Joint Amplitude-Phase Optimization of Broadband Lasers Raises Absolute Two-Plasmon-Decay Thresholds Above Coherence-Time Predictions

Abstract

Broadband lasers suppress the absolute two-plasmon-decay instability that preheats inertial-fusion targets. The usual scaling relates this suppression to the drive's coherence time, a power-spectrum statistic insensitive to spectral phase. By gradient descent through a differentiable enveloped wave solver, we show that at fixed power spectrum phase optimization raises the threshold from the random-phase median of $2.8I_{\mathrm{mono}}$ to $4.1I_{\mathrm{mono}}$, but produces a transform-limited (TL) pulse train with peak-to-average ratio $R=32$. Joint amplitude--phase optimization reaches $5.6I_{\mathrm{mono}}$ at $R=3.6$, above the best tested TL line-count result of $4.5I_{\mathrm{mono}}$ at $R=16$; relaxing the peak constraint raises the joint threshold to $6.4I_{\mathrm{mono}}$. An exact growth-rate budget evaluated inside the simulation separates the two mechanisms. TL suppresses coupling mainly by concentrating the pump field into short bursts, thereby lowering its time-averaged magnitude at fixed average intensity. The joint optima retain near-random values of this amplitude measure while suppressing both the available coupling and the fraction realized through pump--daughter alignment. The advantage of joint optimization persists from $1\%$ to $4\%$ bandwidth and from OMEGA-scale to ignition-scale conditions.