Magnetic flux and heat losses by diffusive, convective, and nernst effects in maglif-like plasma

One component of the MagLIF approach to inertial fusion ignition involves compression and heating of a DT plasma with frozen-in magnetic flux by a heavy cylindrical liner. The liner implosion velocity most of the time is lower than the speed of sound in the compressed DT plasma, which makes the plasma motion subsonic and isobaric. The losses of heat and magnetic flux from the plasma are thereby determined by plasma convection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion and thermomagnetic effects. In the MagLIF-relevant parameter range, the Hall parameter ω_eτ_e and the thermal-to-magnetic pressure ratio β = 8πp / B_z² are both large. Then, according to a theoretical analysis based on the classical collisional Braginskii´s plasma transport equations,^1,2 the heat losses from the hot compressed magnetized plasma to the cold liner wall are dominated by the transverse heat conduction (the ion heat conductivity needs to be accounted for) and convection, and the losses of magnetic flux by convection and the Nernst effect. Here we advance the earlier referenced work and demonstrate that in the limit β(ω_eτ_e)² → ∞ the losses of magnetic flux become asymptotically independent of magnetic diffusivity. For large ω_eτ_e ≫ 1 the effective diffusion coefficients determining the losses of heat and magnetic flux to the liner wall are both shown to be of the order of the Bohm diffusion coefficient ~ cT / (eB), which is commonly associated with low collisionality. We discuss the possibility of using this family of exact solutions for verification of codes that model the MagLIF plasma dynamics.