Effect of external axial magnetic field on the early stage instabilities in magnetized cylindrical liners

Based on the resistive MHD theory, the dispersion relations of instabilities are derived in the liner geometry, where a uniform current flows over the cross section. Both the external axial magnetic field and the electrothermal effect are taken into account. It is found that instabilities act as electrothermal instabilities (ETIs) below a critical wavelength, which is increased by the axial magnetic field. Beyond the critical wavelength, the growth rate increases with the wavelength quickly and approaches the maximum which depends on the gradient scale length of the azimuthal magnetic field. When the axial magnetic field is applied, the m = 1 mode has a higher growth rate than the m = 0 mode although the difference between them is relatively small.