Remarkable charged particle dynamics near magnetic field null lines

Area of Science:

• Plasma physics
• Nonlinear dynamics
• Charged particle motion

Background:

• Guiding center theory effectively describes charged particle motion in strong magnetic fields using adiabatic invariants like the magnetic moment.
• This theory breaks down near magnetic field null lines where the magnetic field strength approaches zero.

Purpose of the Study:

• To investigate the novel phenomena arising from charged particle motion in electromagnetic fields with a magnetic field null line.
• To explore the breakdown of guiding center theory and the behavior of the magnetic moment near these null lines.

Main Methods:

• Analysis of planar motion of a charged particle in a strong stationary perpendicular magnetic field and a strong electric field.
• Examination of particle dynamics switching between guiding center motion and fast traversal along the magnetic field null line.

Main Results:

• Particle dynamics exhibit a switch between slow guiding center motion and rapid traversal along magnetic field null line segments.
• The magnetic moment, an adiabatic invariant during guiding center motion, changes randomly upon traversing the null line.
• This random change causes particles with the same total energy to adopt new guiding center trajectories, resulting in an energy-dependent stationary magnetic moment distribution.
• The observed jumps in the adiabatic invariant are mathematically described by the Painlevé II equation.

Conclusions:

• Magnetic field null lines introduce significant new phenomena in charged particle dynamics and nonlinear dynamics.
• The random variation of the magnetic moment near null lines leads to a predictable distribution of particle trajectories based on total energy.
• The Painlevé II equation provides a mathematical framework for understanding the stochastic changes in adiabatic invariants in this context.