Mutual influence between two spherical conducting grids in a warm isotropic plasma

The multiple water-bag model can be used to describe a uniform warm plasma as accurately as one wishes. Moreover, it makes boundary-value problems in such a plasma tractable. As a special case, the problems of the influence of a point charge on a spherical grid and of the mutual influence between two spherical grids are solved. From these results, the self-impedance of a double-sphere dipole antenna is deduced. If the spheres are widely separated it exhibits a resonance at the plasma frequency, whereas if the spheres are close there is an anti-resonance at this frequency. The mutual impedance of a quadrupole probe comprising two double-sphere antennae is also studied, and is found, usually, to be not very sensitive to the finite radius of the spheres. For determining the electron temperature of the plasma, this last device seems better than a double-sphere antenna alone.