Measurement of the laser pulse phase velocity in plasma channel for DLA optimization

Abstract

We demonstrate a novel, direct method for measuring the phase velocity $v_φ$ of an intense laser pulse within a plasma channel - the crucial parameter that controls the resonance condition in direct laser acceleration (DLA). The technique exploits the second harmonic (SH) radiation generated at the channel sheath - a phenomenon previously observed in laser-wakefield acceleration experiments. The SH emission angle is governed by a phase-matching condition that directly depends on $v_φ$. Experimental measurements performed using a 1 TW, 10 Hz Ti:Sa laser system yield phase velocities in the range $v_φ=(1.010-1.030)c$ for plasma electron densities in the range $n_e=(0.01-0.06)n_{cr}$. The diagnostic is validated through quasi-3D particle-in-cell (PIC) simulations that reproduce the experimental conditions. This work provides a way to optimize DLA schemes by enabling in-situ measurement of the laser pulse phase velocity in plasma channels.

Figures (4)

• Figure 1: Mechanism of SH generation (a). Phase-matching conditions for SH generation from plasma channel sheath, ange of SH emission (see Eq. \ref{['eq1']}) (b).
• Figure 2: (a) Experimental setup. (b) The SH generation angle $\Theta_{2\omega}$ for different delay between ns and fs laser pulses $\Delta t$. (c-g) SH image from CCD camera for different $\Delta t$.
• Figure 3: Hydrodynamic simulation of the PET tape ablation. Carbon atomic density $n_{at}$ in $n_{cr}$ for different delay between ns and fs laser pulses: $\Delta t=-1$ ns (a), $\Delta t=1$ ns (b), $\Delta t=3$ ns (c), $\Delta t=5$ ns (d), $\Delta t=7$ ns (e), $\Delta t=9$ ns (f). The electron density of the ablated film on axis $y=0$ for various values $\Delta t$ assuming that 4 electron ionized (g).
• Figure 4: PIC-simulation results. Electron density $n_e$ and Fourie filtrated SH electric field $E_y^{2\omega}$$n_e=0.035n_{cr}$ (a), $n_e=0.058n_{cr}$ (b). SH angle distribution obtained from spatial Fourier transform of $E_y^{2\omega}$ for $n_e=0.035n_{cr}$ in blue (maximum at $\Theta_{2\omega}=10.7^{\circ}$) and $n_e=0.058n_{cr}$ in orange (maximum at $\Theta_{2\omega}=11.8^{\circ}$) (c). Laser pulse electric field $E_y$ (solid lines) on axis ($y=20\lambda$) at different time instants: $t=70\lambda/c$ (blue), $t=80\lambda/c$ (orange) and $t=120\lambda/c$ (green) and corresponding dashed pulse envelopes at $y=21\lambda$ (approximately the plasma channel sheath) for $n_e=0.035n_{cr}$ (d), $n_e=0.058n_{cr}$ (e). Phase velocity $v_{\phi}$ depending on electron plasma density $n_e$ in experiment (orange), PIC-simulation: calculated from SH angle $\Theta_{2\omega}$ by Eq. \ref{['eq2']} (darkpurple squares) and "directly" measured (lightpurple circles) and the theoretical lower limit of the method's applicability in green (f).