Growth rate (imaginary part of frequency) of antisymmetric (kink) mode vs. normalised wave number k_zd calculated from Eq. (15) when α = 1 and k_y, V_0y = 0 for different ratios of inverse Alfvén Mach number, . Green, blue, cyan, and solid red lines correspond to , 0.7, 0.9, and 1, respectively. Dashed lines show the corresponding solutions for the homogeneous jet α = 0, which is already zero for and 1. Here, ρ₀/ρ_e = 1 and the growth rate is normalised by k_zV_0z.