Linear Integrals for Skew Quad Components,

Improved Field Calculation and Fit,

and

8-Pole Model with Dowel Pin Holes



CESRc Working Group Meeting

1 November 2002

Postscript files are also available.:

Outline

Linear Integral of Bx along Z as a function of X for the 3-pole model where the central pole pair was raised by 100 mils.
This model is meant to simulate the effect of a sag along the length of the wiggler. The green line shows the slope of the measurement by ST performed on Wiggler 1. The observed magnitudes of the skew quad components are comparable.

Progressive linear Integral of Bx along Z as a function of the upper limit of the integral for the 3-pole model where the central pole pair was raised by 100 mils.

Linear Integral of Bx along Z as a function of X for the 3-pole model where the central upper coil was elongated by 100 mils on one side.
The green line shows the slope of the measurement by ST performed on Wiggler 1. The observed magnitudes of the skew quad components are comparable.

Progressive linear Integral of Bx along Z as a function of the upper limit of the integral for the 3-pole model where the central upper coil was elongated by 100 mils on one side.
Note that for this type of error the skew quad component will occur at the position of the coil with the error, while for the sag effect the error will occur in the middle. The ST measurement indicated that the skew quad component in Wiggler 1 appeared closer to one end of the wiggler. Also note that a recent measurement by MGB of the coil displacements of the upper coils of Wiggler 2, which is under construction, yielded a net average displacement of the coils of 50 mils, which corresponds precisely to the displacement simulated here.

As reported on 18 October, a big improvement in the field calculation algorithm has been established. Previously, the field calculation was composed of a contribution from an interpolation of the local mesh for the magnetization part and of a contribution from the integral over current density elements for the current part. The new method avoid use of the local mesh and gets the two contributions from an integral over the mesh in the iron and one over the mesh in the coils. It requires 25 hours of computer time rather than 5 hours. The upper plot shows BY as a function of Z for both the table and the fit for the old field table. The lower plot shows the residuals of the fit, which can reach 5 gauss. Superposed in green are the differences between the old table and the new one. The differences can reach 40 gauss, which is much larger than the residuals of the old fit.

The curl and divergence values for the new field table show only improvement in the tails of the values for the Y component of the curl.

Example of residuals for the old fit.
Same example of residuals, but for the new fit.
This pattern shows the general result that there are places along Z where the new fit has much better residuals. Also BY versus Y shows smaller residuals. Note that one difference between the old and new fit procedures is that the errors on the field values provided by the OPERA software were included in the minimization function in the old fit, while the new fit uses 1-guass errors for all contributions to the function to be minimized. Also, the new fit uses all 72982 field points, while the old algorithm excluded about 20% of them from the minimization function.

First integral of BY for the old table.
First integral of BY for the new table.
Though the field values themselves have big differences of up to about 40 gauss, the X-dependence of the first integral of BY shows little change, the only difference being an overall shift by about 3 gauss-meters. DLR's tracking result shows similarly that the transfer functions through the old and new tables are nearly indistinguishable.

Picture of 8-pole model including the dowel pin holes.
Closeup of the finite-element mesh in the region of the dowel-pin holes.
The OPERA software successfully made a fine mesh in the locality of the holes, ensuring the accuracy of the results, which will be available next week.




Creation date: 11/01/02.