Mathematical simulation of precision scanning by a H− beam

Abstract

A method and a computer program are developed for computing the dynamics of precision beams. The numerical method used for integrating differential equations is conservative. Within a paraxial approximation, the method ensures strict conservation of the phase volume at every step of calculations. Geometrical aberrations up to the third order are included and the space charge is taken into consideration within the paraxial approximation. The method is valid for relativistic beams. Controlling fields can have arbitrary longitudinal distributions. An accompanying frame of reference with a moving base is used where a trajectory of one of the particles is chosen to be a curvilinear axis. If a beam axis does not coincide with that of the device through which the beam travels, or if the angle of the beam axis deviation from that of the device (e.g. a scanner) considerably exceeds the angular divergence, within the given accuracy the method allows to be restricted with calculations of aberrations of lower order than in the case of a fixed frame of reference with a rectilinear axis. The method ensures simultaneous calculations of dynamics of any number of particles. For the case when a set consists of a large number of particles, a gain in the calculation time is obtained in comparison with times for calculation of the dynamics of all the individual particles. Dynamics of a broad H− beam having a small angular divergence at the inlet is studied in the scanner field. In order to keep the angular divergence at a small level at the outlet either distortion of the angular divergence of the beam should not be allowed or appearing angular distortions should be incessantly suppressed. Distributions of fields acting upon the beam while scanning are found when a small angular divergence at the outlet is provided.