Formation of a cylindrical ion beam in the field of an axisymmetric system of ring currents at a low Hall current

A study is made of the structure of an accelerating layer with a closed Hall current and the geometry of an ion beam in an external magnetic field created by an arbitrary axisymmetric system of ring currents under conditions such that the Hall current can be ignored. It is shown that the ion trajectories are perpendicular to the magnetron cutoff surface for electrons and that the cathode plasma boundary coincides with a magnetic field line. A magnetic field configuration is found in which the cutoff surface is a plane surface perpendicular to the axis of the system. It is shown that, for a small ratio of the gyroradius of the electrons (in terms of the maximum energy acquired by them in the layer) to the characteristic size of the structure, such a configuration provides sufficient means to ensure the formation of slightly converging ion beams or those that are essentially parallel to the system axis.     

Specific features of virtual cathode formation and dynamics with allowance for the magnetic self-field of a relativistic electron beam

The conditions and mechanisms of virtual cathode formation in relativistic and ultrarelativistic electron beams are analyzed with allowance for the magnetic self-field for different magnitudes of the external magnetic field. The typical behavior of the critical current at which an oscillating virtual cathode forms in a relativistic electron beam is investigated as a function of the electron energy and the magnitude of the uniform external magnetic field. It is shown that the conditions for virtual cathode formation in a low external magnetic field are determined by the influence of the magnetic self-field of the relativistic electron beam. In particular, azimuthal instability of the electron beam caused by the action of the beam magnetic self-field, which leads to a reduction in the critical current of the relativistic electron beam, is revealed.     

Effect of the external magnetic field on the critical current for the onset of a virtual cathode in an electron beam

The critical current at which an unsteady oscillating virtual cathode forms in an electron beam is studied as a function of the external magnetic field guiding the beam electrons. It is shown that the critical beam current decreases with external magnetic field and that there is an optimum magnetic induction at which the critical current for the onset of an oscillating virtual cathode in the beam is minimum. For a strong guiding magnetic field, the critical beam current is described by relationships derived under the assumption that the motion of the beam electrons is one-dimensional. Such behavior is explained by the characteristic features of the dynamics of the beam electrons in longitudinal and radial directions in the interaction space at different inductions of the external magnetic field.     

Possible mechanism for radial ion acceleration in a beam-plasma discharge

A mechanism is proposed that can lead to radial ion acceleration in a plasma discharge excited by an electron beam in a relatively weak longitudinal magnetic field. The mechanism operates as follows. The beam generates an azimuthally asymmetric slow potential wave, which traps electrons. Trapped magnetized electrons drift radially with a fairly high velocity under the combined action of the azimuthal wave field (which is constant for them) and a relatively weak external longitudinal magnetic field. The radial electron flux generates a radial charge-separation electric field, which accelerates unmagnetized plasma ions in the radial direction. The ion flux densities and energies achievable in experiments with kiloelectronvolt electron beams in magnetic fields of up to 100 G are estimated.     

Dynamics of beam instability in a finite plasma volume: Numerical experiment

Results are presented from numerical simulations of the dynamics of beam instability in a finite plasma volume (plasma-filled cavity) in a weak magnetic field. It is shown that, in such a system, the low group velocity of the plasma waves excited by an electron beam can result in the generation and amplification of an electric field; strong electron heating in the axial region; and, as a consequence, the generation of a high potential at the axis. The quasistatic radial electric field so produced accelerates ions toward the periphery of the plasma column, forming a directed ion beam with an energy much higher than the thermal energy of the bulk plasma electrons.     

Acceleration and stability of a high-current ion beam in induction fields

A one-dimensional nonlinear analytic theory of the filamentation instability of a high-current ion beam is formulated. The results of 2.5-dimensional numerical particle-in-cell simulations of acceleration and stability of an annular compensated ion beam (CIB) in a linear induction particle accelerator are presented. It is shown that additional transverse injection of electron beams in magnetically insulated gaps (cusps) improves the quality of the ion-beam distribution function and provides uniform beam acceleration along the accelerator. The CIB filamentation instability in both the presence and the absence of an external magnetic field is considered.     

Theory of nondiffusive penetration of a magnetic field into a conducting medium

The penetration of a current and, accordingly, a magnetic field into the plasma of pulsed systems characterized by short temporal and spatial scales can be investigated in electron magnetohydrodynamics. A study is made of the rapid penetration of the magnetic field of an injected high-current ion beam into a plasma.     

Investigation of the helicon discharge plasma parameters in a hybrid RF plasma system

Results of an experimental study of the helicon discharge plasma parameters in a prototype of a hybrid RF plasma system equipped with a solenoidal antenna are described. It is shown that an increase in the external magnetic field leads to the formation of a plasma column and a shift of the maximum ion current along the discharge axis toward the bottom flange of the system. The shape of the plasma column can be controlled via varying the configuration of the magnetic field.     

Mechanism for ion acceleration along the normal to the axis of a beam-plasma discharge in a weak magnetic field

The mechanism responsible for the previously discovered phenomenon of acceleration of an ion flow along the normal to the axis of a beam-plasma discharge in a weak magnetic field is investigated. It is suggested that the ions are accelerated in the field of a helicon wave excited in the discharge plasma column. It is shown theoretically that, under actual experimental conditions, a helicon wave can be excited at the expense of the energy of an electron beam. The spectral parameters and spatial structure of the waves excited in a beam-plasma discharge in the frequency ranges of Langmuir and helicon waves are studied experimentally and are shown to be related to the parameters of the ion flow. Theoretical estimates are found to agree well with the experimental results.     

Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.     

Investigation of the chaotic dynamics of an electron beam with a virtual cathode in an external magnetic field

The effect of the strength of the focusing magnetic field on chaotic dynamic processes occurring in an electron beam with a virtual cathode, as well as on the processes whereby the structures form in the beam and interact with each other, is studied by means of two-dimensional numerical simulations based on solving a self-consistent set of Vlasov-Maxwell equations. It is shown that, as the focusing magnetic field is decreased, the dynamics of an electron beam with a virtual cathode becomes more complicated due to the formation and interaction of spatiotemporal longitudinal and transverse structures in the interaction region of a vircator. The optimum efficiency of the interaction of an electron beam with the electromagnetic field of the vircator is achieved at a comparatively weak external magnetic field and is determined by the fundamentally two-dimensional nature of the motion of the beam electrons near the virtual cathode.     

Simulation of the development and interaction of instabilities in a relativistic electron beam under variation of the beam wall thickness

The development and interaction of Bursian and diocotron instabilities in an annular relativistic electron beam propagating in a cylindrical drift chamber are investigated analytically and numerically as functions of the beam wall thickness and the magnitude of the external uniform magnetic field. It is found that the interaction of instabilities results in the formation of a virtual cathode with a complicated rotating helical structure and several reflection regions (electron bunches) in the azimuthal direction. It is shown that the number of electron bunches in the azimuthal direction increases with decreasing beam wall thickness and depends in a complicated manner on the magnitude of the external magnetic field.     

Formation of space-charge bunches in a multivelocity-electron-beam-based microwave oscillator with a cathode unshielded from the magnetic field

The influence of the magnitude and configuration of the magnetic field on the parameters of electron bunches formed in a multivelocity electron beam is analyzed. It is shown that the use of a cathode unshielded from the magnetic field and a nonuniform magnetic field increasing along the drift space enables the formation of compact electron bunches. The ratio between the current density in such bunches and the beam current density at the entrance to the drift space reaches 10⁶, which results in a substantial broadening of the output microwave spectrum due to an increase in the amplitudes of the higher harmonics of the fundamental frequency.     

Nonlinear oscillations of a semiconductor plasma with a nonrelativistic electron beam

Nonlinear oscillations of a semiconductor plasma with a low-density electron beam in the absence of an external magnetic field are studied in the hydrodynamic approximation. The beam is assumed to be nonrelativistic and monoenergetic. Cases are studied in which the Langmuir frequency of the electron oscillations in a semiconductor is much higher or much lower than the electron momentum relaxation rate. The self-similar solution obtained for the first case describes the damping of the nonlinear oscillations of the wave potential. Numerical analysis of the second case shows that the electric field distribution in the beam may correspond to that in a shock wave.     

Ion acceleration in a dipole vortex in a laser plasma corona

Particle-in-cell simulations show that the inhomogeneity scale of the plasma produced in the interaction of high-power laser radiation with gas targets is of fundamental importance for ion acceleration. In a plasma slab with sharp boundaries, the quasistatic magnetic field and the associated electron vortex structure produced by fast electron beams both expand along the slab boundary in a direction perpendicular to the plasma density gradient, forming an extended region with a quasistatic electric field, in which the ions are accelerated. In a plasma with a smooth density distribution, the dipole magnetic field can propagate toward the lower plasma density in the propagation direction of the laser pulse. In this case, the electron density in an electric current filament at the axis of the magnetic dipole decreases to values at which the charge quasineutrality condition fails to hold. In electric fields generated by this process, the ions are accelerated to energies substantially higher than those characteristic of plasma configurations with sharp boundaries.     

2.5-Dimensional numerical simulation of a high-current ion linear induction accelerator

Results are presented from numerical particle simulations of the transport and acceleration of a high-current tubular ion beam through one to five magnetically insulated accelerating gaps. The ion beam is neutralized by an accompanying electron beam. The possibility of transporting a high-current neutralized ion beam through five cusps is demonstrated. It is shown that the quality of the distribution function of a high-current ion beam at the exit from the accelerator can be substantially improved by optimizing the energy of the neutralizing electron beam. It is also shown that, by injecting additional high-current electron beams into the cusps, the accelerated ion beam can be made more monoenergetic and its divergence can be reduced.     

Extension of the neuronal membrane model to account for suppression of the action potential by a constant magnetic field

A biophysical explanation of the reduced excitability in neurons exposed to a constant magnetic field is based on an extended neuronal membrane model. In the presence of a constant magnetic field, reduced excitability is manifested as an increase in the excitation threshold and a decrease in the frequency of action potentials. The proposed explanation for the reduced excitability rests on the well-known Hall effect. The separation of charges resulting from the Lorentz force exerted on moving intracellular ions leads to the formation of a Hall electric field in a direction perpendicular to that of action-potential transmission. Consequently, the ion current for discharging the membrane capacitance is reduced in the presence of a magnetic field, thereby limiting initiation of the action potential. The validity of the proposed biophysical explanation is justified analytically and verified by simulations based on the Hodgkin and Huxley model for the electrical excitability of a neuron. Based on derivation of the current segregation ratio α characterizing the reduction in the stimulating current from first principles, the equivalent circuit model of the neuronal membrane is extended to account for the reduced excitability of neurons exposed to a constant magnetic field.     

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 Ω _e ≡ B − (c/e) ▿ × p _ee ≠ 0 and the corresponding Lagrangian invariant I _e . Such current structures can exist on spatial scales of up to ω _pi ⁻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 r _B = B/(4πen _e )—the main property of such current structures in a Hall medium with σB/(en _e c) ≫ 1—is stressed. Since the minimum size of a vortex structure is the London length c/ω _pe , the structures under consideration correspond to the condition r _B > c/ω _pe or B ² > 4πn _e m _e c ², 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 10⁷ J/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 I _e and I _i . 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.     

Magnetorotational instability of a weakly ionized accretion disk with vertical and azimuthal magnetic fields

Magnetorotational instability of a weakly ionized accretion disk with an admixture of charged dust grains in a magnetic field with the axial and toroidal components is analyzed. The dispersion relation for perturbations perpendicular to the disk plane is derived with allowance for both the Hall current and the finite transverse plasma conductivity. It is shown that dust grains play an important role in the disk magnetic dynamics. Due to the effect of dust grains, the Hall current can reverse its direction as compared to the case of electron-ion plasma. As a result, the instability threshold shifts toward the short-wavelength range. Under certain conditions, electromagnetic fluctuations of any length can become unstable. It is established that the instability criterion for waves of any scale length is satisfied within a finite interval of the density ratio between the dust and electron plasma components. The width of this interval and the instability growth rate as functions of the plasma parameters and the configuration of the magnetic field in the disk are analyzed.     

Relativistic diamagnetic equilibrium of a thin-walled annular electron beam in an external magnetic field

A self-consistent equilibrium state of a thin-walled annular electron beam in an external magnetic field is investigated with allowance for diamagnetic effect and relativistic effects in the beam rotational motion. An equation for the relativistic angular velocities of the beam rotation is derived in the hydrodynamic approximation. The main parameters of the beam equilibrium state are obtained analytically and are calculated numerically. The parameters of a longitudinally homogeneous, relativistic diamagnetic high-density electron beam are determined.