Formation of bound states of electrons in spherically symmetric oscillations of plasma
Maxim Dvornikov
备注：
9 pages in LaTeX2e, no figures; paper was significantly modified, 2 new references added, some inessential mathematics was removed, many typos were corrected; final variant to be published in Physica Scripta
We study spherically symmetric oscillations of electrons in plasma in the frame of classical electrodynamics. Firstly, we analyze the electromagnetic potentials for the system of radially oscillating charged particles. Secondly, we consider both free and forced spherically symmetric oscillations of electrons. Finally, we discuss the interaction between radially oscillating electrons through the exchange of ion acoustic waves. It is obtained that the effective potential of this interaction can be attractive and can transcend the Debye-Huckel potential. We suggest that oscillating electrons can form bound states at the initial stages of the spherical plasma structure evolution. The possible applications of the obtained results for the theory of natural plasmoids are examined.
I reply here to the comment of Dr Shmatov on my recent work and demonstrate the invalidity of his criticism of the classical physics description of the formation of bound states of electrons participating in spherically symmetric oscillations of plasma.
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We develop a method for investigating the relationship between the shape of a 1-particle distribution and non-linear electrostatic oscillations in a collisionless plasma, incorporating transverse thermal motion. A general expression is found for the maximum sustainable electric field, and is evaluated for a particular highly anisotropic distribution.
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We present a derivation of the dispersion relation for electrostatic oscillations (ESOs) in a zero temperature quantum plasma. In the latter, degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations. The Poisson equation determines the electrostatic wave potential. We consider parameters ranging from semiconductor plasmas to metallic plasmas and electron densities of compressed matter such as in laser-compression schemes and dense astrophysical objects. Due to the wave diffraction caused by overlapping electron wave function due t…
The self-excitation of plasma series resonance (PSR) oscillations is a prominent feature in the current of low pressure capacitive radio frequency (RF) discharges. This resonance leads to high frequency oscillations of the charge in the sheaths and enhances electron heating. Up to now, the phenomenon has only been observed in asymmetric discharges. There, the nonlinearity in the voltage balance, which is necessary for the self-excitation of resonance oscillations with frequencies above the applied frequencies, is caused predominantly by the quadratic contribution to the charge-voltage relation…
The boundary problem about behavior (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with specular boundary conditions is analytically solved. The kinetic equation of Vlasov--Boltzmann with integral of collisions of type BGK (Bhatnagar, Gross, Krook) and Maxwell equation for electric field are applied. Distribution function for electrons and electric field in plasma in the form of expansion under eigen solutions of the initial system of equations are received. Coefficients of these expansions are found by means of the boundary condi…
The boundary problem about behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with diffusion boundary conditions is analytically solved. The kinetic equation of Vlasov - Boltzmann with integral of collisions of type BGK (Bhatnagar, Gross, Krook) and Maxwell equation for electric field are applied. Distribution function for electrons and electric field in plasma in the form of expansion under eigen solutions of the initial system of equations are received. Coefficients of these expansions are found by means of the boundary co…
Three dimensional rotatory modes of oscillations in a one-dimensional chain of rodlike charged particles or dust grains in a plasma are investigated. The dispersion characteristics of the modes are analyzed. The stability of different equilibrium orientations of the rods, phase transitions between the different equilibria, and a critical dependence on the relative strength of the confining potential are analyzed. The relations of these processes with liquid crystals, nanotubing, and plasma coating are discussed.
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision quasi-neutral (n_i \simeq n_e) Maxwellian electron-ion plasmas. We obtain two branches of electron waves: the ubiquitous one of high-frequency and high-velocity oscillations and the unusual low-velocity one. Taking into account Coulomb collisions in the limit m_e << m_i, \bar{v_i} << \bar{v_e}, and T_e m_e << T_i m_i results in expressions for transversal plasma-elect…
Micron-size charged particles can be easily levitated in low-density plasma environments. At low pressures, suspended particles have been observed to spontaneously oscillate around an equilibrium position. In systems of many particles, these oscillations can catalyze a variety of nonequilibrium, collective behaviors. Here, we report spontaneous oscillations of single particles that remain stable for minutes with striking regularity in amplitude and frequency. The oscillation amplitude can also exceed 1 cm, nearly an order of magnitude larger than previously observed. Using an integrated experi…
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A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the solution in parametric form is obtained. It involves simple elementary functions. Our solution includes all known exact solutions for an ideal cold plasma and a large class of new ones for a more realistic plasma. A new nonlinear effect is found of splitting of the largest density maximum, with a saddle point between the peaks so obtained. The method may sometime…
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Plasma dipole oscillation (PDO) depicted as harmonic motion of a spatially localized block of electrons has, until now, been hypothetical. In practice, the plasma oscillation occurs always as a part of a plasma wave. Studies on radiation burst from plasmas have focused only on coupling of the plasma wave and electromagnetic wave. Here we show that a very-high-field PDO can be generated by the electrons trapped in a moving train of potential wells. The electrons riding on the potential train coherently construct a local dipole moment by charge separation. The subsequent PDO is found to persist …
Five-moment approximation in hydrodynamics includes not only continuity equation and momentum balance equation, but also energy equation. Set of hydrodynamic equations is presented for system of non-relativistic quantum particles with Coulomb interaction. This set of equations is linearized, and dispersion relation for Langmuir waves in quasi-neutral system of electrons and immobile ions is obtained.
It is shown that a Friedel type oscillations accompany skin effect in degenerate plasma of a metal. It was learnt earlier that Friedel oscillations take place under charge screening in quantum plasma. However the nature of Friedel oscillations is not in the quantum character of the plasma, but in the features of degenerate Fermi distribution, namely, in its sharp transformation into zero directly just the other side of the Fermi surface. This circumstance leads to the Frieldel-type oscillations under anomalous skin effect.
A two-fluid model developed originally to describe wave oscillations in the vacuum arc centrifuge, a cylindrical, rapidly rotating, low temperature and confined plasma column, is applied to interpret plasma oscillations in a RF generated linear magnetised plasma (WOMBAT), with similar density and field strength. Compared to typical centrifuge plasmas, WOMBAT plasmas have slower normalised rotation frequency, lower temperature and lower axial velocity. Despite these differences, the two-fluid model provides a consistent description of the WOMBAT plasma configuration and yields qualitative agree…
We study the spatio-temporal evolution of the nonlinear electrostatic oscillations in a cold magnetized electron-positron (e-p) plasma using both analytics and simulations. Using a perturbative method we demonstrate that the nonlinear solutions change significantly when a pure electrostatic mode is excited at the linear level instead of a mixed upper-hybrid and zero-frequency mode that is considered in a recent study. The pure electrostatic oscillations undergo phase mixing nonlinearly. However, the presence of the magnetic field significantly delays the phase-mixing compared to that observed …
The results of experimental investigations of electron ejection from gas-discharge nonneutral electron plasma at the formation and radial oscillations of vortex structure have been presented. The electrons are injected from the vortex structure and the adjacent region of electron sheath in the form of pulses the duration and periodicity of which are determined by the processes of evolution and dynamics of this structure. The possible mechanisms of pulse ejection of electrons are considered. The influence of electron ejection on other processes in discharge electron sheath is analyzed.
In the present paper the linearized problem of half-space plasma oscillations in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the plasma boundary are considered. Coefficients of continuous and discrete spectra of the problem are found, and electron distribution function on the plasma boundary and electric field are expressed in explicit form.
We evidence the existence of plasma oscillations of electrons-positron pairs created by the vacuum polarization in an uniform electric field with E < Ec. Our general treatment, encompassing also the traditional, well studied case of E > Ec, shows the existence in both cases of a maximum Lorentz factor acquired by electrons and positrons and allows determination of the a maximal length of oscillation. We quantitatively estimate how plasma oscillations reduce the rate of pair creation and increase the time scale of the pair production. These results are particularly relevant in view of the exper…
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The self-excitation of Plasma Series Resonance (PSR) oscillations plays an important role in the electron heating dynamics in Capacitively Coupled Radio Frequency (CCRF) plasmas. In a combined approach of PIC/MCC simulations and a theoretical model based on an equivalent circuit, we investigate the self-excitation of PSR oscillations and their effect on the electron heating in geometrically symmetric CCRF plasmas driven by multiple consecutive harmonics. The discharge symmetry is controlled via the Electrical Asymmetry Effect, i.e. by varying the total number of harmonics and tuning the phase …
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The linearized problem of plasma oscillations in layer (particularly, in thin films) in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the plasma boundary are considered. Coefficients of continuous and discrete spectra of the problem are found, and electron distribution function on the plasma boundary and electric field are expressed in explicit form. Absorption of energy of electric field in layer is calculated.
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We study the frequency of the plasma oscillations of electron-positron pairs created by the vacuum polarization in an uniform electric field with strength E in the range 0.2 Ec < E < 10 Ec. Following the approach adopted in [1] we work out one second order ordinary differential equation for a variable related to the velocity from which we can recover the classical plasma oscillation equation when E -> 0. Thereby, we focus our attention on its evolution in time studying how this oscillation frequency approaches the plasma frequency. The time-scale needed to approach to the plasma frequency and …
The influence of the shape of a sample on the type of uniform dipole collective electrons oscillations is discussed. In samples of a bulk shape uniform bulk dipole oscillation (Langmuir oscillation) cannot exist. It exists in samples of a thin slab shape only. As uniform bulk dipole oscillations cannot penetrate ellipsoidal samples of conductive material, they exist in the surface layer of a sample only (Mie oscillations). Frequencies of Mie oscillations are alculated for a sample of the shape of an arbitrary ellipsoid.
Research of influence of collisions on Friedel oscillations in quantum degenerate collisional plasma (T=0) is carried out for the first time. It is shown that presence of collisions in plasma leads to exponential decreasing of amplitude and phase shift of the Friedel oscillations. In linear approximation the phase shift is equal to the half of quantity inverse to product of Fermi's wave number by free length path of electrons. The correct expression for longitudinal dielectric permeability of the quantum collisional plasma found by the authors (see arxiv:1001.3937 [math-ph] 22 Jan 2010) is use…
