Dimensionless Joule damping −τ_Ω/|1 − Ω₀| of tidal instability (solid blue line), as a function of magnitude |k₀|. Dashed magenta line is given by formula (31), delimiting the two hydromagnetic regimes. Red shaded areas show the typical strength of the diffusionless growth rate of tidal instability σ ∼ 𝒪(β₀), with β₀ ∈ [10⁻⁴, 10⁻²] for close binaries. Computations at Le = 10⁻⁵ and Ek/Pm = 10⁻¹² for the dimensionless fossil field B₀ = 1_z aligned with the spin axis.