Abstract
A new method for the calculation of the magnetic field of beam guiding elements is presented. The method relates the calculation to measurement data of the magnetic field in a direct way. It can be applied to single beam guiding elements as well as to clusters of elements. The presented description of the magnetic field differs from the classical approach in that it does not rely on power series approximations. It is also both divergence free and curl free, and takes fringe field effects up to any desired order into account. In the field description, pseudodifferential operators described by Bessel functions are used to obtain the various multipole contributions. Magnetic field data on a two-dimensional surface, e.g., a cylindrical surface or median plane, serve as input for the calculation of the three-dimensional magnetic field. A boundary element method is presented to fit the fields to a discrete set of field data, obtained, for instance, from field measurements, on the two-dimensional surface. Relative errors in the field approximation do not exceed the maximal relative errors in the input data. Methods for incorporating the obtained field in both analytical and numerical computation of transfer functions are outlined. Applications include easy calculation of the transfer functions of clusters of beam guiding elements and of generalized field gradients for any multipole contribution up to any order.
Highlights
The transport of charged particle beams through particle optical devices, such as beam-transport lines, particle accelerators, and spectrometer equipment, depends strongly on the shape of their electric and magnetic fields
The presented description of the magnetic field differs from the classical approach in that it does not rely on power series approximations
The solution to the trajectory equations for a beam guiding element is generally presented as a function, called the transfer map of the element, that maps the initial location of a charged particle in phase space on its final location
Summary
The transport of charged particle beams through particle optical devices, such as beam-transport lines, particle accelerators, and spectrometer equipment, depends strongly on the shape of their electric and magnetic fields. For the calculation of the transfer map of a magnetooptical element, an accurate description of the magnetic field of the element is essential This is often done by expanding the scalar potential of the field in a Taylor-Fourier series, as given by, among others, Szilagyi [18], for straight elements having their design orbit along the z axis. The aim of this approach is to overcome the above-mentioned difficulties by using a magnetic field description that is not based on power series expansions In this way, we do not have to deal with an explosively growing number of higher order terms, which is usually the case in higher order perturbative methods. Once the electrostatic scalar potential has been obtained, it can be introduced into the description of the transfer function of the device, much in the same way as the magnetic vector potential
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
