Stochastic heating of electrons by a large-amplitude extraordinary wave in plasma

Stochastic heating of plasma electrons by a large-amplitude electromagnetic wave propagating across a strong external magnetic field is studied theoretically and numerically. An analytic estimate of the threshold wave amplitude at which heating begins is obtained. The dependence of the average electron energy on the magnetic field and plasma density is investigated using particle-in-cell simulations.     

Kinetic Simulations of EC Plasma Heating and Current Drive in the L-2M Stellarator

The ECHLAB code, intended for a self-consistent numerical analysis of the evolution of the electron distribution function and the spatial structure of the electromagnetic field during EC plasma heating in a stellarator, is described. The results from calculations of plasma heating and current drive under conditions corresponding to experiments on EC plasma heating by an X2-mode in the L-2M stellarator are presented. It is shown that, at the existing level of microwave power, the energy deposition region displaces only slightly during heating. The energy is mainly absorbed by relatively fast passing electrons. The influence of locally trapped electrons on the efficiency of current drive is insignificant.     

Trapping of electrons and acceleration of the electron bunch in a wake wave

The process of electron trapping by a wake wave excited by a laser pulse in a plasma channel in the case where the electron bunches are injected into the vicinity of the maximum of the wakefield potential at a velocity lower than the wave phase velocity is considered. The mechanism for the formation of a compact electron bunch in the trapping region when only the electrons of the injected bunch that are trapped in the focusing phase mainly undergo the subsequent acceleration in the wakefield is analyzed. The influence of the spatial dimensions of the injected bunch and its energy spread on the length of the trapped electron bunch and the fraction of trapped electrons is studied analytically and numerically. For electron bunches with different ratios of their spatial dimensions to the characteristic dimensions of the wake wave, the influence of the injection energy on the parameters of the high-energy electron bunch trapped and accelerated in the wake-field is studied.     

Effect of plasma nonlinearity on the beam-plasma interaction in a hybrid plasma waveguide

A study is made of the characteristic features of the effect of plasma nonlinearity in a slow-wave structure on microwave generation by an electron beam and on electron beam energy losses. Theoretical results on the plasma density variation, the amplitude of the excited microwaves, and the velocity distribution function of the beam electrons are compared with the experimental data. It is shown that the self-consistency between the decreasing plasma density gradient and the spatial variation of the amplitude of an amplified wave in a slowwave structure leads to a significant (severalfold) increase in the efficiency with which the electron beam energy is converted into microwave energy in short pulses. The predictions of the theoretical model developed to describe the non-steady-state beam-plasma interaction agree well with the experimental data.     

Electron energy balance and ionization in the channel of a stationary plasma thruster

The paper presents results of numerical simulations of the electron dynamics in the field of the azimuthal and longitudinal waves excited in the channel of a stationary plasma thruster (SPT). The simulations are based on the experimentally determined wave characteristics. The simulation results show that the azimuthal wave displayed as ionization instability enhances electron transport along the thruster channel. It is established that the electron transport rate in the azimuthal wave increases as compared to the rate of diffusion caused by electron scattering from neutral atoms in proportion to the ratio between the times of electron? neutral collisions responsible for ionization and elastic electron scattering, respectively. An expression governing the plasma conductivity is derived with allowance for electron interaction with the azimuthal wave. The Hall parameter, the electron component of the discharge current, and the electron heating power in the thruster channel are calculated for two model SPTs operating with krypton and xenon. The simulation results agree well with the results of experimental studies of these two SPTs.     

Nonlinear relativistic plasma resonance: Renormalization group approach

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.     

Electron-Ion collisions in relativistically strong laser fields

Electron-ion collisions in relativistically strong electromagnetic fields are considered. Analytical and numerical analyses both show that all qualitative effects characteristic of collisions in nonrelativistic strong fields [1–3] occur at relativistic intensities of an electromagnetic wave as well. Expressions for Joule plasma heating and for the energy distributions of fast particles are derived from simple analytic considerations and are confirmed by numerical simulations. It is found, in particular, that, due to the relativistic increase in the mass of a scattered electron, Joule heating in ultrarelativistic fields becomes more intense as the field amplitude grows.     

Nonlinear properties of two-dimensional wake waves excited by relativistic electron bunches in plasma

The properties of a nonlinear plasma wake wave excited by an axially symmetric relativistic electron bunch are studied. It is shown that the nonlinear dependence of the wake wavelength on the transverse coordinate leads to distortion of the phase front of the wake wave and to steepening and oscillations of the transverse profile of the wakefield. The magnetic field of the wake wave is nonzero and oscillates at a frequency higher than the plasma electron frequency. Because of nonlinearity, the amplitude of the excited wake wave changes with distance from the bunch. The increase in nonlinearity leads to the development of turbulence and chaotization of the wakefield and results in the switching-on of the thermal effects and plasma heating.     

Spatial distribution of the plasma temperature under ion-beam fast ignition

Results are presented from theoretical studies of the formation of the spatial temperature distribution in plasma heated by a high-energy ion beam under the conditions in which the free path lengths of ions of different parts of the beam in plasma varies in the course of its heating. Special attention is paid to ionbeam heating of deuterium-tritium (DT) plasma under the conditions of fast ignition of inertial confinement fusion (ICF) targets. The influence of the initial energy spectrum of the heating beam ions on the spatial temperature distribution is investigated. For beams with different ion charges, masses, and initial energy spectra, criteria are determined for the formation of different types of spatial temperature distributions, namely, a distribution with a negative temperature gradient and a quasi-uniform distribution, which correspond to the edge ignition of a precompressed ICF target, as well as a distribution with a temperature peak, which corresponds to the ignition in the inner region of the target.     

Displacement of the electron cyclotron resonance heating region and time evolution of the characteristics of short-wavelength turbulence in the 3D magnetic configuration of the L-2M stellarator

Reflection of the heating extraordinary microwave incident obliquely onto the surface of the electron cyclotron resonance (ECR) at the second harmonic of the electron gyrofrequency in the 3D magnetic configuration of the L-2M stellarator was studied experimentally. The plasma was heated using two gyrotrons with a total power of 600–700 kW, the specific heating power being 2.4–2.8 MW/m³. The displacement of the ECR region in the course of heating was monitored by measuring the phase of the reflected extraordinary wave. It is found that the growth of the plasma density is accompanied by the displacement of the ECR heating region from the center of the plasma column toward its periphery. The coefficient of reflection of the heating microwave beam from the ECR region was measured. The spectra of short-wavelength (k _s ≈ 30 cm^?1) plasma density fluctuations were explored by analyzing backscattered microwave radiation. A tenfold increase in the energy of short-wavelength density fluctuations and the growth of the spectral density of fluctuations in the frequency range of 0.3–1.5 MHz were observed.     

Acceleration of electron bunches injected into a wake wave

The process of trapping and acceleration of nonmonoenergetic electron bunches by a wake wave excited by a laser pulse in a plasma channel is investigated. The electrons are injected into the vicinity of the maximum of the wakefield potential with a velocity lower than the wave phase velocity. The study is aimed at utilizing specific features of a wakefield with substantially overlapped focusing and accelerating phases for achieving monoenergetic electron acceleration. Conditions are found under which electrons in a finite-length nonmonoenergetic bunch are accelerated to high energies, while the energy spread between them is minimal. The effect of energy grouping of electrons makes it possible to obtain compact high-energy electron bunches with a small energy spread during laser plasma acceleration.     

Quasilinear modification of the spectra of cyclotron emission from a toroidal plasma near the ECRH frequency

A study is made of the modification of the spectra of electron cyclotron emission from an ECR heated plasma in a toroidal magnetic confinement system into which the heating radiation is launched from the low-field side. It is shown that, at frequencies close to the heating frequency, cyclotron emission can become more intense because of the deformation of the distribution function of the resonant electrons. This effect can be used to diagnose the slightly pronounced quasilinear perturbations of the electron distribution in the thermal energy range, which are typical of experiments on ECR plasma heating. Results of a qualitative analysis carried out for model electron distribution functions are presented, and examples of three-dimensional numerical simulations of a circular tokamak are described.     

Effect of microwave reflection from the region of electron cyclotron resonance heating in the L-2M stellarator

In experiments on electron cyclotron resonance (ECR) heating of plasma at the second harmonic of the electron gyrofrequency in the L-2M stellarator, the effect of partial reflection of high-power gyrotron radiation from the ECR heating region located in the center of the plasma column was revealed. The reflection coefficient is found to be on the order of 10^?3. The coefficient of reflection of an extraordinary wave from the second-harmonic ECR region is calculated in the one-dimensional full-wave model. The calculated and measured values of the reflection coefficient are found to coincide in order of magnitude.     

Influence of the plasma density and heating power on the intensity of electron cyclotron emission in the L-2M stellarator

Results are presented from experiments on studying the plasma behavior in the L-2M stellarator in regimes with a high power deposition in electrons during electron cyclotron heating at the second harmonic of the electron gyrofrequency (X mode) at heating powers of P _in=120–400 kW and average plasma densities from n _e≤3×10¹⁹ to 0.3×10¹⁹ m^?3. It is shown that, as the plasma density decreases and the heating power increases, the electron cyclotron emission spectrum is modified; this may be attributed to a deviation of the electron energy distribution from a Maxwellian and the generation of suprathermal electrons. At low plasma densities, the emission intensity at the second harmonic of the electron gyrofrequency increases, whereas the plasma energy measured by diamagnetic diagnostics does not increase. This poses the question of the correctness of determining the plasma electron temperature by electron cyclotron emission diagnostics under these conditions.     

Diagnostics of plasma oscillations by the field of surface waves guided by a dielectric waveguide

The potentialities of the diagnostic method for determining the plasma parameters by recording the surface waves guided by a dielectric waveguide and scattered by plasma oscillations are discussed. The use of surface (slowed) waves makes it possible to improve both the sensitivity and spatial resolution of measurements. The scattering is the most intense near the waveguide cutoff, at which the dependence of the wave propagation constant on the plasma density is the steepest. It is shown experimentally that the method proposed makes it possible to determine the discharge plasma density and electron energy and to estimate the amplitude of the RF field of the plasma waves forming the discharge and the amplitude of plasma density oscillations in these waves. The data obtained from the measurements of the amplitudes of both high-and low-frequency plasma density oscillations by the proposed method agree satisfactorily with theoretical predictions. The experimental data on the plasma density are confirmed by other diagnostic measurements. The ways of reducing measurement errors are proposed.     

Excitation of helicons by current antennas

Depending on the angle θ between the wave vector and the magnetic field, helicons are conventionally divided into two branches: proper helicons (H mode), propagating at small θ, and Trivelpiece–Gould waves (TG mode), propagating at large θ. The latter are close to potential waves and have a significant electric component along the external magnetic field. It is believed that it is these waves that provide electron heating in helicon discharges. There is also commonly believed that current antennas, widely used to ignite helicon discharges, excite essentially nonpotential Н modes, which then transform into TG modes due to plasma inhomogeneity. In this work, it is demonstrated that electromagnetic energy can also be efficiently introduced in plasma by means of TG modes.     

Mechanism for ion acceleration along the normal to the axis of a beam-plasma discharge in a weak magnetic field

The mechanism responsible for the previously discovered phenomenon of acceleration of an ion flow along the normal to the axis of a beam-plasma discharge in a weak magnetic field is investigated. It is suggested that the ions are accelerated in the field of a helicon wave excited in the discharge plasma column. It is shown theoretically that, under actual experimental conditions, a helicon wave can be excited at the expense of the energy of an electron beam. The spectral parameters and spatial structure of the waves excited in a beam-plasma discharge in the frequency ranges of Langmuir and helicon waves are studied experimentally and are shown to be related to the parameters of the ion flow. Theoretical estimates are found to agree well with the experimental results.     

Multimode parametric instability during electron cyclotron heating

A study is made of the generation of electron Bernstein waves in the interaction of a microwave field with a magnetized plasma during electron cyclotron heating. Parametric resonance accompanied by simultaneous conversion of microwave-field energy into the energy of numerous waves is analyzed. The relevant dispersion relation is investigated using the Hill method, which has recently been applied for the first time to examine the parametric interaction between high-power microwave radiation and plasmas. It is shown that the dispersion relation can be used to describe the onset of modulational instability at multimode parametric resonance. The growth rate of the modulational instability is obtained. Efficient energy transfer from the microwave field into Bernstein modes and, accordingly, into plasma electrons may be one of the main mechanisms for electron cyclotron resonance plasma heating.     

Electron bunch acceleration in the wake wave breaking regime

Results are presented from theoretical analysis and 2D PIC simulations of electron acceleration in a breaking wake plasma wave generated by a short intense laser pulse during its interaction with a finite-length underdense plasma layer. The high energy electron energy spectrum and transverse emittance are obtained. It is shown that, for laser pulse lengths above the plasma wake wavelength, the wakefield-accelerated electrons are further accelerated by the electromagnetic wave. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 4, pp. 291–310. The text was submitted by the authors in English.     

Determination of the power absorbed during plasma ECR heating from diamagnetic measurements

Probable reasons are discussed why the absorbed energy determined from diamagnetic measurements in experiments on electron cyclotron resonance plasma heating is less than the input microwave energy.