Wake Potential Research Articles

Wake Potential for Dust Grains in a Flowing Plasma

The wake effect among dust grains in a flowing plasma is studied by the linear-response dielectric theory within the linear hydrodynamics model. The expression of potential is derived, and it can be divided into two parts: one is the screened Coulomb short-ranged repulsive potential, and the other is the long-ranged oscillatory wake potential. The numerical results show that both the amplitude and wavelength of the wake potential depend on the Mach number, in such a manner that the wavelength of the oscillating potential increases, while its amplitude decreases, with increasing Mach number.

Wakes in viscous quark-gluon plasma

With the dielectric function derived from the chromohydrodynamic approach, we investigate wakes in induced charge density and wake potential induced by a fast parton traveling through the viscous quark-gluon plasma (QGP). When the fast parton moves with a speed v = 0.55c which is less than the phase velocity of plasmon vp in QGP, the equicharge lines show a sign flip in the backward-forward spaces. While for v = 0.99c which is larger than vp, the equicharge lines show an oscillatory behavior. A Lennard-Jones potential and an oscillatory wake potential are found in the backward direction for v = 0.55c and v = 0.99c respectively. In addition, the viscous effect on wakes is also speed-dependent. When v = 0.55c, shear viscosity has a trivial impact on the wakes. While for v = 0.99c, shear viscosity modifies the strength and structure of the wakes significantly.

Energy levels of a heavy ion moving in dense plasmas

In this paper, the potential of a slowly moving test particle moving in collisional dense plasmas is studied. It is composed of the Debye-shielding potential, wake potential, and collision term. The Ritz variational-perturbational method is developed for calculating relativistic binding energy levels of a heavy ion moving in dense plasmas. Binding energy levels of a heavy ion moving in plasmas are calculated. The results show that both non-relativistic energy levels and relativistic energy levels become more negative as the temperature becomes high. They also become more negative as the number density decreasing. Relativistic correction is important for calculating binding energy levels. Both relativistic energy levels and non-relativistic energy levels vary minutely as the speed of heavy ion varies.

The plasma wake field excitation: Recent developments from thermal to quantum regime

AbstractTo describe the transverse nonlinear and collective self-consistent interaction of a long relativistic electron or positron beam with an unmagnetized plasma, a pair of coupled nonlinear differential equations were proposed by Fedele and Shukla in 1992 (Fedele, R. and Shukla, P. K. 1992a Phys. Rev. A 45, 4045). They were obtained within the quantum-like description provided by the thermal wave model and the theory of plasma wake field excitation. The pair of equations comprises a 2D Schrödinger-like equation for a complex wave function (whose squared modulus is proportional to beam density) and a Poisson-like equation for the plasma wake potential. The dispersion coefficient of the Schrödinger-like equation is proportional to the beam thermal emittance. More recently, Fedele–Shukla equations have been further applied to magnetized plasmas, and solutions were found in the form of nonlinear vortex states and ring solitons. They have been also applied to plasma focusing problems and extended from thermal to quantum regimes. We present here a review of the original approach, and subsequent developments.

Self-modulation of a long externally injected relativistic charged-particle beam in a laser wake field acceleration scheme. A preliminary quantum-like investigation

Recent investigations indicate that sufficiently long beams of charged particles, travelling in a plasma, experience the phenomenon of self-modulation. The self-modulation is driven by the plasma wake field excitation due to the beam itself, and it may become unstable under certain conditions. A preliminary theoretical investigation of the self-modulation of a relativistic charged-particle beam in overdense plasma in the presence of a preformed plasma wave is carried out, within the quantum-like description of charged particle beams provided by the Thermal Wave Model. A simple physical model for the self-modulation is put forward, described by a nonlinear Schrödinger equation coupled with the Poisson-like equation for the plasma wake potential (so-called Fedele–Shukla equations). The physical mechanism is based on the interplay of three concomitant effects, the radial thermal dispersion (associated with the emittance ε), the radial ponderomotive effects of a preexisting plasma wave (which provides the guidance for the beam), and the self-interaction of the plasma wake field generated by the beam itself.

Ion wake formation with dust charge fluctuation in complex plasma

In complex plasma, the interaction mechanism among dust grains near the plasma sheath is significantly influenced by the downward ion flow towards the sheath and dust charge fluctuation over grain surface. Asymmetric ion flow towards the sheath gives rise to well known attractive wake potential in addition to repulsive Yukawa type of potential. The present work shows that the charging dynamics play a significant role in modification of plasma dielectric response function and hence the interaction mechanism among test dust particulates. The effective Debye length is found to be a characteristic of dust size and background plasma response towards the grain along with ion flow speed. The potentials thus obtained show a damping in strength of interaction in the presence of dynamical charging of dust as compared to that of constant charge dust grains. The result also shows decrease in focal length of ion lensing with increase in grain size.

Resonance properties of low-energy electron beams radiation in a two-layer waveguide

We obtain an approximating formula for the low-energy impedance of a two-layer cylindrical waveguide, which allows constructing explicit expressions for the space-time functions that characterize the radiation of a charged particle in a waveguide. The general laws of the evolution of impedance and wake potentials with increasing particle energy and with the change of geometric and electrodynamical parameters of the waveguide are obtained. The settings of waveguides convenient for experimental research and having resonance properties at energies of about 20 MeV are revealed.

Wake potential in collisional anisotropic quark-gluon plasma

Within the framework of Boltzmann transport equation with a Bhatnagar-Gross-Krook (BGK) collisional kernel, we study the wake potential induced by fast partons traveling through the high-temperature QCD plasma which is anisotropic in momentum-space. We calculate the dielectric response function of a collisional anisotropic quark-gluon plasma (AQGP) for small $\xi$ (anisotropic parameter) limit. Using this, the wake potential for various combinations of the anisotropy parameter ($\xi$) and the collision rate ($\nu$) is evaluated both for parallel and perpendicular directions of motion of the fast parton. It is seen that the inclusion of the collision modifies the wake potential and the amount as well as the nature of the potential depends on the combinations of $\xi$ and $\nu$

Collisional effects on nonlinear ion drag force for small grains

The ion drag force arising from plasma flow past an embedded spherical grain is calculated self-consistently and non-linearly using particle in cell codes, accounting for ion-neutral collisions. Using ion velocity distribution appropriate for ion drift driven by a force field gives wake potential and force greatly different from a shifted Maxwellian distribution, regardless of collisionality. The low-collisionality forces are shown to be consistent with estimates based upon cross-sections for scattering in a Yukawa (shielded) grain field, but only if non-linear shielding length is used. Finite collisionality initially enhances the drag force, but only by up to a factor of 2. Larger collisionality eventually reduces the drag force. In the collisional regime, the drift distribution gives larger drag than the shift distribution even at velocities where their collisionless drags are equal. Comprehensive practical analytic formulas for force that fit the calculations are provided.

Shielding effect and wakefield pattern of a moving test charge in a non-Maxwellian dusty plasma

By using the Vlasov-Poisson equations, we calculate an expression for the electrostatic potential caused by a test charge in an unmagnetized non-Maxwellian dusty plasma, whose constituents are the superthermal hot-electrons, the mobile cold-electrons with a neutralizing background of cold ions, and charge fluctuating isolated dust grains. The superthermality effects due to hot electrons not only modify the dielectric constant of the electron-acoustic waves but also significantly affect the electrostatic potential. The latter can be decomposed into the Debye-Hückel and oscillatory wake potentials. Analytical and numerical results reveal that the Debye-Hückel and wakefield potentials converge to the Maxwellian case for large values of superthermality parameter. Furthermore, the plasma parameters play a vital role in the formation of shielding and wakefield pattern in a two-electron temperature plasma. The present results should be important for laboratory and space dusty plasmas, where hot-electrons can be assumed to follow the non-Maxwellian distribution function.

Fast Ion Surface Energy Loss and Straggling in the Surface Wake Fields

We have measured the stopping powers and straggling of fast, highly ionized atoms passing through thin bilayer targets made up of metals and insulators. We were surprised to find that the energy losses as well as the straggling depend on the ordering of the target and have small but significantly different values on bilayer reversal. We ascribe this newly found difference in energy loss to the surface energy loss field effect due to the differing surface wake fields as the beam exits the target in the two cases. This finding is validated with experiments using several different projectiles, velocities, and bilayer targets. Both partners of the diatomic molecular ions also display similar results. A comparison of the energy loss results with those of previous theoretical predictions for the surface wake potential for fast ions in solids supports the existence of a self-wake.

Effect of magnetic field on production of wake field in laser–plasma interactions: Gaussian-like (GL) and rectangular–triangular (RT) pulses

In this paper, by considering a weakly relativistic case and using the hydrodynamics fluid equations in plasma and Maxwell's equations, the general equation for the wake potential is obtained. The analytical solutions of the wake potential are gotten for Gaussian-like (GL) and rectangular–triangular (RT) pulses in presence and absence of magnetic field. It is shown that the wake field depends on length and wavelength of pulses, electron number density of plasma and external magnetic field. The effect of magnetic field on the production of the wake field is also considered.

Coherent quantum hollow beam creation in a plasma wakefield accelerator

AbstractA theoretical investigation of the propagation of a relativistic electron (or positron) particle beam in an overdense magnetoactive plasma is carried out within a fluid plasma model, taking into account the individual quantum properties of beam particles. It is demonstrated that the collective character of the particle beam manifests mostly through the self-consistent macroscopic plasma wakefield created by the charge and the current densities of the beam. The transverse dynamics of the beam–plasma system is governed by the Schrödinger equation for a single-particle wavefunction derived under the Hartree mean field approximation, coupled with a Poisson-like equation for the wake potential. These two coupled equations are subsequently reduced to a nonlinear, non-local Schrödinger equation and solved in a strongly non-local regime. An approximate Glauber solution is found analytically in the form of a Hermite–Gauss ring soliton. Such non-stationary (‘breathing’ and ‘wiggling’) coherent structure may be parametrically unstable and the corresponding growth rates are estimated analytically.

Point-charge wakefield calculations from finite length bunch wake potentials

We present a new method to accurately calculate point-charge geometric wakefields and/or short-bunch wake potentials from wake potentials due to a much longer bunch, typically obtained with a time-domain electromagnetic (EM) field solver. By allowing a long bunch in the EM solver, this method can significantly reduce the need for computer resources as well as drastically shorten the computing time. After explaining the method we give examples of longitudinal wakefield calculations for several 2D accelerator structures of various complexity.

Binding energy levels of a slowly moving ion in dusty plasmas

The near field electric potential of a slowly moving ion in complex plasmas is studied. We find that the potential consists of the Debye-Hückel potential, the wake potential, and the potential associated with charge fluctuations. The binding energy levels of the ion are calculated by use of the Ritz variation method. The results show that the binding energy levels are related to the magnetic quantum number m. The binding energy levels are affected by speed of the ion and dust grain number density. In contract to isolated ion or static ion in plasmas, the binding energy levels of the ion are pushed up and even become unbounded.

Some Aspects of Anisotropic Quark-Gluon Plasma

We review the various aspects of anisotropic quark-gluon plasma (AQGP) that have recently been discussed by a number of authors. In particular, we focus on the electromagnetic probes of AQGP, inter quark potential, quarkonium states in AQGP, and the nuclear modifications factor of various bottomonium states using this potential. In this context, we will also discuss the radiative energy loss of partons and nuclear modification factor of light hadrons in the context of AQGP. The features of the wake potential and charge density due to the passage of jet in AQGP will also be demonstrated.

Wake in anisotropic quark-gluon plasma

We calculate the wake in charge density and the wake potential due to the passage of a fast parton in an anisotropic quark-gluon plasma. For the sake of simplicity, a small $\ensuremath{\xi}$ (anisotropic parameter) limit has been considered. When the velocity ($v$) of the jet is parallel to the anisotropy direction ($\stackrel{^}{n}$) and remains below the phase velocity (${v}_{p}$), the wake in induced charge density shows a little oscillatory behavior in anisotropic quark-gluon plasma, contrary to the isotropic case. With the jet velocity greater than the phase velocity, the oscillatory behavior increases with $\ensuremath{\xi}$. Also for $v>{v}_{p}$ one observes a clear modification of the conelike structure in the presence of anisotropy. For the parallel direction in the backward region, the depth of the wake potential decreases with the increase of $\ensuremath{\xi}$ for $v<{v}_{p}$, and the potential becomes modified Coulomb-like for higher values of $\ensuremath{\xi}$. In the forward region, the potential remains modified Coulomb-like with the change in magnitude for nonzero $\ensuremath{\xi}$, for both $v>{v}_{p}$ and $v<{v}_{p}$. In the perpendicular direction, the wake potential is symmetric in the forward and backward regions. With the increase of $\ensuremath{\xi}$, the depth of negative minimum is moving away from the origin irrespective of the jet velocity. On the other hand, when the jet velocity is perpendicular to the anisotropy direction, we find significant changes in the case of both wake charge density and potential in comparison to the isotropic case. For nonzero $\ensuremath{\xi}$, the oscillatory nature of the color charge wake is reduced at $v>{v}_{p}$. Also the oscillatory behavior of the wake potential along the direction of motion of the parton is attenuated in the backward direction for anisotropic plasma at parton velocity $v>{v}_{p}$. In the presence of anisotropy, for $v<{v}_{p}$, the screening potential along the perpendicular direction of the parton is transformed from the Lennard-Jones type to a modified Coulomb-like potential.

Quantum ring soliton formation by strongly nonlocal plasma wake field response to a relativistic electron beam

The relativistic electron/positron particle beam propagation in overdense magnetized plasmas is studied theoretically, using a fluid plasma model and accounting for the quantum properties of individual particles. The collective character of the particle beam manifests through the macroscopic, beam created, plasma wake field. The transverse dynamics is described by the quantum Schrödinger equation for the single-particle wave function, within the Hartree mean-field approximation, coupled with the Poisson equations for the wake potential. The resulting nonlinear nonlocal Schrödinger equation is solved analytically in the strongly nonlocal regime, yielding breathing/wiggling Hermite-Gauss ring solitons. The nonstationary rings may be parametrically unstable. The conditions for instability and the growth rates are estimated analytically.

Coherent-states calculation of electronic density fluctuations associated to the excitation of plasmons

We study the fluctuations in the electronic density associated with the wake potential generated by an external charged particle, using a coherent-states description for the plasmon states excited in planar geometry. We consider different trajectories of the external particle and analyze the effect of parameters such as its velocity, and distance to the surface.

Effect of wake potential on Coulomb crystallization in the presence of magnetic field

The formation of dust crystal in plasma under the influence of repulsive Yukawa (Debye-Hückel) potential is a well known phenomenon. The regular structure of dust particles is affected by anisotropic ion flow near the sheath region. The bombardment of the ions over dust grains distorts their Debye sphere by overshielding the dust cloud and gives rise to an attractive oscillatory wake potential. In this paper, we have obtained an expression for wake potential along with the Yukawa type of potential in a complex plasma in the presence of magnetic field, for subsonic ion flow towards the plasma sheath. In the presence of magnetic field, interaction potential gets modified and becomes anisotropic. We have studied the combined effect of the attractive wake potential as well as repulsive Yukawa potential on a 2D dust crystal, both in the presence and absence of magnetic field, using molecular dynamic simulation.