A. V. Gordeev

Nonquasineutral current equilibria as elementary structures of plasma dynamics

A study is made of the fundamental features of current filaments with a nonzero electron vorticity Ωe ≡ B − (c/e) ▿ × pee ≠ 0 and the corresponding Lagrangian invariant Ie. Such current structures can exist on spatial scales of up to ωpi−1. It is shown that the dissipative stage of the plasma evolution and the violation of Thomson’s theorem on vorticity conservation in an electron fluid are of fundamental importance for the onset of electron current structures. A key role of the screening of electric and magnetic fields at distances on the order of the magnetic Debye radius rB = B/(4πene)—the main property of such current structures in a Hall medium with σB/(enec) ≫ 1—is stressed. Since the minimum size of a vortex structure is the London length c/ωpe, the structures under consideration correspond to the condition rB > c/ωpe or B2 > 4πnemec2, which leads to strong charge separation in the filament and relativistic electron drift. It is demonstrated that the specific energy content in current structures is high at a filament current of 10–15 kA: from 100 J/cm3 at a plasma density of 1014 cm−3 (the parameters of a lightning leader) to 107J/cm3 for a fully ionized atmospheric-pressure air. Estimates are presented showing that the Earth’s ionosphere, circumsolar space, and interstellar space are all Hall media in which current vortex structures can occur. A localized cylindrical equilibrium with a magnetic field reversal is constructed—an equilibrium that correlates with the magnetic structures observed in intergalactic space. It is shown that a magnetized plasma can be studied by using evolutionary equations for the electron and ion Lagrangian invariants Ie and Ii. An investigation is carried out of the evolution of a current-carrying plasma in a cylinder with a strong external magnetic field and with a longitudinal electron current turned on in the initial stage—an object that can serve as the simplest electrodynamic model of a tokamak. In this case, it is assumed that the plasma conductivity is low in the initial stage and then increases substantially with time. Based on the conservation of the integral momentum of the charged particles and electromagnetic field in a plasma cylinder within a perfectly conducting wall impenetrable by particles, arguments are presented in support of the generation of a radial electric field in a plasma cylinder and the production of drift ion fluxes along the cylinder axis. A hypothesis is proposed that the ionized intergalactic gas expands under the action of electromagnetic forces.

Nonquasineutral relativistic current filaments and their X-ray emission

Nonquasineutral electron current filaments with the azimuthal magnetic field are considered that arise due to the generation of electron vorticity in the initial (dissipative) stage of evolution of a current-carrying plasma, when the Hall number is small (σB/enec ≪ 1) because of the low values of the plasma conductivity and magnetic field strength. Equilibrium filamentary structures with both zero and nonzero net currents are considered. Structures with a zero net current type form on time scales of t < tsk = (r0ωpe/c)2tst, where tsk is the skin time, tst is the typical time of electron-ion collisions, and r0 is the radius of the filament. It is shown that, in nonquasineutral filaments in which the current is carried by electrons drifting in the crossed electric (Er) and magnetic (Bθ) fields, ultrarelativistic electron beams on the typical charge-separation scale rB = B/(4πene) (the so-called magnetic Debye radius) can be generated. It is found that, for comparable electron currents, the characteristic electron energy in filaments with a nonzero net current is significantly lower than that in zero-net-current filaments that form on typical time scales of t < tsk. This is because, in the latter type of filaments, the oppositely directed electron currents repel one another; as a result, both the density and velocity of electrons increase near the filament axis, where the velocities of relativistic electrons are maximum. Filaments with a zero net current can emit X rays with photon energies ℏ ω up to 10 MeV. The electron velocity distributions in filaments, the X-ray emission spectra, and the total X-ray yield per unit filament length are calculated as functions of the current and the electron number density in the filament. Analytical estimates of the characteristic lifetime of a radiating filament and the typical size of the radiating region as functions of the plasma density are obtained. The results of calculations are compared with the available experimental data.

Hydrodynamic Model of the Penetration of a Magnetic Field into a Plasma with Two Ion Species

AbstractHydrodynamic equations are presented that describe the dynamics of a plasma with two ion species in a magnetic field such that . It is shown that there exists a range of values of the ratio of the plasma density to the magnetic field, νii/ωBi<(Z2M/m)1/4, within which the frictional force caused by ion-ion collisions dominates over that caused by electron-ion collisions. In this range, the effective conductivity, which governs the magnetic field diffusion, is lower than the conventional electron-ion conductivity by a factor of

Localization of Magnetized Electrons in Current Filaments as a Fundamental Cause of Coulomb Explosion

\sqrt {M/m}

Electron leakage mechanism in a plasma-filled magnetically insulated transmission line

and can be as low as σ ≃ enc/B. The equations derived for this three-component plasma make it possible to self-consistently incorporate local changes in the partial mass and partial charge of each of the ion species in relative motion. The characteristic features of the equations obtained are analyzed by applying them to describe the propagation of a current sheath in a transmission line filled with a multispecies plasma. An analogy is drawn between magnetic phenomena in a plasma with two ion species and in a so-called dusty plasma.

Formation of a Z-Pinch during Electromagnetic Compression of a Nonquasineutral Current Filament

A nonquasineutral vortex structure with a zero net current is described that arises as a result of electron drift in crossed magnetic and electric fields, the latter being produced by charge separation on a spatial scale of about the magnetic Debye radius rB = |B|/(4πene). In such a structure with a radius of r ∼ rB, the magnetic field is maintained by a drift current on the order of the electron Alfvén current JAe = mec3/(2e) and can become as strong as B ≃ mec2/(er). Estimates show that, in a plasma with a density of ne = 1021−1023 cm−3 and with nonzero electron vorticity driven by high-power laser radiation on a time scale on the order of θpe−1, magnetic fields with a strength of B ∼ 108−109 G are generated on micron and submicron scales. The system with closed current that is considered in the present paper can also serve as a model of hot spots in the channel of a Z-pinch.

Suppression of the rayleigh-taylor instability of a low-density imploding liner by a longitudinal magnetic field

Mechanisms for generating current filaments in a dense plasma under the action of focused laser pulses and in a Z-pinch configuration are discussed. The main properties of current filaments with a zero and nonzero electron vorticity Ωe=B−(c/e)∇×pe that originate at magnetic fields in the range 4πnemec2≪B2≪4πnimic2 are investigated under the conditions of Coulomb explosion at currents below the ion Alfvén current. A study is made of the equilibrium configurations of nonquasineutral current filaments in a purely longitudinal (Bz) and a purely azimuthal (Bθ) magnetic field and also in a more general case of a helical magnetic field, having two components, under conditions such that the charge separation occurs on a spatial scale on the order of the magnetic Debye radius rB ≃ |B|/(4πene. It is shown that strong electric fields generated in the current filaments are comparable in magnitude to the atomic field and are capable of accelerating ions to energies of several tens of megaelectronvolts. The ion dynamics in strong electric fields of the filaments is calculated numerically and is shown to lead to the formation of collisionless shock waves on time scales on the order of several inverse ion plasma frequencies ωpi−1. The possible formation of current filaments on different spatiotemporal scales is considered.

Non-quasineutral model of an equilibrium z - pinch

The motion of a nonquasineutral plasma in a strong magnetic field such that is analyzed. It is shown in simple examples that, when the plasma pressure and dissipation are neglected, the only dynamic process in a magnetized plasma is the evolution of the charge-separation electric field and the related magnetic field flux. The equations derived to describe this evolution are essentially the wave Grad-Shafranov equations. The solution to these equations implies that, in a turbulent Z-pinch, a steady state can exist in which the current at a supercritical level is concentrated near the pinch axis.