Stochastic Ion Heating from Many Overlapping Laser Beams in Fusion Plasmas

In this Letter, we show through numerical simulations and analytical results that overlapping multiple ($N$) laser beams in plasmas can lead to strong stochastic ion heating from many ($\propto N^2$) electrostatic perturbations driven by beat waves between pairs of laser beams. For conditions typical of inertial-confinement-fusion experiment conditions, hundreds of such beat waves are driven in ${\mathrm{mm}}^3$-scale plasmas, leading to ion heating rates of several $\mathrm{keV}/\mathrm{ns}$. This mechanism saturates cross-beam energy transfer, with a reduction of linear gains by a factor $\sim 4–5$ and can strongly modify the overall hydrodynamics evolution of such laser-plasma systems.

Figure 1

Upper half of a NIF hohlraum, where 96 of the 192 NIF laser beams, grouped in 24 quadruplets, overlap in a ${\mathrm{mm}}^3$-scale plasma at the upper laser entrance hole (the lower half, not shown, has identical geometry), leading to 276 possible individual pairs. Each pair of quads ($m$, $n$) drives a beat wave with a phase velocity ${\mathit{v}}_{\varphi ,k}=\mathit{k}{\omega }_k/k^2$, where ${\omega }_k={\omega }_n-{\omega }_m$ and $\mathit{k}={\mathit{k}}_n-{\mathit{k}}_m$. The beat waves’ ${\mathit{v}}_{\varphi ,k}$ are represented on the right (green arrows), for a wavelength separation between inner and outer beams of $\Delta \lambda =2\AA$ (with ${\lambda }_{\mathrm{out}}=351\mathrm{nm}$ and ${\lambda }_{\mathrm{inn}}=351.2\mathrm{nm}$).

Figure 2

Ion velocity distribution function $\log [f_i(\mathit{v})]$ from our particle code, plotted vs $v_z$ and $v_r$ (the distribution is axisymmetric along $z$) at times $t=0$, 40, 200, and 500 ps. The cyan contour line represents the ion acoustic velocity $c_s$, and the green dots represent the 276 beat waves’ phase velocities for the NIF geometry with $\Delta \lambda =2\AA$. The initial plasma conditions are $T_e=2.8\mathrm{keV}$, $T_i=0.8\mathrm{keV}$, $n_e/n_c=3\%$, and $Z=2$ (He), and the laser intensities are $5\times {10}^{14}$ and ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ for the “inner” and “outer” quads, respectively.

Figure 3

Time evolution of (a) ion temperature (defined as $k_B{T}_i=\frac{1}{3}{m}_i(⟨v^2⟩-⟨v{⟩}^2)$), (b) average velocity, and (c) average exponential CBET spatial gain for a NIF inner beam. The black curves are the results from the particle code, and the dashed red curves are from the quasilinear reduced model.