PFC/RR-93-7
ITER/US/93/EV-MAG/A.
Radovinsky/1 1.9/1
Joule Heating of the ITER TF Cold Structure
Effects of Vertical Control Coil Currents and ELMS
A. Radovinsky and R.D. Pillsbury, Jr.
November 9, 1993
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA
Supported under US DOE Grant DE-FC02-93-ER-54186
Table of Contents
Page
1.0
Introduction and Summary
1
2.0
Model
1
3.0
Joule Heating of the ITER TF Cold Structure due to the
Vertical Control Coil Currents
2
3.1
Current versus Time Scenarios
2
3.2
Joule Heating of the TFCS
10
4.0
Joule Heating of the ITER TF Cold Structure due to ELMs
32
4.1
Current versus Time Scenarios
32
4.2
Joule Heating of the TFCS
37
References
50
List of Figures
Figure No.
Caption
2.0-1
One sixth of the TF cold structure
2.0-2
The finite element model
2.0-3
Structural elements models
3.1-l.a
Vertical control coils current simulation, tr=3 s, Opt.#1a
3.1-1.b
Vertical control coils current simulation, tr=1 s, Opt.#la
3.1-1.c
Vertical control coils current simulation, tr=1/
3.1-2.a
Vertical control coils current simulation, tr=3 s, Opt.#lb
3.1-2.b
Vertical control coils current simulation, tr=1 s, Opt.#lb
3.1-2.c
Vertical control coils current simulation, tr=1/3 s, Opt.#lb
3.1-3.a
Vertical control coils current simulation, tr=3 s, Opt.#2
3.1-3.b
Vertical control coils current simulation, tr=1 s, Opt.#2
3.1-3.c
Vertical control coils current simulation, tr=1/
3.1-4.a
Vertical control coils current simulation, tr=3 s, Opt.#3
3.1-4.b
Vertical control coils current simulation, tr=1 s, Opt.#3
3.1-4.c
Vertical control coils current simulation, tr=1/
3.2-1.a.
Power deposition in the TF cold structure, tr=3 s, Opt.#la
3.2-1.b
Power deposition in the TF cold structure, tr=1 s, Opt.#1a
3.2-1.c
Power deposition in the TF cold structure, tr=1/
3.2-2.a
Power deposition in the TF cold structure, tr=3 s, Opt.#lb
3.2-2.b
Power deposition in the TF cold structure, tr=1 s, Opt.#lb
3.2-2.c
Power deposition in the TF cold structure, tr=1/3 s, Opt.#lb
3.2-3.a
Power deposition in the TF cold structure, tr=3 s, Opt.#2
3.2-3.b
Power deposition in the TF cold structure, tr= 1 s, Opt.#2
3.2-3.c
Power deposition in the TF cold structure, tr-=1/3 s, Opt.#2
Page
ii
3
3
3
s, Opt.#la
s, Opt.#2
s, Opt.#3
3
s, Opt.#1a
3.2-4.a
Power deposition in the TF cold structure, tr=3 s, Opt.#3
29
3.2-4.b
Power deposition in the TF cold structure, tr=1 s, Opt.#3
30
3.2-4.c
Power deposition in the TF cold structure, tr=1/
3.2-5.a
Eddy currents in the model, Opt.#la
33
3.2-5.b
Eddy currents in the structural elements, Opt.#1a
34
3.2-6
Eddy currents in the model, Opt.#3
35
4.1-1
ELM2 Current Simulation, Opt.#1
36
4.1-2
ELM6 Current Simulation, Opt.#1
38
4.1-3
ELM2a Current Simulation, Opt.#1
39
4.1-4
ELM2b Current Simulation, Opt.#1
40
4.1-5
ELM2c Current Simulation, Opt.#1
41
4.2-1
Power deposition in the TFCS, Opt.#1, ELM2
42
4.2-2
Power deposition in the TFCS, Opt.#1, ELM6
43
4.2-3
Power deposition in the TFCS, Opt.#1, ELM2a
44
4.2-4
Power deposition in the TFCS, Opt.#1, ELM2b
45
4.2-5
Power deposition in the TFCS, Opt.#1, ELM2c
46
4.2-6
Eddy currents in the TFCS, Opt.#1, ELM2
48
4.2-7
Eddy currents in the TFCS, Opt.#1, ELM6
49
iii
3
s, Opt.#3
31
List of Tables
Table No.
Caption
h
2.0-1
Coil Dimensions
6
iv
1.0
Introduction and Summary
The toroidal field coil and support structures for ITER are maintained at
cryogenic temperatures. The time-varying currents in the poloidal field coil
system will induce eddy currents in these structures. The associated Joule
dissipation will cause local heating and require heat removal which will show
up as a load on the cryogenic system.
Studies of Joule heating of the ITER TF cold structure (TFCS) due to the
currents in the poloidal field coil system are presented. The two regimes
considered in this study are the plasma vertical stability control and the Edge
Loss Mode (ELM) events. The 3-D, thin-shell, eddy current program, EDDYCUFF
[1], was used to analyze the eddy currents and Joule losses in the cold structure.
The current versus time scenarios were defined by [4-12].
Four control coil options were studied. All schemes use coils external to
the TF cold structure. The four options are:
(la)
(lb)
(2)
(3)
in which
in which
in which
in which
coils PF2 and PF7 are active,
all the coils PF2-PF7 are active,
PF3 and PF5 are used, and
a pair of coils separate from the PF system is used.
Analyses of power depositions during the plasma vertical stability
control were performed for each of the four options. For each of these options
three different recovery times were assumed. The times were 3, 1, and 1/3
seconds. Option #1a showed the minimum power deposition in the TF cold
structure.
Sets of four sequential ELMs, as well as isolated ELMs have been studied
for various sets of active PF coils. The results showed that the lowest average
power dissipation in the TF cold structure occurs when a subset of PF2 and PF7
are active, and all the other PF coils are passive.
The general conclusion is that to minimize power dissipation in the TF
cold structure it is preferable that only coils PF2 and PF7 are active. The other
coils (PF3-PF6) should be passive and driven by a condition of constant flux. It
is recommended in particular, that coils PF3 and PF5 be allowed to change
currents to conserve flux, since they provide the maximum shielding of the
TFCS from the fields caused by the active coils. It is highly undesirable to use
any of the coils close to the TFCS (PF3-PF6) as active coils.
2.0
Model
The program EDDYCUFF was used in these analyses. EDDYCUFF assumes
that the conducting medium is a shell which is thin relative to the skin depth.
This implies a uniform distribution of current density through the thickness
of the material. This also implies that there is no current flow perpendicular to
the plane of the shell.
1
The TF cold structure (TFCS) modeled in the study consists of six
segments. One segment is shown in Fig. 2.0-1. EDDYCUFF can take into account
the symmetry of the structure as well as the symmetry of the eddy current
patterns. Thus, only one half of a 1/6-th segment of the entire structure was
included in the model, as shown in Fig. 2.0-2. The model is symmetric with
respect to the plane Y=O. As is shown below, it is essential to take into account
the shielding effect of the vacuum vessel (VV) and the blanket (BL). These
elements were also included in the model if not specified differently. The
meshes of these structural elements are shown separately in Fig. 2.0-3.
The bolted joints of the TF cold structure were modeled by the boundary
condition for an insulated edge. The dimensions of the model correspond to [2].
The resistivity of the TF cold structure material is 5*10- 7 ohm*m.
The vacuum vessel and the blanket were modeled as toroidal segments
with boundary conditions permitting current flow in the circumferential
direction. The resistivity was modified to produce a toroidal resistance of 10
pL..
The dimensions of the PF coils involved in the study are listed in Table
2.0-1, unless specified below. They are based on [3]. All the dimensions are the
same as in the cited document except for the radii of the PF4 and PF5 coils
which have been increased to provide a 15 cm gap between the inner surface
of the coils and the outer bore of the TF cold structure.
3.0
Joule Heating of the ITER TF Cold Structure due to the
Vertical Control Coil Currents
The analysis of power deposition during the plasma vertical stability
control shows that Option #1a, in which coils PF2 and PF7 are active, dissipates
less average power in the TF cold structure than either Option #1b, in which
all the peripheral coils, PF2-PF7, are active, or Option #2, in which PF3 and PF5
are used, or Option #3, in which a pair of coils separate from the PF system is
used.
3.1
Current versus Time Scenarios
The current versus time scenarios were defined as follows.
Option #1a:
Option #1a is defined by [4]. The three cases considered correspond to
the three current versus time scenarios (shown in Figs. 3.1-l.a - 3.1-1.c) with
recovery times tr=3 , 1 and 1/3 seconds, respectively. Coils PF2 and PF7 are
active; all the other peripheral PF coils (PF3-PF6) are passive and maintain
constant flux; currents in PF1 are constant.
2
I-
I
(Z
(Z
Q
(9 Gill
A
44
Fig. 2.0-1 One sixth of the TF cold structure
3
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5
Coil Dimensions
Table 2.0-1
Coil
Rc (m)
Zc (m)
dR (m)
dZ (m)
PFR
2.498
0.000
0.775
12.120
PF2
5.947
9.981
1.098
1.161
PF3
13.017
7.197
1.000
0.537
PF4
15.365
-2.445
1.000
0.745
PF5
15.463
-5.745
1.196
1.027
PF6
9.650
-9.635
1.098
1.161
PF7
5.184
-9.485
1.098
1.161
6
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Option #lb:
Option #lb is defined by [5]. The three cases considered correspond to
the three current versus time scenarios (shown in Figs. 3.1-2.a - 3.1-2.c) with
recovery times tr=3 , 1 and 1/3 seconds, respectively. Peripheral coils PF2-PF7
are active, currents in PF1 are constant.
Option #2:
Option #2 is defined by [6]. The three cases considered correspond to the
three current versus time scenarios (shown in Figs. 3.1-3.a - 3.1-3.c) with
recovery times tr=3 , 1 and 1/3 seconds, respectively. A subset of PF3 and PF5 is
used here. The dimensions of the coils were different from those in Table 1,
and were defined as in the task description as follows:
PF3:
PF5:
R=13.017 m, Z=6.702 m, dR=0.565 m, dZ=0.160 m;
R=15.193 m, Z=-5.228 m, dR=0.785 m, dZ=0.116 m.
The currents in the two coils are opposite to each other. All the other PF coils
maintain constant currents.
Option #3:
Option #3 is defined by [7]. The three cases considered correspond to the
three current versus time scenarios (shown in Figs. 3.1-4.a - 3.1-4.c) with
recovery times tr=3 , 1 and 1/3 seconds, respectively. In this option the vertical
control coils were modeled by two solenoids of R=15.193 m, dR=dZ=0.05 m,
placed at Z=+7.345/-4.035 m. The currents in the two coils are opposite to each
other. The vertical control coils are separate from the main PF coils, and are
outside the vacuum vessel as described in the task description. The currents in
the PF coils are held constant.
The magnetic fields caused by the PF coils due to the normal scenario
were not taken into account in these studies.
3.2
Joule Heating of the TFCS
The Joule losses for the three cases have been calculated. The power
dissipation in the entire TF cold structure versus time is shown in Figs. 3.2-l.a 3.2-1.c for Option #1a, Figs. 3.2-2.a - 3.2-2.c for Option #1b, Figs. 3.2-3.a - 3.2-3.c
for Option #2, and Figs. 3.2-4.a - 3.2-4.c for Option #3, respectively.
The finite element model used in Options #2 and #3 included only the TF
cold structure, whereas the model used for Options #1a and #1b also included
the VV and the BL An analysis performed for Options #2 and #3 showed that
such simplification of the model has a negligible effect on the calculated
power dissipated in the TFCS, whereas in Options #1a and #1b such
simplification would cause a consistent error. Figure 3.2-2.a shows a
comparison of power depositions in the TF cold structure for Option #1a (tr=3 s)
obtained using two different finite element models: the one described above
which includes the VV and the BL (solid line), and a model taking into account
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only the TFCS (dashed line). The results show that the effect of shielding the
TFCS with the vacuum vessel and the blanket is significant in this case,
accounting for about 40% of the power deposited in the TFCS. It can be
explained by the fact that in these cases the magnetic field is driven primarily
by coils PF2 and PF7 which are located near the top and the bottom of the
vacuum vessel, where, as is shown in Figs. 3.2-5.a and 3.2-5.b, the highest
density of eddy currents occurs. The same is applicable to Option #1b. The eddy
current patterns shown in Figures 3.2-5.a and 3.2-5.b are obtained for Option
#1a and are typical for Option #1b. Figure 3.2-6 shows the pattern of the eddy
currents in the TFCS for Option #3, which is typical also for Option #2.
The average power dissipation over the 10-second time period modeled
is:
tr
3s
1 s
1/3 s
Option #1a
3.32 W
13.0 W
97.1 W
Option #1b
9.08 W
101 W
1242 W
Option #2
76 W
380 W
3380 W
Option #3
160 W
490 W
4190 W
The dramatic drop in power dissipation in the TFCS in Option #1a is
primarily due to the fact that in this case currents in coils PF3 and PF5 driven
by the flux caused by PF2 and PF7 provide a shielding effect to the TFCS.
Another reason is that in Option #1a the driving coils PF2 and PF7 are much
farther from the TFCS than coils used in Options #1b, #2, or #3.
4.0
Joule Heating of the ITER TF Cold Structure due to ELMs
Sets of four sequential ELMs, as well as isolated ELMs have been studied
for various sets of active PF coils. The results showed that the lowest average
power dissipation in the TF cold structure occurs when PF2 and PF7 are active,
and all other PF coils are passive.
4.1
Current versus Time Scenarios
The current versus time laws were defined as follows.
Case ELM2 :
ELM2 is defined by [8]. Coils PF2 and PF7 are active, coils PF1 and PF3-PF6
are passive and are driven by a condition of constant flux. The ampere-turns
versus time scenario is shown in Fig. 4.1-1. Four ELMs were modeled over a
time interval of 4 seconds.
Case ELM6 :
ELM6 is defined by [9]. Coils PF2-PF7 are active, coil PF1 is passive and
carries only the current induced under the condition of constant flux. The
32
Cd
LUI
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i*n1
E
I
In
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340
-- ITER TF CS
TIME(SEC-
JOULE LOSSIU)
1992.8
1.000
Et0I
*2.0645SEt0I
2
9.53737E+02 A/M
Fx
Fig. 3.2-6
Nh
Eddy currents in the model, Opt.#3
35
LL
cL
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CL
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v 'wenno poo
36
0
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C
0
C
0
C6
current versus time scenario is shown in Fig. 4.1-2. Four ELMs were modeled
over a time interval of 4 seconds.
Case ELM2a :
ELM2a is defined by [10]. Coils PF2 and PF7 are active, coils PF1 and PF3PF6 are passive and carry only the currents induced under the condition of
constant flux. The current versus time scenario is shown in Fig. 4.1-3. One ELM
was modeled over a time interval of 3 seconds.
Case ELM2b :
ELM2b is defined by [11]. Coils PF2 and PF7 are active, while currents in
coils PF1 and PF3-PF6 are not allowed to change. The current versus time
scenario is shown in Fig. 4.1-4. One ELM was modeled over a time interval of 3
seconds.
Case ELM2c :
ELM2c is defined by [12]. Coils PF2 and PF7 are active, while currents in
coils PF1 and PF3-PF6 are not allowed to change. The current versus time
scenario is shown in Fig. 4.1-5. Four ELMs were modeled over a time interval of
4 seconds.
In all cases the perturbation currents given were used directly without
the addition of normal scenario currents.
4.2
Joule Heating of the TFCS
The Joule losses for the five cases have been calculated. The power
dissipation in entire TF cold structure versus time is shown in Fig. 4.2-1 for
ELM2, Fig. 4.2-2 for ELM6, Fig. 4.2-3 for ELM2a, Fig. 4.2-4 for ELM2b, and Fig.
4.2-5 for ELM2c.
The average power dissipated over the characteristic time periods are:
Case
Time period
(s)
Number
of ELMs/time
Average power
dissipation (W)
period
ELM2
ELM6
ELM2a
ELM2b
ELM2c
1
1
0
0
0
3
3
1
1
4
<
<
<
<
<
t
t
t
t
t
<4
<4
<3
<3
<4
1580
4120
2582
1117
4144
Cases ELM2 and ELM6 show that from the point of view of minimizing
the power dissipation in the TF cold structure it is preferable to use only coils
PF2 and PF7 (corresponding to ELM2). In ELM6, where coils PF2-PF7 are all
active, the coils close to TFCS, principally PF3-PF5, produce very high power
37
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dissipation (note the high spikes in Fig. 4.2-2). In ELM2 coils PF3 and PF5 act in
the opposite direction, i.e., the currents induced in them cancel the flux
through the TFCS due to PF2 and PF7. The eddy current patterns in the TFCS at
time t=1.113 s corresponding to the spike are shown in Figs. 4.2-6 and 4.2-7 for
ELM2 and ELM6, respectively. The patterns in Fig. 4.2-7 (ELM6) show a much
stronger coupling between the coils and the TFCS than those in Fig. 4.2-6
(ELM2). Note the scale factor of the vectors for ELM6 is almost twice that for
ELM2. Cases ELM2a-ELM2c served the purpose of confirming this suggestion.
47
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49
References
1. A.Kameari, "Transient Eddy Current Analysis on Thin Conductors with
Arbitrary Connections and Shapes," Journal of Computational Physics, Vol. 42,
No.1, July 1981, pp. 124-140.
2. NAKA CO-CENTER Fax, Ref NO.N 11 MD 01 93-07-26 F of 7-27-93.
3. Draft Design Description Document for ITER Magnet System, Ref NO.N AO RI
02 93-09-06 W.
4. R.H. Bulmer, private communication, 10-17-93.
5. R.H. Bulmer, private communication, 10-21-93.
6. R.H. Bulmer, Memorandum, "ITER Vertical Control Task, Option #2", 8-10-93.
7. R.H. Bulmer, Memorandum, "ITER Vertical Control Task, Option #3", 7-30-93.
8. LD.Pearlstein, private communication, 10-29-93.
9. LD.Pearlstein, private communication, 10-29-93.
10. LD.Pearlstein, private communication, 11-1-93.
11. LD.Pearlstein, private communication, 11-1-93.
12. LD.Pearlstein, private communication, 11-3-93.
50