Counterintuitive Particle Confinement in a Helical Force-Free Plasma

The force-free magnetic field solution formed in a high-aspect ratio cylinder is a non-axisymmetric (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>), closed magnetic structure that can be produced in laboratory experiments. Force-free equilibria can have strong field gradients that break the usual adiabatic invariants associated with particle motion, and gyroradii at measured conditions can be large relative to the gradient scale lengths of the magnetic field. Individual particle motion is largely unexplored in force-free systems without axisymmetry, and it is unclear how the large gradients influence confinement. To understand more about how particles remain confined in these configurations, we simulate a thermal distribution of protons moving in a high-aspect-ratio force-free magnetic field using a Boris stepper. The particle loss is logarithmic in time, which suggests trapping and/or periodic orbits. Many particles do remain confined in particular regions of the field, analogous to trapped particles in other magnetic configurations. Some closed flux surfaces can be identified, but particle orbits are not necessarily described by these surfaces. We show examples of orbits that remain on well-defined surfaces and discuss the statistical properties of confined and escaping particles.