Role of Frequency Chirp and Energy Flow Directionality in the Strong Coupling Regime of Brillouin-Based Plasma Amplification

A detailed analysis is presented of the various stages of strong coupling Brillouin plasma amplification, emphasizing the importance of the chirp which can be of threefold origin: the intrinsic one driven by the amplification process, the one originating from the chirped-pulse-generated laser pulses, and the one associated with the plasma profile. Control of the overall chirp can optimize or quench the energy transfer. The time-dependent phase relation explains the energy flow direction during amplification and is characteristic for this strong coupling process. The study is also of potential importance to understand and maybe control cross-beam-energy transfer in inertial confinement fusion.

Figure 1

(a) Evolution in time of the phases of the pump (${\phi }_p$, blue line) and of the seed ($-{\phi }_s$, green line) and the density perturbation ($-\phi$, red line) in units of $\pi$. (b) Time evolution of the total phase $\vartheta ={\phi }_p-{\phi }_s+\varphi -\phi$, in units of $\pi$. The green shadowed regions indicate the values of $\vartheta$ for which the pump amplifies the seed; the blue ones correspond to a reversed flow energy direction. (c) Electric field amplitudes, in $\mathrm{V}/\mathrm{m}$, of the pump (blue line) and of the seed (green line) as a function of time. The data are taken at $x_{\text{cross}}=350\mu \mathrm{m}$, the point where seed and pump initially collide in the plasma.

Figure 2

Electric field amplitudes, in $\mathrm{V}/\mathrm{m}$, of the pump (blue lines, propagating to the right) and of the seed (green lines, propagating to the left) at $t=1.5\mathrm{ps}$. Dashed lines are for $\alpha =0$. Solid lines are for (a) $\alpha ={\alpha }_{\mathrm{opt}}\approx -3.3\times {10}^{-7}$ and (b) $\alpha ={\alpha }_q\approx 1.28\times {10}^{-6}$.

Figure 3

Electric field amplitude of the seed as a function of space for $\text{const}$, constant density profile at $n_e/n_c=0.05$ and no chirp; $\text{const}(-)$, constant density profile with $\alpha =-2.7\times {10}^{-7}$; $\text{const}(+)$, constant profile with $\alpha =+2.7\times {10}^{-7}$; and $trl$ and $trr$, triangular density profiles with $n_{\max }/n_c=0.1$.