This is a tutorial and selective review explaining the fundamental concepts and some currently open questions concerning the plasma phenomenon of the electron hole. The widespread occurrence of electron holes in numerical simulations, space-craft observations, and laboratory experiments is illustrated. The elementary underlying theory is developed of a one-dimensional electron hole as a localized potential maximum, self-consistently sustained by a deficit of trapped electron phase-space density. The spatial extent of a hole is typically a few Debye lengths; what determines the minimum and maximum possible lengths is explained, addressing the key aspects of the as yet unsettled dispute between the integral and differential approaches to hole structure. In multiple dimensions, holes tend to form less readily; they generally require a magnetic field and distribution-function anisotropy. The mechanisms by which they break up are explained, noting that this transverse instability is not fully understood. Examp...

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Electron Holes in phase-space: what they are and why they matter

The nonlinear features of dust-acoustic waves (DAWs) propagating in a multicomponent, collisional, magnetized dusty plasma whose constituents are negative dust grains, superthermal ions, and electrons are investigated. The hydrodynamic fluid equations are reduced to a damped Zakharov–Kuznetsov (DZK) equation, using the reductive perturbation technique. The DZK equation is solved using both the generalized $$(G^{{\prime }}/G)$$
 –expansion method and the Painleve analysis method. Each method gives a class of solutions. This indicates that these methods are sufficient to give all possible solutions of the DZK equation. These solutions successfully describe different kinds of nonlinear waves such as explosive, soliton, shocklike, periodical, and cnoidal waves. Additionally, the effects of different plasma parameters such as relative densities and temperatures as well as superthermality parameters of ions and electrons on the behavior of the obtained diverse waves are investigated. The relevance of the present investigation can be used to understand the cosmic dust-laden plasmas.

Propagation of dust-acoustic nonlinear waves in a superthermal collisional magnetized dusty plasma

\n The aim is to state the properties of ion acoustic solitary waves in course of collision and extract characteristics of the daughter wave in a magnetized electron–ion plasma. The magnetized plasma medium that is a constituent of white dwarfs and astrophysical plasmas that possesses relativistically degenerate electrons and thermal ions in the presence of a constant background magnetic field. The model is based on the extended Poincaré–Lighthill–Kuo (ePLK) method where a set of Korteweg–de Vries equations is obtained to show the phase shifts of colliding waves together with the amplitude and width of the born daughter solitary waves. The numerical results and presented figures regarding the amplitude and width of solitons provide a description of the influence of plasma parameters on soliton interactions, namely ion to electron temperature ratio (σi), ion cyclotron frequency (ωci), and angle between magnetic field and collision line (θ) together with their interplay in shaping the character of solitary waves. It is concluded that only rarefactive electrostatic non-linear waves are able to propagate in such plasma media. The daughter wave amplitude possesses a scaling behaviour regarding the impact angle. Interplay of the parameters on the phase shifts is presented. Ratio of amplitude and width of the daughter wave is directly proportional to the background field, the impact angle controls its maximum. It is observed that the magnetic field elevates ratio of the solitary wave amplitude to width leading it to a shorter life and hence interaction range with neighbouring sites.

The characteristics of daughter waves emerging from colliding solitary waves in astrophysical plasma media

An alternative way for calculating the magnetic field in the Lee Model Code has been used. The effects of the various anode-tip shapes on the DPF behavior have been studied. The current and impedance calculations have been employed for these investigations. For the conical anode tip, the best pinch current and soft x-ray radiation have been seen in simulations which was in good agreement with the empirical results. The investigations were carried out for the voltages of 11, 12, and 13 kV and the pressure range of 1–6 Torrs. The asymmetry in the discharging current has been investigated through three arbitrarily defined cathode current distribution patterns. The simulations showed that asymmetry in the axial discharge current increased the plasma Impedance and consequently reduced the soft x-ray emission.

The Effect of the Shape of the Anode Head on the Nitrogen Soft X-Ray Emission from a Dense Plasma Focus Device: a Numerical Investigation Using the Modified Lee Model Code Accompanied by Experiments

Increasing the lifetime of plasma semiconductors that exposed to an electron beam is an important challenge. The dynamical features of growing nonlinear waves, which transfer the energy through the semiconductors to produce defects, are examined. For this purpose, a quantum fluid model including degenerate pressures, exchange-correlation effects, and Bohm potentials are considered for GaAs semiconductor plasma composed of electrons, holes, and electron beam. The basic equations are reduced to Kadomtsev-Petviashvili (KP) equation. The latter is solved analytically using the Painleve analysis method, which yields three different nonlinear solutions describe cnoidal, periodic, and soliton waves. It is found that positive and negative nonlinear wave potentials can exist. The polarity of the wave depends on an electron streaming velocity and moving frame speed. Furthermore, controlling the streaming electron density, electron streaming velocity, and direction of transverse perturbation has great importance to minimize the effects of unfavorable nonlinear waves. The relevance of electron streaming velocity and transverse perturbation direction on nonlinear wave existence is highlighted.

Generation of soliton, cnoidal, and periodic waves during pumping GaAs by an electron beam

This paper introduces a physical solution in order to overcome the damage to semiconductors, due to increasing temperature during the pumping process. For this purpose, we use quantum hydrodynamic fluid equations, including different quantum effects. This study concludes that nonlinear acoustic waves, in the form of soliton and shock-like (double layer) pulses, can propagate depending on the electron beam temperature and the streaming speed. Therefore, one can precisely tune the beam parameters in order to avoid such unfavorable noises that may lead to defects in semiconductors.

Optimum performance of electron beam pumped GaAs and GaN

The diagnostic of magnetized radio frequency complex plasma via probing techniques and spectroscopy is challenging. However, a self-excited dust ion acoustic waves (DIAWs) have been observed employ...

Dynamics of dust-ion acoustic cnoidal and solitary pulses in a magnetized collisional complex plasma

Criteria of the electron pumping in electron-hole quantum plasma

The hollow electrode Z-pinch (HEZP) experiment is a new construction for the electromagnetic propulsion application in which the plasma is formed by the discharge between a plate and ring electrodes through which the plasma is propelled. The experimental results for 8 kV charging voltage shows that the peak discharge current is about 109 kA, which is in good agreement with the value obtained from the simulation in the slug model that simulates the sheath dynamics in the HEZP. The fitting of the discharge current from the slug model indicates that the total system inductance is 238 nH which is relatively a high static inductance accompanied with a deeper pinch depth indicating that the fitted anomalous resistance would be about 95 mΩ. The current and mass factors vary with the changing the gas pressure and the charging voltage. The current factor is between 0.4 and 0.5 on average which is relatively low value. The mass factor decreases by increasing the gas pressure indicating that the sheath is heavy to be driven by the magnetic pressure, which is also indicated from the decreases of the drive factor, hence the radial sheath velocity decreases. The plasma inductance and temperature increase with the increase of the drive factor while the minimum pinch radius decreases.

Dynamics of current sheath in a hollow electrode Z-pinch discharge using slug model

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