Particle energization through time-periodic helical magnetic fields.

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 probability density function of kinetic energy is, at late times, close to a Gaussian but with steeper tails.

Chaotic magnetic fields in Vlasov-Maxwell equilibria.

Stationary solutions of Vlasov-Maxwell equations are obtained by exploiting the invariants of single particle motion leading to linear or nonlinear functional relations between current and vector potential. For a specific combination of invariants, it is shown that Vlasov-Maxwell equilibria have an associated Hamiltonian that exhibits chaos.