Nonlinear ablative Rayleigh-Taylor instability: Increased growth due to self-generated magnetic fields

The growth rate of the nonlinear ablative Rayleigh-Taylor (RT) instability is enhanced by magnetic fields self-generated by the Biermann battery mechanism; a scaling for this effect with perturbation height and wavelength is proposed and validated with extended-magnetohydrodynamic simulations. The magnetic flux generation rate around a single RT spike is found to scale with the spike height. The Hall parameter, which quantifies electron magnetization, is found to be strongly enhanced for short-wavelength spikes due to Nernst compression of the magnetic field at the spike tip. The impact of the magnetic field on spike growth is through both the suppressed thermal conduction into the unstable spike and the Righi-Leduc heat flow deflecting heat from the spike tip to the base. Righi-Leduc is found to be the dominant effect for small Hall parameters, while suppressed thermal conduction dominates for large Hall parameters. These results demonstrate the importance of considering magnetic fields in all perturbed inertial confinement fusion hot spots.

Figure 1

Density and change in temperature due to MHD effects at three different times during the ARTI evolution for a perturbation of $20\mu \mathrm{m}$ wavelength. Select magnetic field strength contours have been indicated. The change in temperature due to MHD is calculated by taking the electron temperature profile with MHD and subtracting the temperature of a separate simulation with no MHD included.

Figure 2

These three figures demonstrate the effectiveness of the scalings proposed in this Letter by comparison with xMHD simulations with different perturbation wavelengths and initial heights. (a) is for the magnetic flux generation [Eq. (5)]; (b) is for the compression of magnetic flux at the spike tip [Eq. (8)]; (c) is for the impact of magnetization on the spike velocity [Eq. (1)].

Figure 3

Change in electron temperature of a $\lambda =20\mu \mathrm{m}$ spike due to magnetized thermal conduction (left) and Righi-Leduc heat flow (right). The left-hand plot is the difference in temperature between a simulation with magnetized heat flow (${\kappa }_{\perp }$) and a simulation with purely unmagnetized heat flow (${\kappa }_{\parallel }$). The plot on the right-hand side is the difference in temperature between simulations with and without Righi-Leduc heat flow turned on (where both simulations use magnetized heat flow ${\kappa }_{\perp }$). Density contours for the case including full MHD have been overlaid.

Figure 4

Increase in RT spike velocity with electron magnetization, including separate curves showing the impact of suppressed perpendicular conduction and the Righi-Leduc component.

Figure 5

Increase in spike height vs time due to self-generated magnetic fields for a number of perturbation wavelengths and initialized heights.