TY - JOUR

T1 - Numerical-analytical algorithms for integrating the equations of motion of charged particles in electric fields

AU - Sveshnikov, V. M.

AU - Tretyakov, A. S.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Numerical-analytical algorithms for integrating the equations of motion of charged particles in electric fields are proposed and experimentally investigated. The need to develop such algorithms arose in the simulation of intense beams of charged particles in extended systems. A characteristic task is to determine, as far as possible, the beam expansion and its angular divergence at a considerable distance from the start (emitter) surface. The use of classical numerical algorithms did not give adequate results. Therefore, a proposal arose at each step of numerical integration to use an analytical solution of the equations of motion, making simplifying assumptions about electric fields. Simplifying assumptions within the numerical integration step, which provide sufficient accuracy and, at the same time, a simple solution, were as follows: in the longitudinal direction the field is assumed to be constant, and in the transverse direction - linear in the coordinate, which is characteristic of intense beams. An experimental comparison of numerical-analytical algorithms with numerical algorithms is given, which showed the advantage of the developed approach.

AB - Numerical-analytical algorithms for integrating the equations of motion of charged particles in electric fields are proposed and experimentally investigated. The need to develop such algorithms arose in the simulation of intense beams of charged particles in extended systems. A characteristic task is to determine, as far as possible, the beam expansion and its angular divergence at a considerable distance from the start (emitter) surface. The use of classical numerical algorithms did not give adequate results. Therefore, a proposal arose at each step of numerical integration to use an analytical solution of the equations of motion, making simplifying assumptions about electric fields. Simplifying assumptions within the numerical integration step, which provide sufficient accuracy and, at the same time, a simple solution, were as follows: in the longitudinal direction the field is assumed to be constant, and in the transverse direction - linear in the coordinate, which is characteristic of intense beams. An experimental comparison of numerical-analytical algorithms with numerical algorithms is given, which showed the advantage of the developed approach.

KW - Electron-optical devices

KW - Extended systems

KW - Integration of equations of motion

KW - Intensive beams

KW - Midpoint

KW - Numerical-analytical algorithms

KW - Predictor-corrector

UR - http://www.scopus.com/inward/record.url?scp=85066340738&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85066340738

SP - 5

EP - 10

JO - Applied Physics

JF - Applied Physics

SN - 1996-0948

IS - 1

ER -