Extend the broadband TPD theory to include density gradients and absolute-instability thresholds

Extend the broadband two-plasmon decay dispersion relation developed for a uniform plasma to a plasma with a spatial electron-density gradient and establish how laser bandwidth modifies the absolute instability threshold near the quarter-critical density, devising a method that adapts or replaces the specific plane‑wave manipulations used by Liu (1976) and Simon (1983) within the Wigner–Moyal/CE2 framework.

Background

The paper’s main result is a uniform‑plasma broadband dispersion relation for two‑plasmon decay under arbitrary laser power spectra, closed via the CE2 cumulant expansion and Wigner–Moyal formalism. Absolute instabilities relevant to hot‑electron generation in direct‑drive ICF, however, are strongly influenced by the coronal density gradient near quarter‑critical density.

Classical threshold calculations for absolute instabilities (e.g., Liu 1976; Simon 1983) rely on specialized analytical techniques for plane‑wave pumps that are not directly compatible with the statistical broadband framework introduced here. The authors explicitly state that extending their analysis to include density gradients and bandwidth effects on absolute thresholds remains open.