Violation of adiabaticity in magnetic billiards due to separatrix crossings.

A V Artemyev,A I Neishtadt

doi:10.1063/1.4928473

Abstract

We consider dynamics of magnetic billiards with curved boundaries and strong inhomogeneous magnetic field. We investigate a violation of adiabaticity of charged particle motion in this system. The destruction of the adiabatic invariance is due to the change of type of the particle trajectory: particles can drift along the boundary reflecting from it or rotate around the magnetic field at some distance from the boundary without collisions with it. Trajectories of these two types are demarcated in the phase space by a separatrix. Crossings of the separatrix result in jumps of the adiabatic invariant. We derive an asymptotic formula for such a jump and demonstrate that an accumulation of these jumps leads to the destruction of the adiabatic invariance.

Highlights

Billiards are considered as universal models of many physical processes
We investigate a violation of adiabaticity of charged particle motion in this system
For separatrix crossings in smooth Hamiltonian systems considered in Refs. 9, 32, 33, and 46, the period has a logarithmic singularity on a separatrix, T $ lnj

Summary

INTRODUCTION

Billiards are considered as universal models of many physical processes (see special section devoted to billiard models and review Ref. 19). These are rather simple systems with geometrical laws of particle motion, they are able to simulate various statistical properties, statistical relaxation processes, the property of exponential decay of correlations, ergodicity of gas models, and breaking of time reversal symmetry of motion.. Billiard serves as a simple model of the Fermi acceleration process.. The magnetic billiard serves as a useful model for quantum mechanical problems and modeling of magnetic properties of materials (diamagnetism, paramagnetism, conductance, magnetic edge state, etc.), interaction of matter with laser field, and molecular/atom dynamics.

GENERAL EQUATIONS

JUMP OF THE ADIABATIC INVARIANT

NUMERICAL SIMULATIONS

DISCUSSION AND CONCLUSIONS