Mitigating the Two Plasmon Decay instability by optimizing bandwidth of plane wave lasers

Previous work has shown that broadband lasers can mitigate laser plasma instabilities. Follett et. al considered various amplitude shapes (e.g. uniform, gaussian) and random phases, and showed that the mitigation can be predicted by determining the coherence time and that it is invariant with respect to the amplitude shape given the same coherence time. In this work, we explore whether optimal spectra (in both amplitude and phase) exist, what their characteristics are, and how well or poorly they mitigate the two plasmon instability in comparison to the previous approaches (e.g. uniform amplitude and random phase). We will discuss optimal spectra for realistic plasma parameters. The parameter space that is explored is given by –



2 keV < T_e < 4 keV || 200 um < L_n < 600 um || 10¹⁴ W/cm² < I < 10¹⁵ W/cm²



To do this, we need to perform optimization of the slowly varying enveloped wave partial differential equations in a high-dimensional (O(100)) parameter space. This requires many iterations using gradient descent. We rewrite the LPSE solvers in a differentiable framework to make them amenable to performing gradient descent and to running on GPUs. Each of these are key enabling technologies for performing optimization of multi-dimensional PDEs in a high-dimensional parameter space.