Particle energization through time-periodic helical magnetic fields

TL;DR

This paper investigates how charged particles gain energy in a time-periodic helical magnetic field, demonstrating chaotic motion and indefinite energy growth with specific statistical properties of the energy distribution.

Contribution

It provides the first analysis of particle energization in time-periodic ABC magnetic fields, revealing indefinite energy increase and detailed statistical characteristics.

Findings

Particle motion is chaotic with positive Lyapunov exponents.

Kinetic energy grows indefinitely as a power law in time.

Energy distribution approaches a Gaussian with steep tails at late times.

Abstract

We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients $A=B=C=1$ are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the PDF of kinetic energy is, at late times, close to a Gaussian but with steeper tails.