End design of the SSC 58 mm High Gradient Quadrupole

The ''end'' design of the High Gradient Quad. was done with consideration to the integrated field harmonics, the iron contribution, and the maximum field at the conductor. Magnetic analysis was done on the return end only, however the physical dimension of the lead end were determined as well. Using the cross-section of the windings and Cook's program BEND, we generated the physical end windings around the return end. Placing a single wire at the center of each turn the integrated gradient was computed and iterating on the end block spacers the integrated harmonics minimized. The final geometry was then used for more, extensive calculations, such as the field at the conductor and the 3D field harmonics. For this detailed calculation we have placed a single line current at the center of each strand and included the iron contribution (μ = ∞), see Appendix C. With the termination of the iron serving as a reference, the maximum length of the inner and outer layers are 182 mm and 215 mm respectively. The magnetic length of the end was computed from the gradient function A2 and was found to be 142 mm. In reality we expect the physical length of the end to be somewhat larger, however this should have little or no effect on the magnetic length. The gradient in the straight section is 212.44 T/m at 7000 A and the integrated value of the gradient is -3.01665 E5 (G) in the end region marked by the magnetic length of the end. The respective integrated harmonics for the end 12 pole and 20 pole are -10.6658 (G/CM4) and 0.7279 (G/cm8) corresponding to b6 = 0.351 , b10 = -0.024 units. The above was computed from the values of A2, A6, and A10