Propagation Dynamics Of An Annular Laser Beam In A Parabolic Plasma Channel

With the development of laser technology,various annular laser beams are produced one after another,and a new type of laser is being formed gradually.For the propagation dynamics of annular laser,there are two main concerns at present.One is the propagation dynamics of annular hollow laser beam,the other is the ring formation dynamics of non-annular laser beam in the propagation process.The annular hollow laser beam is a kind of annular beam with zero central intensity.Recently,the annular hollow laser beam with cylindrical vector polarization,especially the radially and azimuthally polarized annular hollow laser beam,has attracted more attention because of the polarization symmetry.As a kind of annular hollow laser beams,the azimuthally polarized first-order Bessel-Gauss laser beam with orbital angular momentum and nearly non-diffractive feature,is a closed-formed solution of the azimuthal paraxial scalar wave equation,and can be widely applied in the field of plasmas,such as particle acceleration and harmonic generation,etc.Therefore,it is very meaningful to study the propagation dynamics of an azimuthally polarized annular hollow laser beam described by a first-order Bessel–Gauss laser beam in plasmas.The ring formation during the propagation of non-annular laser beam may degenerate into filaments under certain conditions,that is to say,the formation of ring is closely related to the filaments.In the field of plasmas,laser beam filament plays an important role in compression process of fast ignition due to the increase of local laser intensity.However,the high intensity filaments can induce stimulated Raman back scattering in plasmas,and it is harmful in the laser energy deposition into the target during the inertial confinement fusion process,so the filament of laser beam and control of stimulated Raman back scattering in plasmas are essential to the success of inertial confinement fusion experiments.Therefore,it is of great physical significance to study the ring formation dynamics of laser beam propagating in plasmas.In this paper,the propagation dynamics of an azimuthally polarized annular hollow laser beam described by a first-order Bessel-Gauss laser beam in a parabolic plasma channel is investigated theoretically and numerically.In theory,the relationship between the ring-beam radius and thickness of a first-order Bessel–Gauss laser beam is given for the first time and their evolution equations are both obtained.It is found that the azimuthal polarization can weaken the vacuum diffraction effect,and the evolution of this annular hollow laser beam may be classified into three typical types,i.e.,propagation with a constant ring-beam radius and thickness,or synchronous periodic defocusing oscillation,or synchronous periodic focusing oscillation.Their corresponding critical conditions and characteristic quantities,such as the amplitudes and spatial wavelengths,are obtained.Further investigation indicates that,with the increase in the initial laser power or the ratio of initial ring-beam radius to channel radius,the laser beam may experience a process from synchronous periodic defocusing oscillation to constant propagation and then to synchronous periodic focusing oscillation,in which the corresponding amplitudes decrease sharply to zero(constant propagation)and then increase gradually,while the spatial wavelength decreases continuously.The evolution type of this annular hollow beam also depends on its initial amplitude but is insensitive to the initial laser profile which,however,has a large influence on the spatial wavelength.These results are well confirmed by the numerical simulation of the wave equation.A two-dimensional particle-in-cell simulation of an azimuthally polarized laser beam is performed finally and also reveals the main results.Secondly,the ring formation dynamics of laser beam propagating in a parabolic plasma channel is studied within considering relativistic,ponderomotive and preformed plasma channel effects.Under the paraxial condition,the evolution equation of laser width parameter,the corresponding dielectric function and condition of ring formation are obtained by means of the high order paraxial theory.The corresponding parameter region of ring formation is given numerically.It is found that the parameter region of ring formation in the parabolic plasma channel is larger than that in the uniform plasma,and the parameter region becomes smaller with the increase of the channel radius or initial axial electron density.In addition,the formation and evolution of ring during the propagation of laser beam in the parabolic plasma channel is studied.It is noted that the laser beam forms a ring gradually after defocusing.With the increase of the propagation distance,the radius of ring becomes larger gradually,and the peak value of ring is stronger,while the central intensity of laser beam is gradually weaker.Further studies show that the ring formation of laser beam in the parabolic plasma channel is later than that in the uniform plasmas,and the ring formation in channel is promoted with the increase of channel radius,initial axial electron density,initial laser intensity or width.