Resistive stability of the cylindrical spheromak

The growth rates for resistive instabilities in a straight circular cylinder with spheromak profiles are computed by using two complementary methods. The first method employs boundary layer analysis and asymptotic matching, most valid for values of the magnetic Reynolds number S ≳ 10 ⁵. The second method solves the full linearized resistive magnetohydrodynamic (MHD) equations as an initial value problem, utilizing zone packing around the mode rational surface. Resolution requirements limit this to S ≲ 10⁷. The results from these two methods agree to better than 1 in 10³ in the overlap region 10⁷ ≳ S ≳ 10⁵. A scan of parameter space reveals that for parabolic q profiles, the least unstable configurations have q₀R / a ∼ 0.67. The Hall term in Ohm's Law is easily incorporated into both methods. Recalculating the resistive MHD growth rates in the presence of this term shows that the resistive interchange mode is completely stabilized for a large enough value of the ion cyclotron time.