Saturation Mechanisms for the Generated Magnetic Field in Nonuniform Laser-Matter Irradiation

Spontaneously generated magnetic fields B can be generated by nonuniform laser irradiation causing sources such as $▽T_e\times ▽n_e{/n}_{e}e$. By considering convective losses and dissipation including the triggering of lower hybrid drift turbulence a universal diagram of saturated B versus $L_{\perp }$, the characteristic transverse scale length for the nonuniformity, is found. For $L_{\perp }$ less than the ion collisionless skin depth $c/{\omega }_{\mathrm{pi}}$ the saturated B scales as $L_{\perp }^{\alpha }$ $\alpha \le 1$. At higher $L_{\perp }$ values B scales as $L_{\perp }^{-1\mathrm{}}$ because convective losses dominate. For resistive plasmas (e.g., high Z, low temperature) B will be limited to $({\mu }_0{\mathrm{kT}}_e/e\eta )\left(L_{\perp }{/L}_{\Vert }\right)$ where $L_{\Vert }$ is $n_e/▽n_e$.