The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas, that relies on the Chapman-Enskog method, as well as to deriving collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rate.
Formulas for calculation of transverse dielectric function and transverse electric conductivity in quantum collisional Maxwellian plasma are obtained. The Wigner -- Vlasov -- Boltzmann kinetic equation with collision integral in BGK (Bhatnagar, Gross and Krook) form in coordinate space is used. Various special cases are in\-ves\-ti\-gated. Comparison with Lindhard's formula has been carried out.
Research of influence of collisions on Friedel oscillations in quantum degenerate collisional plasma (T=0) is carried out for the first time. It is shown that presence of collisions in plasma leads to exponential decreasing of amplitude and phase shift of the Friedel oscillations. In linear approximation the phase shift is equal to the half of quantity inverse to product of Fermi's wave number by free length path of electrons. The correct expression for longitudinal dielectric permeability of the quantum collisional plasma found by the authors (see arxiv:1001.3937 [math-ph] 22 Jan 2010) is use…
Formulas for calculation of transversal dielectric function and transversal electric conductivity in quantum non-degenerate collisional plasmas under arbitrary degree of degeneracy of the electron gas are received. The Wigner-Vlasov-Boltzmann kinetic equation with collision integral in BGK (Bhatnagar, Gross and Krook) form in coordinate space is used. Various special cases are investigated
For the first time the kinetic description of Landau diamagnetism for degenerate collisional plasma is given. The correct expression for transverse electric conductivity of the quantum plasma, found by authors (see arXiv:1002.1017 [math-ph] 4 Feb 2010) is used. In work S. Dattagupta, A.M. Jayannavar and N. Kumar [Current science, V. 80, No. 7, 10 April, 2001] was discussed the important problem of dissipation (collisions) influence on Landau diamagnetism. The analysis of this problem is given with the use of exact expression for transverse conductivity of quantum plasma.
Formulas for transversal electric conductivity and dielectric permeability of quantum collisional plasma are deduced. The kinetic equation for a density matrix in relaxation approaching in momentum space is used. It is shown, that when Planck's constant tends to zero, these deduced formulas pass in classical expressions and when frequency of electron collision tends to zero (i.e. plasma passes in collisionless plasma), the deduced formulas pass in deduced earlier by Lindhard. It is shown also, that when the wave number tends to zero, quantum conductivity passes in the classical one. Graphic co…
The formula for dielectric function of non-degenerate and maxwellian collisional plasmas is transformed to the form, convenient for research. Graphic comparison of longitudinal dielectric functions of quantum and classical non-degenerate collisional plasmas is made.
Formulas for transversal conductance and dielectric permeability (dielectric function) in quantum Maxwell collisional plasma are deduced. The kinetic equation with collision integral in the form relaxation type is used.
The kinetic description of magnetic susceptibility and Landau diamagnetism of quantum collisional plasmas with any degeration of electronic gas is given. The correct expression of electric conductivity of quantum collisional plasmas with any degeration of electronic gas (see A. V. Latyshev and A. A. Yushkanov, Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach. - Theor. and Math. Phys., V. 175(1):559-569 (2013)) is used.
Kinetic model of three component, weakly ionized, collisional plasma with a beam of neutral particles is developed. New dispersion relations for linear perturbations are derived and analyzed in various limiting cases.
The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/ν$-collisionality regime and need to be modified in the $\sqrtν$-regime. The correction due to fini…
The collisional coupling of relativistic electrons and non-relativistic ions in hot plasmas has been analysed. It is found that relativistic effects produce a new feature: while the condition T_e<3T_i guarantees a stable collisional coupling between electrons and ions in low-temperature plasmas, relativistic effects shift the upper T_e/T_i boundary of stability to higher values. Moreover, for sufficiently high temperatures, T_{e,i} > 75 keV, collisional decoupling between relativistic electrons and ions becomes impossible.
We present time-resolved measurements of ion heating due to collisional plasma shocks and interpenetrating supersonic plasma flows, which are formed by the oblique merging of two coaxial-gun-formed plasma jets. Our study was repeated using four jet species: N, Ar, Kr, and Xe. In conditions with small interpenetration between jets, the observed peak ion temperature Ti is consistent with the predictions of collisional plasma-shock theory, showing a substantial elevation of Ti above the electron temperature Te and also the subsequent decrease of Ti on the classical ion-electron temperature-equili…
The evolution of a solar flare accelerated non-thermal electron population and associated plasma emission is considered in collisional inhomogeneous plasma. Non-thermal electrons collisionally evolve to become unstable and generate Langmuir waves, which may lead to intense radio emission. We self-consistently simulated the collisional relaxation of electrons, wave-particle interactions, and non-linear Langmuir wave evolution in plasma with density fluctuations. Additionally, we simulated the scattering, decay, and coalescence of the Langmuir waves which produce radio emission at the fundamenta…
With the use of correct expression of the electric conductivity of quantum collisional degenerate plasmas (A. V. Latyshev and A. A. Yushkanov, Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach, - Theor. and Math. Phys., {\bf 175}(1): 559-569 (2013)) the kinetic description of a magnetic susceptibility is obtained and the formula for calculation of Landau diamagnetism is deduced.
The plasma force on grains of specified charge and height in a collisional DC plasma sheath are calculated using the multidimensional particle in cell code COPTIC. The background ion velocity distribution functions for the unperturbed sheath vary substantially with collisionality. The grain force is found to agree quite well with a combination of background electric field force plus ion drag force. However, the drag force must take account of the non-Maxwellian (and spatially varying) ion distribution function, and the collisional drag enhancement. It is shown how to translate the dimensionles…
With the use of correct expression of the electric conductivity of quantum collisional plasmas (A. V. Latyshev and A. A. Yushkanov, {\it Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach}. - Theor. and Math. Phys., {\bf 175}(1): 559-569 (2013)) the kinetic description of a magnetic susceptibility is obtained and the formula for calculation of Landau diamagnetism is deduced.
We present space- and time-resolved experimental data of head-on-merging, supersonic plasma jets (of an argon/impurity mixture) in an initially collisionless regime for counter-streaming ions. The merging begins with collisionless interpenetration followed by a transition to collisional stagnation. The transition occurs due to an experimentally inferred rising mean-ionization level, which rapidly reduces the counter-streaming ion-ion mean free path. The measurements demonstrate a specific mechanism by which a collisionless interaction transitions to a collisional one and constrain collisionali…
The kappa-distributed fully ionized plasma with collisional interaction is investigated. The Fokker-Planck equation with Rosenbluth potential is employed to describe such a physical system. The results show that the kappa distribution is not a stationary distribution unless the parameter kappa tends to infinity. The general expressions of collisional relaxation rate of multiple-component plasma with kappa distribution are derived and discussed in specific cases in details. For the purpose of visual illustration, we also give those results numerically in figures. All the results show that the p…
An orbit following code is developed to calculate ion beam trajectories in magnetized plasmas. The equation of motion (the Newton's equation) is solved including the Lorentz force term and Coulomb collisional relaxation term. Furthermore, a new algorithm is introduced by applying perturbation method regarding the collision term as a small term. The reduction of computation time is suggested.
We present a new theoretical approach for collisional absorption of laser energy in dense plasmas which accommodates arbitrary frequencies and high intensities of the laser field. We establish a connection between laser absorption by inverse Bremstrahlung and the stopping power. This relation is then applied to include strong correlations beyond the mean field approach. The results show an excellent agreement with molecular dynamics simulations up to very high coupling strength.
The problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attach, both from the theoretical and the numerical point of view, and which requires in general to approximate the original collisional Landau integral by simplified differential operators in reduced dimensionality. In this paper, a Eulerian time-splitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through one-dimensional operators of the Fokker-Planck ty…
The properties of obliquely propagating dissipative electron-acoustic solitary waves (OPdEASWs) have been investigated in a magnetized collisional superthermal plasma consisting of inertial cold electrons, inertialess hot electrons featuring kappa-distribution and static ions via the fluid dynamical approach. By using the reductive perturbation technique, a nonlinear Schamel equation that governs the nonlinear features of OPdEASWS is obtained. The solitary wave solution of the Schamel equation is used to examine the basic features of small, but finite amplitude OPdEASWs in such a magnetized co…
Following an argument by Kirzhnits we rederive an exact expression for the energy loss of a fast charged particle in a relativistic plasma using the quantum field theoretical language. We compare this result to perturbative calculations of the collisional energy loss of an energetic electron or muon in an electron-positron plasma and of an energetic parton in the quark-gluon plasma.
Formulas for transverse conductance in quantum collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at Planck's constant tends to zero the derived formula transfers to the classical one. It is shown also, that when electron collision frequency tends to null (i.e. plasma becomes collisionless), the conductance formula transfers in the known formula inferred earlier by Lindhard.
Formulas for transverse conductance in quantum non-degenerate collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at $\hbar\to 0$ the derived formula transfers to the classical one. It is shown also, that when values of dimensionless wave numbers are small, the conductance formula transfers in the known formula for classical non-degenerate plasmas.
The accumulation of impurities in the core of magnetically confined plasmas, resulting from standard collisional transport mechanisms, is a known threat to their performance as fusion energy sources. Whilst the axisymmetric tokamak systems have been shown to benefit from the effect of temperature screening, that is an outward flux of impurities driven by the temperature gradient, impurity accumulation in stellarators was thought to be inevitable, driven robustly by the inward pointing electric field characteristic of hot fusion plasmas. We have shown in Helander et. al. (2017b) that such scree…
Gyrokinetic simulations of magnetic reconnection are presented to investigate plasma heating for strongly magnetized, weakly collisional plasmas. For a low plasma beta case, parallel and perpendicular phase mixing strongly enhance energy dissipation yielding electron heating. Heating occurs for a long time period after a dynamical process of magnetic reconnection ended. For a higher beta case, the ratio of ion to electron dissipation rate increases, suggesting that ion heating (via phase-mixing) may become an important dissipation channel in high beta plasmas.
We solve the linearised Vlasov-Fokker-Planck (VFP) equation to show that heat flow or an electrical current in a magnetized collisional plasma is unstable to the growth of a circularly polarised transverse perturbation to a zeroth order uniform magnetic field. The Braginskii (1965) transport equations exhibit the same instability in the appropriate limit. This is relevant to laser-produced plasmas, inertial fusion energy (IFE) and to dense cold interstellar plasmas.
In a two-ion-species plasma with disparate ion masses, heavy ions tend to concentrate in the low-temperature region of collisionally magnetized plasma and in the high-temperature region of collisionally unmagnetized plasma, respectively. Moreover, collisional magnetization can be determined as the ratio of the light ion gyrofrequency to the collision frequency of light and heavy ion species, and the behavior of this effect in the intermediate regime of partially magnetized plasma is predominantly dependent on this Hall parameter. Multi-ion cross-field transport has been described before in the…
The effect of ionization and recombination processes on the electrical interactions between a pair of small charged particles in highly collisional plasmas is discussed. In particular, it is shown that these processes suppress the long-range attraction between positively charged particles. The condition corresponding to the vanishing of attraction is derived. The role of the effect for conditions of existing experiments is estimated.
Formulas for transverse conductance in quantum Maxwellian collisional plasma are deduced. The kinetic Von Neumann equation in momentum space with collision integral in the relaxation form is used. It is shown, that at Planck's constant tends to zero the derived formula transfers to the classical one. It is shown also, that when values of dimensionless wave numbers are small, the conductance formula transfers in the known formula for classical Maxwellian plasmas.
Energy losses in a magnetic nozzle radiofrequency plasma thruster are investigated to improve the thruster efficiency, which are calculated from particle energy losses in fully kinetic simulations. The simulations calculate particle energy fluxes with a vector resolution including the plasma energy lost to the dielectric wall, the plasma beam energy, and the divergent plasma energy in addition to collisional energy losses. As a result, distributions of energy losses in the thruster and the ratios of the energy losses to the input power are obtained. The simulation results show that the plasma …
A potential threat to the performance of magnetically confined fusion plasmas is the problem of impurity accumulation, which causes the concentration of highly charged impurity ions to rise uncontrollably in the center of the plasma and spoil the energy confinement by excessive radiation. It has long been thought that the collisional transport of impurities in stellarators always leads to such accumulation (if the electric field points inwards, which is usually the case), whereas tokamaks, being axisymmetric, can benefit from "temperature screening", i.e., an outward flux of impurities driven …
A method is developed to analytically determine the resonance broadening function in quasilinear theory, due to either Krook or Fokker-Planck scattering collisions of marginally unstable plasma systems where discrete resonance instabilities are excited without any mode overlap. It is demonstrated that a quasilinear system that employs the calculated broadening functions reported here systematically recovers the nonlinear growth rate and mode saturation levels for near-threshold plasmas previously calculated from kinetic theory. The distribution function is also calculated, which enables precis…
We investigate the low-frequency wave mode associated with heavy particles and its instability in a collisional complex plasma with drifting ions. The effect of the ion drift on the sound velocity of this mode is discussed. The general condition of the instability is derived for subthermal ion drifts, taking into account strong coupling of the particle component. As a general tendency, strong coupling effects reduce the sound velocity and facilitate the occurrence of the ion drift instability. A wide parameter range is considered from the weakly collisional to strongly collisional regimes for …
For plasma velocity space instabilities driven by particle distributions significantly deviated from a Maxwellian, weak collisions can damp the instabilities by an amount that is significantly beyond the collisional rate itself. This is attributed to the dual role of collisions that tend to relax the plasma distribution toward a Maxwellian and to suppress the linearly perturbed distribution function. The former effect can dominate in cases where the unstable non-Maxwellian distribution is driven by collisionless transport on a time scale much shorter than that of collisions, and the growth rat…
We present experimental data providing evidence for the formation of transient ($\sim 20~μ$s) plasmas that are simultaneously weakly magnetized (i.e., Hall magnetization parameter $ωτ> 1$) and dominated by thermal pressure (i.e., ratio of thermal-to-magnetic pressure $β> 1$). Particle collisional mean free paths are an appreciable fraction of the overall system size. These plasmas are formed via the head-on merging of two plasmas launched by magnetized coaxial guns. The ratio $λ_{gun}=μ_0 I_{gun}/ψ_{gun}$ of gun current $I_{gun}$ to applied magnetic flux $ψ_{gun}$ is an experimental knob for e…
We present results from experiments on the head-on merging of two supersonic plasma jets in an initially collisionless regime for the counter-streaming ions. The plasma jets are of either an argon/impurity or hydrogen/impurity mixture and are produced by pulsed-power-driven railguns. Based on time- and space-resolved fast-imaging, multi-chord interferometry, and survey-spectroscopy measurements of the overlapping region between the merging jets, we observe that the jets initially interpenetrate, consistent with calculated inter-jet ion collision lengths, which are long. As the jets interpenetr…
A drift-kinetic model to describe the plasma dynamics in the scrape-off layer region of tokamak devices at arbitrary collisionality is derived. Our formulation is based on a gyroaveraged Lagrangian description of the charged particle motion, and the corresponding drift-kinetic Boltzmann equation that includes a full Coulomb collision operator. Using a Hermite-Laguerre velocity space decomposition of the gyroaveraged distribution function, a set of equations to evolve the coefficients of the expansion is presented. By evaluating explicitly the moments of the Coulomb collision operator, distribu…
Formulas for transverse conductance and dielectric permeability in quantum degenerate collisional plasma with arbitrary variable collision frequency in Mermin's approach are deduced. Frequency of collisions of particles depends arbitrarily on a wave vector. For this purpose the kinetic Shrödinger - Boltzmann equation with collision integral of relaxation type in momentum space is applied. The case of degenerate Fermi plasma is allocated and investigated. The special case of frequency of collisions proportional to the module of a wave vector is considered. The graphic analysis of the real and i…
The distinction between the plasma dynamics dominated by collisional transport versus collective processes has never been rigorously addressed until recently. A recent paper [Yoon et al., Phys. Rev. E 93, 033203 (2016)] formulates for the first time, a unified kinetic theory in which collective processes and collisional dynamics are systematically incorporated from first principles. One of the outcomes of such a formalism is the rigorous derivation of collisional damping rates for Langmuir and ion-acoustic waves, which can be contrasted to the heuristic customary approach. However, the results…
Kinetic Vlasov equation for collisional Maxwellian plasmas is used. Collision integral of BGK (Bhatnagar, Gross and Krook) type is applied. From Vlasov equation we find distribution function of electrons in square-law approximation on size of transversal electric field. The formula for electric current calculation is deduced. This formula contains an one-dimensional quadrature. It is shown, that nonlinearity leads to revealing of the longitudinal electric current directed along a wave vector. This longitudinal current is perpendicular to known so-called transversal classical current. The class…
The ion-drag force on a spherical dust particle immersed in a flowing plasma with external electric field is self-consistently calculated using the Particle In Cell code SCEPTIC in the entire range of charge-exchange collisionality. Our results, not based on questionable approximations, extend prior analytic calculations valid only in a few limiting regimes. Particular attention is given to the force direction, shown never to be directed opposite to the flow except in the continuum limit, where other forces are of much stronger magnitude.
Magnetized plasma interactions are ubiquitous in astrophysical and laboratory plasmas. Various physical effects have been shown to be important within colliding plasma flows influenced by opposing magnetic fields, however, experimental verification of the mechanisms within the interaction region has remained elusive. Here we discuss a laser-plasma experiment whereby experimental results verify that Biermann battery generated magnetic fields are advected by Nernst flows and anisotropic pressure effects dominate these flows in a reconnection region. These fields are mapped using time-resolved pr…
Formulas for transverse conductance and dielectric permeability in quantum non-degenerate and Maxwellian collisional plasma with arbitrary variable collision frequency in Mermin's approach are deduced. Frequency of collisions of particles depends arbitrarily on a wave vector. The special case of frequency of collisions proportional to the module of a wave vector is considered. The graphic analysis of the real and imaginary parts of dielectric function is made.
The friction in plasmas consisting of two species with different temperatures is discussed together with the consequent energy transfer. It is shown that the friction between the two species has no effect on the ion acoustic mode in a quasi-neutral plasma. Using the Poisson equation instead of the quasi-neutrality reveals the possibility for an instability driven by the collisional energy transfer. However, the different starting temperatures of the two species imply an evolving equilibrium. It is shown that the relaxation time of the equilibrium electron-ion plasma is, in fact, always shorter…
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 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 wave length than the collisionless ones. Transition from the collisionless regime …
Wave-Energy Partition Governs Weak Collisional Damping in Cold Plasmas
School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学技术学院）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）
The profile of a Bennett hole induced by laser field in ionic distribution in collisional plasma is calculated. Influence of Chandrasekhar's dependence of coefficients of velocity space transport on the profile is included into the calculation for the first time. It is found that the hole narrows down as the field detuning frequency increases. Physical cause of the effect is the falling dependence of Coulomb collision frequency on the ionic velocity. Estimations show that the effect is quite observable under conditions of high-current gas-discharge plasma.
A collisional magnetized plasma consisting of two temperature electrons has been investigated numerically to study the sheath structure and the ion energy flux to the wall. The low-temperature electrons are described by Maxwellian distribution, and the high-temperature electrons are described by truncated Maxwellian distribution. It has been observed that high-temperature electrons play a major role in the sheath potential as well as the ion energy flux to the wall. The presence of collision in the sheath has a significant effect on the properties of the sheath. The study of such a system can …
Instabilities of ion-acoustic waves in a dusty plasma with electron-drift, collisional, and dust charge fluctuations effects, have been investigated. The regimes are clearly marked out where the theory is applicable. The critical electron-drift velocity required to drive the instability is predicted. It is also shown that electron thermal conductivity and charged grains concentration enhance the growth of the ion-acoustic mode whereas ion-viscosity, ion-thermal conductivity, and dust charge fluctuations have a stabilizing effect.
This paper develops a unified linear theory of local cross-field plasma instabilities, such as the Farley-Buneman, electron thermal, and ion thermal instabilities, in collisional plasmas with fully or partially unmagnetized multi-species ions. Collisional lasma instabilities in low-ionized, highly dissipative, weakly magnetized plasmas play an important role in the lower Earth's ionosphere and may be of importance in other planet ionospheres, star atmospheres, cometary tails, molecular clouds, accretion disks, etc. In the solar chromosphere, macroscopic effects of collisional plasma instabilit…
The low-frequency instability of a cylindrical poorly magnetized plasma with an inward-directed radial electric field is studied changing the gas pressure and the ion cyclotron frequency. The unstable frequency always decreases when the gas pressure is increased indicating collisional effects. At a fixed pressure, the unstable frequency increases with the magnetic field when the B-field is low and decreases at larger magnetic field strength. We find that the transition between these two regimes is obtained when the ion cyclotron frequency equals the ion-neutrals collision frequency. This is in…
This work, which extends Squire et al. [ApJL, 830 L25 (2016)], explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-beta plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, "interrupting" the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional "Braginskii" reg…
Drift ordered fluid models are widely applied in studies of low-frequency turbulence in the edge and scrape-off layer regions of magnetically confined plasmas. Here, we show how collisional transport across the magnetic field is self-consistently incorporated into drift-fluid models without altering the drift-fluid energy integral. We demonstrate that the inclusion of collisional transport in drift-fluid models gives rise to diffusion of particle density, momentum and pressures in drift-fluid turbulence models and thereby obviate the customary use of artificial diffusion in turbulence simulati…
