Nonthermal Electron Distribution Research Articles

Electron and ion temperature gradients and suprathermal tail strengths at Parker's solar wind sonic critical point

New constraints are placed on the electron and ion temperature gradients at Parker's sonic point, demonstrated here as the location for an ion where the force of gravity and the electric field parallel to the magnetic field are balanced. The equal‐temperature, one‐fluid versions of these results precisely recover Parker's necessary and sufficient conditions for the supersonic expansion. The two species constraints are largely within the Parker envelope. For all possible critical points, the electron partial pressure must exceed 0.2437 of the plasma pressure at this point. The location of the critical point relative to the isothermal critical point is determined by the partial pressure average of the electron and ion logarithmic derivatives of temperature at the critical point. The bulk acceleration at the critical point is controlled by (1) the ion (as distinct from the electron) temperature gradient at this point and (2) the ratio of the ion to electron pressure at the critical point. The sonic point is a velocity space deLaval nozzle rather than a traditional configuration space nozzle. Critical points are most frequently accompanied by positive radial ion and electron temperature gradients. The electron and ion temperature gradients required for a critical point are coupled and not arbitrary. Parker's one‐fluid discussion requires, by this analysis, both electron and ion temperature gradients to have positive radial exponents β = 3/4 near the critical point and a local effective gas polytrope behavior of γ = 10/13 < 1. For equal electron and ion temperatures, all possible critical points require positive ion temperature gradients at the critical point. Nonthermal electron and ion distributions are demonstrated to be generally required near the sonic critical point of a spherically symmetric solar wind. Effective polytrope exponents near the critical point range from γi(r*) < 1 and 1.5 > γe(r*) > 1/3. The allowed critical points with γ < 1 are used to infer a range of nonthermal κ distributions that permit this unusual γ < 1 behavior; ion nonthermal suprathermal tail indices ranging between 2 < κi < 5 are required, reflective of decidedly nonthermal distributions at the critical point and consistent with previous inferences of their size [Scudder, 1992b]. Even when unequal electron and ion temperatures are considered, the vast preponderance of the critical points delineated also is found with 1/3 < γe < 1, with the attendant range of electron nonthermal indices, κe, ranging from 2 to the Maxwellian limit of ∞. Critical points with maximal acceleration invariably occur for a positive electron temperature power law exponent of βe ≃ 1.12 that corresponds to κe ≃ 3.3, whether or not the ions and electrons have a common temperature at the critical point.

Quantum cascade lasers without intersubband population inversion.

The fundamental limits of the operation of quantum cascade intersubband lasers are investigated. Band nonparabolicities combined with the nonthermal electron distribution in the active region make laser action possible even in the absence of global $k$-space population inversion between subbands, i.e., when the lifetime of the lower subband exceeds that of the upper one. A laser based on local $k$-space population inversion with single-quantum-well active regions is demonstrated and its performance compared to that of quantum cascade lasers with double-quantum-well active regions.

Fokker‐Planck modeling of auroral wave‐particle interactions

Observations of electron velocity distributions in the auroral zone, carried out by spacecraft and by rockets, have found high‐energy, magnetic field‐aligned, suprathermal tails in regions where strong wave activity in the lower hybrid range of frequencies is also detected. A causal link between these observations could in principle arise from quasi‐linear diffusion of the electrons, driven by Landau resonant lower hybrid waves. To investigate this, a two‐dimensional finite difference Fokker‐Planck code has been written. The results of the numerical investigations carried out with this code indicate that the observed lower hybrid wave intensities are sufficient to produce strongly nonthermal electron distributions, which are similar to those observed.

Ion Sound Solitary Waves with Density Depressions

We show that a non-thermal electron distribution may change the nature of ion acoustic solitons. If the ions are assumed to respond as a fluid to perturbations in the potential, with no significant trapping in a potential well, then a thermal plasma only supports a solitary waves with a density peak. However, with a suitable distribution of non-thermal particles, solitary waves with both density peaks and density depressions may coexist. This may have applications to magnetosperic observations, where solitary structures with lowered densities have been observed in regions where the electron distribution is also seen to be non-thermal.

Parabolic valence-band dispersion in GaAs for optical interband transitions.

The initial nonthermal electron distribution at densities \ensuremath{\le}${10}^{14}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ is studied in GaAs:Be by investigating the band-to-acceptor luminescence after excitation by picosecond laser pulses. Two peaks are observed originating from electrons generated out of the heavy- and light-hole valence bands, respectively. This assignment is confirmed by polarization dependence. Variation of excitation energy yields the valence-band dispersions for wave vectors 0.04(\ensuremath{\pi}/a), where purely parabolic terms dominate. The light- and heavy-hole masses relevant for optical interband excitation of a 100 GaAs surface close to the band edge are determined to be ${\mathit{m}}_{\mathrm{lh}}$=0.093${\mathit{m}}_{0}$\ifmmode\pm\else\textpm\fi{}0.007${\mathit{m}}_{0}$ and ${\mathit{m}}_{\mathrm{hh}}$=0.54${\mathit{m}}_{0}$\ifmmode\pm\else\textpm\fi{}0.05${\mathit{m}}_{0}$.

On the harmonic structure of solar radio spikes

This paper analyzes the frequency structure of the bands of electron-cyclotron maser instability. The calculations show that each term of the series describing the growth rate provides a double-peak structure, if we accept a nonthermal electron distribution with a ‘two-side’ loss-cone. The ratio of central frequencies is found to be non-integer in general case. We conclude that the harmonic structure of solar radio spikes observed in a number of events can be imitated by electron-cyclotron maser emission of mildly relativistic electrons with a power-law momentum distribution.

Analysis of electron cyclotron emission by lower-hybrid current drive plasmas

Electron cyclotron emission may be used for diagnosing non-thermal electron distribution functions generated by radio-frequency current drive. Our attention is concentrated in theX-mode-downshifted second-harmonic range of frequencies, by inspecting at the radiation collected in the horizontal low-magnetic-field side of a tokamak. The cut-off presence eliminates the thermal first-harmonic emission and the non-thermal one may be observed without other inference. The electron distribution function is modelled by a suitable sum of drifting Maxwellians for reproducing the flat tails usually obtained in the presence of lower-hybrid power injection. This model is time saving as far as the computer simulations are concerned and permits a lot of runs in order to accomplish a wide parameters exploitation. A sensitivity analysis of ECE intensity is performed with respect to the main moments of the suprathermal electrons distribution function. The analysis shown that the radiation spectra are very sensitive to the perpendicular energy and to the number of fast electrons, while only a weak dependence on the parallel energy is found.

Semiconductor-coupled Josephson junctions

Superconductor-semiconductor-superconductor junctions have been studied using 50-nm-thick silicon membranes sandwiched between niobium electrodes. The normal state resistance is determined by barriers at the interfaces. The supercurrent is well described by the Kupriyanov-Lukichev theory for the proximity effect in SINIS (superconductor-insulator-normal metal-insulator-superconductor) structures, whereas the voltage-carrying state is understood as resulting from a nonthermal distribution of electrons in the semiconductor. The details of the distribution depend on elastic and Andreev scattering at the interfaces. By analogy to semiconductor heterostructures, the authors propose that these structures be called superconducting quantum wells, a concept which is applicable to other double-barrier tunnel devices as well. >

Electron cyclotron emission from nonthermal tokamak plasmas

Electron cyclotron emission can be a sensitive indicator of nonthermal electron distributions. A new, comprehensive ray-tracing and cyclotron emission code that is aimed at predicting and interpreting the cyclotron emission from tokamak plasmas is described. The radiation transfer equation is solved along Wentzel–Kramers–Brillouin (WKB) rays using a fully relativistic calculation of the emission and absorption from electron distributions that are gyrotropic and toroidally symmetric, but may be otherwise arbitrary functions of the constants of motion. Using a radial array of electron distributions obtained from a bounce-averaged Fokker–Planck code modeling dc electron field and electron cyclotron heating effects, the cyclotron emission spectra are obtained. A pronounced strong nonthermal cyclotron emission feature that occurs at frequencies relativistically downshifted to second harmonic cyclotron frequencies outside the tokamak is calculated, in agreement with experimental results from the DIII-D [J. L. Luxon and L. G. Davies, Fusion Technol. 8, 441 (1985)] and FT-1 [D. G. Bulyginsky et al., in Proceedings of the 15th European Conference on Controlled Fusion and Plasma Heating, Dubrovnik, 1988 (European Physical Society, Petit-Lancy, 1988), Vol. 12B, Part II, p. 823] tokamaks. The calculations indicate the presence of a strong loss mechanism that operates on electrons in the 100–150 keV energy range.

Radio emission from chemically peculiar stars

In five VLA observing runs the initial survey of radio emission from magnetic Bp-Ap stars by Drake et al. is extended to include a total of 16 sources detected at 6 cm out of 61 observed, giving a detection rate of 26 percent. Of these stars, three are also detected at 2 cm, four at 3.6 cm, and five at 20 cm. The 11 new stars detected as radio sources have spectral types B5-A0 and are He-weak and Si-strong. No classical (SrCrEu-type) Ap stars have yet been detected. The 16 detected sources show a wide range of radio luminosities with the early-B He-S stars on average 20 times more radio luminous than the late-B He-W stars and 1000 times more luminous than Theta Aurigae. Multifrequency observations indicate flat spectra in all cases. Four stars have a detectable degree of circular polarization at one or more frequencies. It is argued that the radio-emitting CP (chemically peculiar) stars form a distinct class of radio stars that differs from both the hot star wind sources and the active late-type stars. The observed properties of radio emission from these stars may be understood in terms of optically thick gyrosynchrotron emission from a nonthermal distribution of electrons produced in a current sheet far from the star. In this model the electrons travel along magnetic fields to smaller radii and higher magnetic latitudes where they mirror and radiate microwave radiation.

Effect of a nonthermal electron distribution on the electron-phonon energy relaxation process in noble metals.

We show experimentally that the electron distribution of a laser-heated metal is a InonthermalR distribution on the time scale of the electron-phonon (e-ph) energy relaxation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{E}}$. We measured ${\mathrm{\ensuremath{\tau}}}_{\mathit{E}}$ in Ag and Au films as a function of lattice temperature (10--300 K) and laser-energy density (0.3--1.3 J ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$), combining femtosecond optical transient-reflection techniques with the surface-plasmon polariton resonance. Calculations support the experimental result that the nonthermal distribution leads to a IslowerR e-ph energy relaxation process below room temperature, compared to the thermalized limit.

Terahertz-frequency-resolved transient conductivity of nonthermal electrons photoexcited in GaAs.

We calculate the terahertz-frequency dependence of the transient linear conductivity \ensuremath{\sigma}(t,\ensuremath{\omega}) of electrons photoinjected in GaAs by a subpicosecond optical pulse. The electrons are assumed to relax to the conduction-band edge mainly by emitting longitudinal-optical phonons. We find that the occurrence of a nonthermal electron distribution, in combination with the time dependence of the mean effective momentum relaxation rate, leads to a non-Drude-like frequency response. In particular, the conductivity at large frequencies (\ensuremath{\omega}/2\ensuremath{\pi}>1 THz) immediately after photoexcitation exceeds the corresponding conductivity after the electrons relax to the conduction-band edge. We also discuss how the Pines-Nozieres conductivity sum rule has to be modified under the nonequilibrium conditions.

Multifrequency observations of a solar microwave burst with two-dimensional spatial resolution

Frequency-agile interferometry observations using three baselines and the technique of frequency synthesis were used to obtain two-dimensional positions of multiple microwave sources at several frequency ranges in a solar flare. Source size and brightness temperature spectra were obtained near the peak of the burst. The size spectrum shows that the source size decreases rapidly with increasing frequency, but the brightness temperature spectrum can be well-fitted by gyrosynchrotron emission from a nonthermal distribution of electrons with power-law index of 4.8. The spatial structure of the burst showed several characteristics in common with primary/secondary bursts discussed by Nakajima et al. (1985). A source of coherent plasma emission at low frequencies is found near the secondary gyrosynchrotron source, associated with the leader spots of the active region.

Non-thermal distribution of electrons for high current density

In the presence of a large current and long energy relaxation times the conduction electrons are not in thermal equilibrium. The energy distribution h(ε) is calculated with an inelastic relaxation time method. An effective electron temperature can be defined. There are clear deviations between the distribution functions of the equilibrium and the non-equilibrium case. However, their effect on physical properties such as electronic transition probabilities is minor.

Vertical-viewing electron cyclotron emission diagnostic for the DIII-D tokamak

The vertical-viewing electron cyclotron emission diagnostic on DIII-D will be used to assess the nonthermal electron distributions resulting from electron cyclotron heating and electron cyclotron current drive experiments. Electron cyclotron emission along a vertical chord is collected using an ellipsoidal focusing mirror and retroreflector (the latter to minimize wall reflections). The emission is then transported ∼20 m using a quasioptical transport system composed of eight lenses and three mirrors, and detected between the 2nd and the 10th harmonics by a fast-scanning (40-Hz) Michelson interferometer. The entire system has been aligned using a Gaussian beam simulator and absolutely calibrated in situ using a cold liquid-nitrogen bath. Details of the design, installation, and calibration will be discussed.

Effects of non-thermal electron distributions on parallel electron cyclotron emission and absorption for energetic electrons in mirror devices

Calculations are presented of the effects of nonthermal features on electron cyclotron emission parallel to the magnetic field from energetic electrons in a mirror geometry. The calculations were performed using a one-dimensional radiation transport model with fully relativistic emission and absorption coefficients and generic axial profiles, which allow comparison of the results to a variety of experiments. Where necessary, specific parameters were chosen to be representative of present-day large mirror devices. Primary focus is on the conditions for which the emission is optically thick and the relationship between the radiation temperature (intensity) and the temperature of a primary hot component. It is demonstrated that for many (but not all) conditions the radiation temperature is a useful measure of the hot electron temperature. In particular, dilute super hot tails on the distribution do not adversely affect the radiation temperature to any great degree.

Diagnosis of mildly relativistic electron velocity distributions by electron cyclotron emission in the Alcator C tokamak

Electron cyclotron emission from nonthermal electron distributions has been measured with a vertical view and control of multiple reflections. The observed intensities at the first few harmonics provide information that can be used to deduce the electron distribution function. Although harmonic overlap restricts the detail that can be obtained when the distribution is very energetic, a fitting procedure enables useful results to be obtained. The distribution functions during Ohmic runaway and lower-hybrid current drive and heating are presented. The current-drive distributions are not inconsistent with theoretical Fokker–Planck calculations, giving perpendicular and parallel ‘‘temperatures’’ around 60 keV and 200 keV, respectively. The runaway cases have quite similar distributions.

Subpicosecond dynamics of electron injection into GaAs/AlGaAs quantum wells

We model the subpicosecond evolution of a nonthermal electron distribution injected into a GaAs/AlGaAs quantum well using an ensemble Monte Carlo simulation which includes electron-electron scattering. The calculated results are in good agreement with the experimental time dependence of the carrier distribution function from recent bleaching experiments with carrier-carrier scattering the dominant mechanism contributing to band filling.

Solar microbursts at meter-dekameter wavelengths

Microbursts are low-brightness temperature bursts observed by the Clark Lake radioheliograph. The bursts occur several times per hour during quiet Sun periods and are seen at the observing frequencies from 30 to 70 MHz. They are stationary at a given frequency, have short rise times, and durations of 2-10 s. Observations of the bursts are presented and given an interpretation in terms of plasma emmission. The burst properties suggest that they are weak type III bursts. The observations imply that energy releases on the Sun continue to be impulsive, with nonthermal electron distributions, for small releases of energy. The relation of the bursts to type III bursts and hard X-ray bursts are discussed.

Measurements of mildly relativistic electron distribution functions during lower hybrid heating and current drive (invited)

Nonthermal electron distribution functions, arising during lower hybrid heating and current drive, have been measured on Alcator C tokamak using vertical electron cyclotron emission and also bremsstrahlung x-ray emission. The methods used for deconvolving the distribution from the radiation measurements are summarized and examples are given of results from different types of plasma, illustrating the present capabilities of the techniques. The cyclotron emission results are consistent with the x-ray analysis but provide additional information, particularly at lower energies (30–100 keV). The x rays are less ambiguous at high energy and give good forward/backward asymmetry diagnosis. The quality of information appears to be already adequate for a quantitative comparison with theory, but further experimental improvements seem possible.