Cold Collisionless Plasma Research Articles

Propagation of twisted laser carrying orbital angular momentum in magnetized plasma

The propagation of electromagnetic beams carrying orbital angular momentum l is investigated in a cold collisionless plasma where a static magnetic field is applied in the axial direction. The relativistic and ponderomotive nonlinearities are taken into consideration simultaneously. A stationary nonlinear Schrödinger equation is derived using the Wentzel–Kramers–Brillouin method and the slowly varying envelope approximation. The critical condition for the self-trapped mode is achieved as a function of orbital angular momentum (OAM), magnetic field, and initial laser intensity of the beam. The response of the medium to the two types of polarizations, i.e., left circular polarization (LCP) and right circular polarization (RCP), is compared, and it is observed that the RCP laser shows better focusing than the LCP laser and also requires a smaller beam radius for achieving the self-trapped mode. The effect of applied magnetic field and OAM of the laser is also studied on the beam width evolution. The laser is found to be focused earlier in the cases of a larger applied magnetic field. A Laguerre–Gaussian laser with higher OAM is observed to show efficient self-focusing. This study enables exploration in the fields of particle acceleration, electron bunch generation, x-ray sources, and more.

Geomagnetic Effect of the Atmospheric Acoustic Resonance Excited by Earthquakes and Volcano Eruptions

AbstractAn analytical model of the vertical acoustic resonance between the thermosphere and the earth's surface and its geomagnetic effect has been constructed. Resonance with a frequency of several mHz occurs when an atmospheric acoustic wave (AW) is excited by vibrations of the earth or ocean surface. The derived analytical relationships give a possibility to examine the dependence of the fundamental resonant frequency on the height of the reflecting atmospheric layer and horizontal AW number. Geomagnetic disturbances caused by the impact of AW on the ionosphere are calculated within the framework of a multi‐layered model of the ground‐atmosphere‐ionosphere system. The E‐layer of the ionosphere is treated in the approximation of a thin layer with an inclined geomagnetic field, while the topside ionosphere is assumed to consist of a cold collisionless plasma. The dependence of the spectral power of magnetic perturbations on the direction of the horizontal AW propagation is examined. The magnetic perturbation spectra are shown to have maxima at frequencies close to the acoustic resonance frequency. The spectral powers of magnetic perturbations and barometric variations measured during the Iwate‐Miyagi Nairik earthquake are in accordance with the model predictions for realistic media and AW parameters. Field‐aligned currents that arise when AWs enter the ionospheric E‐layer is shown to carry measurable electromagnetic disturbances into the geomagnetically conjugated region.

TWO-STREAM NONLINEAR LANGMUIR OSCILLATIONS

Langmuir oscillations of a large amplitude in a cold collisionless plasma are considered in this work. We passed to the conclusion that multiple streams is an inevitable feature of the Langmuir oscillations in the cold collisionless inhomogeneous plasma with resonant point even in the low-signal limit. By extending the equation of the cold plasma oscillations on the multi-stream regimes, we find two-stream modes in the homogeneous plasma, which are stationary solutions of this equation.

Impact of wiggler magnetic field on wakefield generation and electron acceleration by Gaussian, super-Gaussian and Bessel–Gaussian laser pulses propagating in collisionless plasma

In this research, the process of electron acceleration and wakefield generation by Gaussian-like (GL), super-Gaussian (SG) and Bessel–Gaussian (BG) laser pulses through cold collisionless plasma in the presence of a planar magnetostatic wiggler are studied. Three different types of laser spatial profiles, GL, SG and BG, are considered. Additionally, using the hydrodynamics fluid equations, Maxwell's equations as well as the perturbation technique for GL, SG and BG laser pulses in the weakly nonlinear regime and in the presence of a planar magnetostatic wiggler, governing equations for analysing the laser wakefield and electron acceleration have been derived and compared correspondingly. In addition, the effect of some important factors, including the wiggler field strengths, laser intensity, pulse length, plasma electron density and laser frequency on the wakefield and the electron energy gain, have been investigated. Numerical results show that enhancing the wiggler magnetic field results in an increase in the amplitude of the wakefield. Furthermore, it is observed that in comparison with the wakefield amplitude excited by SG and GL laser pulses, the amplitude of the wakefield excited by BG laser pulse is larger when the wiggler field is enhanced. Moreover, it is realized that the type of the laser profile, selected laser parameters and wiggler magnetic field are the most decisive and effective factors in the wakefield amplitude and shape of wakefield generation through cold collisionless plasma. Also, it is seen that as the pulse length declines, the amplitude of the wakefield increases, and correspondingly the resonance positions shift to higher ${({\varOmega _w}/{\varOmega _p})_{max}}$ values.

Second harmonic generation of high power Cosh-Gaussian beam in cold collisionless plasma

The purpose of this study is to explore the second harmonic generation (SHG) of a high power Cosh-Gaussian beam in cold collisionless plasma. The ponderomotive force causes carrier redistribution from high field to low field region in presence of a Cosh-Gaussian beam thereby producing density gradients in the transverse direction. The density gradients so produced the results in electron plasma wave (EPW) generation at the frequency of the input beam. The EPW interacts with the input beam resulting in the production of 2nd harmonics. WKB and paraxial approximations are employed for obtaining the 2nd order differential equation describing the behavior of the beam’s spot size against normalized distance. The impact of well-established laser-plasma parameters on the behavior of the beam’s spot size and SHG yield are also analyzed. The focusing behavior of the beam and SHG yield is enhanced with an increase in the density of plasma, the radius of the beam and the decentred parameter, and with a decrease in the intensity of the beam. The results of the current problem are really helpful for complete information of laser-plasma interaction physics.

Analogy between electro-magnetic waves in cold unmagnetized plasma and shallow water inertio-gravity waves in geophysical systems

The fundamental dispersion relation of transverse electro-magnetic waves in a cold collisionless plasma is formally equivalent to the two-dimensional dispersion relation of inertio-gravity waves in a rotating shallow water system, where the Coriolis frequency can be identified with the plasma frequency, and the shallow water gravity wave phase speed plays the role of the speed of light. Here we examine this equivalence and compare between the propagation wave mechanisms in these seemingly unrelated physical systems.

Simulation of Velocity Evolution of a Cold Collision-less Non-Magnetised Plasma by Particle-in-Cell Method

This work presents simple numerical simulation algorithm to analyse the velocity evolution of high density non-magnetized glow discharge (cold) collision-less plasma using Particle-in-Cell (PIC) method. In the place of millions of physical electrons and background ions, fewer particles called super particles are used for simulation to capture the plasma properties such as particle velocity, particle energy and electrical field of the plasma system. The plasma system which is of interest in this work is weakly coupled plasma having quasi-neutrality nature. Simulation results showed symmetric velocity distribution about zero with slight left skewness, indicating static system. The order of directional velocity of individual particle seems to agree with the input electron temperature of the considered plasma system. The particle and field energy evolution were observed having fluctuations about zero which indicates that the system is equilibrating. This work marks the preliminary work to study the transport of plasma species in plasma column of gliding arc discharge.

Distortion of a twisted beam passing through a plasma layer.

In this paper, we explore what happens to the intensity profile, phase distribution, and centroid position of a vortex beam (VB) when it passes through a cold collision-less magnetized plasma layer. For this purpose, we utilize angular spectral expansion accompanied by a 4×4 matrix method to obtain the total transmission coefficient, intensity and phase profiles, and centroid shifts of VBs in the output plane. Based on numerical analyses, it is found that the evolution of transverse intensity as well as the distortion of the phase profile of transmitted VBs are greatly affected by variation of radial and angular mode numbers, external magnetic field, plasma number density, and incident angle. In addition, displacement of the VB centroid under variation of angular mode numbers is presented quantitatively. It is expected that the results of this study will give more insight into VB communication, radar probing, and plasma diagnostics.

Transient setting of relativistic ponderomotive non-linearity and filamentation of ultra-short laser pulses in collisionless plasmas

AbstractWe study the setting up of relativistic ponderomotive non-linearity in an under-dense collisionless cold plasma. Using the fluid model, coupled system of equations of the laser beam and electron plasma oscillations has been derived. We present the numerical simulation for this coupled system of equations, when the coupling arises through relativistic ponderomotive non-linearity. The filamentation of the laser beam has been found to vary appreciably with perturbation wave number. The results show that with time, localized structures become more complex and the plasma oscillation frequency spectra have several harmonic peaks at terahertz frequencies when the electron plasma frequency is in terahertz range and laser frequency is around 2.35 × 1015 rad/s. We also present the semi-analytical model to capture the underlying physics.

Analytical study of resonant optical solitons with variable coefficients in Kerr and non-Kerr law media

In this article, the extended trial approach has been used for the investigation of traveling wave solutions of resonant nonlinear Schrodinger equation with variable coefficients depending upon time in the presence of different effects such as Kerr law and parabolic law nonlinearity including a Bohm potential term. Many new soliton solutions such as bright, dark, singular and rational function solutions are obtained. This technique proves to be an advantageous and powerful mathematical tool for establishing abundant exact traveling wave solutions in mathematical physics and plasma. The resonant nonlinear Schrodinger’s equation, in specific, governs the propagation of soliton in both quantum potential and uniaxial waves in a cold collisionless plasma.

Poynting vector and wave vector directions of equatorial chorus

AbstractWe present new results on wave vectors and Poynting vectors of chorus rising and falling tones on the basis of 6 years of THEMIS (Time History of Events and Macroscale Interactions during Substorms) observations. The majority of wave vectors is closely aligned with the direction of the ambient magnetic field (B0). Oblique wave vectors are confined to the magnetic meridional plane, pointing away from Earth. Poynting vectors are found to be almost parallel to B0. We show, for the first time, that slightly oblique Poynting vectors are directed away from Earth for rising tones and toward Earth for falling tones. For the majority of lower band chorus elements, the mutual orientation between Poynting vectors and wave vectors can be explained by whistler mode dispersion in a homogeneous collisionless cold plasma. Upper band chorus seems to require inclusion of collisional processes or taking into account azimuthal anisotropies in the propagation medium. The latitudinal extension of the equatorial source region can be limited to ±6∘ around the B0 minimum or approximately ±5000 km along magnetic field lines. We find increasing Poynting flux and focusing of Poynting vectors on the B0 direction with increasing latitude. Also, wave vectors become most often more field aligned. A smaller group of chorus generated with very oblique wave normals tends to stay close to the whistler mode resonance cone. This suggests that close to the equatorial source region (within ∼20∘ latitude), a wave guidance mechanism is relevant, for example, in ducts of depleted or enhanced plasma density.

Nonlinear Interaction of High Power Elliptical Laser Beam with Cold Collisionless Plasma

In the present paper, nonlinear interaction of high power elliptical laser beam with cold collisionless plasma is investigated by taking in to account ponderomotive nonlinearity. Nonlinear differential equations for the beam width parameters of semi-major axis and semi-minor axis of elliptical laser beam have been set up and solved numerically to study the variation of beam width parameters with normalized distance of propagation. Effects of variation in laser intensity, plasma density and plasma temperature on the beam width parameters are also analyzed.

Solitary fast magnetosonic waves propagating obliquely to the magnetic field in cold collisionless plasma

Solutions describing solitary fast magnetosonic (FMS) waves (FMS solitons) in cold magnetized plasma are obtained by numerically solving two-fluid hydrodynamic equations. The parameter domain within which steady-state solitary waves can propagate is determined. It is established that the Mach number for rarefaction FMS solitons is always less than unity. The restriction on the propagation velocity leads to the limitation on the amplitudes of the magnetic field components of rarefaction solitons. It is shown that, as the soliton propagates in plasma, the transverse component of its magnetic field rotates and makes a complete turn around the axis along which the soliton propagates.

Penetration of a radio frequency electromagnetic field into a magnetized plasma: one-dimensional PIC simulation studies

Penetration of a radio frequency (rf) electromagnetic field into a magnetized plasma is discussed by performing one-dimensional particle-in-cell (PIC) simulations. We consider two models: an electrostatic (ES) model using an external rf voltage and an electromagnetic (EM) model using an external rf current. The background magnetic field is perpendicular to the one-dimensional system. In the ES model, the external rf voltage across the plasma produces the rf electric field into the plasma. When ω rf =Ω e /2, where ω rf and Ω e are the externally applied field and electron gyrofrequencies, respectively, the ion-rich sheath is formed due to the electron wall loss caused by the electron polarization drift. When ω rf =ω LH /2, where ω LH is the lower hybrid frequency, the electron-rich sheath is formed due to the ion wall loss caused by its larger gyroradius than the electron. In the EM model, an induced electromagnetic field via the external rf current forms a standing wave in the plasma region bounded by the external antennas. When the diameter of the plasma is equal to the wave length, the spatial/temporal profiles of the rf standing waves are well explained by a cold collisionless plasma linear theory except for the existence of the sheath. When the rf magnetic field is increased to 10 % of the background magnetic field, the waveforms become irregular and complex because of the boundary effects.

An analysis of higher order terms for ion-acoustic waves by use of the modified Poincaré-Lighthill-Kuo method

In this work, by utilizing the modified Poincare-Lighthill-Kuo (PLK) method, we studied the propagation of weakly nonlinear waves in a collisionless cold plasma and obtained the governing evolution equations of various order terms in the perturbation expansion. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is exactly the same with those of the modified reductive perturbation and re-normalization methods. The method presented here is quite simple and based on introducing a new set of stretched coordinates.

Equivalent Circuit Model for the Electric Field Sensitivity of a Magnetic Search Coil of Space Plasma

Magnetic search coils (MSCs) are sensitive to both magnetic and electric fields, but detecting electric fields is unnecessary for magnetic observations of plasma waves. However, it is important to evaluate both sensitivities for different geometries and electrostatic shields to avoid electric field pickup. An equivalent circuit model for the electric field sensitivity of an MSC in a collisionless isotropic cold plasma is developed here using electrical coupling through a sheath capacitance. That sensitivity is defined by a relationship between the MSC impedance and the sheath capacitance. To confirm the validity of the circuit model, the sensitivity to an electric field is measured by imposing an external electric field using charged parallel metallic plates in laboratory experiments. The coupling capacitance between the MSC and charged plates is equivalent to the sheath capacitance in a space plasma. The measured results show good agreement with an approximate expression deduced from the equivalent circuit model.

Energy Distribution Along the Focal Axis of a Metallic Cylindrical Parabolic Reflector Covered With a Plasma Layer

The deviation of the energy distribution along the focal axis of a long metallic cylindrical parabolic reflector, which on its surface contains a uniform cold collisionless plasma, is investigated. In addition, the effects of some physical parameters such as the plasma and wave frequencies and the thickness of plasma layer on this energy distribution and the reflected and the transmitted electromagnetic fields are studied. It is shown that the maximum value of the reflected intensity increases by increasing the incident wave frequency and by decreasing the plasma layer thickness and the plasma frequency.

Extended Reductive Perturbation Method and Its Relation to the Re-normalization Method

Abstract In this work, by utilizing the extended reductive perturbation method, we studied the propagation of weakly nonlinear waves in a collisionless cold plasma and formally obtained the governing evolution equations of various order terms in the perturbation expansion. The result obtained here is exactly the same with that of Kodama and Taniuti [5], who employed “so called” the re-normalization method. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is consistent with the results of Malfliet and Wieers [6], who employed the dressed solitary wave method and Demiray [7], who utilized the modified reductive perturbation method.

Integrability and soliton interaction of a resonant nonlinear Schrödinger equation via binary Bell polynomials

Under investigation in this paper is a resonant nonlinear Schrödinger equation for the response of a hypothetical resonance medium to an action of a quasimonochromatic wave or the propagation of one-dimensional long magnetoacoustic waves in a cold collisionless plasma subject to a transverse magnetic field. Binary Bell polynomials are employed to derive the bilinear form, Bäcklund transformation (BT) and Lax pair in the 3×3 matrix form. Two sets of the binary Bell polynomials are considered. Infinite conservation laws are also constructed from the BT in the binary-Bell-polynomial form. Moreover, two-soliton solutions are obtained through the Hirota method. Finally, the regular, intermediate-state and resonant soliton interactions are analyzed under certain conditions.

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.