DOE/ET-51013-179
PFC/RR-86-10
A Poloidal Field Scenario Generating Code
for Use in the Design and Operation of Tokamaks
Joel H. Schultz
May 15, 1986
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA 02139
I
A Poloidal Field Scenario Generating Code
for Use in the Design and Operation of Tokamaks
Joel H. Schultz
M.I.T. Plasma Fusion Center Research Report PFC/RR-86-10
Introduction
The calculation of energy, power, current and voltage requirements of the coils in a tokamak
poloidal field system is a common design and analysis problem.
The calculation of all circuit
parameters, given a sufficient set of inputs, such as a program of current vs. time, along with coil
dimensions, is straightforward. However, the construction of a general-purpose code is nontrivial.
Several design decisions and physical insights are required, in order to program the coil currents
and voltages. It is thus frequently difficult for one investigator to duplicate the design and analysis
results of another, using a different code. A further, purely teclmical barrier, is that the display
of calculated parameters in a manner that easily permits the selection of the number of turns for
each coil, and the allocation of rectifiers, dump resistors and switches involves a large amount of
graphics postprocessing and typesetting, which has not previously been completed.
There are also a number of important parameters that can be calculated easily by the use
of circuit theory that are usually neglected, including the radial and vertical forces on each coil,
before or after a disruption, at each moment in time. The purpose of the code described below is
to calculate everything of any design importance that, can be deduced through circuit theory, to
display the results in a comprehensive, but easy to use format, and to retain enough flexibility in
inputting to permit collaboration with other groups.
Method
A scenario is specified that includes the dimensions of each of the poloidal field coils, including
the plasma. and the coil currents at a small number of discrete times. These are typically the
begiming and ends of coil charge-up, plasma initiation, start-up, auxiliary heating, burn, plasma
shutdown and coil rampdown. The scenario and coil specifications are input by hand or calculated
by auxiliary algoritlus.
Once the scenario is specified, three inductance matrices are specified. Both mutual and self
2
inductances are calculated using constant current density, rather than filamentary, models, in order
to have the greatest possible accuracy. Mutual inductances are calculated at positions perturbed
by 0.1 nun individually in the radial and axial directions in order to calculate radial and vertical
forces on the coils. The perturbed mutual inductances are used to calculate influence matrices for
radial and axial force that are multiplied by the coil currents to obtain the forces at each moment
of time.
Forces between the coils are simply calculated at each moment in time by precalculating an
influence matrix, based on the conservation of coenergy, so that the per unit force due to 1 ampereturn in coil 1 on 1 ampere-turn in coil 2 is simply:
6A1
12
6r>
Fr,pt,
br:
-6
4
M 12
where the average hoop tension in the coil is related to the fictitious radial force, as:
=F
FT FT-27r
In order to calculate currents and forces in the coils after disruptions, the simplifying assumnption
is made that the coils are connected to low impedance power supplies. in the short circuit
limit, the coil currents will change passively so that the flux linkage of each coil is conserved. A
matrix inversion is performed to calculate the per unit changes in each coil due to a change in
plasia current that satisfv this crit erion. The flux-conserving currents in each coil due to disruptive disappearance of tlie plasma current are then calculated using this influence matrix at each
moment of time in the
scenario. The radial and axial force influence matrices are then used to cal-
culate the forces on each coil at each moment of time. following a flux-conserving disruption. The
radial force
is converted to an average tensile stress over the winding pack cross section, while the
axial force is converted to an average axial compression stress over the coil bearing area. Each case
requires confirmation by more sophisticated analysis. but it has been our experience that average
hoop stresses above 200 MPa will require the addition of steel reinforcement to the winding pack
or case.
3
Guidance is given to the selection of power supplies by monitoring when each coil's current
and voltage have the same polarity, and recording the maximum individual voltage and current
for each polarity. Note that, the product of the maximum voltage and current is invariably higher
than the maximum instantaneous power needed from the power supplies, since the current and
voltage maxima usually do not occur at the same time. Periods of regenerative power flow are also
monitored, in order to aid in the design of switches and dump resistors or to check for inverter
commutation failure.
The energy requirements for the system and for each individual coil are determined merely by
monitoring the power flow through the coil terminals. Therefore, when the power flow is regenerative (negative), the code calculates a reduction in the instantaneous energy requirement. If the
code is used to calculate the rotational stored energy requirements for the system, this output will
always be optimistic, since not all of the regenerated power can be returned to the coils' energy
source. Thus a diagnostic parameter called "Dump Energy" is calculated and displayed. This is the
sum of the integrated regenerative power flow through each pair of coil terminals. The parameter
physically corresponds to the energy ratings of dhunp resistors, if all of the negative coil power were
dissipated in dump resistors. If the calculation of "Dunp Energy" is added to the calculation of
energy required, upper and lower bounds can be calculated for the actual energy drawn from a
source.
Worked Example
An interesting worked example is the limiter discharge, as of March 1986, for the Compact
Ignition Tokamak (ClT ) device T-86]. This poloidal field system provides a 9 MA plasmna current
for a 3.0 s ignited burn. All of the graphics and tabulated output of the code are included in the
Appendix. Selected features of the output are discussed in the text..
Table I shows the posit ions. maxiniun anpere-turns an(d turns in each one of the PF coils. Coils
above and below the equator are routinely tabulated, in order 16 avoid confusion or to handle the
infrequent design case of an asynunetric system (e.g. hitor, Alcator DCT). Table II shows the peak
current density over the winding pack envelope, maximum temperature, maximum energy and peak
power required by the coil. The latter two values are the sums of dissipative and magnetic energies,
thus representing the peak requirements for stored energy sources and power supplies. Table III
4
shows the peak positive and negative current and positive and negative voltage requirements of each
coil. These are not the power supply ratings. The peak positive voltage frequently, even usually,
occurs when the current is negative and vice versa. Since the instantaneous power flow is negative
at that moment, a power supply is not required, and the coil can dump energy into a resistor, if
desired. The values in Table III, then, are used primarily for the design of bus, ground insulation
and switch circuits. Power supply requirements are listed in Table IV. During each moment of
time, the emulator monitors whether the current and voltage have the same polarity, then divides
the scenario for each coil into time intervals that have to be provided for by positive current power
supplies, negative current power supplies or neither. Notice that the power ratings listed in Table
IV are typically much larger than the peak power flowing instantaneously through the coils, being
the product of the peak current and peak voltage during the entire period that current and voltage
have the same polarity. Thus the power requirement tabulated is essentially the product of the
no load voltage-full load current product that typifies the power supply requirement for each coil.
Table V lists the volt-second contributions of each coil to the plasma, which is a source of physical
insight for redesigning the coils or the scenarios.
System requirements as a function of time are illustrated in Figures 1-7. Each total system
requirement is usually illustrated in two different formats, showing the individual contributions of
each coil pair and showing the individual contributions of the magnetic and resistive components
of power or energy. As shown in Figure 1, the resistive energy requirements of the PF system are
higher than the magnetic requirements. The peak total energy requirement of the PF system is 1283
MJ, so the pulsed energy source must be capable of delivering that much energy to the load. The
fmal dissipate(l energy of the PF system is 990 MIJ. so the cryogenic system must remove that much
energy from the coils between pulses. As shown in Figure 2. the dominant energy requirement for
the CIT PF syst em cones from the outermost coil, EF3. that provides most of the plasma's vertical
field. This is a typical situation. since the outermost coil always has the largest major radius and
is usually the most efficient in providing vertical field on axis. The energy that flows through the
coil terminals, however, is always less than the actual energy that an energy source must provide,
because when magnetic energy leaves the coils, it is not returned to the energy source with 100
% efficiency. In particular, during plasma initiation, most or all of the regenerative energy flow
through the coil terminals is dumped in external resistors. A diagnostic of the system dump energy
is included in Figure 3. This is simply the sum of all the energy that could be either returned to the
line or dumped from each coil, whenever its power flow is negative. A typical approach to source
design is to assume that all of the dump energy during the initiation and start-up period, must be
provided by the generator, while the 'dump energy' from the shutdown period can be returned to
the line or provided over a long enough period to constitute a negligible load. As seen in Figure 3,
the total dump energy is - 557 MJ, of which - 270 MJ is dumped during the start-up period. If the
start-up dumped energy is charged to the generator, then it must provide 1553 MJ to the PF load
during a plasma discharge.
Power flow through the system is shown in Figures 3-7. Figure 3 shows the instantaneous
power flow through all of the PF coils. The curve is dominated by the large regenerative power
flow due to plasma initiation, and, therefore, makes all the positive powers somewhat difficult to
read. Therefore, additional curves, labeled 'line power' are included, that only count and sum the
positive power flows in each coil. As seen in Figure 4, the peak line power of 429 MVA, like the
energy, is donnated by the outside PF5 coil at the end of plasma current ranipup, so the dominant
power requirement of the system is simply ramping the vertical field to its final value. There are
three secondary power peaks at the end of coil precharge. auxiliary heating and end of burn. As seen
in Figure 5. the resistive coil losses are climbing rapidly at the end of burn, so there is probably not
much to be gained ramping the plasma more slowly. However, the peaks are sufficientlY separated
that an additional 0.5-1 second of ramp might lower the peak line power by 50 MW or so. Other
tradeoffs that would be created, as shown later would be the final temperature of
OH2. the hottest
coil in the PF system, vs. the more difficult to evaluate benefits of being permitted to take longer
to establish the final plasma.
Figure
6 shows the history of the plasma loop voltage and the contributions of each pair of PF
coils, confirming that 30 V are available for plasma initiation. Figure 7 shows the history of the
volt-second linkage to the plasma, confirming that the specified 26 V-s have been satisfied by the
PF system. The large contribution by the outside PF5 coil is striking. However, since the positive
current polarity coil, PF4, used for elongating the plasma. subtracts a large number of volt-seconds,
the contribution from the two central solenoid coils, PFI and PF2, is still half the total swing.
Figures 8-11 display circuit and force scenarios for the upper 0111 coil. The scenario code
generates total displays of all circuits for each one of the coils individually. The code automatically
checks for synunetry. If the system is asynmetric, as in a recent simulation done for INTOR,
four pages of curves apiece were generated for each of nine asymmetric coils, above and below the
equator. If syrmnetry is satisfied, only the four coils above the equator are displayed. The designer
has to keep this in mind when deciding whether to connect mirror image coils in series, parallel, or
independently. Figure 8 displays the ampere-turns, volts/turn, power flow and energy vs. time for
0111, U. Note that the power flow curve displays not only the bipolar power requirements, but also
the positive and negative power supply requirements. Both resistive and inductive contributions
to energy and power are displayed. Figure 9 displays the conductor current, terminal voltage, flux
linkage and coil temperature vs. time. Note that the flux linkage is the flux linking the coil, not
the coil contribution to the plasma. For inertially-cooled coils, the temperature rise is frequently
the dominant feasibility issue of the PF design. The rise of OH1 to 292 K is substantial, but within
the allowable final temperature specification of 370 K.
The radial and axial force vs. time are displayed in Figure 10. The 'radial force' is really the
product of the average coil circumference and the radially outward force per unit circtumference,
the actual integral of this force being zero. The average hoop tensile stress in the winding pack
is this force divided by 27r times the area of the winding pack. When this average force exceeds
200 MPa, reinforcement of the copper is frequently found to be necessary.
The axial force vs.
time is the vertical bearing force on the top or bottom of the magnet. The average stress is this
force divided by the cross-sectional axial bearing area of the winding pack. If the vertical force
peaks somewhere other than the magnet end, then there will be no particular relation between the
peak and average axial stresses. Whenever any coil has moderately high average stresses, the peak
stresses are calculated. using E. Bobrov's three-dimensional closed-form solution to the stresses in
a solenoid, using a fully anisotropic model of an equivalent composite winding pack [B084].
Figure 11 shows the pre- and post-disruption current and radial force in OH1, U, assuming that
all the PF coils are flux-conserving (i.e.. short-circuited). Although the plasma had a demagnetizing
effect on the OH1 field, the overall effect is a decreased 0111 current, so that the change in the
bursting force on
O1 is negligible at all times during the scenario. Note that disruption forces
are given at every moment of time, so that what is being calculated is not a single scenario, but a
series of hypothetical events, since a disruption might occur at any time, during a pulse.
Conclusions
A simple poloidal magnet scenario emulator has been constructed for use in the design and
evaluation of tokamaks. This code has proven to have a wide utility, being used both in the design
and planning of laboratory experiments, such as Alcator C-Mod at M.I.T., analysis of behavior
on existing machines , such as Alcator C, and design and planning of national and international
'flagship' demonstration tokamaks, such as CIT and INTOR. The code is a simple time integrator
that allows the designer and analyst to calculate all parameters that can be deduced by circuit
theory, including power, energy, voltage, current, and force.
A worked example has been presented from the CIT design, illustrating something of the
extent of the analysis on that machine, along with some discussion of design problems and tradeoffs
suggested by the results of PF system emulation. A complete set of code output for the CIT limiter
discharge is included in the Appendix.
Acknowledgments
Special thanks are owed to A.M. Dawson for the preparation of this report.
References
'B0841 E.S. Bobrov, "Electrically conducting orthotropic cylindrical shell in axial and radial magnet
fields." in The Mechanical Behavior of Electromagnetic Solid Continua, ed. G.A. Maugin, Proc of
the
IUTAM-IUPAP
Symposium, Paris. France, 4-7 July, 198:3, Elsevier Science Publishers (North-
Holland), 1984
TH86] R.J. Thome et a]. "Poloidal field coil system design for the Compact Ignition Tokamak:
Status Report." M.I.T. Plasma Fusion Center Research Report PFC/RR-86-Il, April, 1986
8
Table I
CIT-L System Winding Pack Dimensions
Coil
R
Z
R,
R,
Z,
(ni)
(M)
(i)
(i)
(i)
OH1,U
0.383
0.184
0.259
0.507
0.000
OH1,L
0.383
-0.184
0.259
0.507
OH2,U
0.383
0.684
0.259
OH2,L
0.383
-0.684
EF1,U
1.050
EF1,L
Z1
NI
nttrns
0.368
7.000
200.0
-0.368
0.000
7.000
200.0
0.507
0.368
1.000
12.600
160.0
0.259
0.507
-1.000
-0.368
12.600
160.0
1.748
0.910
1.189
1.518
1.979
7.660
300.0
1.050
-1.748
0.910
1.189
-1.979
-1.518
7.660
300.0
EF2,U
2.050
1.680
1.887
2.213
1.517
1.843
4.220
112.0
EF2,L
2.050
-1.680
1.887
2.213
-1.843
-1.517
4.220
112.0
EF3,U
2.510
0.955
2.351
2.670
0.795
1.115
7.100
160.0
EF3,L
2.510
-0.955
2.351
2.670
-1.115
-0.795
7.100
160.0
9
(in)
(MAT)
Table II
Current Density, Temperature, Energy and Power
Coil
Jetpk
Tmax
Epk,rcq
Pmax
(MA/m 2 )
(K)
(MJ)
(MW)
OH1,U
76.701
292.358
116.791
34.715
OHI,L
76.701
292.358
116.791
34.715
OH2,U
80.390
300.559
207.244
52.526
OH2,L
80.390
300.559
207.244
52.526
EF1,T
59.556
95.636
84.585
53.247
EF1,L
59.556
95.636
84.585
53.247
EF2,U
39.708
95.568
36.884
9.223
EF2,L
39.708
95.568
36.884
9.223
EF3,U
69.771
139.789
348.497
133.600
EF3,L
69.771
139.789
348.497
133.600
10
Table III
Peak Currents and Voltages on PF Coils
Icond,max
lcond,min
Vtcrm,max
Xterm,min
(kA)
(kA)
(kV)
(kV)
OH1,U
29.300
-35.000
0.606
-2.786
OH1,L
29.300
-35.000
0.677
-2.702
OH2,U
78.750
-59.125
0.667
-1.938
OH2,L
78.750
-59.125
0.572
-2.062
EF1,U
25.533
-8.200
2.085
-9.196
EF1,L
25.533
-8.200
2.085
-9.196
EF2,U
37.679
-22.054
0.716
-0.156
EF2,L
37.679
-22.054
0.716
-0.156
EF3,U
5.750
-44.375
3.529
-12.986
EF3,L
5.750
-44.375
3.529
-12.986
Coil
11
Table IV
Positive and Negative Power Supply Requirements
I+PS
V+PS
P+PS
I-PS
V-PS
Pps
(kA)
(V)
(MVA)
(kA)
(V)
(MVA)
OH1,U
29.30
605.86
17.75
-35.00
-991.85
34.71
OH1,L
29.30
676.69
19.83
-35.00
-1699.02
59.47
OH2,U
78.75
667.00
52.53
-59.13
-862.22
50.98
OH2,L
78.75
572.14
45.06
-59.13
-721.88
42.68
EF1,U
25.53
2085.40
53.25
-8.20
-2216.50
18.18
EF1,L
25.53
2085.40
53.25
-8.20
-2216.50
18.18
EF2,T
37.68
288.90
10.89
-22.05
-156.17
3.44
EF2,L
37.68
288.90
10.89
-22.05
-156.17
3.44
EF3,U
5.75
598.59
3.44
-44.38
-3389.14
150.39
EF3,L
5.75
598.59
3.44
-44.38
-3389.14
150.39
Coil
12
Table V
Volt-second Contributions of Each PF Coil
Coil
VSend,start,.jp
VSendfiat
(V-S)
(V-S)
OH1,U
1.384
-1.654
OH1,L
1.384
-1.654
OH2,U
1.969
-1.478
OH2,L
1.969
-1.478
EF1,U
2.067
-0.664
EF1,L
2.067
-0.664
EF2,U
-1.498
2.560
EF2,L
-1.498
2.560
EF3,U
0.906
-6.994
EF3,L
0.906
-6.994
Total
9.657
-16.461
13*
op
PF System Energy (MJ)
Etotal (MJ) =1390.1
Wm,max (MJ) =5.20E+08
14 0 0
-
vs.
Time (s)
PF Total
Resistive
Magnetic
T
--- R--- M--
12001
10
10001
800
C
600
4001
I
-
,
M
2001
0
00
'VT
2
4
6
Time
8
10
12
(s)
Figure 1 - CIT Limiter Discharge: System Energy Requirement vs Time
14
14
PF System Energy (MJ)
Etotal (MJ)
CIT306L
=1390.12
I
1400
T
------
--- 2--
-3_--
1200
vs. Time (s)
T
PF Total
PF1,U+L
PF2,U+L
PF3,U+L
PF4,U+L
...PF5,U+L
1000
800 -
600-
~
400 -/
z
-
--
-
-
-
200
0
2
4
-3--
3 4
--
6
8
10
12
14
Time (s)
Figure 2 - Total PF System and Individual Coil Energy Requirements vs Time
15
PF Dump Energy (MJ)
Edump (MJ)
-- -s PFI,
-- i--
+-
...
- ---------
\+L
'
-
-
- e
-
-
------
-----
-
-2- ---
-
PF2, +L
P F3, +1
PF4,U L\
PF5,U L
-- 3a--
-100
CIT306L
=-548.683
C'
PF
-
vs. Time (s)
-
--2
~
-200
N -300 -
-400
-500 -
-600
0
I
I
I
2
4
I
6
I
8
10
12
14
Time (s)
Figure 3 - Additional Energy Requirements if Regenerative Energy is not Returned to Source
16
PF Line Power (MW)
vs. Time (s)
CIT306L
Pline,max (MW) =437.687
500
I
I
I
I
+T--PF T otal
-T-- PF1, J+L
-2-- PF2, J+L
-3- - PF3, U-L
4PF4, J+L
5- PF5, J+L
400
i
I
I
I
300 1-
I
0
200
5
-5.
1001
//
'/
4,
I,
/
/
K-.
~
-
0
W
0
2
4
6
8
10
12
14
Time (s)
Figure 4 - Individual Power Supply and System Line Power Requirements (MW) vs Time(s)
17
PF Line Power (MW)
CIT306L
=437.687
Pline,max (MW)
500
i
--R-
vs. Time (s)
i
i
i
Total
Resistive
i
I
4001-
300
0
200
100
0 ,,
0
I
2
~i
-i
4
L
-r
6
i
A
8
10
12
14
Time (s)
Figure 5 - System Line Power: Resistive, Magnetic and Total (MW) vs Time (s)
18
Plasma
10
Loop Voltage (V) vs. Time (s)
CIT306L
Vloop,max (V) =6.33104
Vloop,min (V) =-31.4713
I
I I I I I I
r
I
14,--
0
- -4-
-10
K
0
-20
---- 1---- 2---- 3~+ 5
-30
I
-40
0
I
2
I
I
4
I
I
I
6
I
8
I
Total
PF1,U+L
PF2,U+L
PF3,U+L
PF4,U+L
PF5,U+L
I
10
I
I
12
14
Time (s)
Figure 6 - Contributions of Individual PF Coils to Plasma Loop Voltage (V) vs Time (s)
19
Plasma Volt-Seconds
10
(Wb)
CIT306L
=9.65708
=-16.4607
VS,max (Wb)
Vs,min (Wb)
T
-- I5-2-4
-- 3-
5
-
-
t
x
.
-5..-
vs. Time (s)
Total
PF1, +L
PF2,N+ L
PF3,U+L,
PF4,U+L 4
PF5,U+L
4/
S.0
5
0
0
-10
5
5.
5
-15
5 -.-
-
-20 ,
0
2
4
6
8
10
|
12
14
Time (s)
Figure 7 - Contribution of Individual PF Coils to Plasma Volt-Seconds (Wb) vs Time (s)
20
dR (m)
= 0.248
dZ (m)
= 0.368
Volts/Turn vs. Time (s)
OH1,U
Re (i)
=
0.38
Z (n)
=
0.18
MA- urns vs. Time (s)
6
1'1
I
I
I
5
I
0
4
-5
0
-2
I
tI
4
1
-
0
i
1
1
1
*
I
I
-10
-4
-15,
-6
c
-8
0
I
I
I
2
4
6
I
I
8 10
2
4
6
8 10
14
I
Time (s)
14
Time (s)
Power Flow (MW)
I
0
vs. Time
Max power =34.7148
Min power
- 86.7317
+ PS MVA: = 17.7516
- PS MVA: = 34.7148
Energy (MJ)
Emax =116.791
120
-
4 .1-
vs. Time
T
Tot
100 ---- R-- Res
-~I-- Ind
80
R
-20
60
c.
-40
40
0
-60
20
-80
-100
-,
01
-
0
2
-
-20
0 2 4 6 8 10
14
Time (s)
4
6
8 10
14
Time (s)
Figure 8 - Ampere-Turns (MAT), Volts/Turn (V), Power (MW), and Energy (MJ)
vs Time (s) for Upper OHI Coil
21
OH1,U
Current (kA) vs.Time (s)
Re =0.38
Ze =0.18
I,max = 29.30
Voltage (V) vs. Time (s)
I,min =-35.00
.I-
30
1.0
.J ~.J
20
VSmx,=,.04729
0.0
0
C.)
-10
.
-
1
CI
-0.5
0
-1.0
Sw -1.5
1
CO
-20
-2.0
-30
0
C.
0.5
a)
10
-j
nturns = 200.0
Vt,max =6.06E-01
Vt,min =- 2.78598
.
-2.5
S-4
-40
-3.0
0 2 4 6 8 10
14
0
2
Time (s)
Flux Linkage
8
(Wb)
4
6
8 10
14
Time (s)
vs. Time
Temperature (K)
VS,max =7.04729
VS,min =-5.59458
vs. Tia
J 2 t, norm =6.57195
Espec (J/cc) =1057.77
T,max (K ) =292.358
6
. .
300
4
CU
4
4
250
2
a)
5-4
0
1
~
1
.
200
4-,
CU
5.4
150
a)
-4
S
a) 100
-6
50
0
2
4
6
8 10
14
0
Time (s)
2
I
I
4
6
I
.4
8 10
4.
14
Time (s)
Figure 9 - Conductor Current (kA), Terminal Voltage (kV), Coil Flux Linkage (Wb),
and Temperature (K) vs Time (s) for Upper OHI Coil
22
Time (s)
Radial Force vs.
140
120
100
80
60
40
20
z
0
0o
FL
Z
d
= 0.383
R
d
) = 0.248
sigmaTmax (MPa)=
sigmaTmin (MPa)=
(m)
m
= 0.184
= 0.368
221.40
-5.60
Tot
- -
Self
Mut
-7
--
4
I
I
I
I-
-20
2
0
4
8
6
10
12
14
12
14
Time (s)
Axial
2
z
Force vs. Time (s)
sigmaz,max (MPa)=
sigmaz,min (MPa)=
0.59
-16.77
0
-2
0
-4
-6
.44?
-8
-10
-12
K
0
I
2
4
6
*
8
10
Time (s)
Figure 10 - Radial and Axial Force (MN) vs Time (s) on Upper OH
23
Coil
Pre and Post Disruption
R (m)
di (m)
Currents
= 0.383
= 0.248
(MAT)
0.184
Z' (m)
dZ (m)= = 0.368
6
E-
C,,
B
_D
- A---
4
2
01
-2
'o
fter
-
-4
-6
-8
-A
'A- A----
-A'
A
2
0
4
6
10
8
12
-14
Time (s)
Radial Force, Pre and Post-Disruption
sigma'ima
sigma'rmin
140
(MN)
(MPa = 221.40
MPa =
-5.60
120
100
80
60
40
-
20
---
D
A--
Befor
'After
0
-20
~
0
I
2
I
4
6
8
10
12
14
Time (s)
Figure 11 - Current (MAT) and Radial Force (MN) Before and After
Hypothetical Plasma Disruptions at Each Point in Time, Conserving Flux in PF Coils
24
Appendix
Sample Output of PF Scenario-Generating Code
A-1
CIT306L System Winding Pack Dimensions
R
z
R,
R,
Z,
Z2
NI
(m)
(m)
(in)
(m)
(m) (m)
(MAT)
()
OH1,U
0.383
0.184
0.259
0.507
0.000
0.368
7.000
200.0
OH1,L
0.383
-0.184
0.259
0.507
-0.368
0.000
7.000
200.0
OH2,U
0.383
0.684
0.259
0.507
0.368
1.000
12.600
160.0
OH2,L
0.383
-0.684
0.259
0.507
-1.000
-0.368
12.600
160.0
EF1,U
1.050
1.748
0.910
1.189
1.518
1.979
7.660
300.0
EF1,L
1.050
-1.748
0.910
1.189
-1.979
-1.518
7.660
300.0
EF2,U
2.050
1.680
1.887
2.213
1.517
1.843
4.220
112.0
EF2,L
2.050
-1.680
1.887
2.213
-1.843
-1.517
4.220
112.0
EF3,U
2.510
0.955
2.351
2.670
0.795
1.115
7.100
160.0
EF3,L
2.510
-0.955
2.351
2.670
-1.115
-0.795
7.100
160.0
Coil
Coil
JeIpk
(MA/1,
2
)
Tmn,,
Epk,req
Pmax
(K)
(Mi)
(MW)
OH1,U
76.701
292.358
116.791
34.715
OH1,L
76.701
0.000
0.000
0.000
OH2,U
80.390
300.559
207.244
52.526
OH2,L
80.390
0.000
0.000
0.000
EF1,U
59.556
95.636
84.585
53.247
EFIL
59.556
0.000
0.000
0.000
EF2,1U
39.708
95.568
36.884
9.223
EF2.L
39.708
0.000
0.000
0.000
EF3,T
69.771
139.789
348.497
133.600
EF3,L
69.771
0.000
0.000
0.000
A-2
n0.0,
Volt-second Contributions of Each PF Coil
Coil
VSend,atart-up
VSendflattop
(V-S)
(V-S)
OH1,U
1.384
-1.654
OH1,L
1.384
-1.654
OH2,U
1.969
-1.478
OH2,L
1.969
-1.478
EF1,U
2.067
-0.664
EF1,L
2.067
-0.664
EF2,U
-1.498
2.560
EF2,L
-1.498
2.560
EF3,U
0.906
-6.994
EF3,L
0.906
-6.994
Total
9.657
-16.461
A-3
Currents in PF Coils after Flux-Conserving Disruptions
EOS
EOS
EOB
EOB
Iprc
post
pre
Ipost
(MA)
(MA)
(MA)
(MA)
OH1,U
-6.093
-3.868
0.000
0.000
OH1,L
-6.093
-3.868
0.000
0.000
OH2,U
-7.790
-5.776
0.000
0.000
OH2,L
-7.790
-5.776
0.000
0.000
EF1,U
-1.609
-1.164
0.000
0.000
EF1,L
-1.609
-1.164
0.000
0.000
EF2,U
3.774
4.046
0.000
0.000
EF2,L
3.774
4.046
0.000
0.000
EF3,U
-6.658
-6.026
0.000
0.000
EF3,L
-6.658
-6.026
0.000
0.000
Coil
2.941
Total A I
A-4
1.470
Peak Currents and Voltages on PF Coils
Coil
Icond,mar
Icond,min
Vtermmax
Vterm,min
(kA)
(kA)
(kV)
(kV)
OH1,U
29.300
-35.000
0.606
-2.786
OH1,L
29.300
-35.000
0.677
-2.702
OH2,U
78.750
-59.125
0.667
-1.938
OH2,L
78.750
-59.125
0.572
-2.062
EF1,U
25.533
-8.200
2.085
-9.196
EF1,L
25.533
-8.200
2.085
-9.196
EF2,U
37.679
-22.054
0.716
-0.156
EF2,L
37.679
-22.054
0.716
-0.156
EF3,U
5.750
-44.375
3.529
-12.986
EF3,L
5.750
-44.375
3.529
-12.986
A-5
Positive and Negative Power Supply Requirements
CIT306L
Coil
P--PS
I+PS
V+PS
P+PS
I-PS
(kA)
(V)
(MVA)
(kA)
(V)
(MVA)
OH1,U
29.30
605.86
17.75
-35.00
-991.85
34.71
OH1,L
29.30
676.69
19.8-3
-35.00
-1699.02
59.47
OH2,U
78.75
667.00
52.53
-59.13
-862.22
50.98
OH2,L
78.75
572.14
45.06
-59.13
-721.88
42.68
EF1,U
25.53
2085.40
53.25
-8.20
-2216.50
18.18
EF1,L
25.53
2085.40
53.25
-8.20
-2216.50
18.18
EF2,U
37.68
288.90
10.89
-22.05
-156.17
3.44
EF2,L
37.68
288.90
10.89
-22.05
-156.17
3.44
EF3,U
5.75
598.59
3.44
-44.38
-3389.14
150.39
EF3,L
5.75
598.59
3.44
-44.38
-3389.14
150.39
A-6
-PS
PF System Energy (MJ)
CIT306L
Etotal (MJ) =1390.12
1400
P
PF Total
T
- -- 1-----
1200
-
PF1,U+L
PF2,U+L
PF3,U+L
PF4,U+L
2--
-3-
vs. Time (s)
-
PF5,U+L
5
1000
800
600
400
200 --
-1-
02
0
2
-41-
4
6
4
8
Time (s)
A-7
10
12
14
Energy Deposited in PF (MJ)
1200 Edepos
(MJ)
vs.
Time (s)
10
12
CIT306L
=1145.35
Total
----Joule
-- N-Nuclear
-T---
1000
800
600
400
200
0
y
0
2
4
6
8
Time (s)
A-8
14
PF Dump
Edump (MJ)
0
B
N
f
I
.
~
--
a
+-- PF
- PF1, \+L
-2-- PF2,
+L
-3PF3, +Il
+ - PF4,U L\
5
PF5,U L
-1001
vs. Time (s)
Energy (MJ)
CIT306L
548.683
+----------------'-
---
--
---------- 1
-- 2
-- 2- ---
2--
3-3
-200
-300
-400
-500
-600
-
0
I
I
2
I
I
4
I
I
6
I
I
8
Time (s)
A-9
I
I
10
I
I
12
14
PF System Energy (MJ)
vs.
Time (s)
Etotal (MJ) =1390.1CIT306L
Wm,max (MJ) =5.20E+08
1400
PF Total
-- R-- Resistive
--M-- Magnetic
-±T-
12001
1000
800
-M
600
400
,M,
200
0 IYJ
0
IV'
2
4
6
Time
A-10
8
(s)
10
12
14
Power Flow (MW)
PF System
0.5
Psys,max (MW)
Psys,min (MW)
I
I
I
I
vs. Time
(s)
CIT306L
=437.687
=-1.20E+03
I
I
I
I
I
I
I
I
I5
0.0
co
-0.5
0
T--- I---- 2--
PF Total
PF1,U+L
PF2,U+L
-3- - PF3,U+L
-
-1.0
- PF4,U+L
5
PF5,U+L
-1.5
0
2
6
4
8
Time (s)
A-1l
10
12
14
PF System Power Flow (MW)
Psys,max (MW)
Psys,min (MW)
i
I
i
I
0.5
vs. Time (s)
CIT306L
=437.687
=-1.20E+03
I
I
I
I
I
I
1-I
-
-
-
0.01
CO
-0.5
0
PF Totafl
-T-
-1.0
-
-1.5
-
-I-
Resistive
Inductive
-
-
0
2
4
6
8
Time (s)
A- 12
10
12
14
PF Line Power (MW)
vs. Time
(s)
CIT306L
Pline,max (MW)
500
=437.687
i
- +-- -H-
i
I
Total
Resistive
I
I
I
I
I
400
300K-
0
200
I
100
0
I
R
0
2
4
6
Time
A-13
8
(s)
10
12
14
PF Line Power (MW)
vs. Time (s)
CIT306L
Pline,max (MW) =437.687
I
I
I
'
I
I
I
--- F-- PF1 Total
--+-PF1, U+L
--- 2-- PF2, U+L
500
- -3--4
-
I
I
I
I
PF3, UL4PF4, U+L
PF5, U+L
5
400
I
300
T
0
200
-~
5
/
--
5:5
100
2-~
0'
0
2
6
4
8
Time (s)
A-14
10
12
14
Plasma Loop Voltage
(V)
vs.
Time (s)
CIT306L
Vloop,max (V) =6.33104
Vloop,min (V) = -31.4713
10
'
'
'
I
'4--
I
I
I
I
I
A- ------
I
4-4
-
4
I.. . . . .
-10
P-4
0
-20
Total
T- -- 1- -PF1,U+ L
--- 2-- PF2,U+L
-
-345
-30
I
-40
0
I
2
I
I
4
I
I
6
I
.I
8
Time (s)
A-15
PF3,U+L
-
II
PF4,U+L
PF5,U+L
II
10
I
I
12
I
14
Plasma Volt-Seconds
10
(Wb)
vs. Time
(s)
CIT306L
=9.65708
=-16.4607
VS,max (Wb)
Vs,min (Wb)
-- T-- 1~4 _4
-3-
5 -
-4-
0
PF5,U+L
5
/
Total
PF1, )+L
-PF2,N+L
PF3,U+L
PF4,U+L 4
2
0
5
10
'5
-15
-20
0
2
4
6
8
Time (s)
A-16
10
12
14
Plasma Current
I
8
4
0
0
4
vs. Time
(s)
CIT306L
(MA) =10
2
(MA)
6
8
10
14
12
Time (s)
Plasma Volt-Seconds vs. Time (s)
20-
--- Inductive V-S
15
10
T -----------5
0-
0
_L
I
2
4
6
8
Time (s)
A-17
10
12
14
dR (i)
= 0.248
dZ (m)
= 0.368
Volts/Turn vs. Time (s)
OH1,U
R. (i)
=
0.38
Z (m)
=
0.18
MA-Tlurns vs. Time (s)
6
5
'I'll
'
III
'
1111111
0
4
2
-5
U)
0
-2
S -4
0
-10
K
-15
-6
liii
ii
0
-8
0
2
4
. . . . . . . . . . . . ' '
2
4
6
6
8 10
14
Time (s)
14
8 10
liii
Time (s)
(MW)
Power Flow
vs.
Time
Max power =34.7148
Min power =-86.7317
+ PS MVA =17.7516
- PS MVA =34.7148
40
120
20
100
01
-20
0
Energy (MJ)
, . , . , . ,
.
-
.
I
80
-60
20
I
Tot
Res
Ind
60
40
I
T
--- R---- I--
=116.791
,.
-40
-80
Emax
vs. Time
-
--
-
01
I-I
-/
,
-r '
-20
-100
0 2 4 6 810
14
0
Time (s)
2 46
8 10
Time (s)
A-18
14
OH1,U
Current (kA)
vs.Time (s)
0.38
Re
=
Zc-
I,max
Voltage (V) vs.
0.18
=
nturns = 200.0
Vt,max =6.06E-01
Vt,min = -2.78598
29.30
I,min =-35.00
30
1.0
20
0.5
10
0.0
Time (s)
-0.5
0
-1.0
-10
0
4-
-1.5
.C
-20
-2.0
I*
E-
-30
4'
I
-40
0
0 24
''
' 1
6 810
Time
Flux Linkag
-3.0
14
0
I
I
2
4
6
I
I
I
8 10
14
Time (s)
vs.
Time
Temperature (K)
=7.04729
=
I
(s)
(Wb)
VS,max
VS,min
-2.5
-5.59458
vs. Tim
J 2 t, norrr =6.57195
Espec (J/cc) =1057.77
T,max (K ) =292.358
8
6
Juu
4
250
2
200
0
-)
-2
150
E- 100
-4
-6
50
ii
0
2
4
6
8 10
14
0
Time (s)
I
I
I
2
4
6
I
8 10
Time (s)
A-19
I
I
14
Radial
R (in) = 0.383
dh (mn)
= 0.248
sigmaT,,max (MPa)=
sigma,, min (MPa)=
140
120
100
80
60
40
20
0
0
C
Force vs.
-A
Time (s)
0.184
0.368
mW
Z
221.40
-5.60
Tot
Mut
-
-
-M
-20
0
4
2
6
8
Time
Axial
2
z
I
12
14
(s)
Force vs.
sigmaz,max (MPa)
sigmaz,min (MPa)
10
Time (s)
0.59
-16.77
I
*
0
N-,
a.)
C.)
0
-2
-4
-6
C.)
-8
a.) -10
-12
I
0
2
4
6
Time
A-20
8
(s)
I
10
I
12
14
Currents
Post Disruption
Pre and
0.383
0.248
R (m)
dk (W)
(MAT)
0.184
0.368
(m)
dZ
6
-----
4
-A-
2
-N
B
o
fter
'
01
'A
-2
-4
-6
-8
0
4
2
6
Time
Radial
sigmaTmai
12
14
(s)
Pre and Post-Disruption
Force,
sigmaTmax (MPa)=
140
10
8
(MN)
221.40
-5.60
(MPa)=
120
100
80
60
40
I Befor
----- N fter
20
0
-20
0
2
4
6
8
Time (s)
A-21
10
12
14
dR (i)
dZ (i)
OH2,U
Re (i)
Ze (i)
MA-Turns
0.38
0.68
vs. Time
= 0.248
= 0.632
Volts/Turn vs. Time (s)
=
=
5
(s)
' ,
I
I
I II
I
15
0
10
E-,
-5
5
a$
0
0
-5
-10
-15
0
-10
I
I
I
0 2 4 6 8 10
Time
50
0
I
4
6
8 10
Time
14
I
I
14
(s)
(s)
Power Flow (MW)
100
2
I
vs.
Time
Max power =52.5261
Min power =-181.474
+ PS MVA =52.5261
- PS MVA =50.979
Energy
Emax
250
-
T
-
200
=207.244
Tot
Res
d
R--
--- I--
[
vs. Time
(MJ)
R
150
-50
100
-100
50
-150
01
I
-
-200,
I
-50
0 2 4 6 810
14
0
Time (s)
2
4
6
8 10
Time (s)
A-22
14
OH2,U
Current (k.A)
vs.Time
(s)
Voltage
(V) vs. Time (s)
-0.38
Ze
=
I,max
I,min
8Q
0.68
= 78.75
59.13
nturns = 160.0
Vt,max =6.67E-01
Vt,min =-1.93783
.
1.0
60
40
0.0-
-4
20
0
-0.5 -
0
0
-1.0
-20
0
-1.5
E-
-40
U
-60
I
I
I
I
0 2 4 6 810
Time
Flux Linkage
8
14
0
2
4
6
8 10
vs. Time
Temperature (
Jet, norm
Espec (J/cc)
T,max (K)
7.34052
=-4.85
=
350
4
S300
2
250
0
200
-2
4S
150
-4
Q)
100
-6
0
I
I
I
2
4
6
I
8 10
14
Time (s)
6
N-,
. . . I. . . . I. . . . I.
(s)
(Wb)
VS,max
VS,min
-2.0
I
I
50
14
0
Time (s)
2
I
I
4
6
K)
=8.36783
-1370.28
=300.559
I
I
8 10
Time (s)
A-23
vs. Tirn
14
Radial Force vs.
R
m)=
0. 383
d
(m)=0.
248
sigmaT,max (MPa)=
sigma ,Tmin (MPa)=
300
250
200
dZ
0.684
0.632
(m)
291.95
-0.37
Tot
Self
150
0
Time (s)
-Mut
-
100
50
I
II
*
I-
- f
-50
0
2
4
6
8
10
12
14
12
14
Time (s)
Axial Force vs. Time (s)
sigmaz,max (MPa)=
0.00
sigmaz,min (MPa)= -56.31
0
I
I
I
I
-5
-10
0
-15
-20
C.)
-25
-30
-35
0
2
I
I
I
4
6
8
Time (s)
A-24
I
10
Pre and Post Disruption
= 0.383
= 0.248
R (i)
dk (m)
Currents
(MAT)
0.684
0.632
(m)
Z
15
SBef re
10
0
-5
'A-A-----
S -10
0
2
4
6
8
10
12
14
Time (s)
Force, Pre and Post-Disruption
Radial
300
sigmaTmax (MPa)=
sigmaTmin (MPa)=
(MN)
291.95
-0.37
250
200
150
100
-B-Before
50
fter
A-
0
-50
0
2
4
6
8
Time (s)
A-25
10
12
14
dR (i)
= 0.279
dZ (i)
0.461
Volts/Turn vs. Time (s)
EF1,U
R.
(i)
=
1.05
Z (m)
=
1.75
MA-Trurns vs. Time (s)
8
I'
I'
I'
10
I'l'
1111111
I'
0
I'
6
rz)
-10
4
Cii)
Cl)
2
H
-20
0
S
-30
0
-40
a.) -2
ii
0
-4
0
2
I
I
4
6
I
8 10
I
2
liii
4
6
Time
-1
14
Iii
8 10
14
(s)
Time (s)
Power Flow (MW)
100
vs. Time
Max power =53.2472
Min power =-242.749
+ PS MVA =53.2472
- PS MVA =18.1753
Energy (MJ)
Eimax
100
50
80
0
-100
0
=84.5851
T
--- R-
Tot
Res
--- I-s
Ind
60
/
-50
vs. Time
40
a.
-150
20
-200
RR 'I
-250
1.1
0
0
2 4 6 810
Time
0
24
0 24
14
(s)
6
81
6 810
Time (s)
A-26
1
1.4
EF1,U
Current
vs.Time (s)
1.05
(kA)
R =
zc
1.75
25.53
-8.20
I,max
I,min
30
. . . . . .
4
25
4-d
Voltage
0z
0u
10
-2
-4
5
-10
I
I
-10
I
0 2 4 6 810
Flux Linkage
14
0
2
VS,max
VS,min
(Wb)
4
6
8 10
14
Time (s)
vs. Time
vs. Tim
Temperature (K)
=19.5708
- 7.08021
J 2 t, norm =5.95E-01
Espec (J/cc) =30.955
T,max (K) =95.6358
I,
15
-4
I
-8
Time (s)
a)
.1
-6
-5
20
.
-
0
0
U
-H
0
15
0
(s)
nturns = 300.0
Vt,max =2.0854
Vt,min =-9.19584
2
20
(V) vs. Time
10n
I fJI
10
1'1~
I'
I'I~
I
95
5I
E-
90
0
85
-5
80
0 2 4 6 810
14
0
Time (s)
I
I
I
2
4
6
8 10
Time (s)
A-27
I
14
Radial Force vs. Time
R (m)
1.050
d& (m)
0.279
sigma,,max (MPa)=
sigmaTmin (MPa)=
120
100
80
60
40
20
0
-20
-40
z
~-
0
106.61
0.00
(s)
dZ
1.748
0.461
(m)
Tot
-
Self
-
---
-0
2
~
Mut
M
4
8
6
10
12
14
12
14
Time (s)
Time (s)
Axial Force vs.
sigmaz,max (MPa)=
sigmaz,min (MPa)=
5
z
C.)
I
I
I
I
2
4
0.19
-11.27
I
I
I
I
I
6
8
*
0
-5
-10
C.)
-15
-20
-25
0
Time (s)
A-2 8
10
Pre and Post Disruption Currents
R
dk
ICl)
1.050
(in)
Z
0.279
(mn)
(MAT)
1.748
mW == 0.461
8
Be
6
er
-----
4
2
S4
Oj
-2
-4
0
4
2
6
8
10
12
14
Time (s)
Radial
Force,
Pre and
sigmaTmax (MPa)=
sigmaTmin (MPa)=
99. 996
Post-Disruption
(MN)
106.61
0.00
79. 996
59. 996
39. 996
R
Before
--- A-- After
19. 996
-
-0.004
0
2
4
6
Time
A-29
8
(s)
10
12
14
dR (i)
= 0.326
dZ (m)
= 0.326
Volts/Turn vs. Time (s)
EF2,U
R. (m)
=
2.05
Z (i)
=
1.68
MA-Turns vs. Time (s)
5
'I
'I
8
111111
I
I
I
I
6k
4
4
3
Cl)
2
2
1
4-'
H
0
0
0
S -1
-2-2
-2
. . . . . . . . . . . ' '
-3
I
0
I
2
4
I
6
I
I
I
I
0
i
2
I
4
'
I
6
8
Time
14
8 10
I
I
I
i
10 12 14
(s)
Time (s)
Power Flow (MW)
vs.
Time
Max power =9.22343
Min power =--17.3578
+ PS MVA =10.8854
- PS MVA =3.44408
10
Energy
40
Emax
-5
0
.
I
I
vs.
Time
=36.8837
i
III I
I
T
--- R--
Tot
Res
30 ---- I--
Ind
5k
1
(MJ)
I
I
A-- R4,-
---
I.-
{l
-
-
20
-
-10
I'd
Q~)
10
-15
I
-20
I
I-
.
0 2 4 6 8 10
0't
0
0
14
Time (s)
2
4
6
Time
A-30
8
(s)
10 12 14
EF2,U
Current (kA)
vs .Time
(s)
2.05
Ze =
1.68
I,max = 37.68
I,min = -22.05
40
Voltage (V)
ct.)
800
I
I
30
Y
600
0-
400
0
200
M4
0
vs. Time (s)
nturns = 112.0
Vt,max =7.16E-01
Vt,min =-1.56E-01
20
10
0
.)
-10
C
-20
cis
-30
0
1,1,
0 2 4 6
810
Time
Flux Linkage
4
-200
1.1
0
14
I
2
4
vs.
6
I
8 10
14
Time
Temperature (K) vs. Tim
J 2 t, norm =5.61E-01
Espec (J/cc) = 30.9783
T,max (K) =95.5678
VS,max =3.17731
VS,min =- 2.05438
I~
1.1
Time (s)
(s)
(Wb)
I~
I
I'
3
100
1'1'
I'I'I*
2
95
1
0
4-)
a>)
Q.o
90
-1
E-
-2
Ii
-3
0
2
80
1111111
4
6
8 10
85
0
14
2
4
6
8 10
Time (s)
Time (s)
A-31
14
Radial
R
2.050
dk (i)
0.326
sigmaTmax (MPa)=
sigmaTmin (MPa)=
60
40
20
=
(
_
1.680
0.326
30.04
-72.25
-
--
Tot
Se
-20
-40
-60
-80
-100
Pd-
W
Z
-----
-IS
0f
0
Force vs. Time (s)
-
T
T
-M
0
2
4
6
8
10
12
14
Time (s)
Axial
Force vs. Time
sigmaz,max (MPa)=
sigmaz,min (MPa)=
80
(s)
17.04
-0.27
60
40
0
Cz
0
-20
I
0
2
4
I
I
6
8
Time (s)
A-32
I
10
I
12
14
Pre and Post Disruption Currents
R
d
5
4
3
Cl)
S
--
A--
---
2.050
=
(in)
(mn)
1.680
0.326
mW
Z
0.326
(MAT)
Before
After
2
1
0,
-1
-2
-3
2
0
4
8
6
Time
12
sigmaTiax (MPa)=
sigmaTmin (MPa)=
14
(s)
Pre and Post-Disruption
Radial Force,
30
10
(MN)
30.04
-72.25
20
10
01
-10
A-
--
-20
-
-30
e
-Bef
-- A -- After
-40
-50
0
2
6
4
8
Time (s)
A-33
10
12
14
dR (m)
dZ (i)
0.319
0.319
Volts/Turn vs. Time (s)
EF3,U
2.51
0.95
vs. Time
=
=
R 0 (in)
Z (m)
MA -T~lurns
S,
2
, ,
40
(s)
I'I
1111111
I'
20
,
, ,
=
=
0
0
-20
Cl)
-2
H
-40
0
-4
-60
-80
S
-6
-100
0
I
I
2
4
-8
11111
Iii
8 10
6
14
Time (s)
0
2
4
6
8 10
14
Time (s)
Power Flow (MW)
150
vs.
Time
Max power =133.6
- 137.017
Min power
+ PS MVA =3.4419
- PS MVA =150.393
-±-T
--- R-250 -- I-200
150
0
0
Tot
Res
Ind
300
50
vs. Time
=348.497
Emax
350
100
-50
(MJ)
Energy
-
a.)
-
100
-100
-150
-/
I
'
'
0 2 4 6 810
Time
'
-50
'
14
. . 1
0
I-
R'
0i
I
2
1
4
1
1
6
.
1
.
A-34
1
8 10
Time (s)
(s)
-
I
50
1
1
14
EF3,U
Current (kA) vs.Time (s)
Re-
2.51
=
0.95
Z
Voltage (V) vs. Time (s)
I,max
5.75
I,min =-44.38
I10~J
I
I'I
1'I
5
I'
nturns = 160.0
Vt,max =3.52881
Vt,min =-12.9856
'1
-'
0
0
0
-10
0
-20
0
-30
Sz
-10
E-
-15
-40
0
-50
I
U
I
I
I
I
0 2 4 6 8 10
14
-5
-
0
2
Time (s)
Flux Linkage
20
VS,max
VS,min
(Wb)
6
14
8 10
Time (s)
vs. Time
Temperature
=11.4692
-
4
-
57.3432
10
14
0
( K)
vs. Tjm
J 2 t, norm =1.72271
Espec (J/cc) -140.534
T,max (K) -139.789
U
130 -
-10
120
-20
110
-30
E-
-40
100
-50
90
-60
80 L
0 2
I
0 2 4 6 810
14
Time (s)
I
4
6
I
8 10
Time (s)
A-35
I
I
14
Radial Force vs. Time (s)
= 2.510
R (
dk (m) = 0.319
sigmaTmax (MPa)=
sigmaTmin (MPa)=
200
150
~
Cz
100
T
Tot
-S-- Self
-M--Mut
-
-
dZ
0.955
0.319
(m)
272.14
0.00
& - - -8
-
-*-
-
-
-
-
-
-
's,
50
01
-
-
-50
2
0
4
6
8
10
12
14
Time (s)
Axial
sigmaz,max (MPa)=
sigmaz,min (MPa)=
20
z
Force vs. Time (s)
0.27
-16.80
0
-20
0
-40
-60
-80
-100
I
0
2
4
I
I
6
8
Time (s)
A-36
I
10
I
12
14
Pre and Post Disruption
R
df
Currents
2.510
0.319
(in)
(mn)
(MAT)
= 0.955
mW= 0.319
Z
2
e-
- Oe
fter---2
-4
-6
-
-I*
S -8
2
0
4
6
8
10
12
14
Time (s)
Radial
Force,
Pre and Post-Disruption
272.14
0.00
sigmaTmax (MPa)=
200
sigmaTmin
(MN)
(MPa)=
150
I
I
100
A
50
,A
-0
0
Li /\
2
4
6
8
Time (s)
A-37
10
12
14