Collisionless whistler heat-flux instability in ultra-high-$β$ plasmas

Abstract

Kinetic instabilities, notably the whistler heat-flux instability (WHFI), are known to suppress thermal transport significantly in the moderate- to high-$β$ plasmas relevant to many astrophysical systems. This paper explores WHFI-regulated heat transport in a new regime: ultra-high-$β$ plasmas with $β_{e} \gtrsim L_{\mathrm{T}}/ρ_e$. Extrapolating previous theories of the WHFI to ultra-high-$β$ plasmas, we propose that the magnetic energy in unstable whistler fluctuations becomes comparable to that of the background magnetic field at saturation. We corroborate this hypothesis using 1D3V and 2D3V kinetic simulations using the particle-in-cell code OSIRIS. We find that, in ultra-high-$β$ plasmas, the heat flux is localised and no longer regulated primarily by resonant pitch-angle scattering of electrons; instead, thermal energy is transported predominantly by advection at the whistler phase velocity. Heat-flux suppression is observed in 1D3V and 2D3V simulations; however, we show that the saturation of the WHFI and the regulation of heat flux are sensitive to dimensionality in the ultra-high-$β$ regime. The amplitude and phase velocity of the heat-flux-regulating whistler waves scale differently with $β_e$, yielding parallel heat fluxes, normalised to the free-streaming value, of $q_{e\parallel} / q_\mathrm{fs} \approx 4.7 β_{e}^{-1}$ and $q_{e\parallel} / q_\mathrm{fs} \approx 0.3 β_{e}^{-1/2}$ in 2D3V and 1D3V simulations, respectively. We perform 2D3V simulations with background magnetic fields inclined to the temperature gradient, showing cross-field heat transport remains negligible. We develop a heuristic theory from kinetic equations that explains these phenomena. Our work extends our understanding of how the WHFI modifies thermal transport to regimes applicable to high-energy-density physics and the reionised intergalactic medium.