<title>Perturbation techniques in the problems of computational charged particle optics</title>

Abstract

Basing on perturbation technique, discussed are some urgent problems of computational charged particle optics including numerical evaluation of fringe fields and field perturbations caused by small deviation of the shape of electrodes from rotational or planar symmetry as well as aberrational analysis of charged particle beams in the most general tensor form.

Space-Charge Effects in An Electrostatic Multireflection Ion Trap

“…Direct numerical integration of a representative set of particle trajectories is also a very difficult problem since we are looking for the effects on the edge of resolving power and need a computation accuracy of approximately 10 -6 . Instead of direct ray tracing, we actively use the tau-variation technique [25][26][27] to calculate the entire packet of charged particles in one run from the instance of the packet's extraction from the RF trap up to the instance of its impingement on the detector. This method gives directly the coefficient in the Taylor series (aberration coefficients) up to the third order inclusive:…”

Numerical estimation of space-charge interaction in ultrashort electron bunches

“…One side of the difficulties is connected with the so-called temporal chromatic aberration which results in electron bunch widening due to initial energy spread of photoelectrons. This effect, as applied to both stationary and time-depending electric fields, is numerically analyzed in the Section 2 on the basis of the tau-variation method 4 .…”