Trivelpiece-Gould-Modes in an Axial Inhomogeneous Plasma

Experiments on the propagation of TG-modes in a weakly inhomogeneous plasma are reported. The modes travel from the high density part (ω < ω_pe) to that of lower density (ω > ω_pe). The wavelength decreases as expected but an increase of the longitudinal fieldstrength predicted by collisionless theory could not be observed. Two nonlinear effects appear one after another with increasing wave amplitude. These are the sideband instability and a decay into the drift frequency range occuring in the whole plasma column. Neither the region ω ≈ ω_pe nor the very vicinity of the exciter antenna are distinguished. The second instability is accompanied by effective electron heating.     

Return current instability and its effects on beam-plasma system

The return current induced in a plasma by a relativisitc electron beam generates a new electron-ion two-stream instability (return current instability). Although the effect of these currents on the beam-plasma e-e instability is negligible, there exists a range of wave numbers which is unstable only to return current (RC) instability and not to e-e instability. The electromagnetic waves propagating along the direction of the external magnetic field, in which the plasma is immersed, are stabilized by these currents but the e.m. waves with frequencies,ω ²≪Ω _e ² ≪ω _pe ² (Ω _e andω _pe being cyclotron and plasma frequency for the electrons of the plasma respectively) propagating transverse to the magnetic field get destabilized. Heuristic estimates of plasma heating, due to RC instability and due to decay of ion-acoustic turbulence generated by the return current, are made. The fastest time scale on which the return current delivers energy to the plasma due to the scattering of ion-sound waves by the electrons can be ∼ω _pi ⁻¹ (ω _pi being the plasma frequency for the ions).     

Excitation of short-wave oscillations in the ionospheric plasma by the field of a high-power radio wave with extraordinary polarization due to induced scattering by ions

We analyze excitation of electron-cyclotron or upper hybrid oscillations of the ionospheric plasma at a frequency that is close to the pump frequency as a result of induced scattering of a high-power radio wave with extraordinary polarization by ions. The excited oscillations have a small wavelength of the order of the Larmor electron radius, which allows them to propagate near and below the reflection level of an extraordinary radio wave. We found the instability increment and threshold field, which results from collisional absorption of plasma waves. It is shown that the threshold field is minimal near the reflection level of an extraordinary radio wave when the radio wave frequency f₀ is between electron harmonics nf_Be with n≥2. In an ionospheric F layer it is of the order of 1 W/m. Such fields are easily obtained in ionospheric heating experiments allowing for radio-wave field swelling in the reflection region. In the vicinity of electron harmonics f_o≅nf_Be, the threshold field is increasing. For f_o<nf_Be with f_o≅nf_Be the instability does not develop because of the absence of plasma oscillations with a frequency that is close to the pump frequency (the latter also refers to the case f_o<2f_Be). The expressions obtained are generalized to the case in which the instability under consideration is excited by the field of an ordinary radio wave in the region of its quasilongitudinal propagation. We discuss the possibility of using the emergence of very short-wave plasma oscillations for explaining the experimentally observed phenomena. Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow Region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 5, pp. 541–560, May, 1997.     

Resonant decay of a Langmuir wave in the presence of dust grains in a cylindrical plasma

The resonant parametric decay of a Langmuir wave into a backward propagating Langmuir wave and an ion acoustic (IA) wave is studied in a cylindrical dusty plasma. The analysis shows that the frequency of the IA mode decreases with the parameter δ_c (where δ_c is the ratio of the ion density to the electron density) for negatively charged dust grains. The growth rate of the resonance decay instability (RDI) and the threshold required for its onset also decrease with δ_c and are strongly dependent on the electron to ion temperature ratio for both positively and negatively charged dust grains. The results obtained also illustrate the dependence of the threshold of the resonance decay instability (μ_th) on the plasma cylinder radius.     

Plasma satellites of X-ray lines of ions in a picosecond laser plasma

We present the results of our measurements of the spectra for multicharged ions in a plasma produced by moderately intense (about 10¹⁷Wcm^?2) picosecond laser pulses. They suggest the existence of intense plasma oscillations with a frequency appreciably lower than the frequency of the laser radiation. The observed spectrum for the plasma satellites of the Lyman Ly_α doublet of the hydrogenic F IX ion in a dense plasma was modeled theoretically. The resulting doublet profile was shown to have a complex structure that depends non-trivially both on the plasma density and on the frequency and amplitude of the plasma oscillations. The positions of the satellites and their separations allowed them to be associated with intense electrostatic oscillations with an amplitude of (4–6)×10⁸Vcm^?1 and a frequency near (0.7–1)×10¹⁵s^?1. Assuming the oscillation frequency to be determined by the strength of the magnetic field B generated in the plasma, we obtained an estimate of B that is in reasonable agreement with other measurements and estimates of this quantity. Our theoretical analysis allowed explanation of the emission spectra observed when flat fluoroplastic targets were heated by intense picosecond laser pulses.     

Stationary Propagation of Coupled Nonlinear High Frequency Waves and Ion-Acoustic Waves in a Plasma

Stationary solutions of the coupled equations for high frequency transverse waves in a plasma and for the low frequency ion motion (T_e?T_i) are investigated numerically. The use of the nonlinear hydrodynamic equations instead of the linear wave equation for ion acoustic waves allows to look for solutions without restrictions of the Mach number M = V/c_s (V group velocity, c_s ion acoustic velocity) and the ratio ω/ω_pe (ω frequency of the HF-field, ω_pe electron plasma frequency at the undisturbed region). In particular, supersonic soliton-like solutions with n/n_o > 1 were found. Dispersion effects due to charge separation are not included.     

Spectra of high-frequency waves in hot magnetized plasmas

On the basis of numerical solution of the dispersion equation, we obtain the spectra of weakly damped high-frequency waves in a hot magnetized plasma for the case where the electron cyclotron frequency ω_He is below the plasma frequency ω_pe. It is shown that the longitudinal wave propagating at an angle to the magnetic field evolves into the slow extraordinary wave for the refractive index n ≤ 1. For n ≫ 1, the longitudinal-wave frequency increases with the refractive index, and the wave evolves into the wave with anomalous dispersion if the angle θ between the wave vector and the magnetic field is close to 90°. In the same range of θ angles, Bernstein modes appear in the spectrum of plasma eigenmode oscillations. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 3, pp. 258–266, March 2006.     

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)     

On the ponderomotive force and the effect of loss reaction on parametric instability

In this paper, the growth rate, ponderomotive force and the exciting condition for parametric instability are derived by considering the loss reaction using a new method. On the basis of the hydrodynamic equations, we take the production and loss reactions in plasma into account to derive the coupling equations for the electron plasma oscillation and ion acoustic oscillation, and obtain the growth rate for the parametric instability, the ponderomotive force and the exciting condition. The result shows that (a) the production reaction has no effect on the parametric instability, and the effect of loss reaction on the parametric instability is a damping one, (b) the more intensive the external field or pump is, the larger the growth rate is, (c) there exist two modes of the ponderomotive force, i.e.\ the high frequency mode and the low frequency mode, and (d) when ponderomotive force counteracts the damping force, the oscillations become non-damping and non-driving. The ratio of the electron plasma oscillation to ion acoustic oscillation is independent of the loss reaction and the external field.     

Current neutralization and plasma polarization for intense ion beams propagating through magnetized background plasmas in a two-dimensional slab approximation

A two-dimensional electromagnetic Particle-in-Cell （PIC） simulation model is proposed to study the propagation of intense, ion beams with beaIn width wb small compared to the electron skin depth c/wpe through background plaslnas in tile presence of external applied magnetic fields. The effcctive eleetron gyrora,dius wge is found to be an important parameter for ion beam transport in the presence of magnetic fields,In the bealn regions, the background plasmas respond differently to the ion beanl of width wb〈wge and wb 〉 wge for the given magnetic field and beaan encrgy, For the case of beam width wb 〈 wge with relative weak external magnetic fiehts, the rotalion effects of plasma electrons a,re found to be signifieant and contributes to the signitica,nt enilaneeinent of the self electric and seif-magnetic fields. While for the ease of beam width wb 〉 wge with relative strong external magnetic fields, the rotation effects of plasma cleetrons are strongly inhibited and a, well neutraliza, tion of ion beam current can be found. Finally, the influences of diftiuent beam widths. beam energies and magnetic fields on the neutralization of ion bc, anl eurrellt are summarized for the eases of wb 〈 wge〈 c/wpe,wge 〈wb〈c/wbp and wb〈c/wpe〈wge.     

Transverse oscillations of a long-pulse electron beam on alaser-formed channel

An intense relativistic electron beam may be transported in low-pressure gas using an ion channel which focuses and guides the beam. The beam can be unstable to the growth of transverse oscillations caused by the electric force between the beam and channel-the ion hose instability. Beam propagation on channels created by photoionization of gas with an excimer laser is discussed. Ion hose oscillations have been recorded which have a betatron wavelength of approximately 1.5 m. The growth rate of the ion hose instability in the linear regime was measured as 1.67±0.45. At this level of growth, the amplitude of beam oscillations equals the channel radius after a period of one-third of an ion oscillation time     

Is the Abrikosov model applicable for describing electronic vortices in plasmas?

A new model of electronic vortices in plasma is studied. The model assumes that the profile of the Lagrangian invariant I, equal to the ratio I=Ω/n of the electronic vorticity to the electron density, is given. The proposed approach takes into account the magnetic Debye scale r _B ≃B/4πen, which leads to breakdown of plasma quasineutrality. It is shown that the Abrikosov singular model cannot be used to describe electron vortices in plasmas because of the fundamental limitation on the electron vorticity on the axis of a vortex in a plasma. Analysis of the equations shows that in the model considered for the electronic vorticity, the total magnetic flux decreases when the size r ₀ of the region in which I≠0 becomes less than c/ω_pe (ω_pe is the electron plasma frequency). For ω _pe r ₀/c≪1, an electronic vortex is formed in which the magnetic flux decreases as r ₀ ² and the inertial component predominates in the electronic vorticity. The structure arising as ω _pe r ₀/c⇒0 is a narrow “hole” in the electron density, which can be identified from the spectrum of electromagnetic waves in this region. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 461–466 (10 April 1998)     

W-Band Second-Harmonic Gyrotron Traveling Wave Amplifier with Distributed-Loss and Severed Structures

The second harmonic TE₀₂ gyrotron traveling wave amplifier (gyro-TWT) is a high-power, broadband, millimeter-wave amplifier with a low applied magnetic field. Mode-selective interaction circuits were applied to suppressing spurious oscillations. However, the mode-selective interaction circuit may perturb the operating mode in the gyro-TWT. A multi-stage gyro-TWT design with distributed-loss and severed structures is proposed to stabilize the amplification. This study presents a nonlinear analysis of typical oscillations, including absolute instability, gyrotron backward oscillation (gyro-BWO) and reflective oscillation. The lossy and severed sections of the multi-stage gyro-TWT seem to increase effectively the start-oscillation currents of the absolute instability, gyro-BWO, and reflection oscillation. The multi-stage gyro-TWT is predicted to yield a peak output power of 215 kW at 89.9 GHz with an efficiency of 14.3 %, a saturated gain of 60 dB and a bandwidth of 1.7 GHz for a 100 kV, 15 A electron beam with an axial velocity spread _z/ _z = 5%.     

Instability of electromagnetic waves in transversely magnetised semiconductor-plasmas

Using the hydrodynamic model of plasmas the general dispersion relation is derived in the collisiondominated regime when a d.c. magnetic field is applied (Y-axis) transversly to the propagation vector k (Z-axis), and the d.c. electric field is inclined to the Z-axis in the X-Z plane. The dispersion relation is solved for intrinsic and extrinsic semiconductors to explore the possibility of wave instability. The threshold conditions of wave oscillations are obtained. In n-InSb the frequency of the oscillation attains a maximum value when the electron cyclotron frequency is equal to the electron collision frequency. In intrinsic InSb instability is possible only in the long wavelength region for E₀ ? 10 kVm^?1 when B₀> 0.2 T, while for lower values of B₀, E₀ should be greater 20kVm^?1. The energy dependent collision frequency has a significant effect on the threshold frequency of oscillation.     

Propagation of electrostatic energy through a quantum plasma

The theory of propagation of electrostatic energy through an infinite, homogeneous electron–ion quantum plasma is presented. Simple expressions for the energy flow, energy density, and energy velocity of longitudinal oscillation waves in the system are derived using the linearized quantum hydrodynamic theory for the electron fluid, which incorporates the important quantum statistical pressure and electron diffraction force, while the optical response of the ion particles is characterized by the classical frequency‐dependent dielectric function, ?_ion. Both cases of plasmon (high‐frequency) and quantum ion‐acoustic (low‐frequency) waves are considered.     

Review of relaxation oscillations in plasma processing discharges

Relaxation oscillations due to plasma instabilities at frequencies ranging from a few Hz to tens of kHz have been observed in various types of plasma processing discharges. Relaxation oscillations have been observed in electropositive capacitive discharges between a powered anode and a metallic chamber whose periphery is grounded through a slot with dielectric spacers. The oscillations of time-varying optical emission from the main discharge chamber show, for example, a high-frequency (\sim 40~kHz) relaxation oscillation at 13.33Pa, with an absorbed power being nearly the peripheral breakdown power, and a low-frequency ( \sim 3 Hz) oscillation, with an even higher absorbed power. The high-frequency oscillation is found to ignite plasma in the slot, but usually not in the peripheral chamber. The kilohertz oscillations are modelled using an electromagnetic model of the slot impedance, coupled to a circuit analysis of the system including the matching network. The model results are in general agreement with the experimental observations, and indicate a variety of behaviours dependent on the matching conditions. In low-pressure inductive discharges, oscillations appear in the transition between low-density capacitively driven and high-density inductively driven discharges when attaching gases such as SF₆ and Ar/SF₆ mixtures are used. Oscillations of charged particles, plasma potential, and light, at frequencies ranging from a few Hz to tens of kHz, are seen for gas pressures between 0.133 Pa and 13.33 Pa and discharge powers in a range of 75--1200 W. The region of instability increases as the plasma becomes more electronegative, and the frequency of plasma oscillation increases as the power, pressure, and gas flow rate increase. A volume-averaged (global) model of the kilohertz instability has been developed; the results obtained from the model agree well with the experimental observations.     

Allgemeine Berechnung der Elektronenverteilungsfunktion von schwach ionisierten Plasmen in beliebig zeitabhängigen elektromagnetischen Feldern

The behaviour of a weakly ionized plasma in external, arbitrarily time-dependent, electromagnetic fields is treated within the framework of kinetic theory. The Boltzmann kinetic equation is solved using the Lorentz ansatz, taking into account elastic collisions between electrons and neutral particles and assuming that the collision frequency is independent of the electron velocity. The drift velocity of electrons enters into the isotropic part f₀ and into the direction-dependent part f₁ of the electron distribution function. A method is given for the calculation of the drift velocity, which is calculated explicitly for the important but difficult case of a sinusoidal electric field in the presence of a magnetic switching field. f₀ and f₁ are calculated; f₀ is investigated generally. f₀ consists of an expansion in generalized Laguerre polynomials. The influence of the electromagnetic fields on the distribution function and its time variation is discussed and the relaxation behaviour is shown. The following two special cases are calculated explicitly: a linear rising electric field and a sinusoidal electric field, both in the presence of a constant magnetic field.     

Linear and Nonlinear Wavetransformation and Absorption in the Inhomogeneous Plasma Capacitor

The parametric decay process in inhomogeneous layers existing near the plasma boundaries or in front of antennas and probes in a plasma has been investigated. The linear enhancement of the pump field near ω = ω_p, the threshold fieldstrength, the wavenumber selection rules and the influence of spontaneous low frequency fluctuations are discussed in detail using a one-dimensional model of the inhomogeneous plasma capacitor. According to this model the instabilities appear in the layers with maximum linear transformation and (linear) absorption. In addition, a strong nonlinear part of absorption in the presence of the instability has been observed. The level of the spontaneous low frequency fluctuations influences strongly the spectrum of the parametrically excited ion waves. The experiments show a redistribution of the transferred ion acoustic wave energy over the whole wave continuum up to ω_pi, if a sufficient strong spontaneous fluctuation level exists in the plasma. It is impossible, however, to excite ion acoustic turbulence by the decay of the high frequency pump field under the present conditions. The conditions for the linear field enhancement are disturbed by the action of the ponderomotive forces changing the density profile near the critical point before reaching the strong pump amplitude being necessary for the excitation of a cascade of decay processes.     

束—等离子体放电中低频等离子体波的非稳定性研究

本文采用非中性冷等离子体模型,研究了沿磁场入射的电子束和等离子体相互作用引起的低频等离子体波的非稳定性。计算表明,在束-等离子体放电情况下,振动频率和增长率都随电子束密度增加而增加,当束电流一定时,它们随l增加而略有增加。l=1时其频率数量级与离子迴旋频率相同。l≥3时,振动频率几乎不随k_z变化,其振动频率和增长率数量级与低混杂振荡频率相同,实质是低混杂漂移非稳定性。理论结果与实验一致。     

Nonlinear longitudinal oscillations of relativistic plasma

The investigation has been made of nonlinear forced longitudinal oscillations of a relativistic plasma. It was demonstrated that: a) the nonlinear terms (v▽)p arising in the equations of motion do not restrict the electron oscillation amplitude increase in the region of plasma resonance; b) the nonlinear terms due to the relativistic nature of oscillations, firstly, limit the oscillation amplitude in the resonance region and, secondly, lead to the development of a parametric instability. The harmonic, sub- and ultraharmonic oscillations turned out to be unstable. The conditions for the instability as well as expressions for the growth rates of unstable oscillations were obtained.