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

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