Energization of Charged Particles By a Time-Dependent Chaotic Magnetic Field

Energization of particles to ultra high energies remains a challenging problem in the plasma physics community. One possible mechanism involves chaotic magnetic fields. It is noteworthy that the equations describing the spatial evolution of field lines of a magnetic field having dependence on three spatial coordinates are not integrable and such field lines are chaotic. Such chaotic magnetic fields are ubiquitous in nature including many astrophysical scenarios. The motion of charged particles in such magnetic fields comprise an important topic of study since it has been suggested that they may be energized if the field is time-dependent.

We considered a particular chaotic field, which is often called the Sine field, and assumed a simple sinusoidal time dependence. Sine fields were first introduced for chaotic fluid motion in the study of nonlinear dynamos, and it can be shown that such fields are a particular solution of the double curl equation for the magnetic field. We construct the equation of motion of a charged particle in the presence of the time-dependent magnetic field and the induced time dependent electric field using Faraday's Law. These three coupled nonlinear differential equations are solved using the adaptive Dormand-Prince Runge-Kutta method. We calculate the energy of the charged particle and examine the evolution of this energy over time. Our results suggest that the energy of the particle increases indefinitely.