To: Tim Giles cc: Mats Lindroos Subject: ISOLDE quads Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Date: Wed, 27 Sep 2006 07:35:24 -0700 From: Rick Baartman Hi. I hope you are well. Recently, I have been trying to better characterize our electrostatic quadrupoles. I performed a 3D relaxation calculation to find the potential. This yields two things: I integrated the paraxial field to get the effective length, and I also calculated the "fringe field integrals" required as input by GIOS. After having done the TRIUMF quads, it was a very small step to also repeat the calculation for the ISOLDE quads. Here are the results: Effective length: Recall that my measurements while at CERN (5 years ago already!) gave a result of 270mm for the effective length, whereas the standard in use up to that time had been 300mm. The relaxation calculation gives 276mm. This is good agreement with my optical measurement, but for my taste not quite good enough. Part of the discrepancy is attributable to using zero for all the fringe-field integrals. If I use the values given below and re-analyze the optical measurements, the new result is 273mm. This still differs from the relaxation result of 276 mm, but not by much. The difference is probably due to a systematic effect, such as that the boundaries are not given to sufficient accuracy, or machining and alignment tolerances (for example, it can arise from an aperture diameter error of less than 1 mm). Of the two, I would tend to use the experimental effective length of 273 mm. FF integrals: I find I1=0.075, I2=0.000, I3=0.022, I4=-0.216. These are significantly smaller than the GIOS default (F F 1) values. This is not a surprise if you observe that the default values in GIOS for e-quads are the same as for m-quads, and realistically one expects e-quad values to be significantly smaller than m-quads simply because any metal boundary "clamps" an e-field, but one needs a ferromagnetic clamp to reduce the m-fields. In summary, the description in GIOS terms of a single 30cm quad is D L 0.0135 ; F F 0 0.075 0.000 0.022 -0.216 ; E Q 0.273 0.07000 ; F F 0 0.075 0.000 0.022 -0.216 ; D L 0.0135 ; -- rick baartman Here are also the Enge coefficients, in the format required by COSY-infinity: fc 2 1 2 -0.0244 8.8051 1.2809 4.4409 -5.2034 2.6821 ; fc 2 2 2 -0.0244 8.8051 1.2809 4.4409 -5.2034 2.6821 ; Make sure to use fr 3 ; else the integration is too coarse.