From: Arthur W. Brooks
Sent: Tuesday, November 16, 2004 10:52 AM
To: Michael R. Kalish
Cc: Wayne T. Reiersen; 'Nelson, Brad E.'
Subject: Impact of Looser (+/-0.25") Tolerance on TF Outer Leg

Attachments: TF In-plane Deformations.ppt

Mike,

I've take a look at how looser tolerances on the TF coil outer leg affect field errors. The results seem to support our earlier instincts that +/-0.25" in-plane in the TF outer leg would be acceptable, but that we should stick to +/-0.125" (~3mm) out-of-plane. We should reach a consensus, or identify other concerns to analyse.

The attached powerpoint document contains some plots of the imposed deformations and a table of results. The deformations were imposed only to the outer leg; the inner leg was held fixed. Radial deformations were applied in to try and simulate what would be expected (to a first order) if the TF coil outer leg sprang when released from the winding form. The blue curves are the nominal shape and the red curves the deformed shape. 

The coil is assumed to move out at the midplane and in at the top/bottom to roughly preserve length. This is actually applied with a cos(3*th) variation. Two other forms were also analyzed: cos(th) to simulate outward growth over the whole outer leg, and sin(2*th) to simulate top/down assymmetry.

Deformations were applied to first a single coil, then to multiple coils in a single period, all coils of type A, and finally all 18 TF coils. The combinations chosen is not exhaustive, but hopefully representative. Out of plane deformations for some of these were also analyzed.

While the hard critera for field errors is that we not exceed 10% islands from all sources (after correction with trim coils), we are using a rule of thumb of a 1% island limit when investigating individual sources. This can be questioned but appears prudent.

The first conclusion is that for in plane deformations that are the same for all coils, there is no impact, almost regardless of the size of the deformation. The same cannot be said of out-of-plane deformations. For these deformations which are the same for all coils, the concern is with stellarator symmetric modes such as the 3/5, since no assymmetries are excited.

The second conclusion is that for in-plane deformations we are fairly safe at the .25" level for individual and multiple coils, but I would not push it beyond .25". Again for the Out-of-Plane deformations, the single coil deformations are not satisfactory at .25" and should be enforced at 0.125". Multiple coils out-of-plane were not examined since they most likely would only be worse.

The attached data was generated using the VACISLD code which calculates linear perturbations to the VMEC equilbrium. The equilibrium ID 4 (179KA, full beta) was used with TF currents equal to their max expected operation level of 45.3 KAT. This is less than the design value of 194 KAT required for 0.5 T TF operation, but the highest TF current for which we have a plasma equilibrium.



Art