When an intense laser pulse interacts with homogeneous plasma embedded in a transverse magnetic field, transverse current density oscillating with frequency twice that of the laser field is set up. This leads to generation of second harmonic radiation with significant conversion efficiency.
In this paper, evolution of spot size of an intense laser beam in cold, underdense, magnetized plasma has been studied. The plasma is embedded in a uniform magnetic field perpendicular to both, the direction of propagation and electric vector of the radiation field. Nonlinear current density is set up and the source dependent expansion method is used to determine the evolution of the spot size of a laser beam having a Gaussian profile. It is shown that transverse magnetization of plasma enhances the self-focusing property of the laser beam leading to reduction in critical power required to self-focus the beam.
A one-dimensional numerical model to study the evolution of longitudinal electrostatic wakefields, generated by propagation of a circularly polarized laser pulse in magnetized plasma has been presented. The direction of the external magnetic field is considered to be along as well as opposite to the axis of propagation of the laser pulse. Further, two-dimensional particle-in-cell code is used to obtain the generated wakefields. Separatrix curves are plotted to study the trapping and energy gain of an externally injected test electron, by the generated electrostatic wakefields, in the relativistic regime. Under appropriate conditions, an enhancement in the peak energy of an externally injected electron in magnetized plasma, as compared to the unmagnetized case, has been observed.
In this paper, evolution of the spot size of an intense laser beam propagating in axially magnetized, cold, underdense plasma has been studied. The effect of longitudinal magnetization on the laser spot for a left as well as a right circularly polarized laser beam has been considered. Critical power for nonlinear self-focusing of the beam in magnetized plasma has been obtained.
For a one-parameter family of simple metrics of constant curvature (4 for 2 . 1; 1/) on the unit disk M , we first make explicit the Pestov-Uhlmann range characterization of the geodesic X-ray transform, by constructing a basis of functions making up its range and co-kernel. Such a range characterization also translates into moment conditions à la Helgason-Ludwig or Gel'fand-Graev. We then derive an explicit Singular Value Decomposition for the geodesic X-ray transform. Computations dictate a specific choice of weighted L 2 L 2 setting which is equivalent to the L 2 .M; dVol / ! L 2 .@ C SM; d † 2 / one for any 2 . 1; 1/.
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