Multipole Decomposition of Quadrupole Magnets of the Large Hadron Collide
by
Bela Erdelyi
Coauthors: Michael Lindemann and Martin Berz

The Large Hadron Collider (LHC) is the currently largest scientific instrument, a circular particle accelerator under construction at CERN in Switzerland. The dynamics of the particles requires detailed understanding of the electromagnetic fields governing the motion. The most important quantities are the multipole content of the fields, which couple to various high-order derivatives of up to order 20 of the three-dimensional fields. The fields themselves are generated through a superposition of up to 100, 000 wire pieces. It is shown how high-order automatic differentiation methods can be used to efficiently perform the multipole decomposition. It turns out that the accuracy of the computation is highly sensitive to an efficient, cancellation-free coding of the relevant field equations, and the demands increase rapidly with order. Furthermore, the method benefits substantially from the exploitation of the symmetries in the fields imposed by Maxwell's equations, which can be accounted for in an efficient manner using differential algebraic methods.

http://bt.nscl.msu.edu/~hoefkens/ad2000-lhc.ps

Date received: March 3, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cads-98.