Super-Gaussian transport theory and the field-generating thermal instability in laser–plasmas

Abstract

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser–plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal ( anomalous Nernst ) magnetic field advection up gradients in the electron number density n _e , which we associate with a novel heat-flow q _n ∝∇ n _e . Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ , in which case the Nernst effect is reduced by a factor of five, the ∇ T _e × ∇ n _e field generation mechanism by ∼30% (where T _e is the electron temperature), and the diffusive and Righi–Leduc heat-flows by ∼80 and ∼90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux q _n are checked against kinetic simulation using the Vlasov–Fokker–Planck code impact , and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ , we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields.