Electron Larmor Radius Research Articles

Particle simulations of collisionless reconnection in magnetotail configuration including electron dynamics

The role of electron dynamics in collisionless magnetotail reconnection is investigated by using two‐dimensional full particle simulations with ion‐to‐electron mass ratios mi/me set to 1 and 10. The results indicate that the electrons have a stabilizing influence on the ion tearing instability in the sense that growth rates are reduced in runs with the initial electron Larmor radius being sufficiently small in comparison with the ion Larmor radius. A comparison of our results with those obtained by Pritchett [1994] using a significantly different numerical model shows encouraging agreement. The attempt to achieve an approach closer to realistic magnetotail conditions is inhibited by present technical restrictions.

Kinetic model of collective scattering off fast ion generated electromagnetic fluctuations in magnetized Vlasov plasma

From the general three-wave coupling formalism in magnetized nonrelativistic Vlasov plasma, an expression is derived that gives the differential cross section for the scattering of incident radiation off of thermal fluctuations induced by ions in a hot magnetized plasma. The model is valid to any order in thermal parameters, and can thus generalize the previous theory models to regimes where either the electron Larmor radius or the electron cyclotron resonance are significant for the scattered wave.

Electron Surface Cyclotron Waves in the Metallic Waveguide Structures with Two‐Component Filling

AbstractThe dispersion properties of the slow electromagnetic surface waves propagating across external magnetic field in planar metallic waveguides with plasma and dielectric filling on the harmonics of the electron cyclotron frequency are studied in this paper. The external steady magnetic field is supposed to be directed perpendicularly to the waveguide wall. Dielectric layer separates semibounded plasma from the metallic wall. The analytical research is carried out using the kinetic description for plasma particles, the mirror reflection model for the interaction between particles and plasma boundary. Skin depth of the surface cyclotron waves (SCW) is much greater than electron Larmor radius. Effect of the following parameters of the waveguide structures: dielectric constant and thickness of the dielectric layer, plasma density value and number of the cyclotron harmonics, on the SCW dispersion is examined both analytically and numerically.

Parametric excitation of a lower-hybrid drift wave in the ionosphere

Parametric excitation of a lower-hybrid drift (LHD) wave has been studied in the ionosphere due to the propagation of a high-frequency electromagnetic (EM) pump wave (with wave number k0≊0) in the presence of the electron collisions. It is considered to be a four wave interaction process of LHD, electromagnetic pump wave, and two electron plasma waves as sidebands. Nonlinear growth rate of a LHD wave is found to be higher for 1<krLe<1.5 as compared to the case krLe<1, where k and rLe, respectively, are the wave number of the LHD wave and electron Larmor radius. Wavelengths of the excited lower-hybrid drift waves lie in the range of the various irregularities observed by Jicamarca [Farley et al., J. Geophys. Res. 75, 7199 (1970)], and Altair and Tradex radars [R. T. Tsunoda, Geophys. Res. Lett. 7, 848 (1980)]. It is seen that the nonlinear growth rate drops significantly in the presence of the electron collisions.

Hybrid modeling of the tearing instability in collisionless two‐dimensional current sheets: Linear theory

The linear stability of thin magnetic field reversals is analyzed using a hybrid approach. The ion resonant response to electromagnetic perturbations is calculated from the kinetic Vlasov equation, whereas the electron response is derived from fluid equations using a suitably adapted electron pressure model. Effects of off‐diagonal components of the perturbed pressure tensor on the compressional stabilization are taken into account. The results are presented with emphasis on a comparison with the linear fully kinetic theory and hybrid simulations of the same model (Hesse et al., this issue). We find the stability of perturbations with gradient scales greater than the maximum electron Larmor radius. The transition to instability with the increase of the electron mass is illustrated.

Finite Larmor Radius Effects in Two-Dimensional Electrostatic Plasma Turbulence

Low frequency electrostatic turbulence in strongly magnetized, low β-plasmas, is studied in two spatial dimensions. In this limit the guiding center velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E x B 0 /B 0 2 -velocity. The electron Larmor radius can safely be set to zero for most relevant conditions, but the ion-dynamics are noticeably influenced by finite Larmor radius effects. We analyzed the effects of finite Larmor radius corrections on the ion velocity and density by using a fluid model where these effects are included by a computationally simple filtering operation. The equilibrium spectra are investigated and compared with analytical results. The consequences of finite Larmor radius corrections for the turbulent diffusion of charged particles across magnetic field lines are studied by obtaining the Lagrangian correlation functions for passive test particles convected by the plasma flow.

Magnetron plasmas for large-area uniform sputtering

A new magnetron plasma with multi-targets has been investigated for large-area uniform sputter-coating with uniform erosion of all targets. When the electron Hall parameter was larger than unity and the length of the cathode dark thickness was shorter than the gap length for the applied magnetic flux density B > B c ( mT)= 150 d( mm) , the discharge was transferred to magnetron mode. In the magnetron mode, it was found that the current density J d on the target was approximately proportional to B 2, P 2 and V 3 2 , respectively. Here P and V are gas pressure and discharge voltage, respectively. The cathode fall depth was roughly proportional to B −1. From these experimental results and from the numerical analysis for the secondary electrons emitted from the targets, a new expression for the Child-Langmuir law in a magnetized plasma was obtained, in which the sheath thickness was replaced by the equivalent electron Larmor radius.

An assessment of plasma instabilities or planetary lightning as a source for the VLF bursts detected at Venus

VLF signals detected in the nightside ionosphere of Venus have generally been attributed to atmospheric lightning. However it has recently been suggested that these bursts could be generated by either whistler-mode or lower hybrid drift instabilities. It has previously been shown that the growth rate for whistler-mode instabilities in the nightside ionosphere is too small for appreciable growth at altitudes < 200 km, where the VLF burst rate is highest. We show that the bursts are usually observed in regions of low electron β, where whistler-mode attenuation is small. We further show that many of the bursts are detected in regions of high collision frequency, which stabilizes the lower hybrid drift instability. Lastly, the waves are also detected in regions where the wavelength required for Doppler-shift of lower hybrid waves to 100 Hz is shorter than the electron Larmor radius, which also argues against a lower hybrid drift instability. Planetary lightning is consequently a more likely source for the VLF bursts.

Anomalous temperature relaxation and particle transport in a strongly non-unifrom, fully in ionized Plasma in a stromg mangnetic field

In classical kinetic and transport theory for a fully ionized plasma in a magnetic field, collision integrals from a uniform theory without fields are used. When the magnetic field is so strong that electrons may gyrate during electron—electron and electron—ion interactions, the form of the collision integrals will be modified. Another modification will stem from strong non-uniformities transverse to the magnetic field B. Using collision terms that explicitly incorporate these effects, we derive in particular the temperature relaxation between electrons and ions and the particle transport transverse to the magnetic field. In both cases collisions between gyrating electrons, which move along the magnetic field, and non-gyrating ions, which move in arbitrary directions at a distance transverse to B from the electrons larger than the electron Larmor radius but smaller than the Debye length, give rise to enhancement factors in the corresponding classical expressions of order In (mion/mel).

The solution of Vlasov's equation for complicated plasma geometry. I. Spherical type

The asymptotic solution of Vlasov's equation for complicated plasma geometry (spherical type) using the computer algebra system Maple is presented. The approximation of small ion and electron Larmor radii (drift approximation) for a dipole magnetic field configuration modeling the earth's plasmasphere was used. The method of solution introduces elliptic integrals as variables, which makes it possible to obtain results in a relatively simple manner. A bounce resonance factor (connected with trapped particles) different from the one appearing in the Landau damping case is found.

Ion temperature measuring probe in a strongly magnetized plasma

A probe for the measurement of the ion temperature in a strongly magnetized plasma is described. The positive-ion current to a cylindrical probe, whose axis is set parallel to the magnetic field, is calculated in the collision-free regime as a function of the ion temperature and the magnetic-field strength. It is assumed that the electron Larmor radius is negligibly small compared to the radius of the cylinder. Only the ion Larmor radius is treated as finite. The ion temperature can be evaluated from the ratio of ion currents of the two cylindrical electrodes with different lengths, whose surfaces are parallel to the magnetic field. The effect of ion drift along the cylinder axis is also considered. Experiments have been made in the edge plasma of a JFT-2M tokamak to test the above probe for determining plasma parameters during ohmic and NBI heatings.

Turbulence and transport in the magnetopause current layer

The current convective instability is identified as the dominant mechanism for producing turbulence and transport in the magnetopause current layer. A linear stability analysis demonstrates that the instability should be robustly unstable for the parameters of the magnetopause current layer. Three‐dimensional nonlinear simulations indicate that the current layer evolves to a strongly turbulent state. The current convective instability is driven unstable by the cross‐field gradient of the parallel current in collisionless plasma. A simple physical picture of the instability is presented. For narrow current layers with scale length L less than an ion Larmor radius ρi, the growth rates exceed the ion gyrofrequency even when Ti ≫ Te. A set of nonlinear fluid equations are derived in the unmagnetized ion limit ρi &gt; L. In three‐dimensional simulations based on these equations the current layer evolves to a turbulent state with layers of extended but irregular clifflike structures with transverse scale length of the order of ρes, the electron Larmor radius based on Ti. The anomalous cross‐field transport rate D⊥ of current resulting from this instability is given by D⊥ ∼ ρes υy with υy the electron parallel streaming velocity. The present linear theory and simulations are limited to electrostatic disturbances. The implications of these results for understanding the structure of the magnetopause current layer are discussed.

Effect of electron dynamics on collisionless reconnection in two‐dimensional magnetotail equilibria

Analytic theory has yielded contradictory predictions regarding the stabilizing role of electron dynamics on the collisionless tearing instability in a field‐reversal region with finite normal magnetic field component Bz. Two‐dimensional (x, z) simulations in which both electrons and ions are treated as particles demonstrate that, for the case of thin current sheets (Ri/ λ ∼ 1, where Ri is the ion Larmor radius based on the lobe field and λ is the current sheet half thickness) and with weakly chaotic electron orbits, the ion tearing mode is indeed stabilized under the mild condition that kρe ≲ 1, where ρe is the electron Larmor radius in the Bz field.

Application of the Child-Langmuir law to magnetron discharge plasmas

In order to investigate the influence of magnetic field on magnetron plasmas, the dependence of discharge-current density (J/sub d/) on magnetic flux densities (B) perpendicular to the electric field over the whole discharge space in a magnetron apparatus with flat multi-targets has been studied. The dependencies on working gas pressures (P) and voltages (V) have been also studied in the configuration. From the experimental results, it was found that J/sub d/ was approximately proportional to B/sup 2/, P/sup 2/ and V/sup 3/2/. The sheath structure in the apparatus has been investigated as a function of B by both a probe method and a spectroscopic one. The cathode-fall thickness was roughly proportional to B/sup -1/. From a numerical analysis on kinetics of /spl gamma/ electrons emitted from the cathode surface, it was found that the dependence of J/sub d/ on B could be explained by the Child-Langmuir law, in which the sheath thickness was replaced by the equivalent electron Larmor radius.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear evolution of a strongly sheared cross-field plasma flow

A study is presented of the nonlinear evolution of a magnetized plasma in which a localized electron cross-field flow is present. The peak velocity of the flow is denoted by V0; LE represents the flow’s shear scale length; and the regime ρe&amp;lt;LE&amp;lt;ρi is considered, where ρi and ρe denote the ion and electron Larmor radii, respectively. It is shown that if the shear frequency ωs=V0/LE is larger than the lower-hybrid frequency, ωLH, then the system dynamics is dominated by the onset of the electron–ion-hybrid (EIH) mode which leads to the formation of coherent (vortexlike) structures in the electrostatic potential of the ensuing lower-hybrid waves. The wavelength of these structures is on the order of LE, and correlates well with that predicted by the linear theory of the EIH mode. Since the characteristic wavelength is longer than ρe, the corresponding phase velocity is low enough that there results significant direct resonant ion acceleration perpendicular to the confining magnetic field. When ωs≳3ωLH, the system exhibits significant anomalous viscosity (typically an order of magnitude larger than that due to Coulomb collisions), which increases as the shear frequency is increased. As ωs is reduced below ωLH, shear effects are no longer dominant and a smooth transition takes place in which the system dynamics is governed by the short wavelength (on the order of ρe) lower-hybrid drift instability.

Theoretical structure of a magnetospheric plasma boundary: Application to the formation of discrete auroral arcs

In the framework of a kinetic theory for tangential discontinuities we modeled the electrical structure of the sheath that separates magnetospheric particle populations of different densities and temperatures. The model can equally be applied to the plasma sheet boundary layer in the tail or to the boundary of some plasma sheet cloud immersed in the central plasma sheet. With plasma parameters typical of the Earth's outer magnetosphere and plasma sheet, we obtain results bearing many features pertinent to magnetospheric processes, specifically the origin of discrete auroral arcs. Creation of a space‐charge separation electrostatic potential in a direction normal to the magnetic field results from the contact of the two plasma populations. When the large‐scale solar wind potential difference is further imposed across the transition layer, the potential gradients are locally much enhanced, to give rise to large electric fields (several hundreds millivolts per meter) appearing over small distances perpendicular to the magnetic field—just the situation needed for the creation of an auroral arc. The transition itself is characterized by two scale lengths of the plasma and fields variables: the average electron Larmor radius ϱe (or some multiple of ϱe) for thin embedded electron‐dominated layers which generate the sharpest potential gradients, and the ion gyroradius ρp (or some multiple of ρp) for the broader ion‐dominated layers located at the outer edges of the transition. The larger‐scale sizes are appropriate to auroral arcs dimensions. The generated electric potential differences, consistent with the energy acquired by the precipitated electrons associated with discrete aurora, are identified with the source of the electromotive force (EMF) required for the auroral current circuit. Wave particle interactions are likely to scatter the electrons into the atmospheric loss cone, establishing the current system threading both the EMF and the ionosphere by means of field‐aligned currents. The half lifetime of the transition is at least of the order of 1000 s. This is also the time interval during which dissipative processes will not alter significantly the available potential gradients of the initially unloaded EMF.

Ion acceleration and coherent structures generated by lower hybrid shear-driven instabilities.

It is shown that if k = omega(S)/omega(LH) greater than 1 (omega(S) and omega(LH) are the shear and lower hybrid frequencies), a sheared electron cross-field flow excites the electron-ion-hybrid mode, causing significant perpendicular ion acceleration. The electric potential develops coherent structures (vortexlike) longer than the electron Larmor radius, rho(e). For k less than 1, a smooth transition occurs where the wavelength becomes of the order of rho(e), the lower hybrid drift instability dominates, and the formation of vortexlike structures is no longer observed. The results are relevant to laboratory, laser-produced, and space plasmas.

Relativistic electron cyclotron theory, revisited

The stages of the relativistic theory leading from the Maxwell-Vlasov system to the absorption and emission coefficients for electromagnetic electron cyclotron waves in a thermonuclear magnetoactive plasma are critically followed, with a particular attention to the approximations involved. Simple and general forms are obtained, holding to arbitrary order in the electron Larmor radius expansion. The applicability limits of the lowest order in this expansion are analysed.

Static Skin Effect at High Current Densities

AbstractThe nonlinear effects in the conductivity of metals and intrinsic semiconductors placed into a homogeneous magnetic field H0 are investigated under the conditions of the static skin effect. The electric current distribution and the intrinsic magnetic field of the current Hj in the sample are obtained by the asymptotic solution of the system of Maxwell and kinetic equations in the case of a slowly changing total magnetic field over a distance of the order of the electron Larmor radius. It is shown that by varying H0 one can study separately the dynamic nonlinear effect associated with the Hj influence on the ballistics of conduction electrons, and the deviation from Ohm's law due to charge carrier heating by electric current.

Static skin effect at high current densities

The nonlinear effects in the conductivity of metals and intrinsic semiconductors placed into homogeneous magnetic field Ho in the. conditions of static skin effect are investigated. The electric current distribution, Hall field, and intrinsic magnetic field of current H j in the sample are obtained by the asymptotic solution of the system of Maxwell equations and kinetic equation in the case of slowly changing of total magnetic field at a distance of the order of electron Larmor radius. The competition between the static skin effect and the pinch effect is analyzed. It is shown that by varying Ho one can study separately the dynamic nonlinear effect associated with the H j influence on the ballistics of conduction electrons, and the deviation from the Ohm's law due to charge carriers heating by electric current.