Fields of a relativistic beam of charged particles between parallel planes: Exact two-dimensional solutions obtained by the method of images

B. B. Levchenko

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We calculate exact two-dimensional analytic expressions for the electric and magnetic fields and their potentials generated by a linear beam of relativistic charged particles between infinite ideally conducting planes and ferromagnetic poles. We use the method of summing an infinite sequence of fields of linear image charges and image currents to obtain solutions and also calculate the density distribution of the electric charge on the conductor surface induced by the charged particle beam. We obtain new formulas for the linear approximation of the fields near the beam and discuss the mathematical features of the exact solutions and the applicability constraints for the linear approximations.

Keywords: charged-beam electromagnetic field, ideal conductor, parallel infinite planes, exact solution, method of images.

PACS: 02.30.Em, 02.30.Lt, 29.27.−a, 41.75.Ak

MSC: 30B99 , 30E25, 31A25 , 78M99

Received: 11.10.2019
Revised: 26.11.2019

DOI: 10.4213/tmf9833

 English version: Theoretical and Mathematical Physics, 2020, 203:2, 700–708

Bibliographic databases:

• 
• 
• 
• 
•