Measurement of the decay of laser-driven linear plasma wakefields

We present measurements of the temporal decay rate of one-dimensional (1D), linear Langmuir waves excited by an ultrashort laser pulse. Langmuir waves with relative amplitudes of approximately $6\%$ were driven by $1.7\mathrm{J}$, $50\mathrm{fs}$ laser pulses in hydrogen and deuterium plasmas of density $n_{e0}=8.4\times {10}^{17}{\mathrm{cm}}^{-3}$. The wakefield lifetimes were measured to be ${\tau }_{\mathrm{wf}}^{{\mathrm{H}}_2}=(9\pm 2)$ ps and ${\tau }_{\mathrm{wf}}^{{\mathrm{D}}_2}=(16\pm 8)$ ps, respectively, for hydrogen and deuterium. The experimental results were found to be in good agreement with 2D particle-in-cell simulations. In addition to being of fundamental interest, these results are particularly relevant to the development of laser wakefield accelerators and wakefield acceleration schemes using multiple pulses, such as multipulse laser wakefield accelerators.

Figure 1

Schematic drawing of the experimental layout inside the target vacuum chamber. Both beams of the Astra-Gemini TA3 laser were used: one as the drive beam, and the other as the diagnostic probe beam. The $800\mathrm{n}\mathrm{m}$ beams are shown in red and the $400\mathrm{n}\mathrm{m}$ diagnostic beam is shown in blue. After leaving the gas cell, the diagnostic beam was transported to a $400\mathrm{n}\mathrm{m}$ spectrometer located outside the vacuum chamber. The inset shows an example recording of a wakefield in a spectral interferogram, as captured by the spectrometer camera. AO: Adaptive optic; HM: Holed mirror; HWP: Half-wave plate; L1: $\mathrm{f}=500$ mm lens; L2: $\mathrm{f}=-100$ mm lens; L3: $\mathrm{f}=300$ mm lens; P: polariser; $10\mathrm{X}$: microscope objective; SHG: second harmonic generating crystal.

Figure 2

Measured normalized relative wakefield amplitude calculated using the TESS technique [36, 37] as a function of delay for: (a) hydrogen; (b) deuterium, recorded with a backing pressure $P_{\text{cell}}=\left(17.0\pm 1.2\right)\mathrm{mbar}$. For each delay are shown the uncertainty-weighted average wakefield amplitude ($\delta n_e\left(\zeta \right)/n_{e0}$) and the standard error. The uncertainty was calculated using the background noise in the Fourier-transformed interferograms. The wakefield amplitude calculated from the PIC simulations are shown as open circles. Also shown are fits of the exponential function to the data as black lines.

Figure 3

Schematic drawing of the experimental layout inside the target vacuum chamber. Both beams of the Astra-Gemini TA3 laser were used, one beam used as the drive beam and the other beam as the diagnostic beam. The $800\mathrm{n}\mathrm{m}$ beams are shown in red and the $400\mathrm{n}\mathrm{m}$ diagnostic beam is shown in blue. The diagnostic beam was transported to a $400\mathrm{n}\mathrm{m}$ imaging spectrometer located outside the vacuum chamber. AO: adaptive optic; SHG: second harmonic generating crystal; HWP: half wave plate; P: polarizer; L1: $f=500\mathrm{mm}$ (4 in diameter); L2: $f=-100\mathrm{mm}$ (1 in diameter); L3: $f=300\mathrm{mm}$ (1 in diameter).

Figure 4

Plot of the perturbed spectrum of the probe pulse, taken during measurements of the spectral chirp of the probe pulse. The temporal overlap of the probe and drive pulses in the gas cell causes a reduction of the probe pulse intensity as measured on the spectrometer. The red cross marks a low-intensity feature that is tracked as a function of the temporal delay between the drive and probe (or reference) pulses, in order to measure the spectral phase.

Figure 5

Measurement of the spectral phase of the (a) probe and (b) reference pulses. The black dots indicate the location of the ionization front feature in time and frequency. The dashed lines show the fitted first derivative of the temporal phase $d\varphi \left(\zeta \right)/d\zeta$ of each pulse. The dotted lines show a linear fit to the data.

Figure 6

(a) Line outs of the spectral intensities of the probe (red line) and reference pulses (blue line). The dashed lines show Gaussian fits to these spectra. (b) spectral overlap function $\mathcal{F}\left({\omega }_{\mathrm{pe}}\right)$ as a function of the plasma frequency, for the measured spectra and Gaussian spectra fitted to the measured spectra.

Figure 7

(a) Intensity of the Fourier transform of the recorded spectral interferograms. The three TESS satellites on either side of the sideband at $t=\mathrm{\Delta }\zeta =6$ ps, and next to the DC band at $t=0$ ps are indicated. (b) Waterfall plot of Fourier transformed interferograms for a range of cell pressures $P$. For each Fourier transform a $1.7\mu \text{m}$ wide strip, centered on the peak of the satellite, is shown. The dashed line shows a parabolic fit to the satellite-to-sideband separation, using the satellites on the left side of the sideband. The above plots are shown using a logarithmic intensity scale.

Figure 8

Plot showing a fit to the temporal separation $\tau$ between the sideband and the TESS satellites as a function of plasma density. The red points assume that the pressure in the cell is that measured by the gauge, $P_{\text{meas}}$; the blue points assume that the true pressure in the cell is given by $P_{\text{cell}}=\alpha P_{\text{meas}}-P_0$. For both plots that the electron density is calculated assuming complete ionization of the H2 gas at the corresponding pressure. The horizontal error bars correspond to the pressure resolution of 1 mbar of the pressure gauge, and the vertical bars show the estimated error of the TESS satellite location. The solid (dashed) line shows a fit to the red (blue) points of the form $\tau ={\omega }_{\mathrm{pe}}{\phi }^{\left(2\right)}$.