Magnetic field effects on electron heat transport in laser-produced plasmas

The classical treatment of thermal heat transport in the presence of magnetic fields has been modified to include effects associated with steep temperature gradients by extending the one-dimensional model of Shvarts et al. [Phys. Rev. Lett. 47, 247 (1981)] to three dimensions. The effects of magnetic field inhibition are described in terms of the parameter ${\beta }_0={\omega }_c{\tau }_{\mathrm{ei}}$, where ${\omega }_c$ is the electron gyrofrequency and ${\tau }_{\mathrm{ei}}$ the (thermal) electron-ion collision time. The model has been applied to plasmas whose zeroth-order distribution functions ($f_0$) are Maxwellian, and solutions have been obtained for the components of the heat flux across the magnetic field, parallel and perpendicular to the temperature gradient. It is found that it is only for small ${\beta }_0 (\lesssim 0.2)$ that the anisotropic portion of the distribution function (${\overrightarrow{\mathrm{f}}}_1$) is limited, according to the prescription of Shvarts et al., to $\delta f_0$ where $\delta$ is an ad hoc cutoff parameter of value approximately unity; for higher values of ${\beta }_0$, a strong reduction of both components of the heat flux occurs due to the inhibition of the more energetic heat-carrying electrons in the distribution, and the classical Braginskii results are valid (in the sense that $f_1\lesssim f_0$ for heat-carrying electrons). The sensitivity of the results to the parameter $\delta$ is examined. For parameters typical of glass-laser-generated plasmas, strong inhibition may occur for magnetic fields as small as 100 kG.