Effects of laser-plasma parameters on sub-nanosecond evolution of cross-beam energy transfer

Cross-beam energy transfer (CBET) between two lasers is investigated through theoretical analysis and two-dimensional hybrid simulations over sub-nanosecond to nanosecond timescales and millimeter spatial scales. A finite frequency-difference range for CBET development is derived. Ion acoustic wave (IAW) damping is found to broaden this range while reducing the growth rate of stimulated Brillouin scattering (SBS). CBET exhibits distinct nonlinear behaviors across different laser-intensity regimes. Denoting $I_{14}=1\times 10^{14} \mathrm{W/cm^2}$ for a laser wavelength of $351 \mathrm{nm}$, at moderate intensities ($1<I/I_{14}<8$), CBET grows weakly and saturates at a low level due to pump depletion. In the strongly coupled SBS regime ($I/I_{14} \gtrsim 8$), harmonic IAW and nonlinear wave-particle interactions emerge. The generation of harmonic IAW reduces the normal IAW mode, while ion-trapping-induced spectral broadening of normal IAW mode causes frequency mismatch, leading to nonlinear reduction of CBET. After the saturation of harmonic mode, ion trapping broadens harmonic IAW spectrum and weakens it, triggering a secondary growth stage of CBET. After approximately $60 \mathrm{ps}$, CBET approaches quasi-steady-state. The maximum total energy transfer occurs at a frequency difference below the linear matching condition due to the trapping-induced IAW redshift. Based on these two intensity regimes, piecewise scalings of the quasi-saturated total energy transfer rate with $I/I_{14}$ are obtained and shown to be robust against spot size. Speckle effects reduce high-intensity overlap and thus the energy transfer rate. The effects of plasma temperature, density, and flow velocity on CBET are also examined.