Solutions of the antisymmetric (kink) mode (Eq. (15)) in type II spicule conditions: ρ₀/ρ_e = 100, d = 100 km, V₀ = 100 km s⁻¹. Left panels: real (upper) and the imaginary (lower) parts of frequencies, which are normalised by k_zV_0z. Blue lines show the purely hydrodynamic case (i.e. V_A = 0). Red lines show the case when the external Alfvén speed is V_A = 200 km s⁻¹. Right panels: periods and growth times of unstable harmonics vs. wavelength in the interval of k_zd = 0.5−2.5. Here, α = 1 and k_y, V_0y = 0.