Relativistic formulation of curl force, relativistic Kapitza equation and trapping

TL;DR

This paper develops a relativistic formulation of curl forces and the Kapitza equation, analyzing particle dynamics and trapping phenomena both theoretically and numerically in the relativistic regime.

Contribution

It introduces the relativistic version of the Kapitza equation and explores particle trapping and escape behaviors with saddle potentials.

Findings

Numerical results reveal unique trapping and escaping behaviors of charged particles relativistically.

The relativistic Kapitza equation exhibits distinct dynamics compared to the classical version.

Generalization to monkey saddle potentials broadens the understanding of relativistic particle trapping.

Abstract

In this present communication the relativistic formulation of the curl forces with saddle potentials has been performed. In particular, we formulated the relativistic version of the Kapitza equation. The dynamics and trapping phenomena of this equation have been studied both theoretically and numerically. The numerical results show interesting characteristics of the charged particles associated with the particle trapping and escaping in the relativistic domain. In addition, the relativistic generalization of the Kapitza equation associated with the monkey saddle has also been discussed.