Electron Distribution Function In Plasma Research Articles

Innovation for measuring the distribution function with nonextensive single electric probe

In the field of plasma diagnosis, the measurement of the distribution function is significant because the distribution function is the basis for the use of plasma kinetic theory and it is the prerequisite for analyzing many physical phenomena, such as Landau damping (wave-particle resonance phenomenon) and ion sheath. Theoretical analysis and a large number of experiments have proved that plasma components do not obey Boltzmann–Gibbs statistics and can be well described by nonextensive statistical mechanics. The field of nonextensive electric probe has also made great progress, and the invention of the nonextensive single electric probes has developed and strengthened the power of plasma diagnostics. The nonextensive electric probe can not only measure the electron nonextensive parameter of plasma that cannot be measured by traditional probes but can also measure more accurate plasma parameters that can also be measured by traditional probes, such as Te, Φp, ne, Φf, and αqFe. However, diagnosing the plasma distribution function by the nonextensive electric probe has not been thoroughly and systematically analyzed and discussed. Here, we show the measurement of the plasma distribution function with a nonextensive single electric probe. This work expands the diagnostic capabilities of the nonextensive single electric probe. We utilize the nonextensive single electric probe theory to analyze the experimental data points of the I–V curve, measure the plasma electron distribution function fvx, and display the distribution curve (figure f-vx), and we also measure the plasma parameters of qFe, Te, Φp, ne, Φf, αqFe, etc. The proposed method provides a new approach to the diagnosis of the plasma distribution function and contributes to a more accurate and comprehensive grasp of plasma, which creates better conditions for us to take advantage of plasma. These initial results illustrate the potential of the nonextensive electric probe in the field of plasma diagnosis and, more generally, in accelerating the progress of fusion-energy science and helping to understand complex physical systems.

Measurements of the populations of metastable and resonance levels in the plasma of an RF capacitive discharge in argon

The behavior of the populations of two metastable and two lower resonance levels of argon atoms in the plasma of an RF capacitive discharge was studied. The populations were measured by two methods: the method of emission self-absorption and the method based on measurements of the intensity ratios of spectral lines. It is shown that the populations of resonance levels increase with increasing power deposited in the discharge, whereas the populations of metastable levels is independent of the RF power. The distribution of the populations over energy levels is not equilibrium under these conditions. The population kinetics of argon atomic levels in the discharge plasma is simulated numerically. The distribution function of plasma electrons recovered from the measured populations of atomic levels and numerical simulations is found to be non-Maxwellian.

Diagnostic techniques for measuring suprathermal electron dynamics in plasmas (invited)

Plasmas, both in the laboratory and in space, are often not in thermodynamic equilibrium, and the plasma electron distribution function is accordingly non-Maxwellian. Suprathermal electron tails can be generated by external drives, such as rf waves and electric fields, or internal ones, such as instabilities and magnetic reconnection. The variety and importance of the phenomena in which suprathermal electrons play a significant role explains an enduring interest in diagnostic techniques to investigate their properties and dynamics. X-ray bremsstrahlung emission has been studied in hot magnetized plasmas for well over two decades, flanked progressively by electron-cyclotron emission in geometries favoring the high-energy end of the distribution function (high-field-side, vertical, oblique emission), by electron-cyclotron absorption, by spectroscopic techniques, and at lower temperatures, by Langmuir probes and electrostatic analyzers. Continuous progress in detector technology and in measurement and analysis techniques, increasingly sophisticated layouts (multichannel and tomographic systems, imaging geometries), and highly controlled suprathermal generation methods (e.g., perturbative rf modulation) have all been brought to bear in recent years on an increasingly detailed, although far from complete, understanding of suprathermal electron dynamics.

Relativistic electron distribution function of a plasma in a near-critical electric field

A corrected relativistic collision operator is used to derive a Fokker-Planck equation for the distribution function of relativistic suprathermal electrons in a weakly relativistic plasma, which is then solved by a procedure similar to that employed in Connor and Hastie [Nucl. Fusion 15, 415 (1975)]. Analytical expressions are derived for the electron distribution function in plasmas with the electric field close to critical, which is typical of plasmas with grassy sawteeth on the Joint European Torus. A numerical solution is used for determining the normalization constant, which matches the relativistic region onto the weakly relativistic region. It is found that the scaling of the runaway rate with the electric field obtained by Connor and Hastie is a good approximation in spite of their use of an incomplete form of the collision operator not conserving number of particles. The present analysis determines the proportionality constant and introduces corrections to the earlier scaling of the runaway rate with respect to the electric field. The results obtained for the electron distribution function constitute a basis for studies of experimentally observed phenomena in near-threshold electric field plasmas with a significant suprathermal electron population.

Dissipation of strong Langmuir turbulence in nonisothermal non-Maxwellian plasma

The regime of strong Langmuir turbulence characterized by the plasma nonisothermality and by the presence of an appreciable non-Maxwellian hot-electron component was experimentally studied. Turbulence was excited in the preliminary produced plasma by the relativistic electron beam. Thomson scattering of laser IR radiation served as the main diagnostic method. The spatial spectra of the Langmuir turbulence and of the attendant ion-sound turbulence were studied using Thomson collective scattering. Thomson incoherent scattering was used for studying the plasma electron distribution function and searching for the local dips of plasma density. Stark spectroscopy of turbulent microfields and the method of observation of plasma radiation at the double plasma frequency were also used. Based on the experimental data, the mechanism of Langmuir oscillation damping by plasma electrons was analyzed. The Langmuir wave conversion induced by the ion-sound turbulence is the most probable channel for energy transfer from the turbulence to plasma electrons, the low-frequency fluctuations being the direct consequence of the strong Langmuir turbulence.

On the electron energy distribution function in a Hall-type thruster

The electron energy distribution function measured at the channel exit of a small Hall-type thruster is interpreted as a beam–plasma electron distribution function with electron beam energy of several tens of electronvolts. Though unstable, the distribution function does not correspond to the completely quasilinear relaxed beam function. Comparison with the measured function in the vicinity of the channel exit shows that the electron beam energy is about 30 eV for the total voltage applied ∼200 V. The contribution of the electron beam is shown to be essential in the ionization of the working gas, even when only the single ionization processes are considered.

Vlasov theory of Mie resonance broadening in metal clusters

Dynamical electromagnetic properties of metal clusters with radii R<10 nm have been theoretically considered in the dipole approximation in a jellium model taking into exact account the spatial dispersion of free electron gas. The Vlasov equation for the plasma electron distribution function inside a spherical cluster exposed to a low-intensity external electromagnetic field is solved analytically in the linear response approximation for the cases of both diffuse and mirror reflection of electrons from the cluster boundary. The solution found is used to obtain the non-local relation between the current density and the electric field inside the cluster, which is substituted into the Maxwell equations and boundary conditions for the electromagnetic field. In the diffuse reflection case the complete set of field equations is reduced to a single integral equation which has been solved numerically to obtain the distributions of both the electric field and the electron density inside the cluster, as well as the cluster dynamical electric polarizability and the photoabsorption and photoscattering cross sections. It has been found, from the cluster photoabsorption spectra calculated, that in the considered model the width of the dipole Mie resonance is mainly due to the electron reflection from the cluster boundary, it slightly depends on the permittivity 0 of the environment, and in the case of clusters in vacuum it is described with a good accuracy by the conventional expression (R) = +bvF/R with b1.0, vF being the electron Fermi velocity.

On the theory of spherical probes and dust grains

In this paper a theoretical analysis for negatively biased single and double spherical probes in a plasma is presented. It is assumed that the motion of ions with respect to the probes is radial and that the plasma electron distribution function is Maxwellian. Photoemission from the probes and secondary electron emission are not taken into account. The analysis provides a tool which may be used to derive plasma parameters directly from experimentally obtained double probe characteristics. In addition the analysis is applied to the case of an isolated negatively charged dust grain in a plasma. The probe theory indicates that the charge on such a dust grain, in a hydrogen or argon plasma at floating potential, is approximately the same as the charge that the grain would have in a vacuum, for the case in which the grain's radius is less than or approximately equal to one tenth of the Debye length of the ambient plasma. At larger values of the grain radius the charge on the grain increases with the grain radius.

Principle and applications of a floating energy analyser

We describe a new type of energy analyser suitable for the use in plasmas having no external potential reference like ICPs and microwave discharges. It can be used to determine the ion distribution function (IDF) at a negatively biased surface and the high energy tail of the plasma electron distribution function (EDF). The EDF is measured without distortions by ion currents. This analyser was tested in a dc glow discharge and its results compared to measurements with Langmuir probes and a analyser with grounded reference. Some preliminary measurements were also performed in a rf parallel plate discharge.

Experimental study of correspondence between the electron distribution function in plasma and the second derivative of the Langmuir probe I-V characteristic

Experimental results are presented that were obtained in a glow discharge in coaxial geometry. Crossed E and H fields in the gas mixture of 0.8 Torr CO2+2.2 Torr N2+5 Torr He were used. A calculation was made of the radiation power P of a gas-discharge laser (utilizing the studied plasma as the active element) on the basis of the measured probe’s I-V characteristics. The calculated dependence P(H) agrees with the results of direct calorimetric measurements. This agreement verifies that the second derivative of a Langmuir probe I-V characteristic varies in the same way as the distribution function of plasma electrons.

Electron acceleration in plasma under the action of strong electromagnetic radiation

The acceleration of electrons in a laser plasma at the densities below the critical one is investigated by a particle simulation. It is shown that the stabilization of parametric instability and limitation of the energies of the accelerated electrons take place. The structure of the plasma electron distribution function is examined.

Physics of REB–Plasma Interaction

The results of the experimental study of the REB–plasma interaction in the two-stream instability regime are presented. The distribution function of plasma electrons has been studied with the use of the laser scattering system, soft X-ray diagnostics and a multifoil analyzer of fast electrons. It is shown that during an effective REB–plasma interaction the distribution function of heated electrons is strongly non-equilibrium. A high-energy part of the distribution function has been registered in the experiments simultaneously by three independent methods. The density of "hot" electrons with a characteristic energy of about 1 keV constitutes several per cent of the total plasma density. The experimental results obtained are discussed in terms of the two-stream instability of the REB in a plasma.

Quasi-linear theory of beam heating in a non-uniform plasma

The authors study, in a quasi-linear approximation, the absorption of oscillations excited by an electron beam in a non-uniform plasma. They find the change in the plasma electron distribution function with heating for two limiting cases: a plasma in a strong magnetic field, and a plasma without any field.

Velocity distribution of plasma electrons in the negative H2- and He-glow with superimposed longitudinal magnetic field

The negative glow plasma has been found nearly field free in axial direction. Therefore plasma electrons in the stationary glow can thermalize down to the temperature of the neutral gas, whenever their diffusion—and recombination—lifetime is high enough. Applying Boltzmann's equation to this problem, the conditions of thermalization of plasma electrons are derived as a function of the outer parameters of the plasma: vessel diameter 2R, neutral gas pressurep and longitudinal magnetic fieldB. — If plasma electrons have a too short diffusion—and recombination—lifetime to be in thermal equilibrium with the neutral gas, the electron energy increases. For this case the distribution function of plasma electrons is derived using Boltzmann's equation. Approximating the calculated energy distribution by a Maxwellian distribution function, the electron temperature in the glow is obtained as a function of the parameters:R, p, B.

Electron cyclotron interaction in a magnetic mirror compression experiment

A single stage mirror compression experiment was used to study the cyclotron resonance absorption of 3 cm and 8 mm wavelength radiation injected into the plasma early in the compression phase. The results indicate that while the high energy tail of the distribution function was altered by a few electrons that gained significant energy, the main body of the plasma electron distribution function was not significantly heated by the r.f. power. Based on a single particle analysis we are led to believe that the plasma is mainly confined to the midplane region of the magnetic mirror.

Statistical characteristics of HF oscillations excited when instability develops in a plasma-beam system

1. It was demonstrated experimentally that the oscillations that accompany the development of beam instability in plasma are random in nature and that the theory of random processes must be used in investigating them. Statistical handling of the investigated HF oscillations was used for the first time to investigate the instabilities in a plasma-beam system. 2. The authors investigated the variation of the instantantaneous spectra and the correlation functions as functions of the time required for the instability to develop. The experimental determination of the correlation functions made it possible to give a theoretical estimate of the change in the distribution function of plasma electrons in stochastic fields. 3. The distribution function of the investigated oscillations does not depend on the time required for the instability to develop and is close to the distribution function of a normal random process. 4. The time intervals during which the oscillatory processes in the plasma can be treated as stationary in the statistical sense were determined. Their values were found to lie in the 50 to 100 nsec range.

On the influence of fluctuations on the measurement of the electron distribution function in plasmas by langmuir probes

Measuring of second derivatives of probe characteristics in fluctuating plasmas produces crossmodulations between the signal and the fluctuations. Expressions for the distortions by this effect are given and compared with the experiment.

Possibility of the Negative Absorption of a Plasma-Cavity System

It is discussed that the cylindrical cavity of a reflection type, coaxial with a plasma column along the static magnetic field may amplify the incident wave. The Q-value contributed by the plasma (Qp) is calculated under the following conditions : i) The plasma is so tenuous that the perturbation theory is used.ii) The velocity distribution function of plasma electrons is as follows : f° (v) ∝ vq exp (-bys).iii) The effective collision frequency for momentum transfer is dominantly due to the collision of electron with neutral particles and varies with the speed v as νc (v) ∝vh.iV) The radius of the plasma is sufficiently smaller than the radius of the cavity. In the case of Qp>0, the incident wave is always attenuated by the plasma-cavity system. However, when Qp<0, the plasma-cavity system has a possibility of amplification or oscillation. This Characteristic of the plasma-cavity system depends sensibly on the velocity distribution function of plasma electrons.