Oscillations of a capillary jet in the presence of a uniform magnetic field

Abstract

The oscillations of a capillary jet of finite electrical conductivity in the presence of a uniform axial magnetic field are investigated taking into account the presence of Hall current in Ohm's law. The dispersion relation is obtained as the exact solution of the characteristic value equations governing the general perturbations. The special case of axisymmetric perturbations (m = 0) is examined in detail. In particular for the case of high resistivity, it is found that the system does not become overstable and that the Hall current contributes an effect only in the second order in an expansion in terms of a small parameter k = H²k/8πηω_c, where H is the magnetic field, k the wavenumber of the perturbation, η the resistivity, and ω_c is the ion cyclotron frequency.