On the Numerical Solution of Maxwell's Equations and Applications in the Field of Accelerator Physics

Abstract

A discretization ansatz for Maxwell's equations is described that enables treatment of all possible homogeneous and inhomogeneous problems from nonlinear magnetostatics and electrostatics to timedependent field problems that include charges moving freely at any speed.The same method can be used for magnet design, for cavity-mode investigations and wake-force computations in time and frequency domains, antenna problems, and waveguide structures.The method makes direct use of the electric and magnetic field as unknowns, thus yielding uniquely defined vectors in combination with a suitable grid definition.This "natural" ansatz avoids problems arising from the use of artificial functions such as vector potentials or Hertz potentials.Using this ansatz, many computer codes have been developed and applied to various problems.Applications in the field of accelerator physics include magnet and solenoid design; design of accelerating rfcavities and beam-tracking calculations for instability studies.More recently the method has been used to study the new acceleration principle of wake-field compression.