non-Maxwellian Electron Distribution Research Articles

Generation of Electron Suprathermal Tails in the Upper Solar Atmosphere: Implications for Coronal Heating

We present a mechanism for the generation of non-Maxwellian electron distribution function in the upper regions of the solar atmosphere in the presence of collisional damping. It is suggested that finite amplitude, low frequency, obliquely propagating electromagnetic waves can carry a substantial electric field component parallel to the mean magnetic field that can be significantly larger than the Dreicer electric field. This long wavelength electric fluctuation is capable of generating high frequency electron plasma oscillations and low frequency ion acoustic-like waves. The analysis has been performed using 1-1/2D Vlasov and PIC numerical simulations in which both electrons and ions are treated kinetically and self consistently. The simulation results indicate that high frequency electron plasma oscillations and low frequency ion acoustic-like waves are generated. The high frequency electron plasma oscillation drives electron plasma turbulence, which subsequently is damped out by the background electrons. The turbulence damping results in electron acceleration and the generation of non-Maxwellian suprathermal tails on time scales short compared to collisional damping. Bulk heating also occurs if the fluctuating parallel electric field is strong enough. This study suggests that finite amplitude, low frequency, obliquely propagating, electromagnetic waves can play a significant role in the acceleration and heating of the solar corona electrons and in the coupling of medium and small-scale phenomena.

A Heat Transport Model Including the Effect of Non-Maxwellian Electron Distribution and Its Application in Laser Produced Plasma

An electron heat transport model is given for studying laser-to-x-ray conversion of inertial confinement fusion. The electron heat flux is derived based on a non-Maxwellian electron distribution, and the behavior of the heat flux is discussed. The effect of the non-Maxwellian electron distribution on inverse bremsstrahlung heating rate and electron-ion heat transfer rate are also included in the present model. The simulation results show that the effects of the non-Maxwellian electron distribution on laser absorption efficiency, laser-to-x-ray conversion efficiency and electron temperature in the coronal region are important.

Spectrum analysis of three-body recombination rates for non-Maxwellian electron distributions under ultra-fast laser irradiation

Calculation of the three-body recombination rate is reformulated in a manner in which the velocity contribution is more explicit and the recombination rate is spectrum analysed for electron velocity distributions under ultra-fast laser irradiation. Electron distribution functions are calculated by using a two-dimensional Fokker-Planck simulation. The shape of the recombination rate spectrum with respect to the velocity is found to be well described by vf(v) where f(v) is the pitch-angle-averaged velocity distribution. It is shown visually that the increase in the slow electron population effectively enhances the recombination rate. The effect of a model energy loss on the recombination rate is also discussed.

Fast modelling of low-pressure radio-frequency collisional capacitively coupled discharge and investigation of the formation of a non-Maxwellian electron distribution function

The principles of fast modelling (FM) of a low-pressure radio-frequency capacitively coupled discharge are presented. They are based on averaging over fast electron and ion motions and on eliminating a small spatial scale, the Debye radius. As a result, the solution of a self-consistent system of the electron kinetic equation, Poisson and ion continuity equations takes approximately 10 min on a 486 PC. The calculation of discharge parameters has been performed for a wide range of current and pressure. The comparison with full-scale Monte Carlo calculations and experimental data has been performed. The performed comparisons demonstrate that the developed method of fast modelling has a good accuracy for calculating the global parameters such as central plasma density, applied voltage, sheath thickness, ionization rate, etc, and the profiles of plasma density and the electric fields. The accuracy of the electron distribution function (EDF) calculation is high when the EDF form is not enriched by slow electrons, and seems satisfactory in the case of a strongly peaked EDF. The results are in qualitatively good agreement with the experiment. The quantitative agreement is mainly within a factor of two. This discrepancy can be attributed to the fact that the EDF form is very sensitive to the details of plasma description, e.g. small variation of cross-sections results in considerable changes in the EDF. The mechanism of non-Maxwellian EDF formation due to non-locality effects has been analysed. The evolution of the low-pressure radio-frequency collisional capacitively coupled discharge with current and pressure variation has been investigated.

Effect of an electron beam generated in an X-pinch plasma on the structure of the K spectra of multiply charged ions

The first experimental studies of an electron beam generated in an X pinch on the XP machine (Cornell University, USA) and the BIN machine (P. N. Lebedev Physical Institute, Russian Academy of Sciences) are reported. It is shown that it is possible in an X pinch to isolate the effect of a plasma-generated electron beam on the multiply charged ion radiation. The intensities of the satellite lines corresponding to Li-, Be-, B-, and C-like ions are calculated for the Al spectrum on the basis of a collisional-radiative model with a non-Maxwellian electron distribution in the plasma. The effect of an electron beam on the multiply charged light ion radiation in an X-pinch plasma is demonstrated. Comparing our calculations with the experimental spectra, we conclude that the present model can be used to estimate the electron beam intensity.

Stimulated Raman scattering in non-Maxwellian plasmas

Inverse bremsstrahlung heating of laser-produced plasmas can result in a non-Maxwellian electron distribution function. This leads to a modification of Langmuir wave collisional and Landau damping coefficients and may result in changes in the stimulated Raman scattering threshold and scattered light frequency spectra. The importance of these effects for current laser–plasma interaction experiments is discussed.

Investigation of nonthermal particle effects on ionization dynamics in high current density ion beam transport experiments

Light ion inertial fusion experiments require the presence of a moderate density background gas in the transport region to provide charge and current neutralization for a high current density ion beam. In this article, we investigate the effects of nonthermal particles such as beam ions or non-Maxwellian electron distributions on the ionization dynamics of the background gas. In particular, we focus on the case of Li beams being transported in an argon gas. Nonthermal particles as well as thermal electrons are included in time-dependent collisional-radiative calculations to determine time-dependent atomic level populations and charge state distributions in a beam-produced plasma. We also briefly discuss the effects of beam ions and energetic electrons on the visible and vacuum ultraviolet (VUV) spectral regions. It is found that the mean charge state of the gas, and hence the electron density, is significantly increased by collisions with energetic particles. This higher ionization significantly impacts the VUV spectral region, where numerous resonance lines occur. On the other hand, the visible spectrum tends to be less affected because the closely spaced excited states are populated by lower energy thermal electrons.

Ion energy distribution functions in a planar inductively coupled RF discharge

Low pressure inductively coupled plasmas in planar geometry have found increasing interest as a means of plasma surface modification in the last few years. These discharges provide high plasma densities at simultaneously low impact energies of the ions. In this paper the formation of an ion energy distribution at a grounded wall of such a discharge is studied experimentally as well as theoretically. The ion energy distribution functions are measured via a retarding field analyser. The effect of a parasitic capacitive coupling from the induction coil is reported. The ion energy distributions observed experimentally are interpreted as being formed in the collisional presheath and being accelerated in the collisionless sheath. A quantitative analysis is presented on the basis of a simple model, which takes into account the non-thermal character of the electron energy distribution. It is shown that observed ion impact energies are correlated to non-Maxwellian electron distributions and that models that imply the assumption of a Maxwellian overestimate the ion impact energies.

Investigation of hot electrons in electron-cyclotron-resonance ion sources

The hot electrons in the plasma of an electron-cyclotron-resonance ion source are investigated by three passive diagnostics: bremsstrahlung, electron cyclotron emission, and diamagnetism. For this type of plasma the feasibility of the second diagnostic is an innovative development, as is the simultaneous use of two independent plasma diagnostics for either steady-state or transient experiments. In the steady-state experiments the bremsstrahlung and the electron cyclotron emission are interpreted by comparing the experimental spectra with simulated spectra calculated for the first time from a non-Maxwellian electron distribution. The ‘‘perpendicular temperatures’’ obtained by the two diagnostics are in good agreement. In the transient experiments the electron cyclotron emission and the diamagnetic signals are recorded to study the electron density and the electron lifetime. All these experiments performed using the Minimafios ion source working at 18 GHz with oxygen gas demonstrate trends and saturation effects when the gas injection pressure and the radio-frequency power are varied.

Effects of non-Maxwellian electron distributions on charge-state populations in laser-produced plasmas

The effects of a non-Maxwellian electron distribution on the charge-state populations in a plasma with the distribution characterized by the function f(v)=Fm exp[−(v/vm)m] with 2≤m≤5 are investigated. In the underdense region of a laser produced plasma, the parameter m would depend on the electron temperature, electron density, and the average ionization state of the plasma in addition to the optical laser intensity and wavelength. The ion populations are obtained by solving the rate equations in which the coefficients are evaluated by integrating the cross sections over the non-Maxwellian electron distributions. The scaling of m with column density and optical laser intensity in laser exploding foils is obtained. The effects of a non-Maxwellian electron distribution on the charge-state populations in both selenium and molybdenum foils, similar to those used to model recent x-ray laser experiments, are calculated. The effects on the dominant populations are found to be small, less than a dozen of percents.

The ionization balance of the Fe in the solar corona for a non-Maxwellian electron distribution function

The ionization equilibrium of the Fe in the solar corona for a non-Maxwellian electron distribution with an enhanced number of particles in the high-energy tail is presented. A parametric form of the distribution function is used to demonstrate the changes in the ionization equilibrium with changes in the shape of the distribution. The results over the range of temperature 105 K ≤ T ≤ 108 K for different deviations of the distribution from a Maxwellian are given in tabular form. The results can be used for specific applications in the solar corona, especially in the active corona, where deviations from the Maxwellian distribution can be significant.

Spectroscopic measurements of the parameters of the ablation clouds of deuterium pellets injected into tokamaks

Spectroscopic measurements have been made of the parameters of the luminous cloud surrounding deuterium pellets injected into the Princeton Large Torus (PLT) [Phys. Rev. Lett. 55, 1398 (1985)] and the Tokamak Fusion Test Reactor (TFTR) [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1987), Vol. 1, p. 171], with the measurements on the latter described formally here for the first time. The electron densities determined from the Stark broadening of the Balmer alpha and beta lines ranged from 5×1015–1×1018 cm−3, while the temperatures obtained from the line to continuum intensity ratios and the ratio of the intensities of the Balmer alpha and beta lines ranged from 0.9 to 3 eV. Balmer alpha emission powers as high as 100 kW were measured. The electron temperature (1.5±0.2 eV) and density (3±1×1017 cm−3 ) at the time of maximum emission from intact pellets were essentially the same for the two tokamaks, although the volumes of both the discharges and the pellets were roughly ten times larger in TFTR than in PLT. The data were taken in Ohmically heated plasmas, except for a limited number of discharges in PLT with low-power (approximately half the Ohmic heating power) ion cyclotron heating for which the results are the same as with Ohmic heating alone. Various factors that may influence the results of measurements of this type are discussed, including self-absorption, low-density plasma surrounding the most intense region of an ablation cloud, fluctuations in the emission intensity, and non-Maxwellian electron distributions. The results of the present experiments are similar to measurements of the pellet cloud parameters in other machines.

Non-Maxwellian electron distributions in models of the solar atmosphere

In this paper, the solar models of Fontenla et al. (1990) are extended to coronal temperatures using optically thin radiative losses and a semicircular loop geometry. The effects of a non-Maxwellian high-energy tail of the electron distribution function is tested by performing a Fokker-Planck calculation of the tail. The results show that the downward conductive heat flux is very clsoe to that given by Braginskii (1965) for small departures from a Maxwellian distribution. The effects of the high-energy tail of the electron distribution on element ionization are computed and found to be negligible for all ionization states of O, Ne, and Si. It is concluded that, for quiet sun loop models in stationary energy balance, the ionization state of all elements is not significantly affected by the non-Maxwellian tail of the electron velocity distribution, and that the heat flux can be computed by considering only small first-order departures from the Maxwellian distribution.

Continuum wave functions and bremsstrahlung in plasmas based on the ion-sphere and jellium models

We determine the density of states and subject the continuum wave functions to normalization and asymptotic conditions consistent with the ion-sphere and jellium models of the plasma. To illustrate the difference between the two models, we present bremsstrahlung calculations for aluminum and iron plasmas. We also compare the exact quantum-mechanical results with the predictions of the Born-Elwert approximation and with some predictions based on phase-shift calculations. Finally, we discuss briefly the effect of a non-Maxwellian electron distribution.

Synchrotron radiation spectrum for galactic-sized plasma filaments

The radiation spectrum for synchrotron-emitting electrons in galactic-sized Birkeland current filaments is analyzed. It is shown that the number of filaments required to thermalize the emission spectrum to blackbody is not reduced when a non-Maxwellian electron distribution is assumed. If the cosmic background radiation (CBR) spectrum (T=2.76 K) is due to absorption and re-emission of radiation from galactic-sized current filaments, higher-order synchrotron modes are not as highly self absorbed as lower-order modes, resulting in a distortion of the blackbody curve at higher frequencies. This is especially true for a non-Maxwellian distribution of electrons for which the emission coefficient at high frequencies is shown to be significantly less than that for a Maxwellian distribution. The deviation of the CBR spectrum in the high-frequency regime may thus be derivable from actual astrophysical parameters, such as filamentary magnetic fields and electron energies in the model. >

Microwave absorption in stellarators with a non-Maxwellian electron distribution function

The magnetic configurations of two stellarators, ATF [Fusion Technol. 10, 170 (1986)] and TJ-II [Fusion Technol. 13, 315 (1986)], are used as examples to study the influence that a superthermal component in the electron distribution function has upon the electron cyclotron resonance heating absorption process for microwaves propagating in the first and second harmonic of the electron cyclotron frequency. The non-Maxwellian tail is simulated by adding a drifting Maxwellian to a bulk distribution function and an analytical form of the weakly relativistic dielectric tensor is obtained. The quantitative, and more importantly, the qualitative differences between nonrelativistic and relativistic models are also presented. A numerical analysis shows that an increase of up to 50% in the absorption power with respect to the pure Maxwellian models, can be obtained if sufficient superthermal populations are present in the plasma.

A collisional-radiative model applicable to argon discharges over a wide range of conditions. I. Formulation and basic data

A collisional-radiative model with an extended region of applicability is developed for an argon atom plasma. Atom-atom inelastic collisions and diffusion losses of the metastable states along with the electron-atom inelastic collisions and radiative processes are considered in this model, taking into account 65 effective levels. Among the analytical expressions used for the corresponding cross sections, special attention is paid to those determining the set of cross sections for excitation by electrons from the ground state, owing to the possibility of utilising the formulae recommended in kinetic modelling studies of discharges in argon or in mixtures including argon atoms. The numerical method developed makes it possible to investigate the mechanisms by which the excited levels are populated in a non-equilibrium argon plasma characterised (even in the case of a non-Maxwellian electron distribution) by a set of parameters, such as the electron kinetic temperature Te, the atom temperature Ta, the ion temperature Ti, the electron number density ne, the ground state atom population n1, the discharge tube (or the plasma column) radius R and the optical escape factors Lambda mn and Lambda m, which are dependent only on the quantities Ta, n1 and R in many cases of practical interest.

Non-Maxwellian electron distributions and continuum X-ray emission in inverse Bremsstrahlung heated plasmas

The heating of a completely ionized plasma by inverse Bremsstrahlung absorption (IB) is studied by numerically integrating the time varying kinetic equation for electrons, and the resulting distribution functions are used to calculate the continuum X-ray emission. The shape of the distribution functions is determined by the competition between IB and electron-electron collisions, and, in all the uniform plasma simulations, the authors find that the distributions are well fitted by the formula Cmexp(-( nu / nu m)m) where m is between 2 and 5. They find the dependence of m on alpha =Z2 nu osc/ nu th2, where Z is the atomic number, nu osc is the oscillation velocity in the laser field and nu th is the thermal velocity: m( alpha )=2+3/(1+1.66/ alpha 0.724). More importantly, in the realistic case of a space and time dependent kinetic simulation of a Be plasma heated by a Nd laser, including heat flow and ion motion, this fit remains valid for electron densities below 0.75 Nc (with constant m), although other effects come into play closer to the critical surface. Thus, these simple results can be used to determine the continuum X-ray spectrum due to Bremsstrahlung (BR) and to direct radiative recombination (DRR).

Review of transport investigations with ECRH

Localised heating of the electron component of plasmas using electron cyclotron waves has been used in a number of devices in an attempt to determine energy and particle transport. Results have been obtained from conventional power and particle balance analyses, analysis of sawteeth heat pulse propagation and by using phase sensitive detection of plasma perturbations induced by modulated ECRF power. Global particle confinement is generally degraded during ECRH; in most cases, a drop in ne is observed despite an increase in the edge particle source. Increased gas puffing can, however, maintain or raise ne. Local analysis of particle transport indicates higher particle diffusion and, possibly, a reduction of inward convection. Increases in the amplitude of fluctuations of poloidal magnetic field and plasma density in the scrape-off layer seem to be correlated with degradations in particle confinement. Global energy content typically follows an L-mode type of scaling but H-modes have been generated in diverted discharges. Some sensitivity to the shape of the power deposition profile is seen with localised central deposition being favoured. At low ne, when strongly non-Maxwellian electron distributions can be produced, tau E may be increased above the ohmic value. Analysis of temperature waves produced by modulating the ECRH power at frequencies approximately 1/ tau E gives values of the effective thermal diffusivity close to those obtained by other techniques.

Electron cyclotron emission during electron cyclotron heating in tokamaks

Plasma heating and current drive in tokamaks by means of high power electron cyclotron waves result in generating non-Maxwellian electron distribution functions. The properties of the radiation emitted at the electron gyro frequency and its harmonics by such non-thermal distributions are investigated. The electron distribution function is evaluated by means of a 3-D bounce averaged Fokker-Planck code for some typical heating scenarios, and the related emission spectra are computed. It is shown that the peculiar features of the spectra are sensitively related to subtle kinetic processes such as quasi-linear flattening of the electron distribution or formation of perpendicular tails and toroidal effects on the electron orbits, which are known to play an important role in electron cyclotron heating and current drive.