![](media/image1.pct){width="9.768055555555556in" height="0.75in"}

Extension of Operation Range of NSTX to

Ip ≤ 1.5MA

C. Neumeyer

12/8/00

Issues related to increasing Ip up to 1.5MA:

1)  Availability of flux

> \- not addressed

2)  Ability of PF coil set to maintain equilibria

\- addressed by scaling from 1.0MA cases

3)  Range of instrumentation

> \- addressed by R Marsala and J Menard

4)  EM forces during normal operation

> \- addressed

5)  EM forces during disruption

> \- addressed

6)  PF coil voltages during disruption

> \- addressed

Issues have been evaluated thus far without the benefit of a complete
analysis (i.e. TSC, equilibria, SPARK and ANSYS) and without an
exhaustive analysis of disruption behavior.

However, margins seem to be large, and no apparent show-stoppers have
been identified.

Pending review of these findings it is recommended to:

-   approve the higher level of operation at limited Bt (e.g. 4.5kG);

-   resurrect the analysis work on SPARK and ANSYS;

-   establish a disruption database;

-   implement Digital Coil Protection system.

1)  [Ability of PF coil set to maintain equilibria]{.underline}

• Scaled PF coil currents from original equilibria cases by 1.5, except
for OH

• On this basis, 34 of 40 cases can be run within existing PF coil
current limits

# 

# Therefore it is assumed that no increase in PF coil current limits is required 

  ---------- ------- ------- ------ -------- -------- ------- ------- ----
  Config     κ95     δ95     li     Ipf1     Ipf2     Ipf3    Ipf4    

  0          2       0.52    0      0.00     0.00     0.44    0.50    

  ND         1.99    0.52    0.2    0.13     0.00     0.57    0.48    

  ND         2       0.35    0.2    0.31     0.00     0.31    0.33    

  ND         2       0.35    0.2    0.51     0.00     0.43    0.32    

  ND         2       0.36    0.2    0.33     0.00     0.36    0.54    

  ND         2       0.36    0.2    0.53     0.00     0.47    0.53    

  ND         2       0.35    0.2    0.40     0.00     0.39    0.66    

  ND         2       0.35    0.2    0.60     0.00     0.49    0.66    

  ND         1.6     0.53    0.2    0.00     0.00     0.70    0.37    

  ND         1.6     0.53    0.2    0.21     0.00     0.80    0.37    

  ND         1.6     0.29    0.2    1.20     0.00     0.36    0.48    X

  ND         1.6     0.33    0.2    1.20     0.00     0.56    0.47    X

  ND         2       0.47    0.2    -0.26    0.00     0.18    0.79    

  ND         2       0.49    0.6    -0.13    0.00     0.31    0.76    

  ND         2       0.3     0.6    0.00     0.00     0.12    0.81    

  ND         2       0.3     0.6    0.26     0.00     0.23    0.80    

  ND         1.6     0.5     0.6    -0.52    0.00     0.52    0.61    

  ND         1.6     0.5     0.6    -0.31    0.00     0.62    0.61    

  ND         1.6     0.3     0.6    0.32     0.00     0.34    0.69    

  ND         1.6     0.3     0.6    0.59     0.00     0.42    0.69    

  ND         2.11    0.55    0.6    0.00     -0.58    0.87    0.36    

  DN         2.11    0.53    0.2    0.17     -0.38    0.83    0.41    

  DN         2.13    0.41    0.2    0.34     -0.49    0.66    0.23    

  DN         2.13    0.39    0.2    0.55     -0.32    0.65    0.26    

  DN         2.14    0.41    0.2    0.48     -0.51    0.70    0.44    

  DN         2.14    0.39    0.2    0.69     -0.35    0.69    0.47    

  DN         2.16    0.41    0.2    0.59     -0.54    0.73    0.56    

  DN         2.15    0.39    0.2    0.80     -0.38    0.73    0.58    

  DN         1.86    0.58    0.2    0.00     -1.27    1.40    0.20    X

  DN         1.86    0.59    0.2    0.13     -1.11    1.41    0.22    X

  DN         1.9     0.41    0.2    0.99     -1.26    1.13    0.31    X

  DN         1.9     0.41    0.2    1.14     -1.11    1.14    0.33    X

  DN         1.88    0.4     0.2    -0.42    -0.33    0.40    0.72    

  DN         1.92    0.38    0.6    -0.24    -0.13    0.36    0.76    

  DN         1.99    0.29    0.6    0.00     -0.27    0.25    0.78    

  DN         2       0.27    0.6    0.24     -0.13    0.26    0.80    

  DN         1.73    0.4     0.6    -0.28    -0.68    0.67    0.63    

  DN         1.74    0.4     0.6    -0.15    -0.53    0.69    0.64    

  DN         1.77    0.36    0.6    0.00     -0.72    0.62    0.65    

  DN         1.77    0.36    0.6    0.15     -0.57    0.64    0.67    
  ---------- ------- ------- ------ -------- -------- ------- ------- ----

## 2.0 Instrumentation Range

J Menard:

"A 1MA shot generates about 2V of integrator output, so we can probably
double Ip before we run into any risk of saturating integrator/digitizer
signals"

R Marsala:

"The change looks like a cinch. To change from 1.2 MA full scale to 2.0
MA full scale (2 MA suggested by Jon & Dave), I propose the following:

-   Change A3R4 and A6R4 in the Ip&IPF1b Calculator Module from 10K to
    6.04K.

-   Re label test points on Ip&IPF1b Calculator Module.

-   Adjust the two IPF1b input pots on the Ip Calculator Module to give
    200KA/V

-   instead of 120KA/V.

-   Re label test points on Ip Calculator Module.

-   Re label the Permissive Module test points from 120KA/V to 200kA/V.

-   Change transfer functions on a few (6) TD channels.

-   ECN 4 drawings.

-   Software changes"

## 3.0 EM Forces During Normal Operation

### Plasma current generally decreases worst case force on coils, assuming that current directions are consistent with normal operations.

![](media/image2.pct)

####### *Relative Current Directions When Plasma Is Present*

*TF Coil Inner Legs* -- Primary concern is torsion on Inner Leg Bundle
due to J~tf~ x B~r~ which is due almost exclusively to I~oh~ and
I~pf1a~. In any case, since polarities of I~oh~ and I~p~ are opposite
when I~p~ is large, I~p~ tends to reduce the torsion.

![](media/image3.pct){width="5.861111111111111in"
height="3.8472222222222223in"}

*TF Coil Outer Legs* -- Primary concern is overturning moment due to
J~tf~ x B~v~ which is due mainly to I~pf3~ and I~pf5~ and is generated
on the top and bottom portions of the outer legs where J~tf~ is mostly
radial. Since polarities of I~pf3~ and I~pf5~ are opposite to I~p~, the
presence of I~p~ tends to reduce the force generated.

*OH Coil* -- Primary concern is tensile stress in conductor due to J~oh~
x B~z~ which is due almost exclusively to I~oh~ by itself. In any case
since polarities of I~oh~ and I~p~ are opposite when I~p~ is large, I~p~
tends to reduce the field and force.

*PFCoils --* Axial and Radial Force Influence Matrices are used to
assess mutual interactions. Using rated currents in nominal directions
in OH, PF3, and PF5, and considering both polarities of PF1a and PF2, it
is shown that the plasma decreases the force on the coil in nearly all
cases and that stresses are well within allowables under all conditions.

PF Coil Axial Force Coefficients (F~Z~(j) = I(j)\*∑F~z~(i,j)\*I(i))

  ------- ------- ------- ------- ------- ------- ------ -------- ------- -------- -------- -------- -------- ------- -------
          OH      PF1AU   PF1AL   PF1BL   PF2U    PF2L   PF3U     PF3L    PF4U     PF4L     PF5U     PF5L     PLA     PLB

  OH      0       -9.6    9.6     53.3    -54.1   54.1   -27.7    27.7    -4.6     4.6      -5.9     5.9      0       0

  PF1AU   9.6     0       0.05    0.05    -24.2   0.26   -2.55    0.96    3.06     1.56     3.51     2.2      0.13    0.09

  PF1AL   -9.6    -0.05   0       97.2    -0.26   24.2   -0.96    2.52    -1.56    -3.06    -2.2     -3.51    -0.13   -0.09

  PF1BL   -53.3   -0.05   -97.2   0       -0.29   17.9   -1.1     -7.16   -1.84    -4.87    -2.72    -5.81    -0.11   -0.07

  PF2U    54.1    24.2    0.26    0.29    0       1.7    99.0     6.56    33.0     11.1     40.29    16.72    0.54    0.35

  PF2L    -54.1   -0.26   -24.2   -17.9   -1.7    0      -6.6     -99.0   -11.08   -33.0    -16.7    -40.3    -0.54   -0.35

  PF3U    27.7    2.5     0.96    1.1     -99.0   6.6    0        26.0    165.1    44.9     204.6    69.6     1.5     0.95

  PF3L    -27.7   -0.96   -2.5    7.2     -6.6    99.0   -26.0    0       -44.9    -165.1   -69.6    -204.6   -1.5    -0.95

  PF4U    4.6     -3.06   1.6     1.8     -33.0   11.1   -165.1   44.91   0.01     89.8     189.4    138.0    1.27    0.39

  PF4L    -4.6    -1.6    3.1     4.9     -11.1   33.0   -44.9    165.1   -89.8    -0.01    -138.0   -189.4   -1.27   -0.39

  PF5U    5.9     -3.5    2.2     2.71    -40.3   16.7   -204.6   69.6    -189.4   138.0    0        225.9    1.31    0.42

  PF5L    -5.9    -2.2    3.5     5.81    -16.7   40.3   -69.6    204.6   -138.0   189.4    -225.9   0        -1.31   -0.42

  PLA     0       -0.13   0.13    0.11    -0.54   0.54   -1.5     1.5     -1.27    1.27     -1.31    1.31     0       0

  PLB     0       -0.09   0.09    0.07    -0.35   0.35   -0.95    0.95    -0.39    0.39     -0.42    0.42     0       0
  ------- ------- ------- ------- ------- ------- ------ -------- ------- -------- -------- -------- -------- ------- -------

PF Coil Radial (Hoop) Force Coefficients (F~R~(j) =
I(j)\*∑F~r~(i,j)\*I(i))

  ------- --------- ------- ------- ------- ------- ------- -------- -------- -------- -------- -------- -------- ------ ------
          OH        PF1AU   PF1AL   PF1BL   PF2U    PF2L    PF3U     PF3L     PF4U     PF4L     PF5U     PF5L     PLA    PLB

  OH      23112.1   -33.8   -33.8   -57.7   -18.9   -18.9   -15.2    -15.2    -10.5    -10.5    -14.1    -14.1    -0.4   -0.2

  PF1AU   2493.8    439.1   0.5     0.33    -7.14   0.71    -8.69    1.14     -1.27    0.72     -1.65    0.74     0.08   0.04

  PF1AL   2493.8    0.5     439.1   22.7    0.71    -7.14   1.14     -8.69    0.72     -1.27    0.74     -1.65    0.08   0.04

  PF1BL   1283.1    0.57    210.1   302.4   0.88    -56.5   1.52     -14.59   1.21     -0.15    1.43     -0.57    0.11   0.06

  PF2U    942.3     180.4   3.41    2.44    387.2   5.5     -110.4   9.7      4.1      8.4      1.5      10.3     0.67   0.4

  PF2L    942.3     3.41    180.4   290.9   5.5     387.2   9.7      -110.4   8.4      4.1      10.3     1.5      0.67   0.4

  PF3U    1007.4    151.3   13.3    9.68    447.9   21.9    515.4    40.1     44.7     37.6     24.7     47.0     2.64   1.63

  PF3L    1007.4    13.3    151.3   150.9   21.9    447.9   40.1     515.4    37.6     44.7     47.0     24.7     2.64   1.63

  PF4U    667.4     53.8    20.9    14.9    92.4    33.3    166.1    59.0     184.4    56.8     -899.0   57.5     4.28   2.48

  PF4L    667.4     20.9    53.8    40.4    33.3    92.4    59.0     166.1    56.8     184.4    57.5     -899.0   4.28   2.48

  PF5U    903.8     70.7    32.3    23.7    130.0   54.0    264.1    100.2    1284.3   111.8    395.1    127.9    5.8    3.2

  PF5L    903.8     32.3    70.7    55.0    54.0    130.0   100.2    264.1    111.8    1284.3   127.9    395.1    5.8    3.2

  PLA     31.0      0.97    0.97    0.52    0.9     0.9     0.76     0.76     -0.74    -0.74    -1.07    -1.07    0.08   0.04

  PLB     17.2      0.62    0.62    0.33    0.56    0.56    0.39     0.39     -0.52    -0.52    -0.61    -0.61    0.04   0.03
  ------- --------- ------- ------- ------- ------- ------- -------- -------- -------- -------- -------- -------- ------ ------

####   {#section-1 .unnumbered}

#### • Plasma Model

#### ![](media/image4.png){width="3.888888888888889in" height="5.291666666666667in"} 

#### 

#### 

#### 

#### 

#### 

#### 

#### R (m) Z (m) Turn

#### 

#### PL-1U 0.85 0.80 0.066

#### PL-1L 0.85 -0.80 0.066

#### PL-4 1.20 0.00 0.225

#### PL-5 0.65 0.00 0.285

#### PL-2U 1.10 0.55 0.097

#### PL-2L 1.10 -0.55 0.097

#### PL-3U 0.65 0.55 0.082

#### PL-3L 0.65 -0.55 0.082

#### 

####  Total= 1.000

#### 

#### PLA-A represents the sum of PL-1U, PL-1L, PL-4, and PL-5. The PLA-B represents the sum of PL-2U, PL-2L, PL-3U, and PL-3L.

#### Axial Forces For Four Cases

  ------- ------ --------- -------- -------- ------ --------- -------- -------- ------ -------- -------- -------- ------ -------- -------- --------
          Curr   EM Force  EM Force \|∆\|%   Curr   EM Force  EM Force \|∆\|%   Curr   EM Force EM Force \|∆\|%   Curr   EM Force EM Force \|∆\|%
          (kA)   w/o Plas  w/Plas            (kA)   w/o Plas  w/Plas            (kA)   w/o Plas w/Plas            (kA)   w/o Plas w/Plas   
                 (lb)      (lb)                     (lb)      (lb)                     (lb)     (lb)                     (lb)     (lb)     

  OH      -24    25584     25584    0        -24    25584     25584    0        -24    25584    25584    0        -24    25584    25584    0

  PF1AU   15     11866     6916     -42      -15    -11889    -6939    -42      -15    2487     7437     199      15     -2510    -7460    197

  PF1AL   15     -41029    -36079   -12      -15    41052     36102    -12      -15    26676    21726    -19      15     -26653   -21703   -19

  PF1BL   20     -10177    -4777    -53      20     -68503    -63103   -8       20     -54415   -49015   -10      20     3911     9311     138

  PF2U    20     82883     56183    -32      20     97571     70871    -27      -20    -98931   -72231   -27      -20    -84243   -57543   -32

  PF2L    20     -75839    -49139   -35      20     -90527    -63827   -29      -20    91887    65187    -29      -20    77199    50499    -35

  PF3U    -20    -168849   -95349   -44      -20    -170937   -97437   -43      -20    -96961   -23461   -76      -20    -94873   -21373   -77

  PF3L    -20    172153    98653    -43      -20    174241    100741   -42      -20    100265   26765    -73      -20    98177    24677    -75

  PF5U    -20    -47906    3994     -92      -20    -47120    4780     -90      -20    -28264   23636    -16      -20    -29050   22850    -21

  PF5L    -20    51318     -582     -99      -20    50532     -1368    -97      -20    31676    -20224   -36      -20    32462    -19438   -40

  PLU     1500                               1500                               1500                              1500                     

  PLL     1500                               1500                               1500                              1500                     
  ------- ------ --------- -------- -------- ------ --------- -------- -------- ------ -------- -------- -------- ------ -------- -------- --------

#### Stress Implication of Four Axial Force Cases

+-----------+------------+-----------+-------+---------+------------+
|           | Max\*      | Max\*     | \     | SS      | Max SS     |
|           |            |           | |∆\|% |         |            |
|           | w/o Plas   | w/Plas    |       | CSA     | Stress     |
|           |            |           |       |         |            |
|           | (lbs)      | (lbs)     |       | (in\^2) | (psi)      |
+-----------+------------+-----------+-------+---------+------------+
| OH        | 25584      | 25584     | 0     |         |            |
+-----------+------------+-----------+-------+---------+------------+
| PF1AU     | 11889      | 7460      | -37   | 0.8     | 15852      |
+-----------+------------+-----------+-------+---------+------------+
| PF1AL     | 41052      | 36102     | -12   | 0.8     | 54736      |
+-----------+------------+-----------+-------+---------+------------+
| PF1BL     | 3911       | 9311      | 138   | 1.0     | 9311       |
+-----------+------------+-----------+-------+---------+------------+
| PF2U      | 97571      | 70871     | -27   | 4.7     | 20705      |
+-----------+------------+-----------+-------+---------+------------+
| PF2L      | 90527      | 63827     | -29   | 4.7     | 19210      |
+-----------+------------+-----------+-------+---------+------------+
| PF3U      | -94873     | -21373    | -77   | 8.6     | -2474      |
+-----------+------------+-----------+-------+---------+------------+
| PF3L      | 98177      | 24677     | -75   | 8.6     | 11364      |
+-----------+------------+-----------+-------+---------+------------+
| PF5U      | -28264     | 23636     | -16   | 3.9     | 6019       |
+-----------+------------+-----------+-------+---------+------------+
| PF5L      | 31676      | 20224     | -36   | 3.9     | 8066       |
+-----------+------------+-----------+-------+---------+------------+

\* Maximum in direction in which force is weak, e.g. bolts or straps in
tension (35ksi yield)

#### Radial Forces For Four Cases

<table>
<colgroup>
<col style="width: 6%" />
<col style="width: 3%" />
<col style="width: 8%" />
<col style="width: 7%" />
<col style="width: 3%" />
<col style="width: 4%" />
<col style="width: 8%" />
<col style="width: 7%" />
<col style="width: 3%" />
<col style="width: 4%" />
<col style="width: 8%" />
<col style="width: 7%" />
<col style="width: 3%" />
<col style="width: 4%" />
<col style="width: 8%" />
<col style="width: 7%" />
<col style="width: 3%" />
</colgroup>
<tbody>
<tr class="odd">
<td></td>
<td>Curr (kA)</td>
<td>EM Force w/o Plas (lb)</td>
<td>EM Force w/Plas (lb)</td>
<td>|∆|%</td>
<td><p>Curr</p>
<p>(kA)</p></td>
<td>EM Force w/o Plas (lb)</td>
<td>EM Force w/Plas (lb)</td>
<td>|∆|%</td>
<td><p>Curr</p>
<p>(kA)</p></td>
<td>EM Force w/o Plas (lb)</td>
<td>EM Force w/Plas (lb)</td>
<td>|∆|%</td>
<td><p>Curr</p>
<p>(kA)</p></td>
<td>EM Force w/o Plas (lb)</td>
<td>EM Force w/Plas (lb)</td>
<td>|∆|%</td>
</tr>
<tr class="even">
<td>OH</td>
<td>-24</td>
<td>11831281</td>
<td>10096441</td>
<td>-15</td>
<td>-24</td>
<td>15422368</td>
<td>13687528</td>
<td>-11</td>
<td>-24</td>
<td>17231488</td>
<td>15496648</td>
<td>-10</td>
<td>-24</td>
<td>13640401</td>
<td>11905561</td>
<td>-13</td>
</tr>
<tr class="odd">
<td>PF1AU</td>
<td>15</td>
<td>86121</td>
<td>121896</td>
<td>42</td>
<td>-15</td>
<td>111690</td>
<td>75915</td>
<td>-32</td>
<td>-15</td>
<td>221970</td>
<td>186195</td>
<td>-16</td>
<td>15</td>
<td>-24159</td>
<td>11616</td>
<td>-52</td>
</tr>
<tr class="even">
<td>PF1AL</td>
<td>15</td>
<td>148986</td>
<td>184761</td>
<td>24</td>
<td>-15</td>
<td>48825</td>
<td>13050</td>
<td>-73</td>
<td>-15</td>
<td>159105</td>
<td>123330</td>
<td>-22</td>
<td>15</td>
<td>38706</td>
<td>74481</td>
<td>92</td>
</tr>
<tr class="odd">
<td>PF1BL</td>
<td>20</td>
<td>177169</td>
<td>202669</td>
<td>14</td>
<td>20</td>
<td>163381</td>
<td>188881</td>
<td>16</td>
<td>20</td>
<td>-71323</td>
<td>-45823</td>
<td>-36</td>
<td>20</td>
<td>-57535</td>
<td>-32035</td>
<td>-44</td>
</tr>
<tr class="even">
<td>PF2U</td>
<td>20</td>
<td>-97033</td>
<td>-53233</td>
<td>-45</td>
<td>20</td>
<td>-93175</td>
<td>-49375</td>
<td>-47</td>
<td>-20</td>
<td>407263</td>
<td>363463</td>
<td>-11</td>
<td>-20</td>
<td>411121</td>
<td>367321</td>
<td>-11</td>
</tr>
<tr class="odd">
<td>PF2L</td>
<td>20</td>
<td>-119997</td>
<td>-76197</td>
<td>-37</td>
<td>20</td>
<td>-116139</td>
<td>-72339</td>
<td>-38</td>
<td>-20</td>
<td>430227</td>
<td>386427</td>
<td>-10</td>
<td>-20</td>
<td>434085</td>
<td>390285</td>
<td>-10</td>
</tr>
<tr class="even">
<td>PF3U</td>
<td>-20</td>
<td>402499</td>
<td>367999</td>
<td>-9</td>
<td>-20</td>
<td>397969</td>
<td>363469</td>
<td>-9</td>
<td>-20</td>
<td>317465</td>
<td>282965</td>
<td>-11</td>
<td>-20</td>
<td>321995</td>
<td>287495</td>
<td>-11</td>
</tr>
<tr class="odd">
<td>PF3L</td>
<td>-20</td>
<td>408943</td>
<td>374443</td>
<td>-8</td>
<td>-20</td>
<td>404413</td>
<td>369913</td>
<td>-9</td>
<td>-20</td>
<td>323909</td>
<td>289409</td>
<td>-11</td>
<td>-20</td>
<td>328439</td>
<td>293939</td>
<td>-11</td>
</tr>
<tr class="even">
<td>PF5U</td>
<td>-20</td>
<td>226034</td>
<td>276434</td>
<td>22</td>
<td>-20</td>
<td>225488</td>
<td>275888</td>
<td>22</td>
<td>-20</td>
<td>234984</td>
<td>285384</td>
<td>21</td>
<td>-20</td>
<td>235530</td>
<td>285930</td>
<td>21</td>
</tr>
<tr class="odd">
<td>PF5L</td>
<td>-20</td>
<td>226834</td>
<td>277234</td>
<td>22</td>
<td>-20</td>
<td>226288</td>
<td>276688</td>
<td>22</td>
<td>-20</td>
<td>235784</td>
<td>286184</td>
<td>21</td>
<td>-20</td>
<td>236330</td>
<td>286730</td>
<td>21</td>
</tr>
</tbody>
</table>

##### Stress Implication of Four Cases

+---------+------------+------------+------+-----------+------------+
|         | Max        | Max        | \|   | Cu CSA    | Max Avg    |
|         |            |            | ∆\|% |           |            |
|         | w/o Plas   | w/Plas     |      | (in\^2)   | Cu Stress  |
|         |            |            |      |           |            |
|         | (lbs)      | (lbs)      |      |           | (psi)      |
+---------+------------+------------+------+-----------+------------+
| OH      | 17231488   | 15496648   | -10  | 211.3     | 12979      |
+---------+------------+------------+------+-----------+------------+
| PF1AU   | 221970.3   | 186195.3   | -16  | 24.9      | 1419       |
+---------+------------+------------+------+-----------+------------+
| PF1AL   | 159105.3   | 184760.7   | 16   | 24.9      | 1181       |
+---------+------------+------------+------+-----------+------------+
| PF1BL   | 177169.2   | 202669.2   | 14   | 14.5      | 2225       |
+---------+------------+------------+------+-----------+------------+
| PF2U    | 411121     | 367321     | -11  | 25.4      | 2576       |
+---------+------------+------------+------+-----------+------------+
| PF2L    | 434085     | 390285     | -10  | 25.4      | 2720       |
+---------+------------+------------+------+-----------+------------+
| PF3U    | 402498.6   | 367998.6   | -9   | 27.2      | 2355       |
+---------+------------+------------+------+-----------+------------+
| PF3L    | 408942.6   | 374442.6   | -8   | 27.2      | 2393       |
+---------+------------+------------+------+-----------+------------+
| PF5U    | 235529.8   | 285929.8   | 21   | 22.2      | 2050       |
+---------+------------+------------+------+-----------+------------+
| PF5L    | 236329.8   | 286729.8   | 21   | 22.2      | 2056       |
+---------+------------+------------+------+-----------+------------+

In summary, coil forces will not be increased during normal operations
with the higher plasma current.

###### 4.0 EM Forces During Disruption

Toroidal current decay follows, to first order, the rate assumed by the
design. Halo currents appear to be less than assumed (10% of Ip with
toroidal peaking factor of 2).

![](media/image5.pct){width="3.6930555555555555in"
height="5.102083333333334in"}

Variations in the toroidal current decay rate effect the induced voltage
on coupled structures (e.g. coils) but do not significantly effect the
peak current induced in coupled structures whose time constant τ \>\>
decay time, i.e. dI ≈ ∫Vdt/L.

Original NSTX design was based on:

-   1.0 MA decay in 6.0mS

-   toroidal jumpers between passive plates with saddle connection at
    one toroidal gap with resistance ≈ 100µΩ

-   disruption calculations with all OH and PF open circuit ex

-   10% halo current flowing in poloidal direction with toroidal peaking
    factor of 2

-   B~t~ ≤ 6kG

Analysis performed for the original design was as follows:

1)  SPARK was used to assess halo currents on center stack, based on 40%
    assumption (ref. NSTX-CALC-13-2, NSTX-CALC-13-13, 13-970214-JMS-01,
    "Center Stack Halo Current Stress Analysis"). Because of "aspect
    ratio effect", forces were found to be very low and not of concern.

```{=html}
<!-- -->
```
2)  SPARK was used to assess the force on the center stack casing due to
    induced toroidal current (ref. 13-970217-AWB-02, "Loads on CS from
    Plasma Disruption"), and the forces were found to be very low and
    not of concern.

3)  LRSIM and SPARK were used (and cross-checked) to determine induced
    voltages and currents in coils and structure based on axisymmetric
    and midplane symmetric model with 1.0MA/6mS ramp from plasma
    represented using one filament above and one filament below the
    midplane (ref. NSTX-CALC-11-1, 11-980514-CLN-01, "Disruption
    Calculations").

4)  Forces on internal hardware (inner wall, passive plates, outboard
    divertor) from disruption were estimated (ref. NSTX-CALC-11-2,
    11-980223-CLN-01, "Forces on Internal Hardware") by taking the
    disruption currents, multiplying by a factor of 1.5 to account for
    non-centered plasma, and calculating J x B force based on worst case
    combination of PF coil currents to produce max B~r~ and max B~z~ at
    each location.

![](media/image6.pct){width="3.8194444444444446in"
height="4.416666666666667in"}

######## 

######## Current Directions to Maximize Inward Forces 

######## on Internal Hardware Components in the Lower Half Plane

  ---------- ----- ------ ------ ------ ------ ------- ------ ------ ------ ------ ------
                   IW +          IBD +         OBD +          SPP +         PPP +  

                   Fv -   Fr +   Fv -   Fr +   Fv +    Fr -   Fv +   Fr -   Fv +   Fr -

                   Br +   Bv +   Br +   Bv +   Br -    Bv -   Br -   Bv -   Br-    Bv-

  OH         -/0   \-     \-     \-     \-     0       0      0      0      0      0

  PF1au      +/-   0      \+     \-     \-     \+      \+     0      \+     0      \+

  PF1al            \+     \+     \-     \-     \+      \+     \-     \+     \-     \+

  PF1b       +/0   \+     \+     \+     \+     0       \+     0      \+     0      \+

  PF2u       +/-   0      \+     0      \+     0       \+     0      \+     0      \+

  PF2l             \+     \+     \+     \+     \-      \+     \-     \+     \-     \+

  PF3u       -/0   \-     0      \-     0      0       \-     0      \-     0      \-

  PF3l             0      0      \-     0      \-      \-     \-     \-     \-     \-

  PF4 u&l    -/0   \-     0      \-     0      0       \-     0      \-     0      \-

  SPP1u&l    +/0   0      \+     0      \+     \+      0      \+     \+     0      \+

  SPP2 u&l                                                                         

  PPP1 u&l                                                                         

  PPP2 u&l                                                                         

  Case             1      2      3      4      5       6      7      8      9      8

  \|B\|max         0.27   0.37   0.68   0.52   0.31    0.60   0.44   0.56   0.22   0.56
  ---------- ----- ------ ------ ------ ------ ------- ------ ------ ------ ------ ------

*Table of Cases To Determine Worst Case Br and Bz Background Fields*

5)  Forces and stresses on VV were analyzed by H.M. Fan via ANSYS using
    the forces from 4) above in combination with vacuum, normal EM, and
    dead load and found to be acceptable (ref. Report on \"Vacuum Vessel
    Stress Analysis for NSTX Plasma Disruption Loads" by H.M. Fan).

6)  Forces and stresses on the Passive Plates and their support brackets
    were analyzed by ORNL (NSTX-CALC-11-06) using forces from 4) above
    and found to be significant but less than those associated with
    bakeout at 350^o^C which drove the design and the choice of CuCrZr
    alloy for the plates.

7)  Forces from 4) above on the outboard divertor back plates were used
    by G. Barnes in a NASTRAN finite element analysis of the "barbecue"
    mounting assembly (ref. NSTX-CALC-11-03) and found to result in
    acceptable levels of stress (peak EM stress of 4244 psi, peak
    thermal stress 3854 psi, not at same location) in the stainless
    steel rings.

8)  Worst case fields from 4) above were used by ORNL (ref.
    NSTX-CALC-11-04) as input to an analysis of the force on individual
    inner wall, inboard divertor, outboard divertor, and passive plate
    tiles due to halo currents as well as induced eddy currents from
    dB/dt due to 1.0 MA/1mS.

9)  Currents and forces in RF antenna faraday shield were calculated by
    P Bonanos (HHFW Antenna PDR) using worst case fields from any PF
    coil current combination along with induced current due to 1.0MA/6mS
    disruption (ref. 21-971211-CLN-01, "Planning for HHFW Antenna PDR")
    and found to be benign (3.2kA, 2.9lb/in, 1.1ksi).

Disruption analysis has been updated using LRSIM for the following
conditions:

-   1.5 MA decay in 9.0mS

-   toroidal jumpers between passive plates with saddle connection at
    one toroidal gap with resistance 300µΩ on secondary and 400µΩ on
    primary

![](media/image7.pct){width="4.833333333333333in"
height="4.124305555555556in"}

![](media/image8.pct){width="4.891666666666667in" height="4.18125in"}

![](media/image9.pct){width="6.0in" height="5.1194444444444445in"}

![](media/image10.pct){width="5.996527777777778in"
height="3.5229166666666667in"}

Under new conditions, current in passive plates is significantly
reduced, while current in vacuum vessel is significantly increased.

![](media/image11.pct){width="5.402777777777778in"
height="4.541666666666667in"}

*LRSIM Filament Model*

![](media/image12.pct){width="7.027777777777778in"
height="3.986111111111111in"}

*Peak Current Distribution in VV Filaments*

*With and Without Passive Plate Jumpers (1.0 MA Disruption)*

Taking worst case Br and Bz due to PF coils crossed with VV filament
currents:

  ---- ------ ------- ------- -------- ------------ --------- --------- ------------
       Idis   Br      Bz      \|B\|    Fz           Fr        F         Pvv

       (kA)   \(T\)   \(T\)   \(T\)    (lb)         (lb)      (lb)      (lb/in\^2)

  1    9.6    0.060   0.30    0.306    1380.7       6903.4    7040.1    3.5

  2    9.6    0.060   0.30    0.306    1380.7       6903.4    7040.1    3.5

  3    9.4    0.090   0.30    0.313    2027.9       6759.5    7057.2    3.5

  4    8.9    0.090   0.30    0.313    1920.0       6400.0    6681.8    3.3

  5    8.2    0.140   0.56    0.577    2751.8       11007.0   11345.8   5.6

  6    7.5    0.140   0.56    0.577    2516.8       10067.4   10377.2   5.1

  7    6.9    0.220   0.56    0.602    3638.6       9262.0    9951.1    4.9

  8    6.2    0.220   0.56    0.602    3269.5       8322.4    8941.6    4.4

  9    5      0.220   0.56    0.602    2623.5       6678.0    7174.8    3.9

  10   4.5    0.220   0.56    0.602    2314.7       5891.9    6330.3    3.5

  11   4.3    0.220   0.30    0.372    2127.2       2900.7    3597.1    2.1

  12   4.6    0.220   0.30    0.372    2146.0       2926.4    3628.9    1.9

  13   4.6    0.340   0.30    0.453    3082.6       2720.0    4111.1    2.4

  14   4.8    0.340   0.30    0.453    2964.5       2615.8    3953.6    2.5

  15   4.8    0.310   0.60    0.675    2466.3       4773.5    5373.0    3.7

  16   4.5    0.310   0.60    0.675    2084.6       4034.6    4541.3    3.4

  17   3.9    0.310   0.30    0.431    1604.8       1553.1    2233.3    1.9

  18   3.2    0.310   0.30    0.431    1147.9       1110.9    1597.5    1.6

  19   2.5    0.310   0.20    0.369    762.7        492.1     907.6     1.0

  20   1.8    0.310   0.30    0.431    451.2        436.6     627.8     0.9

  21   0.9    0.200   0.30    0.361    113.6        170.4     204.7     0.4

  22   0.4    0.200   0.20    0.283    36.1         36.1      51.1      0.1

  23   0.1    0.200   0.20    0.283    5.4          5.4       7.7       0.0
  ---- ------ ------- ------- -------- ------------ --------- --------- ------------

With most of the current flowing in VV instead of plates, force on VV is
more uniformly distributed than before, since reaction is directly from
VV instead of discrete mounting points of passive plate supports.
However, VV is closer to coils than plates, so field is somewhat higher.

Prior ANSYS work indicated the following non-additive peak stress in the
VV:

Disruption (passive plate supports pulling inward): 18.2ksi

Normal EM loads (PF and TF coil supports) attached to VV: 11.4ksi

Vacuum: 10.9ksi

Dead weight load: 3.8ksi

New disruption load looks more like vacuum load, and the stress can be
scaled from vacuum force approximately by:

> (14.7 + 6)/14.7\*10.9 ≈ 15ksi

Axial forces on PF coil supports are relatively small compared to forces
from coil currents (even if they are summed they add to only 42.8kp).

Radial forces on PF coils are insignificant.

Peak current in OBD increases from 8.6kA to 15.4kA (at 1.0MA w/o
jumpers) to 20.0kA (at 1.5MA w/o jumpers). Stress goes from 4.2ksi to
20/8.6\*4.2 = 9.8ksi, still low.

Non-axisymmetric currents:

With passive plate jumpers removed, net non-axisymmetric currents flow
in plates. Taking a crude plasma model (rectangular cross section) used
by ORNL during the project design, the field B due to the plasma, normal
to the plates, can be estimated, along with the initial value of the
flux φ=B\*A linked by a path around the periphery of the plate.

![](media/image13.pct){width="9.530555555555555in"
height="2.0555555555555554in"}

Then the current induced around the periphery of the plate can be
estimated by ∆I=∆φ/L, where L is estimated via:

L = 0.004 \* {a \* ln(2a/ρ) + b \* ln(2b/ρ) + 2 \* sqrt(a\^2+b\^2) --
a\* arcsinh(a/b)-b\*arcsinh(b/a)-2\*(a+b)+µ/4\*(a+b)}

Where:

a, b = sides of rectangular loop of conductor in cm

ρ = cross section of conductor = cm\^2, assumed square conductor with
width equal to thickness of plate

µ = 1

L = inductance in µH

(from Grover, p. 60, eq. 58)

![](media/image14.pct){width="4.618055555555555in"
height="4.582638888888889in"}

#### *Non-Axisymmetric Currents and Forces in Passive Plates*

Forces of primary interest are those due to the poloidal current which
form torsional couples and act in opposite directions on the supports at
the ends of the plates.

  -------------- ------------- ------------- ------------- ------------- ---------
                 1.0 MA                      1.5 MA                      

                 PPP           SPP           PPP           SPP           

  R1             53.540        43.823        53.540        43.823        in

  Z1             39.594        54.143        39.594        54.143        in

  R2             59.416        52.752        59.416        52.752        in

  Z2             21.775        41.509        21.775        41.509        in

  Lpoloidal      18.763        15.471        18.763        15.471        in

  Theta          71.749        54.749        71.749        54.749        degrees

  T              0.500         0.500         0.500         0.500         in

  a              75.112        64.220        75.112        64.220        cm

  b              47.658        39.296        47.658        39.296        cm

  csa            1.613         1.613         1.613         1.613         cm\^2

  L              1.50668E-06   1.19654E-06   1.50668E-06   1.19654E-06   H

  Bnormal        0.125         0.11          0.1875        0.165         T

  A              0.358         0.252         0.358         0.252         m\^2

  Phi            0.045         0.028         0.067         0.042         weber

  I              29698.4       23199.5       44547.6       34799.3       amp

  Ravg           1.435         1.227         1.435         1.227         m

  R0             0.854         0.854         0.854         0.854         m

  Bφ(R0)         0.600         0.600         0.600         0.600         T

  Bφ(ravg)       0.357         0.418         0.357         0.418         T

  Fn (Iθ)        1137          857           1706          1285          lbs

  Fz (Iθ)        356           494           534           742           lbs

  Fr (Iθ)        1080          700           1620          1049          lbs

  Ir             9301          13390         13951         20085         amp

  Fz (Ir)        356           494           534           742           lbs

  Iφ (n=0)       16100         6400          17700         7300          amp

  Br             0.22          0.44          0.22          0.44          T

  Bz             0.56          0.56          0.56          0.56          T

  Fr (Iφ(n=0))   1522          517           1674          590           lbs

  Fz (Iφ(n=0))   598           407           658           464           lbs

  ∑Fr            2602          1217          3293          1639          lbs

  Fr (design)    14160         5123          14160         5123          lbs

  Fr (% of       18            24            23            32            \%
  design)                                                                

  ∑Fz            1310          1395          1726          1947          lbs

  Fz (design)    5563          4025          5563          4025          lbs

  Fz (% of       24            35            31            48            \%
  design)                                                                
  -------------- ------------- ------------- ------------- ------------- ---------

*Forces are all less than the original design condition*

Halo Currents:

If we reduce the assumed %Ip from 10% to 5%, and increase the plasma
current from 1.0 to 1.5, then there is a net reduction to 5/10\*1.5/1 =
75% of original design criteria. Such a reduction could also come in
part from reduction in peaking factor.

  ------------------- ----------- ----------- ----------- ----------- ------
  \--\>1MA\<\--       Inner Wall  OBD         SPP         PPP         

  Ip                  1.00E+06    1.00E+06    1.00E+06    1.00E+06    Amp

  k                   0.10        0.10        0.10        0.10        

  peaking             2.00        2.00        2.00        2.00        

  Ipoloidal           8333.33     4166.67     16666.67    16666.67    Amp

  R0                  0.854       0.854       0.854       0.854       m

  Bt(R0)              0.600       0.600       0.600       0.600       T

  Bt(Ravg)            2.694       0.561       0.436       0.378       T

  L poloidal          0.152       0.624       0.292       0.582       m

  Fnormal/segment     3421.39     1456.92     2118.99     3667.43     N

                      769.13      327.52      476.35      824.44      lbs

  Fradial/segment     769.13      119.75      408.47      779.25      lbs

  Fvertical/segment   0.00        304.84      245.08      269.20      lbs

  \--\>1.5 MA\<\--                                                    

  Ip                  1.50E+06    1.50E+06    1.50E+06    1.50E+06    Amp

  k                   0.05        0.05        0.05        0.05        

  peaking             2.00        2.00        2.00        2.00        

  #segment            24.00       48.00       12.00       12.00       

  Ipoloidal           6250.00     3125.00     12500.00    12500.00    Amp

  R0                  0.854       0.854       0.854       0.854       m

  Bt(R0)              0.600       0.600       0.600       0.600       T

  Bt(Ravg)            2.694       0.561       0.436       0.378       T

  L poloidal          0.152       0.624       0.292       0.582       m

  Fnormal/segment     2566.04     1092.69     1589.24     2750.57     N

                      576.85      245.64      357.26      618.33      lbs

  Fradial/segment     576.85      89.81       306.35      584.44      lbs

  Fvertical/segment   0.00        228.63      183.81      201.90      lbs
  ------------------- ----------- ----------- ----------- ----------- ------

5.0 PF Voltages During Disruption

For an open coil, MdIp/dt will appear at the coil terminals. If coil is
closed through its power supply in a conducting condition, then
M\*dIp/dt ≈ Lcoil\*dIcoil/dt, i.e. ∆Icoil ≈ M∆Ip/L and little voltage
change will be evident at coil terminals. However, if ∆Icoil is
sufficient to drive the power supply current to zero in a unipolar
circuit, then the MdIp/dt could appear.

![](media/image15.pct){width="4.483333333333333in"
height="3.832638888888889in"}

If the plasma does not disrupt mid-plane symmetric, then different
voltages will appear on upper and lower coils.

Maximum open circuit induced voltages are of order 1.8kV on OH and PF5
with midplane symmetry. Others are of order 1kV.

This should not be a problem because:

-   OH and PF5 systems are very unlikely to be open circuited, if we
    have a 1.5 MA plasma.

-   voltages are in any case ≤ 1/2 of those normally applied by the
    power supplies.

[CONCLUSIONS]{.underline}

Issues have been evaluated thus far without the benefit of a complete
analysis (i.e. TSC, equilibria, SPARK and ANSYS) and without an
exhaustive analysis of disruption behavior.

However, margins seem to be large, and no apparent show-stoppers have
been identified.

Pending review of these findings it is recommended to:

-   approve the higher level of operation at limited Bt (e.g. 4.5kG);

-   resurrect the analysis work on SPARK and ANSYS;

-   establish a disruption database;

-   implement Digital Coil Protection system.