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13_031205_CLN_01.doc

# TO: DISTRIBUTION

***FROM: C NEUMEYER***

***SUBJECT: PF4 AND PF5 FORCES WITH PF4 ENERGIZATION***

References:

\[1\] NSTX_CALC_13_020, "PF Coil Axial and Radial Force Calculations",
12/8/00

The purpose of this memo is to quantify the increase in EM forces which
will occur with the energization of PF4. These changes will primarily
effect the PF4 and PF5 coils and coil supports.

The influence matrix created by H. M. Fan \[1\] is used to perform the
calculation.

*Axial Forces*

For the axial forces, the following combination of currents was found to
produce the maximum forces, as indicated for the case with I_PF4=0.

+-----------+---------------+-------------------+---------------------+
|           | Current (kA)  | EM Force w/o Plas | EM Force w/Plas     |
|           |               | (lbf)             |                     |
|           |               |                   | (lbf)               |
+-----------+---------------+-------------------+---------------------+
| OH        | 24.00         | 25584             | 25584               |
+-----------+---------------+-------------------+---------------------+
| PF1AU     | -15.00        | 12451             | 9151                |
+-----------+---------------+-------------------+---------------------+
| PF1AL     | -15.00        | -41614            | -38314              |
+-----------+---------------+-------------------+---------------------+
| PF1BL     | -20.00        | -6047             | -2447               |
+-----------+---------------+-------------------+---------------------+
| PF2U      | -20.00        | 30093             | 12293               |
+-----------+---------------+-------------------+---------------------+
| PF2L      | -20.00        | -23049            | -5249               |
+-----------+---------------+-------------------+---------------------+
| PF3U      | -5.00         | 38966             | 26716               |
+-----------+---------------+-------------------+---------------------+
| PF3L      | -5.00         | -39792            | -27542              |
+-----------+---------------+-------------------+---------------------+
| PF4U      | 0.00          | 0                 | 0                   |
+-----------+---------------+-------------------+---------------------+
| PF4L      | 0.00          | 0                 | 0                   |
+-----------+---------------+-------------------+---------------------+
| PF5U      | 20.00         | -115386           | -80786              |
+-----------+---------------+-------------------+---------------------+
| PF5L      | 20.00         | 118798            | 84198               |
+-----------+---------------+-------------------+---------------------+
| PLU       | -1000.00      |                   |                     |
+-----------+---------------+-------------------+---------------------+
| PLL       | -1000.00      |                   |                     |
+-----------+---------------+-------------------+---------------------+

The following table and figure show the variation in the axial forces
with I_PF4 non-zero. Here the worst case forces occur w/o plasma.

+-------------+-------------+-------------+-------------+-------------+
| I_PF4       | F_PF4U      | F_PF4L      | F_PF5U      | F_PF5L      |
|             | (lbf)       |             | (lbf)       |             |
| (kA)        |             | (lbf)       |             | (lbf)       |
+-------------+-------------+-------------+-------------+-------------+
| -20         | 117802      | -120486     | -135954     | 139366      |
+-------------+-------------+-------------+-------------+-------------+
| -16         | 99987       | -102134     | -131840     | 135252      |
+-------------+-------------+-------------+-------------+-------------+
| -12         | 79299       | -80909      | -127727     | 131139      |
+-------------+-------------+-------------+-------------+-------------+
| -8          | 55739       | -56812      | -123613     | 127025      |
+-------------+-------------+-------------+-------------+-------------+
| -4          | 29306       | -29842      | -119499     | 122911      |
+-------------+-------------+-------------+-------------+-------------+
| 0           | 0           | 0           | -115386     | 118798      |
+-------------+-------------+-------------+-------------+-------------+
| 4           | -32178      | 32715       | -111272     | 114684      |
+-------------+-------------+-------------+-------------+-------------+
| 8           | -67229      | 68303       | -107159     | 110571      |
+-------------+-------------+-------------+-------------+-------------+
| 12          | -105153     | 106763      | -103045     | 106457      |
+-------------+-------------+-------------+-------------+-------------+
| 16          | -145949     | 148096      | -98931      | 102343      |
+-------------+-------------+-------------+-------------+-------------+
| 20          | -189618     | 192302      | -94818      | 98230       |
+-------------+-------------+-------------+-------------+-------------+

![](media/image2.pct){width="5.997916666666667in"
height="4.720833333333333in"}

*Radial Forces*

For the radial forces, the following combination of currents was found
to produce the maximum forces, as indicated for the case with I_PF4=0.

+-----------+---------------+-------------------+---------------------+
|           | Current (kA)  | EM Force w/o Plas | EM Force w/Plas     |
|           |               | (lbf)             |                     |
|           |               |                   | (lbf)               |
+-----------+---------------+-------------------+---------------------+
| OH        | -24.00        | 16002736          | 17159296            |
+-----------+---------------+-------------------+---------------------+
| PF1AU     | -15.00        | 123516            | 147366              |
+-----------+---------------+-------------------+---------------------+
| PF1AL     | -15.00        | 186381            | 210231              |
+-----------+---------------+-------------------+---------------------+
| PF1BL     | -20.00        | 202049            | 219049              |
+-----------+---------------+-------------------+---------------------+
| PF2U      | -20.00        | 119781            | 148981              |
+-----------+---------------+-------------------+---------------------+
| PF2L      | -20.00        | 96817             | 126017              |
+-----------+---------------+-------------------+---------------------+
| PF3U      | -5.00         | -34842            | -29092              |
+-----------+---------------+-------------------+---------------------+
| PF3L      | -5.00         | -36453            | -30703              |
+-----------+---------------+-------------------+---------------------+
| PF4U      | 0.00          | 0                 | 0                   |
+-----------+---------------+-------------------+---------------------+
| PF4L      | 0.00          | 0                 | 0                   |
+-----------+---------------+-------------------+---------------------+
| PF5U      | 20.00         | 203768            | 237368              |
+-----------+---------------+-------------------+---------------------+
| PF5L      | 20.00         | 204568            | 238168              |
+-----------+---------------+-------------------+---------------------+
| PL-U      | -1000.00      |                   |                     |
+-----------+---------------+-------------------+---------------------+
| PL-L      | -1000.00      |                   |                     |
+-----------+---------------+-------------------+---------------------+

The following table and figure show the variation in the radial forces
with I_PF4 non-zero. Here the worst case forces occur w/plasma.

+-------------+-------------+-------------+-------------+-------------+
| I_PF4       | F_PF4U      | F_PF4L      | F_PF5U      | F_PF5L      |
|             | (lbf)       |             | (lbf)       |             |
| (kA)        |             | (lbf)       |             | (lbf)       |
+-------------+-------------+-------------+-------------+-------------+
| -20         | -453449     | -453993     | 573976      | 574776      |
+-------------+-------------+-------------+-------------+-------------+
| -16         | -378195     | -378630     | 506655      | 507455      |
+-------------+-------------+-------------+-------------+-------------+
| -12         | -295223     | -295549     | 439333      | 440133      |
+-------------+-------------+-------------+-------------+-------------+
| -8          | -204533     | -204750     | 372011      | 372811      |
+-------------+-------------+-------------+-------------+-------------+
| -4          | -106125     | -106234     | 304690      | 305490      |
+-------------+-------------+-------------+-------------+-------------+
| 0           | 0           | 0           | 237368      | 238168      |
+-------------+-------------+-------------+-------------+-------------+
| 4           | 113843      | 113952      | 170047      | 170847      |
+-------------+-------------+-------------+-------------+-------------+
| 8           | 235404      | 235621      | 102725      | 103525      |
+-------------+-------------+-------------+-------------+-------------+
| 12          | 364682      | 365009      | 35403       | 36203       |
+-------------+-------------+-------------+-------------+-------------+
| 16          | 501679      | 502114      | -31918      | -31118      |
+-------------+-------------+-------------+-------------+-------------+
| 20          | 646393      | 646937      | -99240      | -98440      |
+-------------+-------------+-------------+-------------+-------------+

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cc: M Bell P Heitzenroeder M Ono S Ramakrishnan

A VonHalle M Williams I Zatz