Source Dependent Expansion Method Research Articles

Investigation of self-focusing of Gaussian laser beams within magnetized plasma via source-dependent expansion method

Self-focusing emerges as a nonlinear optical phenomenon resulting from an intense laser field and plasma interaction. This study investigates the self-focusing behavior of Gaussian laser beams within magnetized plasma environments utilizing a novel approach, source-dependent expansion. By employing source-dependent expansion, we explore the intricate dynamics of laser beam propagation, considering the influence of plasma density and external magnetic fields. The interplay between the beam's Gaussian profile and the self-focusing mechanism through rigorous mathematical analysis and numerical simulations, particularly in the presence of plasma-induced nonlinearities, is elucidated here. Our findings reveal crucial insight into the evolution of laser beams under diverse parameters, including the ponderomotive force, relativistic factors, plasma frequency, polarization states, external magnetic field, wavelength, and laser intensity. This research not only contributes to advancing our fundamental understanding of laser–plasma interactions but also holds promise for optimizing laser-driven applications.

Nonlinear self-focusing of an intense laser beam in non-Maxwellian plasma with a non-uniform magnetic field

The present article investigates the nonlinear self-focusing of an intense laser beam circularly polarized inside a non-Maxwellian magnetized plasma. It has been assumed that the plasma is embedded in a non-uniform axial magnetic field with a positive slope. Through applying relativistic fluid momentum and Maxwell's equations, the nonlinear equation of electromagnetic wave propagation for a circular polarized laser beam with right-and left-hand polarizations has been derived. Subsequently, a differential equation was obtained for the evolution of the laser spot-size through applying the source-dependent expansion method. The equation was then solved using the fourth-order Runge-Kutta method. Effects of the simultaneous presence of the superthermal particles and non-uniform magnetic field on the evolution of laser spot-size were studied, and variations of the normalized spot-size of the laser with respect to the variables κe and κi were discussed. It was also indicated that the solution of the present study confirms the results of the Maxwellian plasma in extreme conditions. Numerical results indicate that the self-focusing of the laser beam in the presence of an external nonuniform magnetic field inside non-Maxwellian plasma was improved in comparison with Maxwellian plasma. In addition, results show that an increase in the nonuniform external magnetic field leads to the reduction of the critical power required for the self-focusing of the laser beam inside the plasma.

Self-Focusing of High-Power Laser Beam Through Cold Uniform Magnetized Plasma

In present paper the determination of the spot size of an ultra-short laser beam in uniform magnetized plasma with a dominant cold plasma has been studied. The liner dispersion relation of the laser beam propagating in Magnetized plasma have been found. Magnetic field is set up and source dependent expansion method is applied to determining the spot size of the intense laser beam with gaussian profile. The transverse magnetization of plasma and its impact on the self-focusing property of the dense laser governing to reduction in critical power necessary to self-focusing beam is shown.

Evolution of intense laser pulse spot size propagating in collisional plasma embedded in magnetic field with variable direction

In this study, propagation of an intense laser pulse through collisional, homogenous, magnetized plasma has been investigated. The plasma is embedded in an external magnetic field with the amplitude and variable direction being constant. The complex dispersion relation of the plasma medium has been obtained that predicates the Faraday rotation effect. The paraxial wave equation has been used for the study of propagation of laser pulse in plasma. The nonlinear current density vector as a source of wave equation is obtained by motion equation and continuity equation of plasma free electrons. Using the source dependent expansion method, the evolution of laser pulse spot size has been investigated. It is shown that the spot size of the laser pulse is dependent on the strength and direction of the external magnetic field significantly. The effect of collision frequency on the evolution of spot size has been studied. The space damping rate of laser pulse power along the propagation length due to collision is obtained. Results show that the increase in the external magnetic field strength increases the rate of laser energy loss.

Nonlinear interaction of intense hypergeometric Gaussian subfamily laser beams in plasma

Propagation of Hypergeometric-Gaussian laser beam in a nonlinear plasma medium is investigated by considering the Source Dependent Expansion method. A subfamily of Hypergeometric-Gaussian beams with a non-negative, even and integer radial index, can be expressed as the linear superposition of finite number of Laguerre–Gaussian functions. Propagation of Hypergeometric-Gaussian beams in a nonlinear plasma medium depends on the value of radial index. The bright rings’ number of these beams is changed during the propagation in plasma medium. The effect of beam vortex charge number l and initial (input) beam intensity on the self-focusing of Hypergeometric-Gaussian beams is explored. Also, by choosing the suitable initial conditions, Hypergeometric-Gaussian subfamily beams can be converted to one or more mode components that a typical of mode conversion may be occurred. The self-focusing of these winding beams can be used to control the focusing force and improve the electron bunch quality in laser plasma accelerators.

Collisional effects on the modulational instability of intense laser pulses in magnetoactive plasmas

AbstractThe modulational instability associated with propagation of an intense laser pulse through a transversely magnetized plasma is investigated in the presence of collisional effects. The source-dependent expansion method for analyzing the wave equation is employed. The dispersion relation is obtained and modulational instability and its growth rate are studied. It is shown that in the absence of collisional effects the modulational instability is restricted to the small wavenumber region and the constant magnetic field reduces the growth rate of the instability. In contrast, in the collisional plasma, there is no upper limit of wavenumber for the existence of modulational instability. In addition, in this case, the growth rate of instability increases as the collision frequency goes up.

Noncollapsing vectorial twisted laser beam in plasma under the paraxial approximation

Using the source-dependent expansion method and the paraxial approximation, the evolution of the vectorial beam width in laser-plasma interaction is investigated. By considering parabolic nonlinearity, the self-focusing of the Laguerre-Gaussian beam in a plasma medium is studied. It is shown that, at self-focusing of the beam in a plasma with Kerr-type nonlinearity, the effect coming out from the divergence term dominates over modifications related to other vectorial effects. This term is interpreted as nonlinear diffraction which plays the role of an effective saturation. The effect of the vortex charge number l, initial (input) beam intensity and plasma temperature on self-focusing of the vectorial Laguerre-Gaussian beam is explored. Since the Laguerre-Gaussian modes can be used to control focusing forces and improve the electron bunch quality in laser-plasma accelerators, the condition for self-focusing of a doughnut vectorial beam in a Kerr-like plasma medium is established and the expression for critical power is obtained. Also, it is shown that vectorial effects lead to the arrest of catastrophic collapse, and a beam width focusing-defocusing oscillation can occur.

Analysis of twisted laser beam focusing and defocusing in plasma

Using the source dependent expansion method and paraxial approximation, the evolution of the beam spot size (BSS) in laser plasma interaction is investigated. Considering a collisionless mechanism, the self-focusing of a Laguerre–Gaussian (LG) light beam in a plasma medium is studied and the evolution of the BSS is solved analytically for the non-saturating nonlinearity state, and numerically for the saturating state. The self-focusing of a doughnut beam depends on the initial BSS, in which if the initial BSS gets bigger, the beam in the medium will be focused faster. We show that if the nonlinear effect of the plasma medium is saturated, the LG beam profile can remain stable and the BSS oscillates between two values as it propagates. Also, the condition for the self-focusing of the doughnut beam in non-saturating nonlinear plasma is established, and an expression for critical intensity is obtained.

Group velocity dispersion and relativistic effects on the wakefield induced by chirped laser pulse in parabolic plasma channel

The excitation of wake field plasma waves by a short laser pulse propagating through a parabolic plasma channel is studied. The laser pulse is assumed to be initially chirped. In this regard, the effects of initial and induced chirp on the plasma wake field as well as the laser pulse parameters are investigated. The group velocity dispersion and nonlinear relativistic effects were taken into account to evaluate the excited wake field in two dimension using source dependent expansion method. Positive, negative, and un-chirped laser pulses were employed in numerical code to evaluate the effectiveness of the initial chirp on 2-D wake field excitation. Numerical results showed that for laser irradiances exceeding 1018W/cm2, an intense laser pulse with initial positive chirp generates larger wake field compared to negatively and un-chirped pulses.

Self-focusing of intense high frequency electromagnetic waves in a collisional magnetoactive plasma

The self-focusing of an intense electromagnetic beam in a collisional magnetoactive plasma has been investigated by the perturbation method. Considering the relativistic and ponderomotive nonlinearities and the first three terms of perturbation expansion for the electron density and velocity, the nonlinear wave equation is obtained. This wave equation is solved by applying the source dependent expansion method and the evolution of electromagnetic beam spot-size is discussed. It is shown that the laser spot-size decreases with increasing the collision frequency and external magnetic field strength.

Intense laser beam guiding in self-induced electron cavitation channel in underdense plasmas

In underdense plasmas, the transverse ponderomotive force of an intense laser beam with Gaussian transverse profile expels electrons radially, and it can lead to an electron cavitation. An improved cavitation model with charge conservation constraint is applied to the determination of the width of the electron cavity. The envelope equation for laser spot size derived by using source-dependent expansion method is extended to including the electron cavity. The condition for self-guiding is given and illuminated by an effective potential for the laser spot size. The effects of the laser power, plasma density and energy dissipation on the self-guiding condition are discussed.

Self-focusing of intense laser beam in magnetized plasma

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.

Relativistic focusing and ponderomotive channeling of intense laser beams

The ponderomotive force associated with an intense laser beam expels electrons radially and can lead to cavitation in plasma. Relativistic effects as well as ponderomotive expulsion of electrons modify the refractive index. An envelope equation for the laser spot size is derived, using the source-dependent expansion method with Laguerre-Gaussian eigenfunctions, and reduced to quadrature. The envelope equation is valid for arbitrary laser intensity within the long pulse, quasistatic approximation and neglects instabilities. Solutions of the envelope equation are discussed in terms of an effective potential for the laser spot size. An analytical expression for the effective potential is given. For laser powers exceeding the critical power for relativistic self-focusing the analysis indicates that a significant contraction of the spot size and a corresponding increase in intensity is possible.

Laser pulse modulation instabilities in plasma channels

In this paper the modulational instability associated with propagation of intense laser pulses in a partially stripped, preformed plasma channel is analyzed. In general, modulation instabilities are caused by the interplay between (anomalous) group velocity dispersion and self-phase modulation. The analysis is based on a systematic approach that includes finite-perturbation-length effects, nonlinearities, group velocity dispersion, and transverse effects. To properly include the radial variation of both the laser field and plasma channel, the source-dependent expansion method for analyzing the wave equation is employed. Matched equilibria for a laser beam propagating in a plasma channel are obtained and analyzed. Modulation of a uniform (matched) laser beam equilibrium in a plasma channel leads to a coupled pair of differential equations for the perturbed spot size and laser field amplitude. A general dispersion relation is derived and solved. Surface plots of the spatial growth rate as a function of laser beam power and the modulation wave number are presented.

Self-focusing and guiding of short laser pulses in ionizing gases and plasmas

Several features of intense, short-pulse (/spl lsim/1 ps) laser propagation in gases undergoing ionization and in plasmas are reviewed, discussed, and analyzed. The wave equations for laser pulse propagation in a gas undergoing ionization and in a plasma are derived. The source-dependent expansion method is discussed, which is a general method for solving the paraxial wave equation with nonlinear source terms. In gases, the propagation of high-power (near the critical power) laser pulses is considered including the effects of diffraction, nonlinear self-focusing, ionization, and plasma generation. Self-guided solutions and the stability of these solutions are discussed. In plasmas, optical guiding by relativistic effects, ponderomotive effects, and preformed density channels is considered. The self consistent plasma response is discussed, including plasma wave effects and instabilities such as self-modulation. Recent experiments on the guiding of laser pulses in gases and in plasmas are briefly summarized.

Radio-frequency linac-driven free-electron laser configurations

Recent developments in accelerator technology and the optical guiding property of the free-electron laser (FEL) radiation indicate that rf linacs may be a strong contender for driving high average power FEL amplifiers. We discuss two rf linac-driven FEL configurations: the master oscillator power amplifier (MOPA) and the single-state power amplifier (SSPA). Our numerical results are obtained using the source-dependent expansion (SDE) method in the computer code shera. The SDE method and the code shera are discussed and illustrations of the MOPA and SSPA configurations presented.