Cross-Beam Energy Transfer Saturation by Ion Heating

We measure cross-beam energy transfer (CBET) saturation by ion heating in a gas-jet plasma characterized using Thomson scattering. A wavelength-tunable ultraviolet (UV) probe laser beam interacts with four intense UV pump beams to drive large-amplitude ion-acoustic waves. For the highest-intensity interactions, the power transfer to the probe laser drops, demonstrating ion-acoustic wave saturation. Over this time, the ion temperature is measured to increase by a factor of 7 during the 500-ps interaction. Particle-in-cell simulations show ion trapping and a subsequent ion heating consistent with measurements. Linear kinetic CBET models are found to agree well with the observed energy transfer when the measured plasma conditions are used.

Figure 1

(a) The ratio of the output power ($P$) to the incident power ($P_0$) of the probe beam was calculated using a linear kinetic CBET model for the conditions of these experiments over a range of nitrogen ion temperatures. (b) The total laser intensity, pulse shapes, and beam timings for each of the beam groups. (c) Transmitted beam diagnostic (TBD) data showing the input (dashed red curve) and output (solid black curve) probe and pump (blue curve) powers. (d) Time-resolved Thomson-scattering data showing the electron-plasma and ion-acoustic wave spectra of a pump beam with minimal ion heating.

Figure 2

The ion-acoustic wave spectrum measured (points) after the CBET pump beams turned off ($\sim 1600\mathrm{ps}$). A calculated spectrum (red curve) is in excellent agreement with the measured spectrum for the plasma conditions: $T_e=450$, $T_{\mathrm{ion}}^H=750$, and $T_{\mathrm{ion}}^N=900\mathrm{eV}$. The calculated spectrum (blue dashed curve) for the ion temperatures with no ion heating ($T_e=450$, $T_{\mathrm{ion}}^H=120$, $T_{\mathrm{ion}}^N=120\mathrm{eV}$).

Figure 3

The power transferred into the probe beam for four different initial probe beam intensities [$0.1\times {10}^{14}$ (red short-dashed curve), $0.9\times {10}^{14}$ (yellow long-dashed curve), $2.0\times {10}^{14}$ (green dash-dotted curve), $4.1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ (blue solid curve)]. The pulse shape of the pump beams (orange dashed curve) is shown. The energy transfer calculated using kinetic linear theory for the measured plasma conditions (diamonds). Inset: VPIC simulated probe beam amplification corresponding to the lowest (red dashed curve) and highest (blue solid curve) experiment probe intensities.

Figure 4

The plasma conditions for the (a) electrons (b) and ions measured from the Thomson-scattering spectrum. The ion temperatures for nitrogen (green points) and hydrogen (purple points) are shown for two shots corresponding to the lowest ($I_{\text{probe}}=0.1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$) (diamonds) and highest ($I_{\text{probe}}=4.1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$) (circles) probe beam intensities.

Figure 5

VPIC simulations of a plasma prepared identically to the experimental plasma show the 2D nitrogen ion velocity distribution functions for a high probe beam intensity CBET interaction at three time steps: (a) $T=0.01$, (b) $T=10$, (c) and $T=100\mathrm{ps}$. The $x$ axis ($y$ axis) of each subplot is the velocity parallel (perpendicular) to the excited ion wave normalized to the initial nitrogen thermal velocity. A line shows the log of the 1D velocity distribution parallel to the excited ion wave (solid line) compared to the initial distribution (dashed line).