Beam-plasma System Research Articles

Electric potential of a macroparticle in beam-plasma systems

Dusty plasma research is one of the most extensively developed areas of modern plasma physics. In spite of the large number of papers devoted to determining the electric potential of dust grains in gas discharge plasmas, this problem is still far from being resolved completely. In this paper, the behavior of the floating electric potential of a macroparticle in an electron beam-plasma system is studied in the framework of the orbit motion limited model taking into account secondary electron emission.

Collisional effects on the current-filamentation instability in a dense plasma

The collisional current-filamentation instability (CFI) is studied for a nonrelativistic electron beam penetrating an infinite uniform plasma. It is analytically shown that the CFI is driven by the drift-anisotropy rather than the classical anisotropy of the beam and the background plasma. Therefore, collisional effects can either attenuate or enhance the CFI depending on the drift-anisotropy of the beam-plasma system. Numerical results are given for some typical parameters, which show that collisional effects cannot stabilize but enhance the CFI in a dense plasma. Thus, the CFI may play a dominant role in the fast electron transport and deposition relevant to the fast ignition scenario (FIS).

Unstable spectrum of a relativistic electron beam interacting with a quantum collisional plasma: application to the fast ignition scenario

Quantum and collisional effects on the unstable spectrum of a relativistic electron beam–plasma system are investigated through a two-fluids model. Application is made to the near target center interaction of the relativistic electron beam in the fast ignition scenario. Partial degeneracy effects are found to be negligible while the most influential factors are the beam temperature and the electron–ion collision frequency of the plasma. The introduction of the latter triggers some oblique unstable modes of much larger wavelength than the collisionless ones. Transition from the collisionless regime to the resistive one is thus documented and found discontinuous.

Interplay of collisions and temperature on the filamentary structures of a relativistic electron beam in plasmas

A systematic study on the Weibel instability induced filamentation of a relativistic electron beam is made by including the effects of collisions and temperature. The stabilization and de-stabilization of the beam filamentation due to beam temperature and plasma collisions, respectively, is explored through an analytical model and PIC simulations. The de-stabilization of the beam filamentation is attributed to the collision driven negative energy wave generation in the beam plasma system.

Effect of nonisothermal electrons on dressed soliton in ion beam plasma system

Using the reductive perturbation method (RPM) evolution equations, governing the first and second order potentials for ion acoustic wave in an ion beam plasma system with nonisothermal electrons, are derived. Adopting renormalization procedure of Kodama and Taniuti [J. Phys. Soc. Jpn. 45, 298 (1978)] nonsecular dressed soliton solution of these coupled equations is determined. An alternative approach is also used to obtain large amplitude soliton solution, retaining higher order nonlinearities in the expansion of the Sagdeev potential and integrating the resulting energy equation for the system. For small amplitude approximation, this solution reduces to dressed soliton solution obtained for the system using the renormalization in the RPM. Variation of the amplitude (A), velocity (λ), width (W), and the product amplitude×width4 (AW4) are numerically studied for the Korteweg–de Vries, dressed and large amplitude soliton for different values of parameters of the beam-plasma system, and results are summarized.

Electromagnetic beam-plasma interactions in a magnetic field

The excitation of plasma oscillations in a thin-walled annular plasma by an annular electron beam in a cylindrical waveguide is considered in the linear approximation. The instability growth rates and spatial amplification coefficients in the beam-plasma system under the conditions of the Cherenkov and anomalous Doppler resonances are obtained and compared with those in a transversely homogeneous system. The contributions from different instability mechanisms are analyzed.

Collision-Driven Negative-Energy Waves and the Weibel Instability of a Relativistic Electron Beam in a Quasineutral Plasma

A new model describing the Weibel instability of a relativistic electron beam propagating through a resistive plasma is developed. For finite-temperature beams, a new class of negative-energy magnetosound waves is identified, whose growth due to collisional dissipation destabilizes the beam-plasma system even for high beam temperatures. We perform 2D and 3D particle-in-cell simulations and show that in 3D geometry the Weibel instability persists even for collisionless background plasma. The anomalous plasma resistivity in 3D is caused by the two-stream instability.

Theory of type III radio bursts in the interplanetary space: I. Derivation of permittivity tensor for the system consisting of electron beam and solar wind plasma

The tensor of permittivity for the system “electron beam - plasma of the interplanetary space” is derived in the approximation of geometrical optics. The problem is one-dimensional; all parameters such as density of the beam and of the solar wind plasma, and the induction of the interplanetary magnetic field are assumed to be dependent only on the distance to the Sun. The beam is generated by an active region during a solar flare, and it is a source of radio bursts of type III in the interplanetary space. The tensor of permittivity was obtained to close field equations by a material equation. On the basis of these equations it becomes possible to study theoretically the amplitude-frequency characteristics of the radio bursts as disturbances of the above-described beam-plasma system.

Vlasov simulation of Langmuir decay instability

A parametric decay process of beam-generated Langmuir waves is examined by a one-dimensional Vlasov code simulation in the open system. It is confirmed that pump Langmuir waves decay into backscattered Langmuir and ion acoustic waves when the wave energy is higher than the thermal energy of background electrons. In the present Vlasov simulation, a large-amplitude pump Langmuir wave is excited by an electron beam. Then a backscattered Langmuir wave and a forward ion acoustic wave are excited by the parametric decay instability. When the wave energy of the backscattered Langmuir waves is also higher than the thermal energy of background electrons, backward ion acoustic waves are also excited. As a result, the wavenumber spectra of Langmuir and ion acoustic waves are broadened in both forward and backward directions, suggesting possible multiple parametric decay processes of Langmuir waves in a beam-plasma system.

Parametric conversion of a lower hybrid wave into a whistler in a plasma

A large amplitude lower hybrid wave parametrically decays into a whistler wave and a low frequency lower hybrid wave in a plasma. The density perturbation due to the low frequency wave couples with the oscillatory velocity due to the pump wave to produce a nonlinear current, driving the whistler. The pump and whistler exert a low frequency ponderomotive force on electrons, driving the lower hybrid decay wave. The growth rate of the parametric instability scales linearly with the amplitude of the pump wave. It decreases with the electron cyclotron frequency. The process is relevant to beam plasma systems where lower hybrid waves are excited with greater ease and the whistler sideband wave can be seen outside the plasma as electromagnetic emission.

Nonlineart theory of relativistic beam-plasma instabilities in the regime of the collective Cherenkov effect

A general mathematical model is proposed that is based on the Vlasov kinetic equation with a self-consistent field and describes the nonlinear dynamics of the electromagnetic instabilities of a relativistic electron beam in a spatially bounded plasma. Two limiting cases are analyzed, namely, high-frequency (HF) and low-frequency (LF) instabilities of a relativistic electron beam, of which the LF instability is a qualitatively new phenomenon in comparison with the known Cherenkov resonance effects. For instabilities in the regime of the collective Cherenkov effect, the equations containing cubic nonlinearities and describing the nonlinear saturation of the instabilities of a relativistic beam in a plasma are derived by using the methods of expansion in small perturbations of the trajectories and momenta of the beam electrons. Analytic expressions for the amplitudes of the interacting beam and plasma waves are obtained. The analytical results are shown to agree well with the exact solutions obtained numerically from the basic general mathematical model of the instabilities in question. The general mathematical model is also used to discuss the effects associated with variation in the constant component of the electron current in a beam-plasma system.

Collisionless transport of energetic electrons in the solar corona at current-free double layers

Context. Impinging electron beams in the solar chromosphere generate hard X-ray radiation (HXR) through the collisional Bremstrahlung thick target model. The deduced electron distributions usually exhibit a broken-power-law. Assuming that the initial distribution function was a drift-Maxwellian, this indicates that the distribution of energetic electrons changes in the course of their propagation, from the looptop acceleration site to the high density chromosphere, via a collisionless scattering mechanism. Aims. The formation of a broken-power-law spectrum via the particle interaction with the current-free weak double layers (DLs) in a reverse current beam plasma system. Methods. The unstable waves generated in current-free coronal plasmas are first studied by means of a linear instability analysis. For most probable coronal plasma parameters, a one-dimensional electrostatic Vlasov-code simulation is performed to understand the nonlinear evolution of the instabilities and their influences on the electron distribution. Results. DL structures cause a dissipation of low energy beam electrons and a stagnation of return-current electrons. Fast electron holes are formed, a secondary two-stream instability, caused by the DL-accelerated electrons. Electron and ion heating by DLs also takes place. Conclusions. The plasma distributions of energetic electrons in the solar corona evolve via their interactions with nonlinear largeamplitude phase-space structures. At the late stage of evolution, the low-energy electrons are slowed down while the high energy part stays uninfluenced after the appearance of DLs. A major part of the return-current electrons change their direction to that of the injected beam. As a result the distribution becomes a broken-power-law as observed by chromospheric HXR radiation.

Determination of the cyclotron generation suppression band width in a plasma relativistic microwave generator

In a plasma-beam system in a finite magnetic field, along with Cherenkov resonance other resonances of beam and plasma waves occur. In a finite-length plasma waveguide, the concurrent wave excited by a beam at Cherenkov resonance is always partially reflected from the ends of the plasma waveguide. The reflected (counterrunning) wave provides feedback and leads to the occurrence of generation regime in such a system. Under the resonance condition for a normal Doppler effect the feedback is suppressed and the generation may cease. This effect can be used in experiments on creation of plasma microwave amplifiers in which microwave generation is harmful.

The Weibel instability in relativistic plasmas

Aims. We discuss the linear theory of the Weibel instability in a relativistic plasma driven by ultra-relativistic beams, describing the physics of the generation of magnetic fields in the ultra-relativistic shocks associated with Gamma Ray Bursts (GRBs). We perform a detailed analysis of the linear dispersion relation for the benefit of non-linear calculations that we discuss in the companion paper. Methods. We use a covariant approach, where the linear response of the beam-plasma system is determined from the polarization tensor. This tensor relates the four-current density to the four-potential of the electromagnetic field. Showing that two approaches, one based on a fluid model and one on a kinetic description that uses a waterbag distribution for the phase-space density of the beam particles, yield essentially the same result, we compare our results to those obtained by other approaches. We mainly consider the symmetric case of two counterstreaming (but otherwise identical) beams. Results. We show that the effect of an asymmetry in the beam densities is small for typical parameters, and briefly discuss the effect of an ambient magnetic field. The dispersion relation of the Weibel instability driven by ultra-relativistic beams is rather insensitive to the model used to describe the plasma. The properties of the instability, such as the growth rate and the range of unstable wavelengths, are governed by only two parameters: the ratio of the plasma frequency squared of the beam and hot background plasma, and a “Mach number”, which is essentially the ratio of the beam momentum and the momentum associated with thermal velocity (∼sound speed) in the beam plasma. We also show that, at least for the parameters associated with the ultra-relativistic shocks in GRBs, the influence of the magnetic field is small, and the results for an unmagnetized plasma can be used. Conclusions.

Computationally efficient description of relativistic electron beam transport in collisionless plasma

A reduced approach to modeling the electromagnetic Weibel instability and relativistic electron beam transport in collisionless background plasma is developed. Beam electrons are modeled by macroparticles and the background plasma is represented by electron fluid. Conservation of generalized vorticity and quasineutrality of the plasma-beam system are used to simplify the governing equations. The method is suitable for modeling the nonlinear stages of collisionless beam-plasma interaction. A computationally efficient code based on this reduced description is developed and benchmarked against a standard particle-in-cell code. The full-scale two-dimensional numerical simulation of the Weibel instability saturation of a low-current electron beam is presented. Using the present approach, linear growth rates of the Weibel instability are derived for the cold and finite-temperature beams.

Chaotic synchronization in distributed beam-plasma systems with supercritical current

Chaotic synchronization is found to arise in coupled beam-plasma systems with supercritical current. It is shown that, with increasingly stronger coupling, such systems pass from asynchronous behavior via phase synchronization to complete synchronization. Chaotic synchronization is studied according to a method based on the introduction of a continuous set of phases of the chaotic signal. In the case of unidirectional coupling, a generalized chaotic synchronization mode is observed. The mechanism of its emergence in the beam-plasma systems is investigated via the modified-system method.

Beam-plasma dielectric tensor with Mathematica

We present a Mathematica notebook allowing for the symbolic calculation of the 3 × 3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summary Title of program: Tensor Catalog identifier: ADYT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère–Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the dimensionless variables. Restrictions on the complexity of the problem: Temperature effects are limited to small, i.e. non-relativistic, temperatures. The kinetic counterpart of the present Mathematica will usually not compute the required integrals. Typical running time: About 1 minute on a Intel Centrino 1.5 GHz Laptop with 512 MB of RAM. Unusual features of the program: None.

Effects of non-Maxwellian electron velocity distribution function on two-stream instability in low-pressure discharges

Electron emission from discharge chamber walls is important for plasma maintenance in many low-pressure discharges. The electrons emitted from the walls are accelerated by the sheath electric field and are injected into the plasma as an electron beam. Penetration of this beam through the plasma is subject to the two-stream instability, which tends to slow down the beam electrons and heat the plasma electrons. In the present paper, a one-dimensional particle-in-cell code is used to simulate these effects both in a collisionless plasma slab with immobile ions and in a cross-field discharge of a Hall thruster. The two-stream instability occurs if the total electron velocity distribution function of the plasma-beam system is a nonmonotonic function of electron speed. Low-pressure plasmas can be depleted of electrons with energy above the plasma potential. This study reveals that under such conditions the two-stream instability depends crucially on the velocity distribution function of electron emission. It is shown that propagation of the secondary electron beams in Hall thrusters may be free of the two-stream instability if the velocity distribution of secondary electron emission is a monotonically decaying function of speed. In this case, the beams propagate between the walls with minimal loss of the beam current and the secondary electron emission does not affect the thruster plasma properties.

The phenomena occuring by the coupling between an electron solitary wave and an ion wave in a beam–plasma system

Experimental results such as nonlinear Landau damping, induced election scattering and the stochastic acceleration of electrons are explained well by our intensity dependent theory which treats the interaction between beam electrons in the presence of ions. We also explain the mechanism for observing nonlinear waves by the time-of-Hight of solitons.

Investigation of surface roughening of low-k films during etching using fluorocarbon plasma beams

The surface roughness evolution of solid organosilicate glass (OSG) and methylsilsesquioxane spin-on porous low-k films after etching in C2F6∕Ar plasmas was characterized as a function of ion bombardment energy, ion fluence reaching the surface (or, equivalently, the etching time), ion impingement angle, and plasma polymerization propensity in a newly designed plasma beam system in which the plasma chemistry, ion energy, ion flux, and ion incident angle can be adjusted independently. A polymerization-induced micromasking mechanism was proposed to explain the surface roughening of these low-k films. The porous structure in the substrate plays a critical role in the film roughening evolution. This effect can be understood using the concept of pore filling with polymeric deposits that etch more slowly under fluorocarbon plasma exposure. Upon exposure to etching, the polymer forms micromasks that induce roughening. Under the same etching conditions, the solid OSG film remains smooth during etching because only a fairly thin and uniform layer of polymer deposits on the surface of solid OSG substrates during the etching in C2F6∕Ar plasmas. Consequently, the inhomogeneity caused by the polymer deposition is not sufficient to induce micromasking in the absence of surface inhomogeneities. Additionally, the roughness level of the porous low-k film etched in C2F6∕Ar plasma is primarily related to the film thickness removed, although it also increases with the ion bombardment energy; no similar trend was observed on nonporous OSG films under the same etching conditions. Striations formed when etching porous low-k films at grazing angles. The striation formation is mainly due to shadowing effects, although conditions of net polymer deposition quenched the striation formation.