Experimental Validation of the Two-Plasmon-Decay Common-Wave Process

The energy in hot electrons produced by the two plasmon decay instability, in planar targets, is measured to be the same when driven by one or two laser beams and significantly reduced with four for a constant overlapped intensity on the OMEGA EP. This is caused by multiple beams sharing the same common electron-plasma wave. A model, consistent with the experimental results, predicts that multiple laser beams can only drive a resonant common two plasmon decay electron-plasma wave in the region of wave numbers bisecting the beams. In this region, the gain is proportional to the overlapped laser beam intensity.

Figure 1

(a) Schematic of the common-wave region for two beams: Two laser beams of wave vectors $k_{0,1}$ and $k_{0,2}$ share the common-plasma wave $k_c$ located in the bisecting plane fulfilling the necessary condition $|k_c-k_{0,1}|=|k_c-k_{0,2}|$ independent of the polarizations of the laser beams; (b) Schematic of the seven common wave regions when four beams are used: six two beam common-wave planes (red lines) and one four beam common-wave line (green point).

Figure 2

(a) The measured hot-electron temperature is plotted as a function of the measured total energy in $K_{\alpha }$ for the five laser-beam orientations tested. (b) The fraction of laser energy converted to hot electrons ($f_{\mathrm{hot}}$) is plotted as a function of the overlapped intensity. The four-beam hot electron generation is estimated (open diamonds) by multiplying the measured two-beam total hot-electron energy fraction by six and plotting the results at twice the two-beam intensity. The dashed line is a fit to the four beam data [$f_{\mathrm{hot}}=3\times {10}^{-8}{e}^{(8I_{\Sigma }/2)}$]. The solid line is scaled from the fit assuming the four beam results are dominated by the six two beam common wave modes driven at half of the intensity [$f_{\mathrm{hot}}=1\times {10}^{-8}{e}^{(8I_{\Sigma })}$].

Figure 3

Calculation of $({\Gamma }_0^2{)}^{2B}$ in the common-wave plane for (a) two beams polarized perpendicular and (b) parallel to the plane (${\mathbf{k}}_{\mathbf{0},\mathbf{1}}$, ${\mathbf{k}}_{\mathbf{0},\mathbf{2}}$). The dashed black lines correspond to the Landau cutoff ($k_{\max }{\lambda }_{\mathrm{De}}=0.25$ where $k_{\max }=\max [k_c,|{\mathbf{k}}_{\mathbf{c}}-{\mathbf{k}}_{\mathbf{0},\mathbf{i}}|]$) calculated for $T_e=1.6\mathrm{keV}$, which defines the maximum wave vector for TPD [20]. The dashed green lines correspond to the two modified hyperbolas of maximum $({\Gamma }_0^2{)}^{2B}$. (c) Calculation of $({\Gamma }_0^2{)}^{4B}$ along the four-beam common-wave line. ${\mathbf{k}}_{\mathbf{x}}$ is along the projection of ${\mathbf{k}}_{\mathbf{0},\mathbf{i}}$ in the common wave region, ${\mathbf{k}}_{\mathbf{y}}$ is perpendicular to ${\mathbf{k}}_{\mathbf{x}}$, $k_0$ is calculated at quarter-critical density.

Figure 4

The total hot electron energy divided by the laser energy is plotted as a function of the common-wave gain ($G_c$) for the dominant mode.