Oscillation spectrum of an electron gas with a small density fraction of ions

The problem is solved of the stability of a nonneutral plasma that completely fills a waveguide and consists of magnetized cold electrons and a small density fraction of ions produced by ionization of the atoms of the background gas. The ions are described by an anisotropic distribution function that takes into account the characteristic features of their production in crossed electric and magnetic fields. By solving a set of Vlasov-Poisson equations analytically, a dispersion equation is obtained that is valid over the entire range of allowable electric and magnetic field strengths. The solutions to the dispersion equation for the m = +1 main azimuthal mode are found numerically. The plasma oscillation spectrum consists of the families of Trivelpiece-Gould modes at frequencies equal to the frequencies of oblique Langmuir oscillations Doppler shifted by the electron rotation and also of the families of “modified” ion cyclotron (MIC) modes at frequencies close to the harmonics of the MIC frequency (the frequencies of radial ion oscillations in crossed fields). It is shown that, over a wide range of electric and magnetic field strengths, Trivelpiece-Gould modes have low frequencies and interact with MIC modes. Trivelpiece-Gould modes at frequencies close to the harmonics of the MIC frequency with nonnegative numbers are unstable. The lowest radial Trivelpiece-Gould mode at a frequency close to the zeroth harmonic of the MIC frequency has the fastest growth rate. MIC modes are unstable over a wide range of electric and magnetic field strengths and grow at far slower rates. For a low ion density, a simplified dispersion equation is derived perturbatively that accounts for the nonlocal ion contribution, but, at the same time, has the form of a local dispersion equation for a plasma with a transverse current and anisotropic ions. The solutions to the simplified dispersion equation are obtained analytically. The growth rates of the Trivelpiece-Gould modes and the behavior of the MIC modes agree with those obtained by numerical simulation.     

On the influence of Alfvén resonance on ion cyclotron resonance heating

Physical processes determining the excitation of RF electromagnetic fields in a plasma column in a magnetic field are analyzed. The Alfvén resonance plays an important role at frequencies close to the ion cyclotron frequency. It leads to the enhancement of the RF electric field and transformation of Alfvén oscillations with a predominantly transverse polarization of the electric field into lower hybrid ones, which have a significant longitudinal component of the electric field. Lower hybrid oscillations efficiently interact with electrons causing their heating. Difficulties in the implementation of ion cyclotron resonance heating by the magnetic beach method are outlined. The processes considered in this work can be important for the VASIMR plasma engine.     

Means for efficient electron beam generation in wide-aperture open-discharge light sources

The interaction of a plasma in the accelerating gap of an open discharge with a strong external electric field and with the cathode surface has been investigated theoretically and experimentally. In a pulsed nanosecond discharge, the ion inertia and plasma screening of the electric field cause a fast growth of the electric field E in the cathode region and a decrease in the length of the latter. Along with a reduction of the electron multiplication factor at high electric fields, this leads to a substantial decrease in the ion flux toward the cathode, which allows one to develop highly efficient open-discharge light sources with a long lifetime and low cathode sputtering. In this respect, continuous and quasi-continuous discharges are less advantageous because of the smaller increase in the electric field in the cathode region. The Townsend coefficients of charge multiplication and electron emission at high electric fields typical of open discharges have been measured for the first time. Fast ions and atoms extracted from the plasma of the accelerating gap significantly affect the cathode emission properties. In particular, photoemission is enhanced by more than one order of magnitude and becomes the main mechanism for electron generation. This also increases the efficiency and lifetime of open-discharge light sources.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

Nonlinear ineraction of an annular electron beam with azimuthal surface waves

A nonlinear theory is developed that describes the interaction between an annular electron beam and an electromagnetic surface wave propagating strictly transverse to a constant external axial magnetic field in a cylindrical metal waveguide partially filled with a cold plasma. It is shown theoretically that surface waves with positive azimuthal mode numbers can be efficiently excited by an electron beam moving in the gap between the plasma column and the metal waveguide wall. Numerical simulations prove that, by applying a constant external electric field oriented along the waveguide radius, it is possible to increase the amplitude at which the surface waves saturate during the beam instability. The full set of equations consisting of the waveenvelope equation, the equation for the wave phase, and the equations of motion for the beam electrons is solved numerically in order to construct the phase diagrams of the beam electrons in momentum space and to determine their positions in coordinate space (in the radial variable-azimuthal angle plane).     

Ponderomotive force of the low-frequency field and modulational instability of drift waves

A study is made of the processes that occur in an inhomogeneous nonisothermal plasma in a strong external magnetic field and whose characteristic frequencies are lower than the ion Langmuir frequency but higher than the collision frequency. An expression for the ponderomotive force of the low-frequency field is derived. The excitation of a long-wavelength low-frequency drift wave during the development of the modulational instability of a drift pump wave is investigated. The growth rates of the instability are obtained, and the conditions for its onset are determined. The possible relation of the modulational instability to the formation of structures in the plasma is discussed.     

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.     

Conditions for electron runaway under leader breakdown of long gaps

An original hydrodynamic model in which inelastic collisions in the equations of motion and energy balance play a decisive role is developed and applied to simulate electron avalanches in strong electric fields. The mean energy and drift velocity of electrons, as well as the ionization coefficient and electric field in a wide range of mean electron energies, are determined for helium and xenon. A criterion is derived for the runaway of the average electron in discharges with ionization multiplication. It is shown that runaway can take place at any value of E/p, provided that the momentum mean free path exceeds the gap length. The voltage corresponding to electron runaway is found for helium, xenon, and air as a function of the electric field, the electron mean energy, and the parameter pd. Conditions for the formation of a precursor in electronegative gases are analyzed. It is shown that the presence of a precursor with a high electric conductance is necessary for the formation of a new leader step. The voltage and time ranges corresponding to efficient electron runaway and X-ray generation during leader breakdown in air are determined.     

Stability of hybrid modes of a single-component electron plasma containing an admixture of background gas ions

The spectrum of eigenmodes of a waveguide completely filled with a cold electron plasma containing a small admixture of ions produced due to electron-impact ionization of background gas atoms is calculated numerically. The calculations were performed within the entire range of allowable values of the radial electric and longitudinal magnetic fields for both magnetized and unmagnetized ions by using the earlier derived nonlocal dispersion relation [Plasma Phys. Rep. 36, 563 (2010)]. The spectrum consists of three families of electron modes with frequencies equal to the Doppler-shifted upper and lower hybrid frequencies and modified ion cyclotron (MIC) modes. When the Doppler shift caused by electron rotation in the crossed electric and magnetic fields compensates for the hybrid frequency, the electron modes become low-frequency modes and interact with the ion modes. For m = 1, only the lower hybrid modes can be low-frequency ones, whereas at m ≥ 2, both lower and upper hybrid modes can be low-frequency ones. The spectrum of modes having the azimuthal number m = 2 is thoroughly analyzed. It is shown that, in this case, the lower hybrid modes behave similar to the m = 1 modes. The dispersion curves of the upper hybrid modes intersect with all harmonics of the MIC frequency (positive, negative, and zero) and are unstable in the vicinities of the intersections. The maximum value of the instability growth rate is several times higher than the ion plasma frequency. The MIC modes are unstable within a wide range of the field strengths, and their growth rates are two orders of magnitude slower. Instabilities are caused by the relative motion of electrons and ions (the transverse current) and the anisotropy of the ion distribution function.     

Electrostatic electron vortex structure in a plasma in an external magnetic field

A previously developed method for describing vortex structures is used to construct electrostatic vortices in a plasma in an external magnetic field. An equation for the radial electric field that gives rise to azimuthal electron drift in crossed electric (E _r ) and magnetic (B _z ) fields is derived without allowance for the magnetic field of the electron currents. Two types of the resulting electrostatic vortex structures with a positive and a negative electric potential at the axis are analyzed. The results obtained are compared with experimental data on vortex structures.     

Combined action of static and alternating magnetic fields on ion motion in a macromolecule: Theoretical aspects

This is an attempt to solve the energetic problem of the primary detection of weak parallel static (DC) and alternating (AC) extremely low frequency (ELF) magnetic fields. We studied the equations of motion for an ion situated inside a macromolecule under the influence of these fields. The main concern is with the magnetic field influence on thermal motion of the ion in the macromolecule. The resonance effects are revealed at discrete frequencies of the ion thermal oscillations determined by the DC field magnitude and the AC field frequency. These phenomena result from the Larmor precession of the ion thermal motion. When the DC field or, to a greater extent, the combined DC and AC fields with the specific frequencies are turned on or cut off, changes occur in the energy of the ion thermal motion. If, inside the macromolecule, the ion is sufficiently protected against immediate impacts of particles of the medium surrounding the macromolecule, these changes may be enough to trigger alteration in the quantum state of the macromolecule. Bioelectromagnetics 19:279–292, 1998. © 1998 Wiley-Liss, Inc.     

Brain stimulation using electromagnetic sources: theoretical aspects.

We prove that, at the frequencies generally proposed for extracranial stimulation of the brain, it is not possible, using any superposition of external current sources, to produce a three-dimensional local maximum of the electric field strength inside the brain. The maximum always occurs on a boundary where the conductivity jumps in value. Nevertheless, it may be possible to achieve greater two-dimensional focusing and shaping of the electric field than is currently available. Towards this goal we have used the reciprocity theorem to present a uniform treatment of the electric field inside a conducting medium produced by a variety of sources: an external magnetic dipole (current loop), an external electric dipole (linear antenna), and surface and depth electrodes. This formulation makes use of the lead fields from magneto- and electroencephalography. For the special case of a system with spherically symmetric conductivity, we derive a simple analytic formula for the electric field due to an external magnetic dipole. This formula is independent of the conductivity profile and therefore embraces spherical models with any number of shells. This explains the "insensitivity" to the skull's conductivity that has been described in numerical studies. We also present analytic formulas for the electric field due to an electric dipole, and also surface and depth electrodes, for the case of a sphere of constant conductivity.     

Nonlinear mechanism for the generation of electromagnetic fields in a magnetized plasma by the beatings of waves

The modulational instability in a plasma in a strong constant external magnetic field is considered. The plasmon condensate is modulated not by conventional low-frequency ion sound but by the beatings of two high-frequency transverse electromagnetic waves propagating along the magnetic field. The instability reduces the spatial scales of Langmuir turbulence along the external magnetic field and generates electromagnetic fields. It is shown that, for a pump wave with a sufficiently large amplitude, the effect described in the present paper can be a dominant nonlinear process.     

Electric field effect on (6,0) zigzag single-walled aluminum nitride nanotube

Structural, electronic, and electrical responses of the H-capped (6,0) zigzag single-walled aluminum nitride nanotube was studied under the parallel and transverse electric fields with strengths 0-140?×?10(-4)?a.u. by using density functional calculations. Geometry optimizations were carried out at the B3LYP/6-31G* level of theory using a locally modified version of the GAMESS electronic structure program. The dipole moments, atomic charge variations, and total energy of the (6,0) zigzag AlNNT show increases with increase in the applied external electric field strengths. The length, tip diameters, electronic spatial extent, and molecular volume of the nanotube do not significantly change with increasing electric field strength. The energy gap of the nanotube decreases with increases of the electric field strength and its reactivity is increased. Increase of the ionization potential, electron affinity, chemical potential, electrophilicity, and HOMO and LUMO in the nanotube with increase of the applied parallel electric field strengths shows that the parallel field has a much stronger interaction with the nanotube with respect to the transverse electric field strengths. Analysis of the parameters indicates that the properties of AlNNTs can be controlled by the proper external electric field.     

Comparison of coupling of humans to electric and magnetic fields with frequencies between 100 Hz and 100 kHz

Recent laboratory and epidemiological results have stimulated interest in the hypothesis that human beings may exhibit biological responses to magnetic and/or electric field transients with frequencies in the range between 100 Hz and 100 kHz. Much can be learned about the response of a system to a transient stimulation by understanding its response to sinusoidal disturbances over the entire frequency range of interest. Thus, the main effort of this paper was to compare the strengths of the electric fields induced in homogeneous ellipsoidal models by uniform 100 Hz through 100 kHz electric and magnetic fields. Over this frequency range, external electric fields of about 25–2000 V/m (depending primarily on the orientation of the body relative to the field) are required to induce electric fields inside models of adults and children that are similar in strength to those induced by an external 1 μT magnetic field. Additional analysis indicates that electric fields induced by uniform external electric and magnetic fields and by the nonuniform electric and magnetic fields produced by idealized point sources will not differ by more than a factor of two until the sources are brought close to the body. Published data on electric and magnetic field transients in residential environments indicate that, for most field orientations, the magnetic component will induce stronger electric fields inside adults and children than the electric component. This conclusion is also true for the currents induced in humans by typical levels of 60 Hz electric and magnetic fields in U.S. residences. Bioelectromagnetics 18:67–76, 1997. © 1997 Wiley-Liss, Inc.     

Influence of electric fields on photophobic reactions in blue-green algae

The effect of external electric fields on photo-accumulations of Phormidium uncinatum in light traps has been studied. 1. In direct current fields the phobic reaction of trichoms leaving the light field is not impaired if a voltage of 2.5 V is not exceeded. With voltages between 3 and 7 V the trichoms are motile, but phobic reactions are cancelled, provided the organisms are oriented more or less parallel to the electric field lines. Higher voltages cause the algae to die within minutes. 2. Only alternating current fields of very low frequencies (less than or equal 10(-3) Hz) have similar effects. Sine waves are more effective than triangular ones, but less than square waves. A hypothesis is proposed according to which sensory transduction of photophobic reactions in blue-green algae is mediated by changes in the endogenous membrane potential. This potential might be interfered with by the application of an external electric field, thus inhibiting photophobic reactions.     

DC和AC磁场混合作用下的离子运动

本文研讨了在微弱ＤＣ磁场和频率非常低的ＡＣ磁场并行作用下，位于大分子内部的离子运动情况。主要焦点是大分子中磁场对离子热运动的影响，通过一些离散频率的分析揭示了热运动的共振效应。指出当ＤＣ和ＡＣ磁场施加或切断时离子热运动能量将发生变化，如果大分子周围的媒介质的粒子能充分阻止瞬间接触，就会引起大分了子量子态的变化。     

Does direction of induced electric field or current provide a test of mechanism involved in nerve regeneration?

We suggest an experimental comparison of two directions for applying the time-varying magnetic fields which have been found to speed spontaneous regeneration of injured peripheral nerves and in attempts to repair spinal cord injuries. Time-varying magnetic fields induce currents in a plane perpendicular to the magnetic field direction. The lower conductivity of the spinal cord's sheath (dura matter) or of the myelin sheath of peripheral nerves would seem to confine the induced electric fields and currents to the spinal cord or nerve itself. The proposed comparison could allow choosing between two possible modes of action of the fields: (1) Magnetically-induced electric fields or currents may be encouraging ion flow or otherwise helping enzyme, channel or other interactions at the cell membrane, as is thought to be the case in field stimulation of healing in bone. This mechanism should be independent of field direction. (2) Work in developing organisms and with fields applied to nerve cells in vitro has shown that neurite growth is guided parallel to both endogenous and external electric fields. This mechanism would be effective when induced electric fields are parallel, but not when they are perpendicular to the nerve. Any experimental test should seek to produce as close as possible to the same induced current intensity with both field directions. Possible confounding factors, as well as breakdowns in the assumptions of the simple model presented here, would have to be considered. This proposal was motivated by a recent report in which the authors listed a changed field direction as one of several possible reasons for an unsuccessful experiment.     

Geometry of a cylindrical ion beam in a radial magnetic field at a low Hall current

The divergence of an ion beam in a cylindrical accelerator with a closed Hall current is considered under the assumption that the Hall current does not substantially change the external magnetic field. It is shown that the tangent of the angle of inclination of the ion trajectories to the cylinder axis is on the order of the ratio of the electron gyroradius in terms of the total energy of an electron to the characteristic radius of the acceleration channel. The beam divergence can be prevented by applying an external magnetic field in a direction parallel to the cylinder axis.