Energy spectrum of particles accelerated in relativistic collisionless shocks

We analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this relation, we obtain s=(3beta(u)-2beta(u)beta(2)(d)+beta(3)(d))/(beta(u)-beta(d)) for isotropic diffusion, where beta(u) (beta(d)) is the upstream (downstream) fluid velocity normalized to the speed of light. This result is in agreement with previous numerical determinations of s for all (beta(u),beta(d)), and yields s=38/9 in the ultrarelativistic limit. The spectrum-anisotropy connection is useful for testing numerical studies and constraining anisotropic diffusion results. It suggests that the spectrum is highly sensitive to the form of the diffusion function for particles traveling along the shock front.     

Nonlinear propagation of relativistically intense electromagnetic waves in a collisionless plasma

We discuss the nonlinear propagation of relativistically intense electromagnetic waves into collisionless plasmas with special emphasis on one dimensional plane wave solutions of the propagating, standing and modulated types. These solutions exhibit a rich variety of phenomena associated with relativistic electron mass variation and coupling between transverse electromagnetic and longitudinal fields. They have important applications to problems of laser propagation, self-focusing in overdense plasmas, particle and photon acceleration and to electromagnetic radiation around pulsars.     

Ion dynamics in a perpendicular collisionless shock

The behaviour of ions moving in fields modelling those of a perpendicular shock in a collisionless plasma has been investigated. The main result is that heating in excess of the adiabatic level can be produced, even in the absence of any dissipative mechanism.     

Turbulent heating of electrons and ions in a collisionless shock wave

Turbulent heating of a nonisothermal plasma by a collisionless shock wave is analysed in the situation when a small-scale high-frequency instability occurs at the wave front. Effective time of electron and ion heating is estimated.     

On the parallel shock waves in collisionless plasma with heat fluxes

A class of shock wave solutions is discussed for collisionless anisotropic plasma with heat fluxes. For the strictly parallel one-dimensional motions of a plasma the system of equations is written in divergent form and both linear and shock wave solutions are considered. Jump expressions for the parallel shocks are obtained in analytical form as functions of the shock upstream parameters.     

Features of the generation of a collisionless electrostatic shock wave in a laser-ablation plasma

The appearance of a density bump is experimentally revealed in an electrostatic shock wave during the ablation of an aluminum foil by a femtosecond laser pulse. The numerical simulation shows that this phenomenon can be explained by the generation of a packet of ion acoustic waves under the action of high-energy electron flows in a collisionless plasma. It is found that, for the formation and maintenance of the dense plasma layer in the shock wave, the contributions of accelerated ions overtaking it and wave-captured ions of the background plasma formed by a nanosecond laser prepulse in the process of ablation are significant.     

Counterrotating disks of collisionless particles and the hoop conjecture

We construct solutions to the Einstein equations and their sources with a high asphericity using kinetic theory. In particular, we consider all the solutions associated with disk like sources of counter rotating collisionless particles, and find that the hoop conjecture is satisfied.     

Observation of collisionless plasma heating by strong shock waves

The heating of a plasma by collisionless shock waves is investigated by measuring the variation of magnetic field (with magnetic probes), density and electron temperature (from Thomson scattering of laser light) in the shock waves. The compression waves are produced in a tube of 14 cm diameter by the fast rising magnetic field (12 kG in 0.5Μsec) of a theta pinch. For shocks with Mach numbers between 2 and 3 propagating into a hydrogen or deuterium plasma with a localΒ of about 1 (Β=ratio of particle pressure to magnetic pressure) the measured jump in density and magnetic field across the front is 2 to 4, and the electron temperature increases in the front from 3 to 50 eV with a further rise to between 100 and 250 eV in the piston region. Only about 20% of the measured electron heating can be explained by adiabatic heating and resistive heating based on binary collisions, indicating a high turbulent plasma resistance. Both the observed electron heating and the width of the shock front, which is about 0.6 ·c/Ω _p, can be accounted for using an effective collision frequency close to the ion plasma frequencyΩ _p. The ion heating in the almost stationary shock fronts can be inferred indirectly from the steady state conservation relations. For shock waves with Mach numbersM<M _crit it seems to be consistent with an adiabatic heating process, whereas forM>M _crit the calculated ion temperatures exceed those one would except for a merely adiabatic heating.     

Time evolution of collisionless shock in counterstreaming laser-produced plasmas

We investigated the time evolution of a strong collisionless shock in counterstreaming plasmas produced using a high-power laser pulse. The counterstreaming plasmas were generated by irradiating a CH double-plane target with the laser. In self-emission streaked optical pyrometry data, steepening of the self-emission profile as the two-plasma interaction evolved indicated shock formation. The shock thickness was less than the mean free path of the counterstreaming ions. Two-dimensional snapshots of the self-emission and shadowgrams also showed very thin shock structures. The Mach numbers estimated from the flow velocity and the brightness temperatures are very high.     

Stationary collisionless shock waves in an initial plasma with high ion temperature

Stationary collisonless shock waves propagating perpendicularly to an initial magnetic field are produced by the fast-rising magnetic field \((\dot B = 7 \cdot 10^{10} G/sec)\) of a theta pinch (coil diameter 16 cm, coil length 60 cm). The initial plasma is produced by a fast theta pinch discharge (810 kHz). At filling pressures between 5 and 15 mtorr H₂ or D₂ the degree of ionization is about 50%. By choosing the filling pressure properly it is possible to trap a homogeneous magnetic field. The ions of this plasma have a temperature of a few 10 eV. This value is much higher than the electron temperature and results in a local plasmaβ between 0.3 and 5. In this initial plasma stationary collisionless shock waves with Mach numbers between 1.5 and 5 are observed. The snow-plough model is used to derive conditions for the stationary state, attainable Mach number, and velocity of the front which relate the external magnetic field and the parameters of the initial plasma. Strong collisionless dissipation can be demonstrated by measuring the profiles of magnetic field, density, and electron temperature of the shock waves. For the electrons this dissipation mechanism can be described by an effective collison frequency. This phenomenologically introduced frequency determines the width of the shock front at least for subcritical shock waves. It exceeds the classical electron-ion collision frequency by 1–2 orders of magnitude and is roughly equal to one-third of the ion plasma frequency. The ion temperature can be estimated from the steady state conservation relations. The ions are heated in the two degrees of freedom perpendicular to the magnetic field. For shock waves with Mach numbers below the critical one the ions seem to be heated merely adiabatically. In strong shock waves this heating is considerably exceeded, and for high Mach numbers it yields ion temperatures up to about 500 eV. Finally, semi-empirical formulas are derived to estimate the possible temperatures of electrons and ions behind the shock front.     

Dust particles in collisionless plasma sheath with arbitrary electron energy distribution function

Dust particles often appear in industrial plasmas as undesirable product of the plasma-wall interactions. Large particles of several micrometers in diameter are concentrated in a thin layer (the sheath) above the lower electrode of the rf driven parallel plate device, where the electric force is strong enough to compensate particle’s gravity. Experimental and theoretical uncertainties are significantly increased in the plasma sheath. Common models of dust charging in the plasma sheath suppose the Maxwellian electron energy distribution function (EEDF) in conjunction with a flux of cold ions satisfying classical Bohm criterion at the sheath edge. In this paper we generalize this model to arbitrary EEDF with adapted Bohm criterion. We limit our considerations to collisionless or slightly collisional plasma, where the EEDF inside the sheath is expressed through the EEDF in the plasma bulk. Derived theoretical formulas are incorporated into numerical model, describing collisionless radio frequency (rf) plasma sheath together with the electrical charge, various kinds of forces, balancing radius and oscillation frequency of particles.     

Third adiabatic invariant and the collisionless distribution function of particles in a tokamak

It has been shown that the distribution function of an ensemble of particles with a given energy in a collisionless regime in a tokamak is formed as a function primarily of the third adiabatic invariant, particularly in the near-axis region. In the periphery of the plasma column, the contribution of the toroidal component of the canonical momentum/longitudinal adiabatic invariant to the distribution function becomes noticeable. The coordinate dependence of the ensemble distribution function in the velocity space is determined predominantly by the trajectories of charged particles.     

Appearance of a relativistically rotating disk

The appearance of a rotating disk, as perceived by a corotating observer in accordance with two operational procedures is discussed, and the results compared. It is noted that naive generalizations of operational procedures which correctly represent the disk geometry when stationary lead to mutually contradictory pictures when the disk rotates.     

Relaxation of heavy ions in collisionless shock waves in cosmic plasma

We report on the results of hybrid particle-in-cell simulation of shock waves (SWs) in the cosmic plasma with admixture of heavy weakly charged ions. The dependence of ion relaxation and the SW structure on the angle between the magnetic field and the normal to the wavefront is analyzed. The conditions for invariability of the anisotropic ion velocity distribution behind the front of quasi-transverse SWs are indicated on scales substantially exceeding the width of the collisionless SW front (up to the Coulomb relaxation length). The obtained results are essential for determining the effectiveness of heating of heavy ions and observation diagnostic of collisionless SWs in the cosmic plasma.     

Interaction of relativistically strong electromagnetic waves with a layer of overdense plasma

Plasma-field structures that arise under the interaction between a relativistically strong electromagnetic wave and a layer of overdense plasma are considered within a quasistationary approximation. It is shown that, together with known solutions, which are nonlinear generalizations of skin-layer solutions, multilayer structures containing cavitation regions with completely removed electrons (ion layers) can be excited when the amplitude of the incident field exceeds a certain threshold value. Under symmetric irradiation, these cavitation regions, which play the role of self-consistent resonators, may amplify the field and accumulate electromagnetic energy.     

Generation of a purely electrostatic collisionless shock during the expansion of a dense plasma through a rarefied medium

A two-dimensional numerical study of the expansion of a dense plasma through a more rarefied one is reported. The electrostatic ion-acoustic shock, which is generated during the expansion, accelerates the electrons of the rarefied plasma inducing a superthermal population which reduces electron thermal anisotropy. The Weibel instability is therefore not triggered and no self-generated magnetic fields are observed, in contrast with published theoretical results dealing with plasma expansion into vacuum. The shock front develops a filamentary structure which is interpreted as the consequence of the electrostatic ion-ion instability, consistently with published analytical models and experimental results.     

Distortion of a spherical gaseous interface accelerated by a plane shock wave

The evolution of a spherical gaseous interface accelerated by a plane weak shock wave has been investigated in a square cross section shock tube via a multiple exposure shadowgraph diagnostic. Different gaseous bubbles, i.e., helium, nitrogen, and krypton, were introduced in air at atmospheric pressure in order to study the Richtmyer-Meshkov instability in the spherical geometry for negative, close to zero, and positive initial density jumps across the interface. We show that the bubble distortion is strongly different for the three cases and we present the experimental velocity and volume of the developed vortical structures. We prove that at late times the bubble velocities reach constant values which are in good agreement with previous calculations. Finally, we point out that, in our flow conditions, the gaseous bubble motion and shape are mainly influenced by vorticity and aerodynamic forces.