Field Compressing Magnetothermal Instability in Laser Plasmas

The mechanism for a new instability in magnetized plasmas is presented and a dispersion relation derived. Unstable behavior is shown to result purely from transport processes—feedback between the Nernst effect and the Righi-Leduc heat-flow phenomena in particular—neither hydrodynamic motion nor density gradients are required. Calculations based on a recent nanosecond laser gas-jet experiment [D. H. Froula et al., Phys. Rev. Lett. 98, 135001 (2007)] predict growth of magnetic field and temperature perturbations with typical wavelengths of order $50\mu \mathrm{m}$ and characteristic growth times of $\sim 0.1\mathrm{ns}$. The instability yields propagating magnetothermal waves whose direction depends on the magnitude of the Hall parameter.

Figure 1

Snapshots of the instability taken at 700 ps (top), 800 ps (center), and 900 ps (bottom), from CTC simulations of the experiment of Froula et al. [7] for the case of an 8 T field given a 1% perturbation at the laser “switch-on” time.

Figure 2

The theoretical dispersion relation of our reduced model—for a 6 T magnetized plasma at a distance $x\approx 120\mu \mathrm{m}$ from the laser strip center after 500 ps of heating—based on one-dimensional profiles taken from CTC (top plot, solid line), CTC+ (top plot, dashed line) and IMPACT (bottom plot). These may be compared with growth rates measured from full two-dimensional simulations.

Figure 3

A comparison between the spread of thermal energy when the instability is active (solid line) and when it is not (dashed line) after 1 ns of laser heating for the case of an 8 T applied field (cf. Fig. 1). The data, taken from CTC, are averaged in $y$ for each $x$ cross section.