FIG. 4: Panel (a) shows the growth rate, γm, of type 2 SuperHMRI, optimized over a set of parameters (α, k∗z ,Ha ∗, Re∗), and represented as a function of Pm, at fixed Ro = 1.5. Panels (b) and (c) show the corresponding Ha∗m and Re ∗ m, respectively. For both Pm ≪ 1 and Pm ≫ 1, γm tends to constant values. The re-scaled Hartmann and Reynolds numbers vary as Ha∗m ∝ Pm −1/2 and Re∗m ∝ Pm −1 for Pm ≪ 1, and as Ha∗m ∝ Pm 1/3 and Re∗m ∝ Pm −1/4 for Pm ≫ 1. Panels (b) and (c) are compensated by these factors to more clearly highlight these scalings. The dashed lines are at Pmc1 = 0.223 and Pmc2 = 4.46, marking the Pm = O(1) region where no instability exists.
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