Steady-state Electron Distribution Function Research Articles

Effects of trapping electrons on synergy of lower-hybrid wave and electron cyclotron wave

Steady state operation is essential for Tokamak-based fusion reactor, in which the plasma current has to be fully sustained and controlled by non-inductive methods. Lower-hybrid current drive is the most effective radio-frequency current drive method, which, however, has the drawback that the driven current profile is difficult to control. Electron cyclotron current drive has the ability to deposit power and drive current in a highly localized and robustly controllable way, while the efficiency of electron cyclotron current drive is known to be significantly lower than that of lower-hybrid current drive. Due to those complementary features, the combinative usage of lower-hybrid wave and electron cyclotron wave has been proposed. The current driven by simultaneously using the waves might be significantly larger than the sum of the currents driven by the waves individually in the same plasma conditions, which is the so-called synergy effect. While the lower-hybrid current drive and the electron cyclotron current drive are both affected by the trapping effect, which implies that the synergy effect between lower-hybrid current drive and the electron cyclotron current drive may also closely related to the trapping effect. In this paper, the effects of trapping on the synergy of lower-hybrid current drive and the electron cyclotron current drive are investigated by solving the bounce-averaged quasi-linear equation with different trapping angles. The diffusions induced by the lower-hybrid wave and the electron cyclotron wave are considered simultaneously. The resulting steady-state electron distribution function as a balance between the collisions and the wave-induced diffusions is obtained numerically by the CQL3D code, which is then integrated to calculate the driven plasma current. The velocity-space fluxes are analyzed for understanding the mechanism and the physics of the synergy process. It is found that the currents driven by the waves decrease as trapping angle increases. The synergy factors also decrease as trapping angle increases, which means that the current drive processes in the synergy case are more sensitive to the trapping effect than in the single wave case. The current driven by electron cyclotron wave drops rapidly with the increase of trapping angle, while the existence of lower-hybrid wave is helpful in decelerating the dropping. The lower-hybrid wave reduces the dependency of the electron cyclotron current drive on the trapping effect. The decouple effect turns stronger as the resonance region of the lower-hybrid wave becomes wider. Increasing the power of the electron cyclotron wave leads to more accelerated electrons and more electrons with relatively high parallel velocities, which results in stronger synergy effect and less dependence on trapping.

Giant microwave photo-conductance of a tunnel point contact with a bridged gate

We study the microwave photo-response of a quantum point contact (QPC) formed on a GaAs/AlGaAs heterostructure with a high-electron-mobility two-dimensional electron gas. The QPCs are fabricated by two types of gates: a traditional split gate and a specially designed bridged gate. We observe a three orders of magnitude enhancement of the dark QPC conductance in the tunneling regime at the incident microwave power density of ∼10 mW/cm2. The response of the bridged-gate structure is more than ten times larger than that of the split-gate QPC. This giant effect and the difference between the two types of gates are explained by the influence of microwaves on the steady-state electron distribution function in the vicinity of the tunnel contact. Experimental results are in good quantitative agreement with theoretical calculations. The bridged-gate QPC can be used for the creation of highly sensitive detectors of electromagnetic radiation.

ON QUIET-TIME SOLAR WIND ELECTRON DISTRIBUTIONS IN DYNAMICAL EQUILIBRIUM WITH LANGMUIR TURBULENCE

A recent series of papers put forth a self-consistent theory of an asymptotically steady-state electron distribution function and Langmuir turbulence intensity. The theory was developed in terms of the κ distribution which features Maxwellian low-energy electrons and a non-Maxwellian energetic power-law tail component. The present paper discusses a generalized κ distribution that features a Davydov-Druyvesteyn type of core component and an energetic power-law tail component. The physical motivation for such a generalization is so that the model may reflect the influence of low-energy electrons interacting with low-frequency kinetic Alfvenic turbulence as well as with high-frequency Langmuir turbulence. It is shown that such a solution and the accompanying Langmuir wave spectrum rigorously satisfy the balance requirement between the spontaneous and induced emission processes in both the particle and wave kinetic equations, and approximately satisfy the similar balance requirement between the spontaneous and induced scattering processes, which are nonlinear. In spite of the low velocity modification of the electron distribution function, it is shown that the resulting asymptotic velocity power-law index α, where fe ~ v –α is close to the average index observed during the quiet-time solar wind condition, i.e., whereas αaverage ~ 6.69, according to observation.

Electron kappa distribution and steady-state Langmuir turbulence

In a recent pair of papers, the present author discussed a self-consistent theory of asymptotically steady-state electron distribution function and Langmuir turbulence intensity in one [P. H. Yoon, Phys. Plasmas 18, 122303 (2011)] and three [P. H. Yoon, Phys. Plasmas 19, 012304 (2012)] dimensions. The resulting electron distribution function is a type of kappa distribution that features a non-Maxwellian energetic tail component. However, while the one-dimensional solution is rigorously correct, the three-dimensional solution, which was obtained using the cylindrical coordinate representation, contains two features that may be inconsistent for field-free plasmas. One is the assumption that the resonance condition can be approximated by ω-k·v≈ω-k∥v∥. Needless to say, this is not the most general condition. The second inconsistency is that while the electron distribution is isotropic in velocity, the Langmuir turbulence intensity depends on the wave propagation direction. While these features may not be too unrealistic in the presence of an implicit ambient magnetic field, they certainly cannot be correct if the plasma is genuinely unmagnetized. In the present paper, we rectify such shortcomings by properly reformulating the problem using a spherical coordinate system in a truly free-field plasma.

Asymptotic equilibrium between Langmuir turbulence and suprathermal electrons in three dimensions

The suprathermal electron distributions with non-Maxwellian tail are commonly detected in space environment as well as in the laboratory. In a previous article [P. H. Yoon, Phys. Plasmas 18, 122303 (2011)], a self-consistent theory of asymptotically steady-state electron distribution function and Langmuir turbulence intensity was formulated in which the steady-state electron distribution is obtained by balancing the spontaneous (or collisional) drag term and velocity space diffusion term, while the steady-state turbulence intensity was obtained by balancing spontaneous and induced processes. The resulting electron distribution function was a type of kappa distribution that features a non-Maxwellian energetic tail component. However, such a discussion was based upon the assumption that both electrons and Langmuir waves are confined to one-dimensional space along the direction of the implicit ambient magnetic field. However, such an assumption may be invalidated when the implicit ambient magnetic field is sufficiently weak or absent. Consequently, in this paper the assumption of one-dimensionality is relaxed to three-dimensional situation.

Fullwave Simulations of Lower Hybrid Waves Coupled to 3D Fokker-Planck Solver: Comparison with Alcator C-Mod Experiment

Non-inductive lower hybrid current drive (LHCD) experiments have been carried out on the Alcator C-Mod tokamak and the hard x-ray (HXR) spectrum has been measured. An improved analysis technique of the experimental HXR data has been developed to more accurately evaluate the HXR flux for this type of discharge. We have simulated a similar LHCD discharge with the full wave code LHEAF (Lower Hybrid wavE Analysis based on FEM). This code, combined with the newly developed 3D Fokker-Planck (v∥, v⊥, r) and synthetic HXR diagnostic modules, to calculate the steady state electron distribution function in the plasma and the resulting HXR radiation spectrum. The simulated non-thermal x-ray proflle shave been found to be in good agreement with the measured experimental profile. In particular LHEAF simulations were able to reproduce the broad width of the measured HXR profile for a discharge with low n∥, which has been a long standing issue for LHCD simulations on Alcator C-Mod.

The excitation of backward propagated ion-acoustic instability in collision-dominated plasmas

The process of spontaneous excitation of ion-acoustic waves (IAW) of growing amplitude by electron drift, in collision-dominated weakly ionized plasmas placed in external d.c. electric field is considered from the standpoint of the linear kinetic theory based on the one-particle distributionfunction formalism. The longitudinal permeability is evaluated, with both e-n and i-n collisions taken into account, by way of the respective collision integral perturbations. The results are derived for the range of frequencies νen ≫ ω ≫ νin and νen ω ≪ k2vte2, provided that the electron drift-to-thermal velocity ratio satisfies u/vte ≪ kvte/νen ≪ 1. It is found that, for certain forms of the steady-state electron distribution function (EDF), some of which are very probable in experimental situations, the criterion for the onset of the ion-acoustic instability is satisfied not for cos θ > 0, but rather for cos θ < 0 (cos θ = u · k/uk), i.e. one can find instances in which the instability is propagated in the direction opposite to that of the electron drift. In particular, this is found to be the case in some weakly ionized gas-discharge argon plasmas, where the IAW of growing amplitude propagated backwards are expected to set in, if the i-n collision frequency is sufficiently small.

Compton scattering and the gamma-ray power-law spectrum in Markarian 421

view Abstract Citations (54) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Compton Scattering and the Gamma-Ray Power-Law Spectrum in Markarian 421 Zdziarski, Andrzej A. ; Krolik, Julian H. Abstract The nearest BL Lac object, Mrk 421, has a γ-ray spectrum which is approximately flat in EF_E_ from E <~ 50 MeV to E >~ 1 TeV. Inverse Compton scattering can explain this smooth spectrum, despite the structure in the Klein-Nishina cross section, if the injected electron distribution function is proportional to γ^-2^, where γ is the electron Lorentz factor. When this is the case, the structure imprinted on the steady state electron distribution function by the structure in the Klein-Nishina cross section is almost exactly compensated in the radiated spectrum. Because particle acceleration in strong shocks injects particles with this distribution function, this shape injection function is in fact quite plausible. Other blazars may be explained by the same model if the cutoff below TeV energies observed in other objects is due to pair production on the cosmological IR background, as suggested by Stecker et al. Publication: The Astrophysical Journal Pub Date: June 1993 DOI: 10.1086/186853 Bibcode: 1993ApJ...409L..33Z Keywords: Bl Lacertae Objects; Compton Effect; Electron Scattering; Extragalactic Radio Sources; Gamma Rays; Power Spectra; Blazars; Relativistic Electron Beams; X Ray Spectra; Astrophysics full text sources ADS | data products SIMBAD (1) NED (1)

Photon-photon absorption and the uniqueness of the spectra of active galactic nuclei

The effects of the feedback of e(+)-e(-) pair reinjection in a plasma due to photon-photon absorption of its own radiation was examined. Under the assumption of continuous electron injection with a power law spectrum E to the minus gamma power and Compton losses only, it is shown that for gamma 2 the steady state electron distribution function has a unique form independent of the primary injection spectrum. This electron distribution function can, by synchrotron emission, reproduce the general characteristics of the observed radio to optical active galactic nuclei spectra. Inverse Compton scattering of the synchrotron photons by the same electron distribution can account for their X-ray spectra, and also implies gamma ray emission from these objects. This result is invoked to account for the similarity of these spectra, and it is consistent with observations of the diffuse gamma ray background.

Electrical Characterization of Hg1−xCdxTe Alloys

ABSTRACTTheoretical models are described for calculations of charge-carrier concentrations, Fermi energy, and conduction-electron mobility as functions of x, temperature, and ionized- and neutral-defect concentrations in Hg1−xCdxTe alloys. Measurements are reported of electron concentration and electron mobility from 5–300 K for alloys with 0.17 &lt; ˗ &lt; 0.30. The electrical data are in reasonable agreement with theory and were analyzed to obtain estimates of donor and acceptor state concentrations. The electron inobilities are calculated in terms of a microscopic theory of electrical conduction derived from the solution of the Boltzmann equation for the perturbed steady-state electron distribution function and show that longitudinal opticalphonon and charged and neutral defect scattering are the dominant mobility-limiting mechanisms.

Theory of the Runaway Electron Tail

The steady-state electron distribution function of a current-carrying magnetized plasma is determined self-consistenly with the enhanced $\ensuremath{\omega}=\frac{{\ensuremath{\omega}}_{\mathrm{pe}}{k}_{\ensuremath{\parallel}}}{k}$ plasma wave spectrum it generates. Consequences include enhanced fluctuations at $\ensuremath{\omega}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{pe}}$ and energy transport by $\ensuremath{\omega}&lt;{\ensuremath{\omega}}_{\mathrm{pe}}$ waves which is found to be greater than that by neoclassical ion thermal conduction and of the order of the observed transport in intermediate-density tokamaks.

Boltzmann-Fokker-Planck model for the electron distribution function in the Earth's ionosphere

Using Boltzmann-Fokker-Planck methods and the diffusion approximation, we derive coupled non-linear equations for the first two angular moments of the electron distribution function in the Earth's ionosphere. The theory includes a phenomenological treatment of photionization of the neutral species by an externally produced photon flux; electron-ion recombination; electronneutral particle attachment; elastic, excitation, deexcitation, and ionizing electron-neutral particle collisions; and elastic electron-electron and electron-ion collisions. At high and low energies, we obtain approximate analytic solutions for the steady-state electron distribution function. Under certain conditions we also obtain the standard continuous slowing-down formulae for the steady-state electron distribution function in the diffusion approximation.

TA9 - Time-dependent calculations of carbon monoxide laser kinetics

We report here calculations of pulsed CO laser operation by revealing the time evolution of the CO vibrational distribution function in electrically pumped CO-N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -He mixtures. This is accomplished through a time-dependent solution of the coupled rate equations for the first 50 vibrational levels of CO considering V-V and V-T processes, spontaneous and stimulated emission, electron impact excitation, and deexcitation as well as kinetic heating of the lasing medium. The electron excitation rates as a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E/N</tex> are obtained from calculations of the steady-state electron distribution function in the appropriate gas mixtures. In addition to following the time dependence of pulsed operation, CW calculations have been performed for the purpose of comparison with the results of other investigators. Comparisons between the predicted time of appearance of lasing lines and experimental data is quite good for both the free-running and single-line modes of operation.

Ion acoustic instability in collisionless shocks

The effect of temperature, density and magnetic field gradients on ion acoustic instability in perpendicular collisionless shocks is investigated. For typical experimental conditions, the temperature gradient increases the growth rate by as much as an order of magnitude, the other gradients having negligible effect. It is shown that this increase is due to a distortion of the steady-state electron distribution function.

Stationary solutions to the equations of the quasi-linear approximation for a plasma with collisions

One of us [1] has considered the equations of the quasi-linear approximation for a plasma with collisions, which, for a spatially homogeneous plasma without a magnetic field in the stationary case, are as follows: (0.1) $$\begin{gathered} \frac{d}{{dp_i }}\frac{{k_i k_i }}{{k^2 }}\left\{ {\frac{1}{2}\frac{{e_a ^2 |E|^2 v_a }}{{(\omega - kv)^2 + v_a ^2 }}\frac{{df_a }}{{dp_j }}} \right\} + S_a = 0, \hfill \\ \hfill \\ \varepsilon ' = 0,\varepsilon '' = 0, \hfill \\ \end{gathered} $$ (0.2) $$\begin{gathered} \varepsilon (\omega ,k) = \varepsilon ' + i\varepsilon '' = 1 + \hfill \\ \hfill \\ + \sum\limits_a {\frac{{4\pi e_a ^2 n_a }}{{\omega k^2 }}} \int {\frac{{kv}}{{\omega - kv + iv_a }}\left( {k\frac{{df_a }}{{dp}}} \right)} dp, \hfill \\ \end{gathered} $$ in which e(ω, k) is the dielectric constant of the plasma for longitudinal waves (k‖E), fa(P) is the distribution function for particles of type a, Sa is the collision integral (which is put in the Landau form for a Coulomb plasma without allowance for polarization), and va is the reciprocal relaxation time due to collisions in the rapidly varying (pulsating) part of the distribution function. In general, va is a function of velocity, and it can be expressed via the distribution function for the background under the conditions for which the equations of the quasi-linear approximation were derived. The va for a slightly nonequilibrium plasma may be considered as some effective collisional frequency averaged over the momenta, which for the electrons makes a certain contribution to the imaginary part of the dielectric constant, where va can be calculated [2, 3] if fa is known. An important point is that Eqs. (0.1) were derived for a monochromatic longitudinal wave, and so it is not a necessary condition to have a sufficiently large width for the wave packet, which condition is characteristic of the quasi-linear theory previously given. However, as in the quasi-linear theory, it is assumed that the oscillation amplitude is small (so that nonlinear interaction between waves can be neglected), and so (0.3) $$e_a ^2 |E|^2 /m_a T_a \omega ^2 \ll 1,$$ while the dimensionless parameter ea2¦E¦2/maTava 2 may be on the order of, or even much greater than, unity. In §1 of this paper we use the equations for the energy and momentum to derive expressions for the electron drift velocity and the difference Te−Ti (electron and ion temperatures) for a two-component plasma in a given wave field on the assumption of Maxwellian background distribution functions for the electrons and ions. Expression (1.14) for the temperature difference extends to longitudinal waves a result obtained in [4] on the heating of electrons in a strong electric field. Section 2 deals with the amplitudes of steady-state high-frequency Langmuir waves when the plasma contains a steady electron beam. We derive in §3 the steady-state electron distribution function for the one-dimensional case on the basis of a model collision integral, and this differs only slightly from the Maxwellian case in which the spatial dispersion Is slight.

High Field Transport Phenomena in n-InSb at High Temperatures

Earlier theories of transport phenomena in n -InSb have been extended to include medium-high electron concentrations at high lattice temperatures (300° to 500°K) in presence of high electric fields. Polar optical mode of electron-phonon scattering has been considered to be the sole mechanism of electron scattering at these temperatures. The steady state electron distribution function has been chosen to be the Fermi-Dirac distribution function appropriate to the effective electron temperature which is determined by the energy balance condition. Nonparabolicity of the conduction band has been taken care of by the Kane's model. It is seen that the effective electron temperature is not far above the lattice temperature even at the highest attainable fields and that the Galvano-thermo-magnetic transport coefficients do not exhibit any marked dependence on the strength of electric field under the present conditions. Some limitations and approximations have also been mentioned.