Relativistic Eulerian Vlasov simulations of the amplification of seed pulses by Brillouin backscattering in plasmas

Abstract

We apply an Eulerian Vlasov code to study the amplification by Brillouin scattering of a short seed laser pulse by a long pump laser pulse in an underdense plasma. The stimulated Brillouin backscattering interaction is the coupling of the pump and seed electromagnetic waves propagating in opposite directions, and the ion plasma wave. The code solves the one-dimensional relativistic Vlasov-Maxwell set of equations. Large amplitude ion waves are generated. In the simulations we present, the density plateau of the plasma is n e ¼ 0:3 n c (n c is the critical density), which excludes spurious stimulated Raman scattering amplification (which can occur only if n e < n c =4). We also varied the duration and/or amplitude of the short input seed pulse to study how these influence its subsequent behaviour. An initially broad pulse grows more rapidly than an initially narrow pulse. Furthermore, for an initially broader seed pulse, towards the end of the simulation, it is seen to become narrower and to gradually detach from the trailing signal. On the contrary, initially very narrow seed pulses are seen to broaden. The absence of noise in the Vlasov simulations allows to simulate long plasma amplifier lengths, and to follow the evolution of the system with a fully kinetic description and with an accurate representation of the phase-space structures of distribution function. V C 2015 AIP Publishing LLC. [http://dx.

Numerical simulation of Raman and Brillouin laser-pulse amplification in a magnetized plasma

“…Eulerian Vlasov codes have been successfully applied to the problem of the plasma-based laser-pulse amplifiers in the absence of an external magnetic field, for the problems of the backward SRS and SBS (Lehmann et al, 2012Shoucri et al, 2014Shoucri et al, , 2015Toroker et al, 2014). They have also been successfully applied to the problem of wakefield accelerators in an un-magnetized plasma (Shoucri, 2008b).…”

“…In the PIC simulation results for seed-pulse amplification presented by Andreev et al (2006) for instance, the length of the plasma amplifier had to be restricted due to the intrinsic numerical noise, because otherwise the pump would have been depleted by Brillouin scattering on the thermal noise, which is intrinsic in PIC simulations. The parameters of Humphrey et al (2013) were used in a simulation with a Vlasov code by Shoucri et al (2015), who showed the Vlasov code produced much more favorable results. The parameters of Humphrey et al (2013) were used in a simulation with a Vlasov code by Shoucri et al (2015), who showed the Vlasov code produced much more favorable results.…”

Short-pulse amplification by strongly coupled stimulated Brillouin scattering

“…a greater degree of pump depletion is obtained [45,46,57], (3) SBS is more robust than SRS to plasma inhomogeneities in density or temperature [3,39,45,51], (4) SBS is better suited for producing pulses with high total power or energy, in part because the lower sensitivity to inhomogeneity allows larger diameter plasmas to be used [51], (5) only SBS may be used in the regime 0.25 < N < 1 [52], (6) the duration of a Brillouin-amplified pulse can be shortened to within a factor of 8 of that for a Raman compressed pulse [3], suggesting that the two methods are capable of comparable pulse-compression, (7) a shorter interaction length is required for SBS because the energy transfer is fast [3,45,57], which is sometimes quantified as SRS requiring mm to cm scale plasmas whereas SBS can be conducted in 100 µm [46], and (8) SBS may be viable in regimes where SRS is limited by particle trapping and wavebreaking [3] and can therefore support pump amplitudes several orders of magnitude higher than SRS [59]. Additionally, we make the argument (9) that SBS may be appropriate in regimes where Langmuir waves would be collisionally damped.…”

“…The differences between SRS and SBS have been articulated with varying degrees of rigor, though direct comparisons appear mostly in literature on SBS, where the following advantages for Brillouin amplification over Raman amplification have been presented: (1) the pump and seed lasers may have almost the same frequency [3,39,45,48,49,57,59], (2) energy loss to the plasma wave, which results from conservation of energy and is described by the Manley-Rowe relations, may be lower for SBS than for SRS, [3,39,46,52], i.e. a greater degree of pump depletion is obtained [45,46,57], (3) SBS is more robust than SRS to plasma inhomogeneities in density or temperature [3,39,45,51], (4) SBS is better suited for producing pulses with high total power or energy, in part because the lower sensitivity to inhomogeneity allows larger diameter plasmas to be used [51], (5) only SBS may be used in the regime 0.25 < N < 1 [52], (6) the duration of a Brillouin-amplified pulse can be shortened to within a factor of 8 of that for a Raman compressed pulse [3], suggesting that the two methods are capable of comparable pulse-compression, (7) a shorter interaction length is required for SBS because the energy transfer is fast [3,45,57], which is sometimes quantified as SRS requiring mm to cm scale plasmas whereas SBS can be conducted in 100 µm [46], and (8) SBS may be viable in regimes where SRS is limited by particle trapping and wavebreaking [3] and can therefore support pump amplitudes several orders of magnitude higher than SRS [59].…”

“…approximately six times longer than the inverse frequency, so the actual limit on pulse duration may be somewhat longer than the inverse frequencies in Fig. 4. B. Brillouin Scattering Growth Rate (7) The assertion that amplification by stimulated Brillouin scattering requires a plasma of shorter length than that necessary for SRS because the energy transfer is faster [3,45,57] demands some care. In the linear regime, the degree of amplification is set by the growth rate and the amplification distance, so this is fundamentally a statement about the respective growth rates of Raman and Brillouin scattering.…”