces certain simplifications.
In particular,
it does not reveal the peculiarities in the structural behavior of the
magnet caused by the presence of the neutral beam ports.
This especially
relates to the circumferential stress distribution in the vicinity of
the port boundaries. A three-dimensional 22.5' model of the TF Bitter
plate magnet with
symmetry)
neutral beam ports (the torus has 16 planes of mirror
has been generated for the purpose of the detailed analysis.
The FE wedge model was developed in a relatively short time because
the most time-consuming procedures for this model were acquired from the
interactive code for the single-plate model.
This relates especially to
the automatic mesh generation in the vertical radial planes, to the current density and field analyses, and to the generation of the Lorentz body
forces.
The general view of the section representing 1/32 of the TF magnet
structure, is shown in Figure 6.22.
A simplification relating to the
orientation of the central axis of the neutral beam port is used in the
model.
In the model the axis of the beam line is perpendicular to the
plasma axis while in the actual magnet it is angled by about 20*.
Figures 6.23 and 6.24 present isometric views of the FE mesh generated
for this analysis.
In the circumferential direction the wedge is repre-
sented by 9 sectors shown in Figure 6.25.
-102-
The angles subtended by these
I
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cu
0
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c
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CDZ
)
1)
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ct2
-
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-
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04
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ci
2 31
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it/z)
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vn
TO
, to t
to
4.
F
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M-S
00
100
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sectors are not equal.
This is done in order to follow as closely as
possible the variations in the geometry, the Lorentz body forces, and
the material properties with respect to the circumferential coordinate.
Each of the 9 sectors is modelled
metric solid elements of the ANSYS type.
by 112 three-dimensionsl isoparaThe FE mesh in the RZ planes
of the model generated for this analysis is shown in Figure 6.26.
The
model has 3815 degrees of freedom.
In order to avoid complications associated with the laminated structure of the Bitter plates (copper, steel, insulation) a special homogeni-
zation technique was used in this analysis.
Except for the small area
in sectors 5 and 6 adjacent to the port where the cranked turns are located, elements whose centroids have the same coordinates in the RZ planes
were assumed to have constant elastic properties with respect to the cir-
cumferential coordinate.
In accordance with the variation of the relative fractions of copper,
steel, and insulation in the plate cross-section as a function of its
radial coordinate as shown in Figure 6.27, anisotropic compound properties
of finite elements at various radial locations were computed.
35 material
combinations including a material with zero stiffness in the port region,
were used for the finite elements in this analysis.
The classification of
the elements on the basis of their material type is shown in Figure 6.28.
The source properties of copper, steel, and insulation were
same as in the single-plate model.
the
The elastic moduli of the types
of materials shown in Figure 6.28 are assembled in Table 6.1.
-107-
Associated
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CL
0.
t:3
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M
z
-108-
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0
z
C,,D
z
0
ci,
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w
)
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4-)
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zU
ul
zz
-109-
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I
TABLE 6.1
Anisotropic Elastic Moduli of Various Material
Types Used in the 22.5* Wedge Model
2
3
4
ER
(GPa)
EI
(GPa)
EZ
(GPa)
0.0
0.0
0.0
51
162.1
129.8
162.1
52
158.4
131.0
158.4
53
155.7
131.9
155.7
54
153.6
132.5
153.6
55
151.9
133.1
151.9
56
150.6
133.5
150.6
57
149.5
133.9
149.5
58
148.6
134.2
148.6
59
147.8
134.5
147.8
60
147.1
134.7
147.1
61
146.5
134.9
146.5
62
146.0
135.1
146.0
63
146.5
135.8
146.5
66
155.3
143.0
155.3
67
157.7
145.1
157.7
69
161.9
148.9
161.9
70
163.7
150.6
163.7
73
168.4
155.3
168.4
76
172.2
159.1
172.2
78
174.3
161.4
174.3
1
Material
Classification
1*
* Space occupied by the neutral beam port
-111 -
(Table
2
3
4
ER
(GPa)
Ee
(GPa)
EZ
(GPa)
80
176.2
163.5
176.2
81
177.1
164.5
177.1
82
177.9
165.4
177.9
83
178.8
166.2
178.6
84
179.4
167.1
179.4
85
180.1
168.0
180.1
86
180.8
168.7
180.7
87 (17)**
181.4
(137.9)
169.5
(137.9)
181.4
(137.9)
88 (18)**
182.0
(137.9)
179.2
(137.9)
182.0
(137.9)
89 (19)**
182.5
(137.9)
170.9
(137.9)
182.5
(137.9)
90 (20)**
183.1
(137.9)
171.5
(137.9)
183.1
(137.9)
1
Material
Classification
*
6.1 continued)
Materials 87 - 90 are replaced with materials 17 - 20 (copper), respectively, in sectors 5 and 6 where the cranked turns are located.
-V12-
with the material types were the relative current densities.
This takes
into account the increased current densities in the cranked turns.
The Lorentz forces were first calculated on the basis of the singleplate model, after which, for all radii and vertical levels at which the
nodal points are located, the linear load per unit angle was found.
The
nodal forces and face pressures were then computed in accordance with
the angles subtended by respective elements in their sectors.
6.3.2
Discussion of the Results of the Analysis
The results of the three-dimensional FE analysis of the TF magnet
subject to inplane Lorentz forces and precompression are illustrated in
Figures 6.29 through 6.70 in the form .of equal stress lines and deformed
shapes of the plates in various cross-sections. All stresses are given
in MPa averaged over the compound material.
The cross-sections to which
the stresses refer are referenced by the angle of the cross-section as
shown in Figure 6.25.
The distribution of the vertical axial stresses aZ in various crosssections is shown in Figures 6.29 through 6.35.
It is pointed out that
the pattern of the aZ stress distribution in the throat region is exactly
the same in all nine angular cross-section. This means that the singularity caused by the presence of the port in the outer limb does not affect the vertical stresses in the throat region.
In the outer limb region,
between the symmetry plane e = 0 and the side of the port there is a noticeable variation of the aZ - stress pattern.
stress above
Although the magnitudes of the
the port are small there is a variation of the aZ - stress
distribution with respect to the angular coordinate.
-113-
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LU cn
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oc
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LLJ
(
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oz
CD
040
LLLU
o
D0
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Figures 6.36 through 6.42 present the distribution of the circumferential stress a e in various cross-sections.
In the throat and hori-
zontal arm region the patterns of the stress distribution in all 9
cross-sections look almost identical.
However, in the outer limb area
there is an apparent variation in stress values and the pattern of its
distribution with respect to the angular coordinate.
At angles 5 and 6
which are very close to the side of the port which is a stress-free surface, the circumferential stress almost disappers while a stress concentration can be observed above the port, see Figures 6.38 and 6.39.
Directly above the port the stress concentration becomes stronger with
maximum values of about 140 MPa, as shown in Figures 6.40 through 6.42.
The radial stresses are illustrated in Figures 6.43 through 6.47.
In the throat and in- most of the top and bottom horizontal arm regions
there is again almost no variation in the stress pattern with respect
to the angular position of the cross-section.
In all cross-sections
the distribution of the aR - stress shows that the horizontal arm is a
beam in bending.
The nonzero radial stresses on the outer surface of
the torus are due to the radial pressure from the girth-rings.
Figures 6.48 through 6.54 illustrate the distribution of the shear
stress, T Z, in the wedge.
The pattern of the distribution of these
stresses and their values and signs vary substantially with respect to
the angular coordinate.
In the throat region and the inner half of the
horizontal arm the shear stresses change their signs between angles 2
and 4. See Figures 6.49 and 6.50.
Between angles 4 and 6 in the outer
limb region a strong shear stress concentration takes place at the top
of the port.
Directly above the port the shear stress decreases rapidly.
-121-
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The horizontal shear stresses, tRe, acting in the vertical radial
cross-sections are shown in Figures 6.55 through 6.59.
As in the pre-
vious case these stresses vary substantially with respect to o, and
change signs in the entire cross-section at angle 3.
As can be seen in Figures 6.50 through 6.65 the TRZ shear stresses
are almost independent of the e-coordinate.
There is a strong concentra-
tion of this shear stress in the throat region where it reaches a value
of almost 130 MPa.
Figures 6.66 through 6.70 illustrate
the inplane displacements of
the TF coil contours in the 22 1/20 wedge model.
Figure 6.66 shows the
deformed shape of the coil at the symmetry plane e = 0 under the inplane
Lorentz forces.
The maximum inward radial displacement of 1.235 mm
takes place in the outer limb at the horizontal plane Z = 0. The maximum
vertical displacement of 2.246 mm was found
to occur approximately in
the middle of the horizontal arms at the inner contour.
It will be noted
that an apparent discrepancy exists between the deflection calculated
by the single turn and three-dimensional FE models.
mm, the latter 2.246 mm.
The former gives 1.67
This is in fact due to the smaller stiffness
of the three-dimensional wedge model which is in turn due to different
dimensions.
The displacements initiated by the radial precompression of the magnet
in the same cross-section are presented in Figure 6.67.
Figure 6.68 shows the deformed shape of the coil cross-section under
the combined action of inplane Lorentz force and precompression.
-140-
This is
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compared with the underformed shape of the coil.
The maximum resulting
horizontal (1.694 mm) and vertical (2.388 mm) displacements are experienced by the same points of the coil boundary as in the case of loading
by pure Lorentz forces.
To illustrate the effects of these individual and combined forces
on deflection Figure 6.69 shows the deflections caused by precompression,
by inplane Lorentz forces and by the sum of both in comparison with the
undeflected shape of the plates.
Figure 6.70 shows the superposition of the deformed shapes of the
magnet cross-sections at e = 0 and
e = 22.50, center of the port, both
under the cumulative action of inplane Lorentz forces and radial precompression.
The two deformed shapes evidently do not differ much in most
regions of the contour away from the immediate vicinity of the port.
The
major difference which is rather small takes place quite close to the port
and mostly affects the vertical displacements.
6.3.3
Conclusions
The structural details and dimensions used in the FE analyses of both
the single-plate and the 22.50 wedge models relate to early versions of
the Bitter plate TF magnet design.
They are different from those used in
the final version of the design described in this report.
However, the results of the analyses presented in this section and
of several preliminary and intermediate analyses lead to the conclusion
that qualitatively and to a certain degree, quantitatively, the described
results are applicable to the present design.
-156-
Cie
I
Lo
U')
0-
CD)
0
4I-)
LUUI
0
C5-
LULU LUI
C
0)U-P
0Q
LU
-LJ
KL
-L-
L--
-L
-I
LJ
11J 2L
L
20-
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-0--
-157-
0 E
c'J eo
LL-
.-
ILI
I
t
LUJ
0
0
0ow
-:
.-
c.'J
0
CL- -00
G).
c4-3
On
.LU
-a w
0 EE
E cu
u c
z m
LU C
-j a
CL
LU
ro -
W
o4-
0-0
zcn
LO
z cn
NC
L
z
-j
C--L 011z
E
(=LUQ
oLJCDLL N
cr
-158-
-
-
* 0.
E
F=
This applies especially to the throat region where the magnitudes
of the stresses and the patterns of stress distribution are least affected by variations of the outer radius of the torus and by the presence of geometric and material simularities in the outer limb region.
Comparison of results generated by the single-plate and 22.50 wedge
models indicates that the sophisticated three-dimensional analysis generates refined stress and displacement data only in the vicinity of the
ports while the rest of the magnet structure is only slightly influenced
by the presence of the ports.
This is especially clear when the deformed
shapes of the magnet cross-sections at different angular positions are
compared, as shown in Figure 6.70.
The single- plate laminated model which is cheaper and simpler to compute is adequate, both qualitatively and quantitatively for all regions
except those close to the port.
It can be used as a reliable analytical
tool during all major stages of the design.
The three-dimensional model is capable of generating a detailed
picture of magnet structural behavior in all regions.
It is appropriate
to the final design stage when dimensions and structural details of the
system are already established.
-159-
I
Conclusions arising from the FE analysis as to the appropriateness
of the Bitter concept to the TF coil are as follows.
1. The transmission of the vertical force generated in the
horizontal arms of the plate to the steel wedge depends on either
friction and/or bonding between the copper and the steel.
Whether
friction or epoxy is used to achieve this, sufficient lateral pressure
is important.
The FE analysis has shown that clamping by means of
the vertical field coils is essential.
2. The stress concentration at the corners of the neutral beam
ports does not require special support.
Furthermore, the lateral
stress above and below the ports is sufficient to transmit all in-plane
forcesin the modified plates to either side of the port where they can
be carried by the unmodified steel wedges.
3. Computation of deflections has shown that the clamping
exerted by the vertical field coils is not significantly reduced by
inward deflection of the TF coil.
Furthermore it is shown in section
7 that clamping is not significantly decreased by forces in the vertical
field coil not by differential contraction.
6.4
Finite Difference Analysis of Torsional Stresses
Due to Poloidal Field
(This section describes the computation of the shear stress
distribution arising from the overturning force (toroidal current and
vertical field).
No results were available at the time of publication.
Only the method is described here.
An approximate method of calculation
is used in section 7.)
6.4.1
Differential Equation
If a body of revolution is subjected to pure torsional loading, it
can be shown that ar = a = ar = Trz = 0, (6.2) and that the equilibrium
-160-
I
equation for a differential element (Figure 6.71) is
-r/gr
+
Tez /az
+
T
(6.4.1)
/r = 0
The analysis of the Bitter magnet was accomplished by including the bodyforce equivalent of the out-of-plane Lorentz loading, jxB z,
in Equation
(6.4.1) which then becomes:
r//r + 9T
/ z + 2c
/r + (jxBz)
0
(6.4.2)
If the magnet is assumed to be homogeneous and isotropic, the stressdisplacement relations are:
re= Gr(3/Dr)(v/r), rz = Gr(O/Dz)(v/r)
(6.4.3)
where G is the shear modulus, and v is the circumferential displacement.
They may be substituted into Equation (6.4.2).
G[v2 + (2/r)(D/3r)](v/r) + jxBz
using
2
2 +
2 2
/ r + (r/
+
= 0
(6.4.4)
2lr~~
2/az2. The boundary conditions are dis-
cussed below.
Equation (6.4.4) has been solved through use of stress functions for
structures without body forces.
The complex inner contour of the magnet
and the distribution of body forces make a finite difference approach a
more attractive path to a solutioh of Equation (6.4.4) considering the efficiency of high speed computers.
-1
F1-
'r
A
N
0
z
NS
ez
'r z
dz
a'rrz
Trz + azdz
Z
a T re
a r dr
r
Figure 6.71
Coordinates and Stresses in the
Torque Problem
-162-
6.4.2
Finite Difference Solution
Equation (6.4.4) was written in central difference form using the
variable m = v/r.
The surfaces are free of stress.
Consequently, from
Figure 6.71 the boundary condition becomes
T re (dz/ds
-
ez (dr/ds) = 0
where ds is an element of the boundary.
(6.4.5)
Using Equation (6.4.3) we ob-
tain
(gm/3r)(dz/ds) - (3m/dz)(dr/ds) = 0
(6.4.6)
A program had been developed previously to find toroidal currents
and fields by a finite difference solution of Laplace's equation disregarding temperature and conduction effects.
Consequently, jxBz would
be available if the vertical field vector were to be assumed constant
throughout the magnet at a value of 1 T.
-163-
REFERENCES
6.1
G.J. DeSalvo and J.A. Swanson, ANSYS Engineering Analysis System,
User's Manual, Swanson Analysis Systems, Inc., Houston, Pennsylvania,
1978.
6.2
S. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill,
N.Y., 1970.
-164-
List of Symbols
Section 7
(Force
-
newtons,
Distance - meters, Temperature - OK, Current - amperes,
Field
-
teslas)
a
-
area
B
-
vertical field strength
C
-
shape coefficient in thermal stress equation (7.2)
Ec
-
young's modulus for copper
Es
-
Young's modulus for steel
F
-
force
G
-
shear rigidity, usually E/[2 (1 + v)] where v = Poisson's ratio
h
-
half-height of maanet
I
-
moment of inertia
i
-
current in conductor of coil turn
j
-
current density in conductor of coil turn
L
-
half-height of free-hanging throat region
N
-
number of fatigue cycles
n
-
number of turns in magnet coil
P
-
pressure between turns of magnet
r
-
radial distance from magnet central axis
z
of beam cross section
ra,av -
radial distance to throat center
rbav -
radial distance to center of outer vertical leg
s
-
distance alonq median curve of turn
T
-
temperature,
tc
-
thickness of copper in turn
ts
-
thickness of steel in turn
also torsional moment
-165-
List of Symbols
Section 7
(continued)
v
-
tangential deflection (in e direction)
wa
-
radial width of throat
wb
-
radial width of outer leg
y
-
neutral axis distance of cantilever beam
z
-
vertical distance from magnet equatorial plane
-
thermal expansion coefficient, average from RT to 77K
A
-
incremental displacement (linear or angular)
6
-
cantilever beam deflection
cc
-
thermal strain in copper
Cs
-
thermal strain in steel
e
-
angular distance
a
-
general normal stress
Ga
-
basic allowable stress (reference)
ac
-
compressive stress
acu
-
compressive ultimate strength
Cr
-
radial stress
atu
-
tensile ultimate strength
Ctu
-
tensile yield strength
z
-
vertical stress
T
-
general shear stress
Ta,av
-
average TOz throat
b,av
-
average Tez at outer leg
ez
-
tangential stress (on equatorial plane, specifically.
see figure 7.9)
-166-
7.0
STRUCTURES ENGINEERING
7.1
Summary
The structures engineering effort on the ITR TF coil has ensured ade-
quate structural integrity in that component.
The critical regions are
the throat and the zone around each neutral beam port aperture where the
safety factors are 1.19 and 1.23, respectively.
The activities involved examination of the following problems:
1. Tensile stress in the throat due to Lorentz
forces,
2. Thermal stresses in the throat due to joule
heating in the copper,
3. Load transfer between copper and reinforcing
steel,
4. Constraint of the overturning couple due to
the Lorentz interaction between toroidal current and vertical field,
5. Shear strength of the plate assembly around
neutral beam ports,
6. Maximization of the fatigue life of critical
components.
This section of the report presents the details of those investigations.
7.2
7.2.1
Introduction
Basic Design Philosophy
As was stated at the beginning of this report, the ITR Program
has been visualized as a preliminary design effort.
The purpose has been
to generate a configuration that appears capable of satisfying the
-167-
mechanical requirements of the magnet in a manner c-nsistent with the
physics goals.
During the preliminary design process, numerous problem areas
were identified
to
basic philosophy.
Some problems have required close examination of de-
tails.
which
solutions have been found that meet the
Some were treatable in a perfunctory fashion.
However, insofar
as has been possible to identify it, no problem area has been neglected.
As a result of the MIT design studies, it is possible to claim that
'the current configuration appears structurally feasible for the intended
mission of the ITR.
The design has not been optimized.
Also, there are
areas that will require further study during the detail design phase,
when that occurs.
Those areas are identified at the conclusion of the
structures engineering presentation.
7.2.2
Scope of Structures Engineering Activity
This section on structures engineering discusses the structural
function of the magnet configuration, presents the calculated stresses
and describes the materials of the Bitter plate ITR.
The description
of the magnet was presented in Section 3. Finite element method (FEM)
and finite difference method (FDM) structural calculations appear in
Section 6. Strength-of-materials (SOM) analyses and stress summaries
are contained in this section together with material property data and
the description of the materials test program.
Bitter plate stresses have been calculated for Lorentz loads generated
by the TF coil current interacting with the toroidal and poloidal fields
-168-
to produce bursting and twisting forces on the TF coil.
The effects of
temperature gradients and of the coil preload were considered.
ceding were 2D analyses.
The pre-
A 3D FEM program (Section 6) provided toroidal
field stresses in the region of a neutral beam port.
The data were used
for an SOM analysis of frictional resistance to the toroidaT shears between ports.
An SOM analysis of the poloidal field coil backup ring also
is included.
7.2.3
General Structural Requirements of Magnet
The structural requirements arise from the physical performance
demands on the system.
The toroidal field at the radius of the com-
pressed plasma dictates the magnitude of the inplane Lorentz forces and
the vertical field controls the torque to be applied to the TF coil. The
plasma behavior generates the radiant flux spectrum and fluence. The
pulse leads to temperature fields as a function of space and time.
The geometric constraints on the coil are reflected in the magnetic field distribution which, in turn, interacts with the current
pattern to produce the Lorentz forces.
Consequently, the TF coil serves
the dual function of providing a magnetic field and resisting the forces
produced by it.
The backup girth rings have been placed where they are most effective
structurally.
field coils.
Those are also the best locations for the large vertical
It was expedient, therefore, to combine those functions.
.The design of the copper conductor in each plate is dictated primarily
by electrical needs.
The steel acts merely as a spacer material everywhere
-169-
except at the throat where it assists the copper in resisting vertica'
forces and at the outer boundary
where it enables the vertical forces
to transfer between the top and bottom of the magnet between the NB
ports.
The function of this report is to present the details of the verification activities employed to demonstrate the structural integrity of
the Bitter plate ITR magnet.
They include theoretical calculations of
applied stresses, extraction of data from the literature on material
properties and amplification of the data base by tests performed by MIT.
The design verification was not limited to analysis and test.
An
important aspect of the design process was the analysis of possible
failure modes and the structural consequences.
This was not done through
any formal process but was part of the design process.
It is felt that
the procedure is helpful in avoiding troublesome aspects of the design
and achieving a configuration that is realistic from the standpoints of
both performance and fabricability.
7.3
7.3.1
Structural Design Requirements
Purpose of Structural Components
The metallic materials in each TF coil plate react the forces
mentioned above.
The steel in the throat region assists the copper in
carrying the vertical loads.
High strength copper theoretically would
be able to support all forces in the remainder of the magnet structure.
However, the pulse magnetic performance requirements prohibit the use
of copper plates thick enough for that function.
-170-
Therefore, the outer
region includes steel wedge plates that serve primarily as filler.
The
stresses in the outer steel are small wnere they transmit vertical force5
from top to bottom of the magnet.
The thin grp (glass reinforced plastic) insulator material participates in resisting the torsional moment as well as preventing shorts and
breakdown between adjacent plates.
Consequently, it is subjected to
mechanical as well as electrical stresses.
is discussed in this report.
Only the mechanical behavior
However, a preliminary study indicates that
the insulator resistance will be satisfactory to the end of the design
life of the magnet.
The steel-copper composite in the backup rings reacts the inward
radial forces that preload
the magnet.
The grp insulates the coils
and transfers the preload pressure radially outward to each turn of the
vertical field coils.
Temperature gradients initiate thermal stresses only if there is
restraint to the potential thermal deformations.
In that sense, there-
fore, a structure does not resist thermal stresses but merely reacts to
the imposed temperature field.
of that reaction.
However, it must survive the consequences
That is the case with the Bitter magnet structural
materials.
7.3.2
Specific Structural Requirements
The magnet structure must be capable of withstanding 10,000 cycles
of full field with a minimum factor of safety of 10.
This includes with-
standing the plate planar loading and torsional moment from the PF current
-171-
interactions, the stresses induced by thermal gradients and these from
the preload forces.
Survivability entails resistance of the structural materials to
damage from the anticipated fluence of 1020 neutrons per square centimeter and 101
rads of gamma radiation.
Fabrication of the magnet involves erection loads that must be withstood without compromising structural integrity.
7.3.3
Design Constraints
The magnet structure must clear the vacuum vessel in the manner
discussed in Section 3.
It cannot encroach on the cylindrical space
for the ohmic heating coil.
The vertical dimensions offer relative
freedom of choice, as does the outer radius.
However, fabricability,
handling and cost dictate the desire for as small a size as possible.
The two large vertical field coils must be spaced from the outer
cylindrical surface enough to permit jacking pads between them and the
magnet.
The eight neutral beam ports restrict the space available for structural material at the outer boundary of the magnet.
Similar restrictions
exist at the eight flanges that contain the NB ports and the diagnostic
ports.
Support of the vacuum vessel also affects design details of those
flanges as well as the eight split closure flanges.
There are structural complications from the presence of the NB ports
and the cross-over copper turns which cause deviations in the load paths
-172-
from the top of the magnet to the bottom.
The plate thicknesses limit
the amount of bearing area available for transferring load through the
shear pads in the equatorial region between NB ports.
7.3.4
Structural Function of TF Coil
The basic structural function of the TF coil is to retain integ-
rity under the influence of the Lorentz forces, temperature fields and
nuclear radiation.
The backup rings assist the TF coil (via the radial
preload)to resist torsion.
The critical structural regions are found to be at the throat and
at the outer zone between NB ports.
The insulation is thinned in the
throat to avoid circumferential pressures that would tend to raise the
effective combined stress and also to minimize stresses due to the local
temperature increases during a pulse.
Vertical and radial forces are reacted within the plates and the
flanges.
plates.
Tangential (or circumferential) forces are reacted between the
That applies to the regions between the copper and steel com-
ponents of the plates and between plates and flanges.
7.3.5
Shear Load Transfer in Plates
The Lorentz forces are generated in the copper.
Within a plate,
there will be load transfer to the steel by shear more-or-less in a
radial plane.
The finite element analysis (Section 6) reveals the
shearing stresses to be small relative to the available frictional shears
and the shear strength capability of typical epoxy cements.
-173-
For that
reason, there has been no final decision at present on the method of joining plate components in the throat region although metallurgical bonding
between steel and copper has been assumed.
This is discussed in more de-
tail in Section 7.8 on materials investigations.
7.4
7.4.1
Material Strength Requirements
Basic Considerations
In this preliminary design of the ITR, the structure is required
to operate at a membrane stress level, aa, no greater than 2/3 of the
yield strength of the material (alone or as a composite) from which it
is fabricated.
When bending and/or thermal stresses are present, the al-
lowable is considered to be 1.5 aa, generally in compliance with the
ASME Boiler and Pressure Vessel Code (BPVC).
It also is required to
survive fatigue with a factor of safety of 10 on life.
The two major strength requirements are resistance to Lorentz tension in the throat with thermal stress present and survivability of the
insulation under circumferential compression combined with torsional
shear and tension.
The first requires a strong steel to reinforce the
copper while using the smallest possible amount of the throat crosssection area.
The steel must possess adequate toughness at 77 K to mini-
mize crack growth under the 10,000 cycles of pulsed loading.
The second
strength requirement can be met best by an insulator material that can
survive the radiation under the imposed loading while exhibiting good
frictional resistance and cementability..
One of the problems in the ITR is the transmission of Lorentz forces
from the copper, where they originate, to the steel which helps support
-174-
them.
The principal problem area is the throat where the radially in-
ward loading must be resisted by the copper and steel acting as a unit.
This requires bonding the two materials with sufficient strength to resist the shearing stress between them.
A discussion of bonding methods
appears subsequently in the section on materials testing.
However, it
is possible to show that, in the current configuration, the interface
shear stress would be of the order of 5 MPa,
which could be attained
with epoxy cement, for example.
7.4.2
Steel/Copper Composite
The behavior of a composite has been analyzed theoretically by
some investigators through application of a mixture law using relative
areas and stiffnesses of the components in both the elastic and inelastic
regimes.
MIT has adopted a different philosophy.
The composite has been
considered a single material in the same sense that a particular steel
is a single material for which the behavior patterns as functions of
composition and heat treatment are determined by structural testing.
The range of strengths of the components has been confined to highlycold-worked oxygen-free copper and a stainless steel with a yield strength
of the order of 700 to 850 MPa between 77 K and 240 K. That, hopefully,
wonild provide a composite with a yield strength high enough to satisfy
the requirement that the throat membrane tension would be below 2/3 of
that value, together with the ability to avoid fatigue failure within
100,000 cycles (FS = 10 on life).
Table 7.1 and Figure 7.1 display data
to indicate that these values can be achieved in a steel/copper composite.
They have in fact obtained in the MIT test program (Section 7.8).
-175-
Table 7.1
Typical Properties of Unirradiated Materials for ITR
77K
RT
Cold-Worked
A-286
ety
(MPa)
620
atu
(MPa)
1100
aty
(MPa)
970
atu
(MPa)
1500
elong.
M
23
Red.in A
M
30
321
---
830
970
1460
26
27
304 LN
690
1380
920.
1400
26
24
---
280
310
450
--
--
550
700
700
970
50
5
--
--
Steels
60%
Cold-Worked
Copper
Steel-Copper
Composites
(22% steel 78%
copper, 70%
cold worked)
Fiber Reinforced
Plastics
350
cu
700
> 310
-176-
to
0
0
Ld
:c
0
H-
Uf)
uj
0
w
(f)z
I
0
I
0
0
0
I
I
0
0
O
Dd
-177-
N '0
0
Table 7.1 lists yield strengths for a variety of stainless steels to
indicate availability for use in ITR.
growth resistance.
terest.
316-LN and A-286'exhibit good crack
Figure 7.1 exhibits fatigue data in the range of.in-
The table and figure indicate that choices exist for an effective
steel for ITR.
Copper strength data appear in Table 7.1 and Figure 7.1.
They in-
dicate that highly cold worked oxygen-free copper can contribute effectively to achievement of a reliable composite for ITR.
7.4.3
Insulator
The extensive insulator research program (described in Section 7.8)
has yielded candidates for the ITR environment.
have yet to be conducted.
Shear and tension tests
However, the compression data (Figure 7.2) indicate
the possibility of a fatigue factor of safety of 2 on stress and 10 on life.
7.5
7.5.1
Toroidal-Field Induced Stresses in TF Coil
Introduction
The toroidal field and plate current interact to induce Lorentz
loadings that tend to burst the magnet somewhat in the manner of a toroidal pressure vessel.
The vertical force is of the order of 5 x 108
newtons, of which approximately 60 percent is reacted at the throat. The
inverse radial variation of the toroidal field generates a net centripetal force on each plate.
This induces a circumferential pressure every-
where except in the throat close to the equatorial plane where the insulation is thinned.
The radial equivalent of the pressure is a centrifugal
force that reacts the centripetal force.
-178-
However, the distances from the
)
T)
0
o~)
(0
CD
0
I
I
Ld
to)
0
C,)
I
I
I
I
I
I
0
itJ
0
(D (D
Iz
<z
z
uLO
fb
tO
0
N
I t
I
I
I
I
0
IS)4'SS3:iLS
0
I
0
>1V3d
-179-
magnet equatorial plane are Rot the same for the two forces.
They thus
comprise a couple that tends to increase the throat tension.
The two main vertical field coils are also backup rings for radial
preload of the magnet.
pression.
This loading increases the circumferential com-
It also reduces the throat tension because the planes of the
radial preload are removed from the equatorial plane.
Lorentz forces on the horizontal legs of each plate cause moderate
bending stresses.
This contrasts with the throat region which appears
to be almost free of bending (See section 6).
Temperatures rise throughout the magnet during each pulse.
Most of
the effect is confined to the throat.
The FEM analyses (and SOM calculations, also) indicate that the
throat is the critical structural region of the magnet.
The 2D FEM analysis (Section 6) was performed for Lorentz loads.
Temperatures were determined by a finite difference method (See section 5).
Thermal stresses were computed using SOM.
7.5.2
General Character of Stresses
The FEM results are discussed in Section 6. Some of the data are
presented here in a modified form to accentuate features of the structural
behavior and to aid in determining combined stresses.
Planar stresses only would be induced in a magnet without port openings by the preload, by the Lorentz forces from the toroidal field current
-180-
interaction and by the temperature gradients.
The 2D finite element stresses
are essentially the same as the 3D stresses for combined preload and Lorentz
loadings, at radial locations inside the center of the uncompressed plasma.
Beyond that position, the three-dimensional effects from the ports begin
to increase and become greatest at the outer cylindrical boundary.
The Lorentz loads would induce shears between the copper and steel
of the composite because of transmission of part of the load from the
copper (where the loads originate) to the reinforcing steel.
The effects
would be greatest in the throat region where the Lorentz loads are mainly radially inward and largest in magnitude.
They would tend to vary
somewhat as 1/r toward the outer boundary and would act approximately
normal to the mean current contour in a plate to produce the equivalent
of a bursting load.
The circumferential compression (the reaction to
the centripetal loading on each plate) would tend to provide reaction
shears through friction, everywhere except in the thin-insulation region
of the throat.
The cement would help, as would the keys at the outer
boundary.
There would be shears acting parallel to the current paths on each
side of a neutral beam port to transfer the plate vertical tension load
around the port.
Those local stress fields would not be planar, however.
They would split at the top and bottom of a port and detour around the
port.
They would be symmetrical about the equatorial plane.
The shears
would be greatest near port corners while the vertical tension would increase near the port sides.
This behavior is comparable to the stress
field at a small hole in a membrane under uniaxial load.
-181-
7.5.3
Lorentz Plus Precompression
Figure 7.3 delineates the normal Lorentz stresses in the com-
posite from the 2D and 3D FEM analyses.
Force balances
indicate
the agreement of the results from the two methods despite the
differences in geometric and structural details of the two models.
peak copper stress is a
induced.
The
in the throat, where a magnitude of 310 MPa is
This would be increased slightly because of the thinned insulation,
as shown in the following section.
7.5.4
Effect of Thinned Insulation
The FEM calculations were performed on plates that were in con-
tact over the entire surface.
throat.
The insulation was not thinned in the
The effect of the thinned insulation is to remove the circum-
ferential pressure from that region and shift it symmetrically above
and below the equatorial plane to a new reaction position.
That would
generate a couple that would increase the tension in the throat and
reduce it on the outer leg.
The analysis of that effect (Figure 7.4) was performed by applying
the Tresca criterion and finding the location (above and below the
equator) at which the average tension at the throat (290 MPa, approximately)equals the vertical tension minus (algebraically) the circumferential compression.
The algebraic difference drops below 290 MPa at
approximately 0.3 m from the magnet equatorial plane.
The average cir-
cumferential pressure is 70 MPa over the region which is 0.33 m in radial
width so that the area is approximately 0.1 m2 . The equivalent
radial
-182-
350
AVERAG E az AT THROAT
2Q
b
300
_
3D
R = 0.74m
R =0.4m
100
AVE RAGE
ONR AT R = 1.50 M
ON
RADIAL ARM
0
3D
b
-100
LO VER
ED GE
Figure 7.3
UPPER
EDGE
2D and 3D stresses at selected locations
-183-
z
2
0)
0
E
0)
dz
0
Z
0-j0:
E
w0
0
.
r(
zJ
C'J
do
6
~
crE
0
C
z
[I
E
I
Ef
0')
M
0
6i
I-
z
2
0
-184-
w
force is 0.17 MN (each plate angle is 1.4 degrees) acting approximately
0.15 m above the equatorial plane.
The radial reaction is assumed to be
located at 0.9 m above th.e equator so that th'e couple arm is 0.75 m. The
vertical reaction (with approximately 2.6 m between the center of the
throat and the center of the outer leg) would be (0.75/2.6)0.17 = 0.049
MN.
The increase in tension stress would be approximately 10 MPa, or 3
percent of the vertical stress shown in Figure 7.3.
The total peak
vertical stress in the composite would be 320 MPa which yields a FS of
1.46 compared to 2/3 yield.
The peak shear, Tez, was found to occur near each port corner at
a magnitude of 20 MPa on the outer boundary (Figure
value is approximately 17 MPa.
6.51).
The current plate leg width is 0.5 m com-
pared to 0.2 m used in the 3D analysis (Figure 6.29).
are proportioned inversely
The average
If the stresses
to the leg widths then the peak and average
values would become 8.0 and 6.8 MPa, respectively.
The horizontal
arms of
each plate are in bending combined with a
small radial compression (Figure 6.43).
The compression is the net ef-
fect of compression from the preload and tension from the Lorentz forces
that act radially outward on the outer leg of the magnet.
The peak com-
bined stress of nominally 100 MPa is a small fraction of the allowable.
The transition from the throat steel reinforcement plate to the
outer steel filler
occurs at the zone of the point of inflection (Figure
6.43) where no bending strength is required.
in that region is
7 MPa
The vertical shearing stress
(Figure 6.48) which can be provided by frictional
-185-
shear since the circumferential compression is of the order of 60 MPa
(Figure 6.36).
This is the region in which a vertical splice would be made in the
copper plate.
It is apparent that no problem would occur by welding
since the shear stress is well below the 40 MPa
shear yield strength of
annealed copper.
7.5.5
7.5.5.1
Thermal Stresses
Introduction
The temperature field may be decomposed into four components:
1. Differential shrinkage of steel, copper and insulation due to slow cooling to 77 K from RT,
2. Differential expansion of steel, copper and insulation during pulse heating,
3. The average temperature rise along the mean
toroidal path during pulse heating,
4. The components normal to the mean toroidal path
during pulse heating.
Stresses from (1) and (2) are calculated for reference purposes only.
As discussed subsequently, they would have little influence on magnet
life.
Thermal strains for stainless steel, oxygen-free copper and G-10
appear in Figure 7.5 as functions of temperature, referred to 273 K.
The computations for cases (1) through (4) were made on the assumption that Young's moduli for steel, copper and G-10 are 200, 120 and 20
GPa, respectively.
Those values indicate that the thin insulator cannot
resist the deformations of the copper and steel components of the composite.
-186-
H
-0
Q0
z
(M
Ld~
Li..
..
-li
0
0
NLLJ
LL.~
o
z>
LLJ
UL
0.H
z
rf
0..
H
_LL
0
00
O
0
D
o
cr-
LL
-187-
0U
7.5.5.2
Slow Cooling From RT
If the plates were free in space, the difference in thermal ex-
pansion (steel vs copper) would lead to the three dimensional equivalent
of the bimetallic strip action.
cal surfaces without stress.
The plates would tend to curve to spheri-
However, if the plates are constrained to
remain flat, the equality of strains and balance of forces would lead to
the relation:
ac/Ec
c
-
Application of the data on the thermal strains (ec
moduli and thicknesses, will lead to ac
a
=
25 MPa.
(7.1)
£s) [tcEc/tsEs + 1]1
~ Es = 0.00028), Young's
= 15 MPa and as = (200/120) 15 or
Those results would apply to the throat region where tc is
2ts, on the average.
Away from the throat, tc and ts are more nearly equal
and ac = 21 MPa while as = 34 MPa.
Near the plate boundaries, shears
could exist at magnitudes that would be slightly
lower than ac'
The above stresses are maxima.
If the plates are not constrained to
be perfectly flat, the stresses would be less.
The precise behavior can
be identified only through more sophisticated analysis than shown here.
7.5.5.3
Differential Expansion From Pulsed Heating
During a pulse, heat is generated in the copper.
The time to the
end of the flat top is too short for appreciable radial heat flow away from
the site of heat generation.
The temperature of the steel will follow the
heat rise in the copper closely, however, where they are in intimate contac.t (as through metallurgical bonding, for example).
-188-
That was the assumption
made in calculating the temperature distributions shown in Section 5.
The mean temperature rise is greatest at the throat where the change
is from 77 K to 180 K. The differential thermal strain is reduced to
0.0001 which reduces the stresses from the slow-cool values to 8 MPa in
the copper and 12 MPa in the steel outside the throat.
The precise values
will depend upon the degree of flatness achieved in the plates.
7.5.5.4
Pulsed-Induced Toroidal Gradient
The data from Figure 5.6
have been reproduced in Figure 7.6 to
show decomposition of the pulse-induced temperature field into a mean
toroidal gradient and normal gradients.
duce two effects.
The toroidal gradient would in-
One would be an increase of the plate height in the
throat zone that would be resisted by frame action in the magnet.
The
other would be a stress field comparable to that generated by longitudinal
gradients in a long strip.
Each will be analyzed separately.
The frame analysis model is depicted in Figure 7.7.
This approach
is feasible since the thinned insulation at the throat avoids cylinder
action, which could increase the stresses over the values shown in this
calculation.
are small.
Simplifying assumptions have been made since the stresses
The bending stress is found to be 17 MPa at the throat and
the compression is virtually zero.
The long-strip calculation was adapted from the result.in reference
1 on the assumption that the strip width is constant.
is depicted schematically in Figure 7.7.
Stress is induced by the vertical
variation of the transverse thermal expansion.
-189-
The temperature
,-WI DTH0.34m
TRANSVERSE STRESS
DISTRIBUTION AT THROAT
14
MPa
(T)
I.Om
7MPa
(C)
IIOK
250
z
AT EQUATORIAL PLANE
200
T
*
T
0
( K)
)
150
M IDWAY
10 0
AT TOP OF INNER
LEG
AT=40K
0
190K
LONGITUDINAL
(TO ROI DAL)
GRADIENT
Figure 7.6
R=0.4M
TRANSVERSE
R =0.74M
GRADIENTS
Decomposition of temperature field at end of flat top
-190-
T=O
51
T=O
10I
AT
THROAT
AR =AZ =A6=0
Y=
=
FRAME ANALYSIS MODEL
0.4mi+-
(ASSUMED
TO
BE COSINE
~I.2m
VARIATION)
T
TOP HALF OF ASSUMED
EQUIVALENT
STRIP
O.33mV
FRAME IN THROAT
REGION
LONG
Figure 7.7
STRIP.MODEL
Models used for thermal stress analysis
-191-
The equation for the tension at the edges is (Reference 2)
a = CaEAT
(7.2)
where C is of the order of 0.1 for the proportions of the gradient
shown in Figure 7.7.
as
The edge tension is 14 MPa while the center com-
pression is approximately half that value, or 7 MPa.
7.5.5.5
Normal Gradient
The normal gradient is reducible to a linear component
deviation from the linear (Figure 7.8).
where AT is the local temperature
and a
The deviation stress is aEAT
deviation from linear.
The peak ten-
sion is at the edges where AT = 3 K. The stress is equal to 7 MPa using
equal to 18 x 10-6 per degree K at 215 K.
The linear gradient is virtually constant over the magnet height at
58 K radially across the throat (0.34 m wide),
The frame analysis for
that case yields a throat bending stress of 34 MPa.
The direct com-
pression is negligible.
7.5.5.6
Total Thermal Stresses
The slow-cool and pulse-heating thermal stresses virtually offset
one another.
At the end of the pulse, the remaining stress is 8 MPa in
the copper and 12 MPa in the steel (Section 7.5.5.2).
These are self-
equilibrating and are considered to be of minimal significance
to the structural integrity of the TF coil.
Consequently, they have been
neglected in the final analysis of stresses in the magnet.
-192-
215
LINEAR GRADIENT
200-
212
LOCAL AT
-DEVIATION FROM
LINEAR GRADIENT
157
154
0.34 m
R= 0.40m
Figure 7.8
Normal gradient in the throat region
-193-
The remaining tension thermal stresses have a total value of
17 + 14 + 7 + 34 = 72 MPa.
7.5.6
Total Stresses
The sum of the mechanical stresses (320 MPa, Section 7.5.4) and
thermal stresses (72 MPa) is 392 MPa.
It yields a safety factor of
1.19
based on 2/3 yield and a safety factor greater than 10 based on life using
the properties of the composite shown in Table 7.1 and Figure 7.1.
The stresses in the steel and copper are considerably smaller at
the outer boundary.
The combination of vertical shear with the torsional
shears is discussed in 7.6.4.
The insulation at the throat will be strained the same amount as
the copper-steel composite. If.the ratio of Young's moduli is assumed to
be 1/10, the combined membrane plus thermal' stress would be 39 MPa.
sequently, the safety factor would be 3 based on 1/3 of ultimate.
-194-
Con-
7.6
7.6.1
Torsional Stresses in TF Coil
Introduction
Interaction of the poloidal field and the TF current induces Lorentz
loadings that act perpendicular to the plane of each Bitter plate.
vectorial senses of the loadings are opposite,
The
above and below the equatorial
plane of the magnet, so that self-reacting torsional moments are generated
in the magnet (Fig. 7.9).
The magnet axisymmetry causes only shearing
stresses on, and perpendicular to, each vertical radial plane.
7.6.2
Analysis
The circular shears on the equatorial plane react the torques.
If
average values are used, the torque balance (Fig. 7.9) would be
T = nftr(i X BZ)da = 2 (Ta,avwa ra, 2av + Tbav b rb, 2 av)
The plate proportions yield wara, 2av << wbrb, 2av.
are comparable (as will be shown).
(7.3)
Also, ca,av and Tb,av
Therefore, it is reasonable to neglect
the first term in parentheses for estimation purposes.
Also, if Bz is
constant then it is possible to simplify the integral with the aid of
Fig. 7.9 to obtain
Tbav = n(iBzrb, 2av/2)/(2arb, 2avWb) = niBz/(4nWb)
This is reasonably close to preliminary finite difference results.
It also indicates that (as a conservative approximation when raav
is small) -ris independent of magnet shape and size.
only on i, Bz and the width of the
outer leg, wb.
-195-
It is dependent
(7.4)
0
0
0
N.0
<0
N
Nl
N
z.
N
m
0.A
'-4
cF-
a
-4
c1.
'I
N
.1,
N
CL
Q-0
*;;
LU
U)
-W
-
F-
Q)N
4
-
LL
114
co
0
N
co
0r-4
H-L
U.H
LUJ
z
0r
_
_
v
-196-
_
The internal resistance of the magnet to Tb,av is supplied by the
cement, the keys and frictional shear.
The frictional shear, in turn,
depends on the tangential pressure from the clamp ring preload and the
inplane Lorentz centripetal forces., A complication arises at each neutral
beam port aperture which alters the circumferential compression in the
equatorial zone and also reduces the available shear surface.
A preliminary torsion analysis was conducted on a magnet without
beam penetrations by amplifying the classical axisymmetric differential
equation to include Lorentz forces and by solving the equation with finite differences.
The circumferential pressures were calculated
by 2D FEM (Section 6.2 ) for a magnet without ports
bursting
loads.
under Lorentz
A localized 3D FEM calculation was then performed for
one magnet- octant (under the same loads) including a port and cranked conductors (Section 6.3).
The final determination of magnet torsional structural
integrity was performed by SOM computations.
7.6.3
Results
The total plate current is 242,000 amperes and the vertical field
is 0.86 T. From preliminary FDM it is found that, at the equatorial
plane, the maximum shear stress, Tez, on the outer leg is 8.4 MPa and
has a maximum value of 13.3 MPa on the inner leg.
The conservative SOM
value at the outer leg (Equation 7.4) is 8.5 MPa which agrees reasonably
well with the peak FDM value at that location.
The horizontal shearing
stress at the midspan of each horizontal arm is 6.6 MPa.
The maximum rotational deflection from the FDM analysis occurs
at the outermost corners at a value of 0.11 mm.
-197-
If the vertical shearing stress
is assumed to be parabolic (Fig. 7.9) then the circumferential deflection
at each extreme corner would be
v = (1/2)(T/G)h
If 1
(7.5)
8.4 MPa, G = 4 x 104 MPa and h = 1.215 m, then v = 0.13 mm.
The
agreement would be better if the mean shear stress were to be used.
At the top and bottom of the unbonded section in the throat, the
deflection is 0.10 mm.
7.6.4
Shear Between Ports
The average shear stresses would increase in magnitude between
ports because of the reduced shear resistance length (Fig. 7.10).
If
the achievable shear stress level were to come from friction alone, the
stress would be zero at the port edges and could vary somewhat as shown
in Fig. 7.10.
The 3D finite element analysis for a magnet without apertures reveals a circumferential compression distribution as shown in Fig. 7.10.
However, that was applied to an earlier magnet design in which the outer
wall thickness was
value of 50 cm.
25 cm at the equatorial plane instead of the current
The greater wall thickness could result in greater cir-
cumferential pressure due to the increased stiffness of the cylinderlike region of the outer leg.
When these factors are taken into account, the available resisting
shear will comoare with the applied shear as shown in Table 7.2.
The
friction coefficient of fiberglass on copper was taken at 0.30, which is
-198-
PORT
PORT
4-50
PORT WIDTH=9*
PORT
360
M AGNE T
EQUATOR
-EFFECTIVE p 15 MPa
MAX:y
3
MPa
NORMAL PRESSURE
4.5 MPa
ACHIEVABLE CEMENT
SHEAR STRENGTH
Figure 7.10
Shear between ports
-199-
Table 7.2
Torsional Shears Between Neutral Beam Ports
45 degrees
Angle Between Port Centerlines
9 degrees
Assumed Port Width
Assumed Effective Width of Material Between Port Edges
36 degrees
Effective Normal Pressure (Figure 7.10)
15 MPa
Equivalent Frictional Shear Stress
4.5 MPa
Achievable Cement Shear Strength
7.0 MPa
11.5 MPa
Total Achievable Shears
Effective Shear Between Ports, (36/45) 11.5
9.2 MPa
Average Applied Shear Stress Without Ports
7.5 MPa
Safety Factor
1.23
-200-
the lower bound of data shown in Reference
3. The shear factor of safety
is seen to be 1.23.
The peak vertical shear at a port corner, by 3 D FEM analysis, is
approximately 20 MPa (Fig. 6.72) which translates to approximately 12
MPa in the current design.
The normal pressure is 120 MPa at the same
location (Fig. 6.40) which is more than enough to prevent frictional
sliding.
The torsional shear in the same location would be approximately
6 MPa from the FDM analysis of the magnet without ports.
However, trhe
torsional shears would be negligible at the port edges.
Consequently,
it is reasonable to disregard the latter stress and not combine the
torsional stresses with the port-corner "inplane" stresses.
The applied torque is 2.71 x 108 N-m
it would appear to be realizeable.
precaution.
Eq. (7.3). Theoretically,
However, keys have been added as a
The keys are spaced vertically 0.3 meters on centers.
Conse-
quently, the vertical force per key on either side of the equatorial plane
is 1.26 MN using the peak vertical shear of 8.4 MPa and the 0.5 m width of
the outer leg.
The key bearing surface is 0.4 m by 0.020 m or 0.0080
sq. m in area.
Consequently, the bearing pressure is 160 MPa.
The key
height is 0.1 m which leads to a shear area of 0.04 sq. m and a shearing
stress of 32 MPa.
The bearing stress is 80 percent of the allowable
compression of G-10 and the shear is 7 percent of the allowable for 316
LN steel.
-201-
7.6.5
Throat Lateral Bending
Each plate hangs free over a height of 0.3 m in the throat region
(Fig. 7.4) because of the thinner insulation.
This causes bending at
the top and bottom of the free region from the relative lateral displacements due to twisting.
The finite difference analysis indicated a lateral
motion of 0.10 mm relative
to the equatorial plane.
If the free-hanging
plate region is assumed to be a cantilever, the bending stress at each
end can be found from
a = 3Ey6/L
With E = 4 x 104 MPa, y = 7.1 mm, 6
found that a is 0.5 MPa.
2
(7.6)
0.10 mm and L = 0.4 m, it is
If the shearing stress between the steel
and copper is assumed to be T = 3V/2A, the ratio, T/O, will be equal to
(1/4)(t/L) and, therefore, the shearing stress would be negligibly small.
-202-
7.7
Poloidal Field Coil
Introduction
7.7.1
The poloidal field coil is integral with the backup ring.
It con-
sists of 50-50 copper/steel composite bands with the flat sides vertical.
10 percent of the cross-section area will be grp insulation.
The radial preload is 37.2 MPa to maintain a high level of circumferential pressure during coil activation, which tends to induce radial
growth due to Lorentz loading and temperature rise and,thereby, diminish
the preload pressure.
The Lorentz mutual attraction of the coils is assumed to be resisted
by frictional shear on the jacks that are used to apply the preload
(Figure 3.2 ).
7.7.2
Analysis
The peak poloidal current of 3.12 MA
induces an outward radial load-
ing of 0.28 MN/m which corresponds to a pressure of 0.56 MPa during each coil
pulse.
The concurrent temperature rise is 12 K. The mutual vertical attraction
is 0.23 MN/m.
The jack-induced preload is equivalent to a radial pressure on
the TF coil outer surface (R = 3.3 m) of 37.2 MPa.
No radial deflection occurs
at toe center of tne cuil (Figure 6.67) when the TF coil is energized.
How-
ever there is an outward movement of 0.256 mm at the top of tne coil due to
local tilting of each plate.
The coil cross-section (0.5 meters square) is considered to be
95 percent effective vertically and 95 percent horizontally, -or 90 percent
-203-
effective on a vertical radial plane.
pr/t,
Therefore, the circumferential stress,
is 37.2 (3.3/0.5)/0.9 = 273 MPa on the composite.
The effective
radial pressure (at 95 percent radial effectiveness) is 37.2/0.95 = 39.2 MPa.
The Tresca combined stress then would be 312 MPa.
The outward movement due to plate tilt would induce a hoop strain
(r = 3,300 mm) of 0.256/3,300 = 7.76 x 10-5 which corresponds to a stress
of 12.0 MPa if E = 1.55
x
105 MPa, which would increase the Tresca stress
to 324 MPa.
The radial Lorentz poloidal loading would increase the radial position
of the ring by 1.5 percent.
That would tend to decrease the preload by
1.5 percent since the ring is much more flexible than the TF coil.
Conse-
quently, no increase in ring stress would occur, nor would there be any
significant decrease in radial load on the TF coil.
The ring thermal growth strain would be 10~.
It would correspond
to a ring tension stress reduction of 16 MPa which would tend to reduce
the preload by (16/273) 37.2 = 2.2 MPa, or about 6 percent.
The mutual attraction of the coils would lead to a required frictional shear stress of 0.23/0.5 = 0.45 MPa to avoid vertical slippage.
It can be resisted easily by the radial pressure of 37.2 MPa in combination with a friction coefficient of 0.3.
7.8
7.8.1
Materials Investigations
Introduction
The materials investigations involved a literature survey and
-204-
material property testing.
The literature survey indicated that metals
could survive the ITR fluence (except for a 30 percent increase in
resistivity in CDA 101 or 102 copper).
ators.
The uncertainty lay with insul-
Consequently, the MIT test program on irradiated materials was
confined to insulators.
A few tests were performed on unirradiated metal
composites.
7.8.2
Literature Survey
Steels and nickel alloys have been shown to suffer little damage
under 1022n/cm (references 4 and 5).
The tests were conducted at 300 K
so that a direct inference for 77 K survivability cannot be drawn.
How-
ever, the data indicate that inappreciable change occurred up to 1020
n/cm 2 , which is the ITR dose.
The publications identified in references
4 and 5 shed no additional light on 77 K performance.
These factors, to-
gether with limited available funding, formed the basis for delaying the
start of a test program on irradiated metals.
The general status of published insulator data is compared to fusion
reactor requirements in Table 7.3 which indicates a weak relation.
Specific information appears in Table 7.4 (covering three pages).
data were derived from references 6 through 15.
The
Little help was avail-
able for the ITR program for which thin sheet insulators with good friction
coefficients must be capable of surviving 10l1l
raso
amsad120
rads of gammas
and 10
n/cm 2
In designing the MIT test program, guidance was sought on the choices
of matrix and fiber materials.
suggested boron-free E glass.
In private discussions, some investigators
However, Figure 7.11 vitiates the value of
that choice.
-205-
Table 7.3
Fusion Reactor
Insulator Environment
1. NUCLEAR RADIATION FLUX
2. LORENTZ (AND PRELOAD) NORMAL PRESSURES, INTERLAMINAR SHEARS AND INPLANE
BENDING PLUS MEMBRANE LOADS.
3. 10
TO 106 CYCLES.
STATIC LOAD DURATION - MONTHS.
4. LIQUID HELIUM TEMPERATURE (CONSTANT) FOR SOME.
TEMPERATURE, FOR OTHERS.
PULSE, STARTING AT LN2
ALL ACT TOGETHER
INSULATOR TEST CONDITIONS
1. MOSTLY RT IRRADIATION, SOME CRYOGENIC
2. MOSTLY STATIC, SOME CYCLIC, LITTLE CREEP TESTING,NO COMBINED LOAD TESTS
3. MOST TESTING AT RT, SOME AT 77 K, SOME AT 4 K.
ALL TESTING AFTER APPLICATION OF TOTAL FLUENCE
-206-
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Utility of Inorganic
Damage
:
MZ// =/
Mcgnesium oxide
Aluminum oxide
=
Incipient to mild
Mild to moderate
Nearly always usable
Moderate to severe
Limited use
Often satisfactory
I-
Ouartz
Glass (hard)(<lO'6n/cmn)( a)
Glass (boron free)
Sapphire
Forsterite7
/
..
Spinel
777-77-,T
,
'/
/A
1s
.-
44
Beryllium oxi.de
lo l
l08
102
1020
lo9
Neutron Flue nce, n/cm2(E>O.1 MeV)
109
10"
1010
1Q12
Gamma Dose, rods(C)(b)
(a) Unsatisfactory at l0' n/cmz
(b) Approximate gamma dose (4 x 108 n/cm 2 = I rod (C))
(C) Varies greatly with temperature
Figure 7.11
Survivability of irradiated nonmetallics
-210-
l0'
It is important to know the relationship of strength loss as a function of the range of dose level.
such a relation.
Figure 7.12 reveals the uncertainty of
No information was found on friction coefficient of ir-
radiated materials.
However, data exist on unirradiated G-10 from pro-
jects performed at (and sponsored by) MIT (reference 15). Micaglass was
mentioned as an inorganic insulator candidate (reference 16).
However,
tests performed during the MIT insulator program showed a friction coeficient on copper too low for the ITR.
Insulator Testing Program
7.8.3
7.8.3.1
Introduction
This section is, for the most part, a reproduction of the paper
presented at the ICEC Conference in Geneva on August 2, 1980(Reference 15).
The term "radiation damage", as applied to structural behavior, can
be defined as the reduction in load-carrying ability resulting from exposure to radiation.
It has been observed that the radiation induced
loss of strength of a material could depend upon the type of load to be
resisted.
The data in this paper indicate that the structural configuration
could be of major importance.
The reactor magnet consists of large flat plates of copper/steel
composite separated by thin insulator sheets.
-211-
The insulator must survive
4I
-1__
-_1_____I
I
N~II
-
Fig. 6
ERL 0510
DAN
0
4
Fig. 8
2
1
0
DER 332
DDM
N.-
4
-I
Fig. 9
DER 332
2
BF
3
4
1B
4
Fig. 10
1
DER 332
DDS
04
3
2
0
2
4
3
Fig. II
EPON 826
EPI CURE 841
-B
-T
Fi g.- 12
EPON 826
4
0DM
2
Fig. 13
0
EPON 826
OTOL
1010
Figure 7.12
101
RADS
8 =Broke
Epoxy strength loss as a function of dose level
-212-
10,000 cycles of 140 MPa pulsed pressure together with 8.4 MPa
pulsed interlaminar shear stress and a lifetime radiation fluence of
1020 n/cm 2 . The pulses could occur at 30 minute intervals.
Further-
more, each cycle would start at 77 K and end near 150 to 200 K. In
addition, the insulator must have a coefficient of friction of at least
0.30.
Most of the existing test data on insulator radiation survivability
have been obtained from static flexural and compression tests on rods.
It may be apparent that those results would not apply to thin sheets
under cyclic compressive load.
Preliminary studies on unirradiated in-
sulators indicated that a 1/2-millimeter-thick fiberglass composite with
an organic matrix might withstand the ITR environment.
Consequently, a
program of irra-diation and test was carried out to explore that possibility.
7.8.3.2
Rationale
The failure mode in a compressed thin sheet of brittle material
is different from that of a rod.
The stress distribution in a rod is
uniaxial and failure usually occurs on the familiar diagonal shear plane,
more or less at 45 degrees to the rod axis.
The thin sheet also would
be under uniaxial compression if a pure pressure were to be applied.
However, the insulators on the ITR are compressed between large flat
plates.
As a result, there is friction-induced restraint in the plane
of the sheet'similar to the behavior studied by Bridgman
The diagonal shear failure planes cannot form easily.
(reference 14).
Observations
reveal that the insulator specimens are reduced to powder by extensive
-213-
compressive cycling, in support of that hypothesis.
Failure of G-10 and similar grp materials may begin by crushing at
the intersections of the cloth warp and fill fibers.
Tendency for the
cloth to spread would be resisted by friction from the metal plates retarding breakage until the fibers begin to crush between intersections.
The matrix material would help to support the fibers during that process.
The onset of failure has been observed to be accompanied by rapid
degradat-ion of stiffness.
Development of a quantitative theoretical explanation would require
more extensive study.
Until that time, the above rationale has been
adopted as part of the basis for believing that materials like grp can
withstand the ITR fluence at the design compression stress for the required number of cycles.
7.8.3.3
Failure Criterion
It is a simple matter to observe failure in compressed brittle
rods.
A break occurs and the testing machine load drops suddenly toward
zero.
In thin sheets, however, the failure process is not so obvious.
This is particularly true of fatigue loading.
It was noticed, during exploratory tests on unirradiated specimens,
that the stiffness appeared to increase by a few percent up to approximately 5,000 to 10,000 cycles after which the stiffness reduced by
several percent during each successive interval of 10,000 cycles.
same phenomenology was observed during the INEL tests bn irradiated
-214-
The
specimens except that the degradation in stiffness occurred in a few
hundred cycles (Figure 7.13).
Subsequent examination showed that at
least one disk in a stack of five had been reduced to powder.
It was decided to define failure in thin sheets as the rapid reduction of stiffness.
The relevant data were chosen as the stress level
and the number of cycles at which that rapid reduction occurred.
7.8.3.4
Initial Tests
Experiments were carried out with sheets of fiber-reinforced
plastics and one common inorganic electrical insulator.
Unirradiated
specimens of G-7, G-10 and micaglass were subjected to compression fatigue
at RT.
Both G-7 and G-10 are commercial E-glass reinforced plastics.
The matrix system of G-7 is silicone while that of G-10 is epoxy.
The
test fixture and loading scheme are shown in Fig. 7.14.
The initial test results appear in Table 7.5.
The grp survived
pressures twice as high as in ITR for the required 10,000 cycles.
The
micaglass, however, did not survive under pressures 50 percent greater
than in ITR.
The 1 Hz frequency was chosen as a practical compromise
between the low ITR cycle and the need for shorter test times to collect
data from several samples.
Additional tests (Table 7.5) were performed on unirradiated specimens selected from the composite formulations described below.
results also indicated high potential for survival.
-215-
Those
F
-C~p.~
U
'1
t~W;~~ j
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3
57o
yL
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0
p.
0
~
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5
0
I
~
0
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z
C
C
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~
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1700
.j ~-d
C~~CC
in-
-
2~C--
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A
~ <i~ 72~
T
FOL 5.
LOAD DEFLECTION->
Figure 7.13
Compressive degradation
cyclic loading
-216-
curve from
-J
U
11.
1 MM DIA.
TYPICAL
STEEL PAD
6.4 MM
t4
+--
TYPICAL G-10 SPECIMEN
ARRANGEMENT IS TYPICAL FOR G-10
I
PMAX
LOAD
0
1 SEC.+
TIME
Figure 7.14
Test fixture schematic and loading cycle
-217-
TABLE 7.5
RESULTS OF COMPRESSION FATIGUE TESTS OF
UNIRRADIATED SAMPLES AT RT
(5 Specimens of Each Type Tested in Stack Shown in Figure 7.14)
INITIAL TESTS
Material
Thickness
(mm)
G-7
Max. Applied
Stress
(MPa)
Number of
Cycles
207
10,000 S
276
10,000 S
207
100,000 F
0.3
G-10
0.50
310
60,000 S
Mica-Glass
0.50
207
10,000 F
S = Survived, F = Failed
ADDITIONAL TESTS
Material
Matrix System
Kerimid
Thickness
Reinf.
601
S
0.50
Max. Applied
Stress
(MPa)
Number of
Cycles
All
TGPAP
+
DCA
S2
0.50
All
DGEBA
+
DDS
S2
0.50
310
TGPAP
+
DDM
E
0.46
TGPAP
+
DDM
S2
0.48
TGPAP
+
DDS
S2
0.50
Tests were halted arbitrarily at indicated number of cycles.
mens survived.
-218-
60,000
All speci-
7.8.3.5
INEL Tests on Irradiated Specimens
Disks were cut from thin sheets of G-7, G-10 and G-11 CR*. They
were irradiated in the Advanced Test Reactor at Idaho National Engineering
Laboratory.
The nuclear flux was calculated from a standard code used at
INEL and is stated to be within 20 percent of actual values.
The total
fluence was 1.6 x 10 19 n/cm 2 for neutron energies greater than 0.1 Mev,
1020 n/cm 2 for the total neutron spectrum and 3.8 x 10l rads of gamma
radiation.
That dose is somewhat higher than the fluence expected in
ITR.
The specimen temperature was reported to be 320 K. All specimens
were found to be highly radioactive after months of cooldown.
Consequent-
ly, testing was conducted in a hot cell.
The compression fatigue tests were conducted in the same manner as
for the unirradiated samples (Figure 7.14).
7.6.
The results appear in Table
In addition the G-10 data are plotted on the graph of Figure 7.15.
All tests were stopped arbitrarily at 200,000 cycles if no failure had
been observed.
It is clear that the observed strengths are much greater than reported previously for rods irradiated at 4.9 K
for which G-10 CR
static compression values of about 69 MPa were obtained.
The INEL re-
sults also exceed the ITR requirements.
The stress level of 345 MPa
is more than twice the ITR requirement.
Furthermore, 200,000 cycles
*Diglycidyl ether of bisphenol A reinforced by E-glass.
-219-
TABLE 7.6
RESULTS OF INEL COMPRESSION
FATIGUE TESTS ON IRRADIATED INSULATORS
For all Specimens D = 11.1 mm
Material
Thickness
(mm)
Temperature
Max. Applied
Stress (MPa)
Number of
Cycles
G-7
0.30
RT
207
10,000 F*
G-11
4.00
RT
207
10,000 F
207
200,000 S
241
200,000 S
276
21,900 F
310
3,570 F
345
460 F
207
20,000 S
241
40,000 S
276
36,000 S
310
30,000 S
345
30,000 S
RT
G-10
0.50
77 K
* Paired disks broke, singles survived
-220-
D Dd I
0
O()
10
10
00
I0
x
N
0
___
U)
Lu
-
0
vJ
I-
0
O
w
II
z
I
M'
b
0
--
N
.
I#
a
I
I
I
0
0
0
IS~l S
0
I
S38.
LS
-221-
corresponds to 20 times the required life.
If it is assumed that the low temperature fatigue strength is twice
the RT value, which matches the ratio for static ultimate compression
of G-10 rods, then the 77 K fatigue curve would be as shown on Figure
7.15.
The observed survivability of the 77 K specimens is consistent
with that curve.
7.8.3.6
MIT Tests
The INEL tests were considered to support the rationale that
G-10 might survive th-e ITR environment.
dependent data as a further check.
It was important to obtain in-
It also was decided to broaden the
scope of the program by including other potential candidate insulators.
A search of the literature showed that epoxy and polyimide resins
with fiberglass reinforcement could be considered as candidate insulators
for ITR.
Among epoxy resins, glycidyl amines were concluded to be more
radiation resistant.
The aromatic amine hardeners lead to resin sys-
tems which appear to be more stable under radiation than do anhydride
hardeners.
According to reference 7, glycidyl amine and glycidyl ether
resins are best when combined with anhydride whereas novolac is best
when combined with an aromatic amine.
Most radiation tests had been carried out with commercial laminates
with E-glass reinforcement (References 10,11).
Because of greater purity,
S-glass appears to provide a more useful reinforcement than E-glass for
radiation resistant insulators.
In reference 6 it is shown that boron-
free E-glass begins to show damage under 1016 n/cm 2 while quartz shows no
-222-
damage up to 1021 n/cm 2 (E > 0.1 MEV).
Sheets of composite were prepared from two epoxy resins (glycidyl
amine and glycidyl ether) mixed with aromatic amine and anhydride
hardeners in combination with E-glass, S-glass and quartz fiber reinforcement.
Polyimide resins were also employed with these types of
reinforcements.
The components are shown in Table 7.7.
Twenty-eight types of specimens (Table 7.8) of various thicknesses
were evaluated for residual radioacti.vity. They were irradiated in the
MIT Reactor for 96 hours.
The total fluence was 1.4 x 1018 n/2 and
5 x 109 rads of gamma radiation.
The activation of each specimen was measured 258, 330 and 450 hrs.
after irradiation.
The S-glass composites were of the order of 1/10 as
active as E-glass composites.
This agrees with the INEL observations
regarding the high residual activity of E-glass composites.
The composite combinations in Table 7.8 were irradiated in the
M.I.T. reactor to 2.3 x 1010 rads of gamma radiation, 1.06 x 1019 n/cm 2
at E > 1 Mev and 2.16 x 10
1/5 of the ITR fluence.
total n/cm2.
It is roughly equivalent to
The compression test results appear in Table 7..
As can be seen, the strengths exceed the ITR requirements.
they are higher than for the INEL fluence.
This may follow from the fact
that the INEL fluence was at least 5x the M.I.T. fluence.
-223-
Furthermore,
TABLE 7.7
COMMON RESINS, HARDENERS AND REINFORCEMENTS USED IN INSULATORS
RESINS
Designation
Classification
Chemical Name
Trade Name
TGPAP
Epoxy
Triglycidyl
p-amino phenol
Ciba 0500
DGEBA
Epoxy
Diglycidyl ether
of Bisphenol A
Ciba 6010
KERIMID 601
Polyimide
Bis-maleimide
amine
Rhodia
Kerimid 601
HARDENERS
DDM
Aromatic
Diaminodiphenol
methane
Ciba 972
DDS
Aromatic
Diaminodiphenol
sulfone
Ciba
Eporal
OCA*
Anhydride
I
*
Proprietary,
Owens-Corning_
M.I.T. Designation
WOVEN FABRIC REINFORCEMENT
(All specimens contained approximately 70 percent glass by volume)
Material
Designation
Weave Stype
Finish
Manufacturer
E-glass
181
A-1100
Clark-Schwebel
El-glass
181
P-283B
Owens-Corning
S-glass
181
901
Owens-Corning
S2-glass
6581
GB-770B
Burlington
Quartz
527
A-1100
J.P. Stevens
-224-
TABLE 7.8
SPECIMENS IRRADIATED IN M.I.T. REACTOR
Material
Specimen
Type
I
-- ~Reinforcement
Matrix System
Thickness
mm
E
0.50
El
0.50
S
0.56
4
S
2.79
5
S2
0.50
6
None
3.05
7
E
0.50
El
0.50
2
3
8
DGEBA + OCA
TGPAP + OCA
9
S
0.56
10
S2
0.50
11
None
3.18
12
E
0.46
13
El
0.50
S2
0.48
15
Quartz
0.43
16
E
0.46
S2
0.50
E
0.46
14
17
TGPAP + DDM
TGPAP + DDS
18
19
DGEBA + DDS
S2
0.50
20
E
0.46
21
S
0.50
22
KERIMID 601 1
Quartz
0.50
23
POLYIMIDE NR-150B2
Quartz
0.50
E
0.50
APF 2
24
PNE +
25
G-7
0.30
26
G-11 CR
0.50
27
28
1
-
2
-
4.00
G-10
0.50
Some specimens of Kerimid 601 with E-glass were cured under 360'F,some
under 440 0 F. S-glass - style 6528, A-110 finish
Phenolic novalac epoxy + aniline modified epoxy.
-225-
TABLE 7.9
RESULTS OF M.I.T. COMPRESSION TESTS ON INSULATORS
(5 Specimens of Each Type Tested in Stack Shown in Figure 7.14)
Materia
Reinf.
Thickness
(mm)
601
601
DGEBA + OCA
S
S
S2
0.50
0.50
0.50
KERIMID
601
S
0.50
- 310
10,000
KERIMID
KERIMID
+
+
+
+
601
601
OCA
OCA
OCA
OCA
S
S
S
S2
S2
S
0.50
0.50
0.56
0.50
0.50
0.56
310
310
310
310
310
310
60,000
168,000
30,000
30,000
60,000
30,000
TGPAP +
OCA
S2
0.50
310
30,000
Matrix System
nirradiated
rradiated
KERIMID
KERIMID
DGEBA
DGEBA
DGEBA
TGPAP
Max. Applied
Stress
(MPa)
310
345
310
Tests arbitrarily halted at indicated number of cycles.
-226-
Number of
Cycles
168,000
60,000
60,000
All specimens survived.
7.8.3.7
Friction Tests
One of the first insulation candidates was mica paper which was
considered to be free of damage at the ITR fluence level.
The potential
use was tentatively ruled out partially as a result of tests that revealed
a coefficient of friction of 0.033 to 0.049 at RT and 0.079 to 0.092
at 77 K. The relatively poor showing in the preliminary compression tests
(Table 7.4) was another reason.
G-10, on the other hand, exhibited a minimum coefficient of 0.33 between RT and 4.2 K.
The above results were obtained on unirradiated materials.
If ir-
radiation reduces structural strength then it might also reduce frictional
resistance.
7.8.3.8
Test data are required in this area.
Conclusions
Evidence has been obtained at RT to support the rationale that
thin sheet grp can withstand the ITR radiation and compression loading
environment.
It remains to conduct combined interlaminar shear and com-
pression tests during irradiation at 77 K before the survivability of
grp can be established reliably for use in ITR.
7.8.3.9
Future Testing
It is planned to conduct compression testing at RT and at 77 K on
the remainder of the large variety of specimens irradiated at M.I.T.
A fixture has been designed and built for explorato'ry tests under
combined normal compression in conjunction with interlaminar frictional
-227-
shear (C-S tests).
Static load and fatigue experiments will be conducted
in that fixture at BNL on irradiated grp specimens at RT and 77 K. M.I.T.
also plans C-S tests on specimens already irradiated in the M.I.T. reactor.
Inpile compression fatigue testing at 77 K is now being planned.
A
friction test program also is being designed to obtain data at RT and
77 K on irradiated specimens.
7.8.4
7.8.4.1
Metal Composites Program
Introduction
Experiments were conducted at room temperature on bare copper
and on copper in combination with steel to obtain a preliminary evaluation of fatigue life.
The results were compared to data from the litera-
ture such as in Table 7.1
7.8.4.2
Little information on composites is avai!able.
Bare Copper
Stress-strain curves were obtained on bare oxygen-free
copper with nominally 50 percent cold work.
ments were run.
In addition, fatigue experi-
Typical results appear in Figure 7.16.
It can be
seen that the test poinc is close to the smooth specimen line taken froi
reference 17 .
That would appear to indicate little influence from
scratches and abrasions since no particular care was taken in fabricating
the fatigue specimen.
7.8.4.3
Copper/Steel Composite Tests
Stress-strain curves were obtained and fatigue tests were con-
ducted on copper/steel composites made by rollbonding and subsequent
-228-
(Dd WA)XDW-0
00
0
0
0
0
00
00
Li
U
a_
00
Z
Z
00
z
c
w
4J
a.
Ot
0L~
-
0
z
(i
0
00
00
0
(lS>4) DW
-229-
-D
-
-
cold rolling, by explosive bonding and, finally, by cementing.
bonded specimens revealed considerable scatter.
The roll-
The explosively bonded
The
specimens exhibited low strength because of the low steel strength.
best result was obtained from the cemented composite.
The rollbonded stress-strain curves appear in Figure 7.17.
The
Inspection of rollbonded plates for
fatigue data appear in Table 7.10.
other test programs has revealed extensive cracking of the steel when
sandwiched between copper plates.
Apparently, the greater the steel
strength and cold reduction, the greater the cracking.
explained as limited ductility of the hard steel.
the scatter shown in
The
This might be
It also might explain
Table 7.10.
property data for the components of the explosively bond-
ed composite are shown in Table 7.11.
It can explain the fact that
static failure occurred during loading at a stress level of 414 MPa,
which is close to the mixture-rule value of 427 MPa.from the strengths and
material percentages shown in Table 7.11.
The properties and proportions of the components of the unbonded
specimens are shown in Table 7.11 together With the fatigue data.
The
width variation in the reduced zone corresponds approximately to the
variation in the throat region of the ITR.
The large fatigue life at 483
MPa for the cemented specimen is encouraging since it may provide a
structurally useful alternative to metallurgical bonding.
-230-
It can be important
ERT= 22 MSI
E 7 7 =23MSI
(152 GPa)
(159 GPa)
77 K
O*tu
-
100
RT
77K
100.5 KSI
Tty-=
81.1 KSI
140 KSI/
(559MPa) (966 MPa)
690
(693 MPa)
RT
C/)
ty
e
= 79.7 KSI
C0 *
(550 MPa)
b
b
78 PERCENT OXYGEN-
50
345
FREE COPPER
22 PERCENT STEEL
(NITRONIC 40)
COMPOSITE COLD WORKED
66 PERCENT
0
0
0.005
0.010
E
Figure 7.17
Representative stress-strain curves for rollbonded
copper/stainless composite.
-231-
0
Table 7.10
Fatigue Test Results on Rollbonded Copper-Steel Composites
Specimen No.
Test Temperature
Maximum Stress
Cycles of Failure
3-5-14
L
RT
70 KSI
43500
3-5-15
L
RT
75 KSI
8380
3-5-18
L
770 K
75 KSI
7420*
3-5-22
T
RT
70 KSI
46820
3-5-23
T
RT
75 KSI
38150
4-5-14
RT
(Failed on Loading)
KSI
28580
4-5-22
T
RT
KSI
58030
4-5-23
T
RT
70
75
70
60
KS I
4-5-15
L
L
RT
KSI
1 x 106 Run Out
*Test halted at end of day due to need for personnel to monitor liquid
nitrogen level. Test will be continued.
-232-
Table 7. 11
Static and Fatigue Strengths of Explosively Bonded and Cemented Composites
A. Explosive Bonding
(22 percent type 301 steel, 78 percent of 60 percent cold worked oxygenfree copper
Copper
aty = 338 MPa, %tu = 338 MPa
Steel
a ty = 317 MPa, atu = 745 MPa
During loading, specimen failed at 414 MPa during cycling at 1Hz while
increasing the applied stress level.
3.
Cement Bonding
25 percent nitronic 40 steel , 75 percent of 60 percent cold worked
oxygen-free copper
Copper
aty = 259 MPa,
atu = 275 MPa
Steel
aty = 621 MPa,
atu
800 MPa
Maximum Cyclic Stress
Cycles to Failure
(MPa)
No cement
414
61,800
No cement
483
19,910
Cemented
483
39,700
-233-
since the unbonded cementpd arrangement offers the possibility of
complete control over the properties of the components, which is not
achievable to the same degree with any bonding process.
7.8.4.4
Selection of Joining Method
The primary metal strength problem is in the throat where the available cross-section area is smallest and the applied vertical forces are
highest.
M.I.T. has investigated several types of steels and several
methods of joining steel to copper to form a composite.
Consideration
has been given to the likelihood that fatigue strength, or crack propagation, will control the life of the TF coil in the throat.
It also
would be desirable to employ a composite with high yield strength.
These
factors conflict since high yield strength usually is accompanied by low
resistance to crack propagation.
M.I.T. has conducted tests on rollbonded and explosion-bonded composites that appear to offer high static strength at room temperature.
However, several test specimens exhibited very low strengths.
Further-
more, cracks have been observed in the steel of both types of bonded
specimens after fabrication.
This indicates a degree of unreliability
in both methods which may require some unknown amount of development
to correct.
IPP has been exploring galvanic bonding and subsequent rolling. The
strengths obtained to date do not appear to be high enough for ITR.
The cementing procedure offers the advantage of being able to employ
existing steel and copper production methods, which have known reliability.
-234-
The properties are reasonably well established for a variety of those
materials, many of which have strength and toughness adequate for ITR.
However, test data are required to establish the survivability of the
cementing procedure in the ITR environment.
For the above reasons, no decision has been made on a plate-composite
joining procedure for ITR.
7.9
Areas for Further Study
The principal problem areas are related to material properties and
fabrication.
It appears possible to obtain a metallic composite that would have
sufficient electrical conductivity combined with high strength and
toughness.
However, the effect of the ITR radiation fluence has yet to
be determined at the temperature range
dition
and under the cyclic load con-
expected in ITR.
The achievement of a satisfactory metallurgical bond is still an
open question because of the numerous low-strength failures that have
been observed for rollbonding, cold rolling after explosion bonding and
cold rolling after hot isostatic pressing.
Furthermore, no form of
bonding has been subjected to irradiation, as yet, to determine that
effect.
Glass reinforced organic composites have shown promise for ITR under
compression loading only.
It is necessary to extend the activities to
include shear and tension, all in combination. Also the effect of cyclic
loading at cryogenic temperature must be explored during irradiation to
determine whether that could cause problems.
Furthermore, the ratio of
gammas to neutrons could have an influence on survivability.
-235-
REFERENCES
1. Anon; "Handbook on Materials for Superconducting Machinery", 1979.
2. S. Timoshenko, "Theory of Elasticity", McGraw-Hill, 1934.
3. R.S. Kensley, "An Investigation of Frictional Properties of MetalInsulated Surfaces at Cryogenic Temperatures", MIT SM Thesis,
June 1979.
4. C.R. Brinkman, R.E. Korth and J.M. Beeston, "Influence of Irradiation
on the Creep/Fatigue Behavior of Several Austentric Stainless Steels
and Incoloy 800 at 700 C". ASTM STP 529, 1973.
5. G.E. Korth and R.E. Schmunk, "Low-Cycle Fatigue of Three Irradiated
and Unirradiated Alloys" 9th ASTM Int. Symposium on Effects of
Irradiation on Structural Materials.
6. Anon., "Radiation Effect Design Handbook", Section 3. Electrical
Insulation Materials and Capacitors. NASA CR 1787, July 1971.
7. E. Laurant, "Radiation Damage Test on Epoxies for Coil Insulation",
NAL, EN-110, July 1969.
8. D. Evans, J.T. Morgan, R. Sheldon, G.B. Stapleton, "Post-Irradiation Mechanical Properties of Epoxy Resin/Glass Composites", RHEL/
R200, Chilton, Bershire, England, 1970.
9. M.M. Von de Voorde, "Selection Guide to Organic Materials for Nuclear
Engineering", CERN 72-7, May 1972.
10.
G.R. Imel, P.V. Kelsey and E.H. Ottewitte, "The Effect of Radiation
on TFTR Coil Materials", 1st Conference on Fusion Reactor Materials,
January 1979.
11.
R.R. Coltman, Jr., C.A. Klabunde, R.M. Kernohan and C.J. Long, "Radiation Effects on Organic Insulators for Superconducting Magnets", ORNL/
TM-7077, November 1979.
12.
H. Brechna, "Effect of Nuclear Radiation on Organic Materials; Specifically Magnet Insulations in High-Energy Accelerators", SLAC Report No.
40, 1965.
13.
K. Shirasishi, Ed. "Report of Group Materials", IAEA Workshop on INTOR,
June 1979.
14.
P.W. Bridgman, "The Physics of High Pressure", G. Bell, London, 1931.
-236-
15.
E. Erez and H. Becker, "Radiation Damage in Thin Sheet Fiberglass
Insulators", ICMC Conference, Geneva, August 1980.
16.
R. D. Hay and E.J. Rapperport, "A Review of Electrical Insulation in
Superconducting Magnets for Fusion Reactors", MEA Report, 21 April
1976.
17.
Aron, "OFHC Brand Copper, Properties and Applications. AMAX Copper,
Inc., 1973.
-237-
8.0
COMPONENT FABRICATION
8.1
General
The fabrication problems of the components of the TF magnet have been
given preliminary considerations in order to confirm that no fundamental
constraint prevents manufacture.
Machining of copper and stainless steel, bonding of copper to stainless steel, electron beam welding, epoxy bonding of copper and stainless
steel and GRP insulation have been examined.
8.2
Component Fabrication
8.2.1
Throat Composite
The composite consists of hard rolled copper bonded to high strength
stainless steel, for instance, 316 LN.
The steel is of constant thick-
ness, .427 cm; the copper is tapered, but of minimum thickness at the inside
radius, .427 cm.
The composite fabrication methods being considered are
hot isostatic pressing, hot rolling, electroplating, explosive bonding or
adhesive bonding.
Of these,explosive bonding, hot pressing and adhesive
bonding are considered equally promising.
It is neither necessary nor desirable to extend the high strength
reinforcement beyond the throat.
Therefore, electron beam welding is being
examined as a method of joining the throat region to the horizontal arms
of the conductor.
stress.
The welds as shown in Figure 3.8 lie along lines of low
The size of the composite would thus be only 90 cm x 240 cm.
-238-
Explosive bonding is routinely carried out by loading the cladding
plate
with explosive, placing it at a predetermined standoff distance
from the baseplate and setting off the charge.
The result is a wave of
high pressure and localized heating that travels the area of the interface
dnd generates the bond.
Experimental investigation and limited small scale production is
carried out at the Battelle Columbus Laboratories in Columbus, Ohio. Production Facilities are located at Deltaclad,a division of the Dupont
Company, in New Jersey, and at Explosive Fabricators, Inc. in Columbus
where large plates are routinely fabricated.
Hot isostatic pressing involves surrounding the cladding and base
plates with a sheath and heating the combination while subjecting them
to uniform hydrostatic pressure on all outer surfaces.
Research on sample pieces can be conducted by the Turbine Generator
Division of GE at Schenectady, New York, in
2 ft (61 cm) long vessel.
in Andover, Mass.
an 8 in. (20 cm) diameter by
Production on a large scale is done at IMT
in a 38 in (97 cm) diameter by 5 ft (152 cm) long
vessel and at Wyman Gordon in Grafton, Mass. in a 48 in (122 cm) diameter
by 5 ft (152 cm) long vessel.
Machining of the throat composite material involves rough milling
and finish grinding to
as shown in Figure 3.8.
the tapered shape defined by the dashed lines
Joining the throat pieces to the copper plates
by electron beam welding follows and produces a joint with minimum
distortion.
Experimental welds in copper plates ranging in thickness
-239-
from 2.5 cm to 3.8 cm have produced joints with heat affected zones 1.3
mm to 2.5 mm wide.
Copper Plate
8.2.2
The top and bottom arms and the outer limb of the conductor are
constant thickness copper joined to the throat by electron beam welding
as described above.
The top and bottom units are separate in order to
provide the break in the outer limb necessary for current transfer between
turns.
Thus the size of the copper plates is 201 cm
These units are made from plates 4.90 cm thick.
x
122 cm.
Internal keys are
machined on both sides to a height of 1.22 cm leaving a plate thickness
of 2.45 cm.
If
keys were not incorporated in the copper plates Blanchard
grinding would be employed; instead a planer-miller or a bridge type grinder
is used.
'(The closure flange plate shown in Figure 3.13 must in
any case use a planer-miller or bridge grinder because of the double
taper on one face.)
Two United States suppliers are able to furnish plates in the required sizes.
The Anaconda Company can supply plate coldworked to
30% with an ultimate tensile strength of 276 mpa (40,000 psi).
Revere
Copper and 3rass can supply plate coldworked to 60% naviig an ultimate
tensile strength of 380 mpa (55,000 psi).
-240-
8.2.3
Wedge Reinforcement
Wedges .of type 304 stainless steel provide the support for the
copper top and bottom arms and outer limb.
Because of its great thick-
ness toward the outer radius of the magnet the steel wedge can be made
up, if necessary, from units welded together along vertical lines near
the outer limb .
However,
the complete wedge must be machined to plasma
faces after welding.
Sources for the welding have not been addressed because the problem is routinely tackled on larger scales in pressure vessel welding
and is not considered to need development.
Facing of the plates would be by Blanchard grinding.
The largest
standard Blanchard grinder available employs a 317 cm diameter table and
will just accept the steel reinforcement plate provided allowance is
made for a 5 cm overhang at the corners.
Modified Blanchard or specially
built rotary grinders exist with the capacity to accept larger closure
and diagnostic flange plates.
Some of these machines are located at
the General Electric Company, Schaffer
Steel Services Company.
Grinding, Castle Metals, and
Guaranteed control of thickness by these fabri-
cators is .13 mm.
The diagnostic flange shown in Figure 3.10 having dimensions of
243 cm by 290 cm would be faced on the larger rotary grinders because
of its larger area.
-241-
8.2.4
Insulators
The use of full size sheets of G-10 type insulator is envisioned.
The sheets would be bonded to the adjacent copper, high strength steel
or low strength steel wedge by a B-stage epoxy, during assembly.
Full size sheets are not essential however, provided smaller sheets
of accurately matched thickness and other properties are used.
Sources of G-10 sheet have been investigated.
be no serious problem of plan dimensi-ons.
There appears to
However, uniformity of thick-
ness may be a problem requiring machining.
Sanding appears to be possible for controlling the thickness to
0.05 mm and could be used to form a thinner local area at the throat. A
local vendor, AAA Plastics of Boston, Mass, routinely supplies sheets to
such accuracy.
However, sanding is limited to widths up to 90 cm.
A search for large capacity sanders is yet to be made.
-242-
EXTERNAL DISTRIBUTION
Institutions
Argonne National Laboratory
Association Euratom-CEA
Grenoble, France
Fontenay-aux-Roses, France
Atomics International
Austin Research Associates
Bank of Tokyo
Brookhaven National Laboratory
CNEN-Italy
College of Wiliam and Mary
Columbia, University
Cornell University
Laboratory for Plasma Studies
Applied & Engineering Physics
Culham Laboratory
Culham Laboratory/Project JET
E G & G Idaho, Inc.
Electric Power Research Institute
Gneral Atomic Company
General Electric Company
Georgia Institute of Technology
Grumman Aerospace Corporation
Hanform Engineering Development Lab.
Hiroshima University
Japan Atomic .Energy Research Institute
Kernforshungsanlage/Julich GmbH
Kyoto University
Kyushu University
Lawrence Berkeley Laboratory
Lawrence Livermore Laboratory
Los Alamos Scientific Laboratory
Max Planck Institut fi'r Plasma Physik
McDonnel Douglas Astronautics Co.
Nagoya University
Naval Research Laboratory
New York University/Courant Institute
Nuclear Service Corporation
Oak Ridge National Laboratory
Osaka University
Physics International Group
Princeton University/Plasma Physics
Sandia Research Laboratories
Science Applications, Inc.
Fusion Energy Development
Lab for Applied Plasma Studies
Plasma Research Institute
Stanford University
University of California/Berkeley
Dept. of Electrical Engineering
Dept. of Physics
University of California/Irvine
University of California/Los Angeles
Dept. of Electrical Engineering
Dept. of Physics
Tokamak Fusion Laboratory
School of Eng. & Applied Science
University of Maryland
Dept. of Electrical Engineering
Dept. of Physics
Inst. for Physical Science & Tech.
University of Michigan
University of Rochester
University of Texas
Dept. of Mechanical Engineering
Dept. of Physics
University of Tokyo
University of Washington
University of Wisconsin
Dept. of Nuclear Engineering
Dept. of Physics
Varian Associates
Westinghouse Electric Corporation
Yale University
EXTERNAL DISTRIBUTION
Individuals
Amheard, N.
Electric Power Research Institute
Balescu, R.C.
University Libre de Bruxelles
Bartosek, V.
Nuclear Res. Inst., Czechoslovakia
Berge, G.
University of Bergen, Norway
Braams, C.M.
FOM/Inst. for Plasma Phys., Netherlands
Brunelli, B.
C.N.E.N.-Centro Frascati, Italy
Brzosko, J.S.
Inst. of Physics, Warsaw University
Cap, F.
Inst. fur Theor. Physik, Innsbruck
Conn, R.W.
Chemical Engineering, UCLA
Consoli, T.
Residence Elysee I, Claud, France
Cuperman, S.
Dept. of Physics, Tel-Aviv University
Engelhardt, W.
I
Max-Planck Institute fur Plasmaphysik
Engelmann, F.
FOM/Inst. for Plasma Phys., Netherlands
Fiedorowicz, H.
Kaliski Inst. of Plasma Physics, Warsaw
Frolov, V.
Div. of Research & Laboratories, Vienna
Fushimi, K.
Science Council of Japan, Tokyo
Gibson, A.
JET/Culham, Abingdon, England
Goedbloed, J.P.
FOM/Inst. for Plasma Phys., Netherlands
Goldenbaum, G.
Lawrence Livermore Laboratories
Hamberger, S.M.
Australian National University
Hellberg, M.A.
University of Natal, South Africa
Hintz, E.A.K.
Kernforschungsanlage/Julich GmbH
Hirose, A.
University of Saskatchewan
Hirsch, R.
EXXON Research & Engineering Co.
Hosking, R.J.
University of Waikato, New Zealand
Ito, H.
Osaka University
Jacquinot, J.G.
CEN/Fontenay-aux-Roses, France
Jensen, V.0.
Riso National Lab, Denmark
Jones, R.
National University of Singapore
Kadomtsev, B.B.
Kurchatov Institute, Moscow
Kostka, P.
Central Res. Inst., Budapest
Kunze, H.-J.
Ruhr-Universitat, F. R. Germany
Lackner, K.
Max-Planck Inst. fur Plasmaphysik
Lee, S.
University of Malay
.Lenhert, B.P.
Royal Inst. of Technology, Sweden
Malo, J;O.
University of Nairobi, Kenya
Mercier, C.H.B.
C.N.E.N./Fontenay-aux-Roses, France
Nodwell, R.A.
University of British Columbia, Canada
Offenberger, A,A.
University of Alberta, Canada
Ortolani, S.
Centro di Studio/C.N.R., Italy
Palumbo, D.
Rue de la Loi, 200, Bruxelles
Pellat, R.
Centre National, Palaiseau, France
Paquette, G.
Universite de Montreal, Canada
Rabinovich, M.S.
Lebedev Institute, Moscow
Razumova, K.A.
Kurchatov Institute, Moscow
Rogister, A.
Kernforschungsanlage/Julich GmbH
Rosenau, P.
Technion, Haifa, Israel
Rosenblum, M.
Soreq Research Center, Yavne, Israel
Rudakov, L.I.
Kurchatov Institute, Moscow
Ryutov, D.D.
Nuclear Physics Instit., Novosibirsk
Salas, J.S.R.
Inst. Nacio'nal de Investig. Nucleares
Shafranov, V.D.
Kurchatov Institute, Moscow
Smirnov, V.P.
Kurchatov Institute, Moscow
Spalding, J.-J.
Culham Laboratory, Abingdon, England
Tachon, J.
CEN/Fontenay-aux-Roses, France
Tewari, D.D.
Dept. of Physics, IIT, New Dehli
Trocheris, M.
CEN/Fontenay-aux-Roses, France
Vandenplas, P.E.
Ecole Royale Militaire, Bruxelles
Verheest, F.
Rijksuniversiteit, Gent, Belgium
Watson-Munro, C.N.
University of Sydney, Australia
Wesson, J.A.
Culham Laboratory, Abindgon, England
Wilhelm, R.
Inst. fur Plasmaphysik, Stuttgart
Wilhelmsson, K.H.B.
Chalmers Univ. of Technology, Sweden
Wobig, H.
Max-.Planck Inst. fur Plasmaphysik