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.     

Electron kinetics in collisionless shock waves

We study the kinetic model of the formation of the energy spectrum of nonthermal electrons near the front of a quasilongitudinal, supercritical, collisionless shock wave. Nonresonant interactions of the electrons and the fluctuations generated by kinetic instabilities of the ions in the transition region inside the shock front play the main role in the heating and preacceleration of electrons. We calculate the electron energy spectrum in the vicinity of the shock wave and show that the heating and preacceleration of electrons occur on a scale of the order of several hundred ion inertial lengths in the vicinity of the viscous discontinuity. Although the electron distribution function is significantly nonequilibrium near the shock front, its low-energy part can be approximated by a Maxwellian distribution. The effective electron temperature T _eff ² behind the front, obtained in this manner, increases with the Mach number of the shock wave slower than it would if it followed the Hugoniot adiabat. We determine the condition under which the electron heating is ineffective but the electrons are effectively accelerated to high energies. The high-energy asymptotic behavior of the distribution function is that of a power law, with the exponent determined by the total compression ratio of the plasma, as in the case of acceleration by the first-order Fermi mechanism. The model is used to describe the case (important for applications) of acceleration of electrons by shock waves with large total Mach numbers, with the structure of these waves modified by the nonlinear interaction of nonthermal ions and consisting of an extended prefront with a smooth variation of the macroscopic parameters and a viscous discontinuity in speed with a moderate value of the Mach number. Zh. éksp. Teor. Fiz. 115, 846–864 (March 1999)     

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.     

Effect of multiple ion reflections on the structure of an ion-sound shock wave

It is shown that multiple ion reflection, arising as a result of collisional dissipation, from a shock front can produce an ion-sound shock wave with an arbitrarily large Mach number. For an exponentially small number of reflected ions, the ion-sound shock wave “degenerates” into a collisionless quasishock wave. The comparative role of viscosity and sound dispersion with different initial nonisothermality of the plasma is discussed. Zh. Tekh. Fiz. 69, 52–56 (December 1999)     

Effect of neutral pressure on the He plasma flow measurement in a linear device

Axial and azimuthal flow velocities have been measured in a linear plasma device called NAGDIS-II (NAGoya DIvertor Simulator-II), along with plasma density and electron temperature, using a vector Mach probe composed of two Mach probes, one of which is for the axial flow, and the other is for the azimuthal flow. To study the effect of neutral pressure on the deduction of the Mach numbers, the ratio of upstream to downstream currents are measured by changing the neutral pressure for the deduction of flow velocities. Helium plasma was generated with pressure of 2–35 mTorr. Since the ion gyro-radius at the magnetic flux of 300 G is larger than the probe size, an unmagnetized collisionless Mach probe theory was used for the deduction of Mach numbers and their variations. In order to check the range of collisionality, plasma density (n_e = 10¹⁰–10¹¹ cm^?3) and electron temperature (T_e = 2–9 eV) are measured by a single electric probe using a conventional collisionless probe theory. Variations of Mach number, electron temperature and plasma density with collisionless models are to be compared with those using collisional models for different pressures where ionization and ion-neutral collision are included. Mach numbers by the collisionless model are found to be overestimated by 120% for the maximum difference even in weakly collisional plasmas. A clear flow reversal exists in the axial direction with higher pressure plasma, even in the linear machine. Azimuthal flows are also measured simultaneously along with axial flows, yet they seem to be very small in the present cold ion plasma (T_i/T_e << 1).     

Die Energieaufnahme der Ionen in einem sehr schnellen Theta-Pinch

In a theta pinch with an extremely fast rising magnetic field (dB/dt 10¹¹ G/sec), a strong compression wave is produced in an initially fieldless low-density deuterium plasma. Assuming simple plasma models, a high-energy gain of the ions is expected already during the implosion of the plasma. In agreement with these calculations for a filling pressure of 20 μ D₂, a mean ion energy of 1–2 keV is determined from the first neutron emission at the end of the implosion, only 150 nsec after ignition. Decreasing the initial pressure to 10 μ D₂ does not cause any further increase of the achieved ion energy. This limitation of the ion heating is explained by a strong broadening of the current carrying layer at low densities which is observed by magnetic probe measurements. In the adiabatic compression, the mean ion energy attains values of several keV. During the first part of this phase, the energy distribution function of the ions is found to be essentially anisotropic, and monoenergetic rather than Maxwellian.     

Collisionless Plasma Expansion in the Presence of a Dipole Magnetic Field

The collisionless interaction of an expanding high–energy plasma cloud with a magnetized background plasma in the presence of a dipole magnetic field is examined in the framework of a 2D3V hybrid (kinetic ions and massless fluid electrons) model. The retardation of the plasma cloud and the dynamics of the perturbed electromagnetic fields and the background plasma are studied for high Alfvén–Mach numbers using the particle–in–cellmethod. It is shown that the plasma cloud expands excluding the ambient magnetic field and the background plasma to form a diamagnetic cavity which is accompanied by the generation of a collisionless shock wave. The energy exchange between the plasma cloud and the background plasma is also studied and qualitative agreement with the analytical model suggested previously is obtained (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Propagation of ion-acoustic waves in a dusty plasma with non-isothermal electrons

For an unmagnetised collisionless plasma consisting of warm ions, nonisothermal electrons and cold, massive and charged dust grains, the Sagdeev potential equation, considering both ion dynamics and dust dynamics has been derived. It has been observed that the Sagdeev potential V(ϕ) exists only for ϕ > 0 up to an upper limit (ϕ ≃ 1.2). This implies the possibility of existence of compressive solitary wave in the plasma. Exhaustive numerics done for both the large-amplitude and small-amplitude ion-acoustic waves have revealed that various parameters, namely, ion temperature, non-isothermality of electrons, Mach numbers etc. have considerable impact on the amplitude as well as the width of the solitary waves. Dependence of soliton profiles on the ion temperature and the Mach number has also been graphically displayed. Moreover, incorporating dust-charge fluctuation and non-isothermality of electrons, a non-linear equation relating the grain surface potential to the electrostatic potential has been derived. It has been solved numerically and interdependence of the two potentials for various ion temperatures and orders of non-isothermality has been shown graphically.      

Untersuchung der Ionenenergieverteilung in einer starken stoßfreien Kompressionswelle

In a strong collisionfree implosion wave generated by a fast theta pinch discharge the density profile and the distribution of ion energies are investigated by spectroscopic methods. At low initial pressures (20 mTorrD ₂) an overturning of the ion sheath leads to an extended density profile and an effective thermalization of the ions in the plane perpendicular to the magnetic field with energies up to 500 eV, which are comparable with the energies of the directed ion motion. However, the thermal ion energies parallel to the direction of the magnetic field are lower by more than a factor of 2. This anisotropy may not be destroyed by ion two-stream instabilities, but possibly by anisotropy instabilities.     

New interior solution describing relativistic fluid sphere

Nonlinear low-frequency electrostatic waves in a magnetized, three-component plasma consisting of hot electrons, hot positrons and warm ions have been investigated. The electrons and positrons are assumed to have Boltzmann density distributions while the motion of the ions are governed by fluid equations. The system is closed with the Poisson equation. This set of equations is numerically solved for the electric field. The effects of the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle are investigated. It is shown that depending on the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle, the numerical solutions exhibit waveforms that are sinusoidal, sawtooth and spiky. The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E ₀ was reduced. The results are compared with satellite observations.     

Stability of electrostatic ion cyclotron waves in a multi-ion plasma

We have studied the stability of the electrostatic ion cyclotron wave in a plasma consisting of isotropic hydrogen ions (H⁺) and temperature-anisotropic positively (O⁺) and negatively (O⁻) charged oxygen ions, with the electrons drifting parallel to the magnetic field. Analytical expressions have been derived for the frequency and growth/damping rate of ion cyclotron waves around the first harmonic of both hydrogen and oxygen ion gyrofrequencies. We find that the frequencies and growth/damping rates are dependent on the densities and temperatures of all species of ions. A detailed numerical study, for parameters relevant to comet Halley, shows that the growth rate is dependent on the magnitude of the frequency. The ion cyclotron waves are driven by the electron drift parallel to the magnetic field; the temperature anisotropy of the oxygen ions only slightly enhance the growth rates for small values of temperature anisotropies. A simple explanation, in terms of wave exponentiation times, is offered for the absence of electrostatic ion cyclotron waves in the multi-ion plasma of comet Halley.     

Decay instability of ion-acoustic wave train (or soliton) and formation of the shock profile

The stability of a periodic ion-acoustic wave of a finite amplitude propagating in a nonisothermal plasma is investigated. It is demonstrated that such a wave is unstable with respect to the splitting into a large number of satellite waves with effective wave numbers different from the wave number of the initial wave. The phase velocity of the satellite waves differs therefore from that of the initial pulse. Hence, the satellite waves with bigger phase velocity will “overtake” the initial pulse and turbulize the upstream plasma. The scattering of ions and electrons by the fluctuations of electric field of turbulent oscillations will cause the energy dissipation of the initial ion-acoustic wave translational motion and produce a collisionless shock wave.     

Decay of an electronic vortex of a collisionless shock wave as a possible mechanism of a “Coulomb explosion”

A new mechanism of a “Coulomb explosion,” where ions are accelerated by the electric field separating charges at the magnetic Debye radius r _B∼B/4πen _e, is proposed on the basis of a nonquasineutral model of electronic vortices in a magnetic field. It is shown by means of numerical calculations that in the process of acceleration of the ions a collisionless shock wave, whose front has an effective width of the order of δ∼r _B, determined by the breakdown of quasineutrality, is formed in a time of the order of ω _pi ⁻¹ , where ω_pi is the ion plasma frequency. The origin of such explosive dynamics is the formation of “holes” in the electron density at characteristic times of the order of ω _pe ⁻¹ (ω_pe is the electronic plasma frequency) as a result of the generation of electronic vorticity by the Weibel instability of an electromagnetic wave. Calculations for a laser pulse with intensity J∼6×10¹⁸ W/cm² show that the ions expand in the radial direction with velocities up to 3.5×10⁸ cm/s. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 10, 669–674 (25 November 1999)     

Overturning of nonlinear Alfvén waves in a collisionless plasma

An analysis is made of the overturning of nonlinear Alfvén waves in a collisionless plasma. It is shown that overturning is followed by the appearance of a region which broadens with time and consists of two collisionless shock waves which can be joined at the point s²=1. If only one Riemann invariant changes in the region of the collisionless shock waves, the waves are simple. The structures of the collisionless shock waves are constructed for different initial conditions of the nonlinear wave. The Whitham averaging method is used for this purpose. Conditions are obtained which are similar to the Rankine-Hugoniot adiabats for passage through the collisionless shock waves. The effect of overturning one of the collisionless shock waves, involving the zeroing of the density at the soliton peak on its trailing edge, is treated as a bifurcation for which a discontinuity occurs in an analog of the hydrodynamic velocity and phase of the nonlinear Alfvén wave. The width of one of the collisionless shock waves decreases with an increase in the parametera which determines the magnitude of the field discontinuity when overturning occurs.L. N. Tolstoi State University, Checheno-Ingushk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 62–67, January, 1993.     

Study of dust ion-acoustic wave propagation in the Lorentzian magnetized dusty plasma

Dust ion-acoustic waves propagation in the magnetized dusty plasma including ions, electrons and dust particulates are studied by using kinetic equation. For unbounded and collisionless plasma and in the presence of uniform external magnetic field B₀, electrons and ions with Lorentzian distribution function and dust particles with Maxwellian one are considered. Calculating dielectric tensor through the Vlasov equation solution, in the parallel propagation, dispersion relation is derived and suprathermal particle effects on the Landau damping is studied. It is shown that the Landau damping effect vanishes for parallel propagation.     

Sheath characteristics in multi-component plasma with negative ions

Properties of steady state ion sheath formed in front of a negatively biased metal plate under the influence of negative ions have been investigated in collisionless argon/SF₆ plasma. This experiment is carried out at a fixed discharge voltage and fixed filament heating power. In this experiment, the decrement in plasma pre-sheath potential drop as well as positive ion drift velocity toward the plate is experimentally recorded in the presence of negative ions. It is also found that the plasma positive ion density and plasma electron temperature decrease in the presence of negative ions. These factors attribute to the decrease of ion current toward the plate. Hence the usual ion sheath expands. Article presented at the International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

Observation of stable,high-mach-number electrostatic shocks in a collisionless plasma

Observation of stable, large amplitude ion acoustic shocks with a high Mach number M> 1.6 in a collisionless plasma is described. Discussions about the nature and behavior of the waves are also given.     

Comparison of the directional characteristics of swift ion excitation for two small biomolecules: glycine and alanine

The characteristics of ions that enter the plasma sheath with an oblique incident angle have been investigated in the presence of an external magnetic field. The ion dynamics in a collisional and collisionless magnetized plasma sheath have been numerically calculated by using a fluid model. Several values for the ion velocity at the sheath edge, orientation and strength of the magnetic field and the ion-neutral collision frequency have been considered. The results show that in a collisionless magnetized plasma sheath, the behaviour of ions that obliquely enter the sheath with some specific velocities at the sheath edge and at some specific orientations and strengths of magnetic field, is more complicated than that of ions with normal entrance angles. For the oblique entrance of ions, the weak magnetic fields cause some fluctuations in ion velocity around its boundary value, i.e. the ion velocity does not accelerate. However, the numerical calculations show that the ion dynamics in a collisional magnetized plasma sheath are the same for both normal and inclined entrance of ions into the sheath.     

Effect of ionic temperature on the modulational instability of ion acoustic waves in the presence of a magnetic field

The modulational instability of ion acoustic waves is studied in the presence of a dc magnetic field, taking the ion temperature into account. It is well known that the instability sets in for wave numbers exceeding 1.47 k_D when there is no magnetic field and the ion temperature is negligible. The instability behaviour, however, changes drastically when either the magnetic field is switched on or the ion temperature becomes important or both. In general three different regions emerge wherein the waves becomes modulationally unstable. The relative sizes of these regions change as the magnetic field, the angle of propagation and the ion temperature are varied.     

Obliquely propagating ion-acoustic solitary and shock waves in magnetized quantum degenerate multi-ions plasma in the presence of trapped electrons

The properties of obliquely propagating ion-acoustic waves have been investigated in multi-ions magnetized plasma comprising of inertial, positively and negatively charged ion fluids, trapped electrons, and negatively charged stationary heavy ions. The propagation of the waves is oblique to the ambient magnetic field which is along the z-direction. Only fast type of modes exists in the linear regime. The reductive perturbation method was adopted to derive the Korteweg– de Vries (KdV) and Burger equations, as well as the solitary and shock wave solutions of the evolved equations, have been used to analyze the properties of the small but finite amplitude waves. The effects of the constituent plasma parameters, namely, the trapping effect of electrons, the electron degenerate temperature and the viscosity coefficient on the dynamics of the small amplitude solitary and shock waves have been examined. The influence of the magnetic field and the obliquity parameter on the propagation characteristics of ion-acoustic waves are discussed.