Magnetic dynamics of simple collective modes in a two-sphere plasma model

TL;DR

This paper models a two-sphere plasma system to analyze magnetic effects on collective modes, revealing inductive inertia and diamagnetic properties, with implications for plasma oscillation frequencies and magnetic responses.

Contribution

It introduces a simplified two-sphere plasma model incorporating magnetic interactions, providing insights into collective modes, inductive inertia, and diamagnetism not previously detailed.

Findings

Magnetic effects induce inductive inertia affecting oscillation frequencies.

Coulomb attraction causes oscillations with frequencies lower than Langmuir plasma frequency.

The model explains the neglect of resistivity due to dominant magnetic effects.

Abstract

A plasma blob is modeled as consisting of two homogeneous spheres of equal radius and equal but opposite charge densities that can move relative to each other. Relative translational and rotational motion are considered separately. Magnetic effects from the current density caused by the relative motion are included. Magnetic interaction is seen to cause an inductive inertia. In the relative translation case the Coulomb attraction, approximately a linear force for small amplitudes, causes an oscillation. For a large number of particles the corresponding oscillation frequency will not be the Langmuir plasma frequency, because of the large inductive inertia. For rotation an external magnetic field is included and the energy and diamagnetism of the plasma in the model is calculated. Finally it is noted how the neglect of resistivity is motivated by the results.