Multiple Beam Two-Plasmon Decay: Linear Threshold to Nonlinear Saturation in Three Dimensions

The linear stability of multiple coherent laser beams with respect to two-plasmon-decay instability in an inhomogeneous plasma in three dimensions has been determined. Cooperation between beams leads to absolute instability of long-wavelength decays, while shorter-wavelength shared waves are shown to saturate convectively. The multibeam, in its absolutely unstable form, has the lowest threshold for most cases considered. Nonlinear calculations using a three-dimensional extended Zakharov model show that Langmuir turbulence created by the absolute instability modifies the convective saturation of the shorter-wavelength modes, which are seen to dominate at late times.

Figure 1

The LW spectrum $⟨|E_1(k_x,k_y,k_z=0,t){|}^2{⟩}_t$ averaged over times $t=2.4$ to 4.2 ps (a) and $t=12.0$ to 15.0 ps (b). The two EM wave vectors ${\overrightarrow{k}}_{0,1}$ (lower green arrow), ${\overrightarrow{k}}_{0,2}$ (upper white arrow), and their polarization vectors lie in the plane shown ($k_{\mathrm{z}}=0$) (i.e., $p$ polarization). The dashed green (white) hyperbolas correspond to the maximum single-beam homogeneous growth rate for beam 1 (2) and the red circle is the Landau cutoff $|\overrightarrow{k}|{\lambda }_{\mathrm{De}}=0.25$ (see text for parameters).

Figure 2

Slices of the LW spectrum $⟨|E_1(\overrightarrow{k},t){|}^2{⟩}_t$ (averaged over times $t=1.0$ to 2.0 ps) in the planes $k_y=0$ and $k_z=0$ for a four-beam calculation ($\parallel$ polarization). The beam geometry and polarization are shown in the inset.

Figure 3

Normalized single-beam threshold intensities $(I_s{)}_{\text{thr}}$ for absolute instability with irradiation by $N$ beams of incidence angle ${\theta }_s=27°$ (except where indicated) for various polarization states (see text). The red numbers are the maximum convective gains evaluated at the absolute threshold.

Figure 4

The transverse averaged LW intensity $⟨|{\overrightarrow{E}}_1{|}^2{⟩}_{y,z}(x,t)$ as a function of the $x$ coordinate (initial density, upper axis) and time. The white lines mark the time windows corresponding to Figs. 1 and 1. The inset shows the temporal dependence of $⟨|{\overrightarrow{E}}_1{|}^2{⟩}_{\perp }(x,t)$ at the locations $x=26\mu \mathrm{m}$ (black dashed line), $x=31\mu \mathrm{m}$ (red dashed line), and $x=36\mu \mathrm{m}$ (blue dashed line).