Optimization of plasma amplifiers

Plasma amplifiers offer a route to side-step limitations on chirped pulse amplification and generate laser pulses at the power frontier. They compress long pulses by transferring energy to a shorter pulse via the Raman or Brillouin instabilities. We present an extensive kinetic numerical study of the three-dimensional parameter space for the Raman case. Further particle-in-cell simulations find the optimal seed pulse parameters for experimentally relevant constraints. The high-efficiency self-similar behavior is observed only for seeds shorter than the linear Raman growth time. A test case similar to an upcoming experiment at the Laboratory for Laser Energetics is found to maintain good transverse coherence and high-energy efficiency. Effective compression of a $10\mathrm{kJ}$, nanosecond-long driver pulse is also demonstrated in a 15-cm-long amplifier.

Figure 1

Schematic of the Raman amplifier scheme in an underdense plasma, where the long pump pulse (dashed) counterpropagates with a short seed pulse (solid line) downshifted from the pump by the plasma frequency. To achieve high-energy transfer and pump depletion, as shown here, Eq. (4) must be satisfied.

Figure 2

Simulated energy transfer efficiency of Raman compression, including kinetic effects, for the three different electron temperatures of (a) $0\mathrm{eV}$, (b) $100\mathrm{eV}$, and (c) $400\mathrm{eV}$. The plots show the maximal amplifier efficiency in the nonlinear regime, as found from 1200 one-dimensional particle-in-cell simulations covering the parameter space. The pump pulse dimensionless amplitude is $a_{\mathrm{pump}}$ and the plasma electron density $n$ is normalized to the pump pulse critical density. Above the theoretical Langmuir wave-breaking threshold for cold plasma (blue solid line), the amplifier efficiency rapidly decreases.

Figure 3

Investigation of the optimal seed pulse with six one-dimensional PIC simulations. The plasma had zero temperature and constant density $n=n_{\mathrm{crit}}/100$, with constant pump amplitude $a_{\mathrm{pump}}=0.003$. The development of six seed pulses, varied in initial duration at constant energy, is shown with a separate color for each seed pulse. (a) The development of the duration versus the dimensionless peak amplitude of each seed on logarithmic scales. Equation (4) is shown by the black line. The total propagation time was $60000{\omega }^{-1}$ for each seed pulse. (b) The energy transfer efficiency from the pump to the main peak of the seed pulse, as a function of propagation time. Note that the peak efficiency of 0.6 agrees with Fig. 2.

Figure 4

(a, b) A two-dimensional simulation of a primary stage amplifier with finite focal length, demonstrating that the process is possible in a focusing geometry and that transverse coherence is retained. Panel (a) shows the amplified pulse at the time of best focus in vacuum, propagating upwards, whereas panel (b) compares this transverse profile (at the position of peak intensity) with that of the seed pulse focused with no plasma interaction. The plasma profile had the form $1.5\times {10}^{19}exp[-{(x/2\mathrm{mm})}^6]/{\mathrm{cm}}^3$, meaning $n/n_{\mathrm{crit}}=0.015$, with fixed temperature $400\mathrm{eV}$. The seed and pump were Gaussian in space and time, with durations $50\mathrm{fs}$ and $25\mathrm{ps}$, wavelengths 1200 and $1054\mathrm{nm}$, both with peak intensity $3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ in the plasma $\left(a_{\mathrm{pump}}=0.016\right)$. Both pulses had transverse width $800\mu \mathrm{m}$ in the plasma and focus $15\mathrm{mm}$ beyond the plasma. (c) Output similar to the first-stage amplifier in (a), albeit at a shorter wavelength, is used to seed a larger secondary stage amplifier using the seed ionization scheme, simulated in one dimension. The simulation used a $10\mathrm{kJ},1\mathrm{ns},1054\mathrm{nm}$ pump pulse at ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and a $15\mathrm{J},50\mathrm{fs},1081\mathrm{nm}$ seed pulse at $3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The electron density was $6\times {10}^{17}/{\mathrm{cm}}^3(n/n_{\mathrm{crit}}=0.0006)$ across a $1\times 1\times 15\mathrm{cm}$ region. The intensity across the space time diagram is shown in a frame moving right, at the group velocity of the amplified pulse.