[NSTX CALCULATION]{.underline} Page 1 of 1

TITLE[\_\_\_\_\_\_\_\_\_\_PF Coil Axial and Radial Force
Calculation\_\_\_\_\_\_\_\_\_\_\_]{.underline}

CALC. NO.[\_NSTX-CALC-13-020]{.underline} DATE [\_\_\_\_12/8/00
\_]{.underline}

ORIGINATOR\_\_\_[C.
Neumeyer\_\_]{.underline}CHECKER\_\_\_\_\_\_\_\_\_\_\_\_
[\_]{.underline}\_\_Rev.\_\_\_[0\_]{.underline}\_

[PURPOSE:]{.underline}

This calculation determines the axial and radial forces on the NSTX PF
coils, considering plasma current up to 1.5MA.

[REFERENCES:]{.underline}

[ASSUMPTIONS:]{.underline}

[CALCULATION:]{.underline}

See attached spreadsheet.

[CONCLUSION:]{.underline}

Plasma generally tends to decrease forces on PF coils, so that an
increase up to 1.5MA will not increase the forces which must be reacted.
PF1aL interaction with PF1b can potentially put a large stress on the
PF1aL hangers. Therefore combined operations must be constrained.

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
  ------- --------- ------- ------- ------- ------- ------- -------- -------- -------- -------- -------- -------- ------ ------

#### *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       |
+---------+------------+------------+------+-----------+------------+