UCLA

The nonlinear optics of plasmas (NLOP) is a fundamental topic within plasma physics. A sub-area of NLOP is laser-plasma interactions (LPI) that involve three-wave coupling. Three wave LPI processes are of interest for inertial fusion energy (IFE) and are a fundamental nonlinear plasma physics research area. Stimulated Raman scattering (SRS) is one LPI of interest where an incident pump laser decays into a scattered electromagnetic wave (EM) and an electron plasma wave (EPW). There is much interest in SRS backscatter where the direction of the scattered EM wave is opposite that of the pump. Much previous research on SRS has involved the study of how plane waves propagate in plasmas. However, in IFE the lasers are broken up into multiple finite-width and length speckles which are related to Gaussian-limited laser pulses, which can be decomposed into Laguerre-Gaussian modes. A Laguerre-Gaussian mode can have orbital angular momentum (OAM).The interaction of finite-width Gaussian laser pulses with plasmas is investigated through theory, fluid simulations, and fully kinetic particle-in-cell simulations. As a starting point, the reasoning for why a finite-width laser can have orbital angular momentum in vacuum is carefully reviewed, including the conclusion that within a Laguerre-Gaussian mode defined by a spot size w0 with an angular dependence e iℓφ each photon has an angular momentum ℓℏ. This is referred to as the photon’s orbital angular momentum (OAM). The properties of Laguerre-Gaussian modes are examined in terms of the laser’s power, peak intensity, and spot size. The regimes of growth for one-dimensional SRS backscatter are also outlined and reviewed. A regime of interest for IFE is the strongly damped regime where damping of the EPW is sufficiently large that its spatio-temporal growth is altered.Starting from the coupled envelope equations for SRS in a uniform plasma within the paraxial ray approximation including a phenomenological damping term for the EPW, multidimensional conservation laws for wave action, energy, axial and transverse momentum, and angular momentum are derived. Sink terms for the otherwise conserved quantities from the EPW damping are included. The expression for OAM in SRS is shown to be the sum over the OAM expression for each of the three waves. The expression for the OAM of each of the EM waves in plasma is identical to the known expressions for an EM wave in vacuum. In normalized units the OAM of the EPW has the same form as that for the EM wave. However, for the EPW the OAM is shown to be the result of the angular momentum of the currents within the finite-width wave and not from the Poynting flux as is the case for the EM waves.It is shown that conservation of energy and momentum are equivalent to ω and k matching of the three waves because ω and k are constant properties of the carrier and not the envelope. A general wave is not a pure azimuthal harmonic so an effective or average ℓ is defined. The average ℓ number is a property of the envelope and not the carrier of the wave. It is thus argued that ℓ matching is not an absolute concept and is only true when the ℓ of each wave is constant.Simulations of SRS of a single Gaussian speckle are studied using the fluid code pF3D which solves the three coupled envelope equations for SRS and the fully kinetic particle-in-cell code OSIRIS. Results from an ensemble of pF3D simulations are presented that explore the effects of OAM, intensity, power, and spot size of the laser, as well as the temperature of the plasma which controls the dimensionless parameter, kλD, which is a key determiner of the collisionless damping of the plasma wave where k is the wavenumber of the plasma wave and λD is the Debye length. The pF3D simulations show that for both SRS growing from noise or well-defined seeds, OAM can be transferred from the pump to the decay EM and EPW waves. It is found that the degree of SRS growth is mostly determined by the peak intensity of the Laguerre-Gaussian mode indicating that for constant power and spot size, SRS is reduced for pumps with larger ℓ numbers. Conservation of the effective ℓ number arises for pumps with the highest intensities and the decay waves are not pure LaguerreGaussian modes even when the effective ℓ number is near an integer. When SRS grows from a well-defined seed and the reflectivity is low the EM mode often has no OAM.Fully kinetic particle-in-cell (PIC) simulations of SRS from a single Gaussian speckle reveal a different behavior. For pumps without OAM, SRS grows more rapidly with higher peak and average reflectivity for otherwise similar parameters in the PIC simulations, and it comes in narrower and more intense bursts. However, the trend that SRS reflectivity is reduced for pumps with OAM and fixed laser power and spot size is also seen in PIC simulations. OAM is seen to be transferred from the pump to the scattered light wave and angular momentum is transferred to the particles. In cases where the pump has OAM, no obvious additional kinetic effects of the EPW are observed.