Ratio Of Larmor Radius Research Articles

Performance improvement of particle-in-cell method for numerical modelling of open magnetic system

The work is connected with numerical simulation of plasma dynamics in open magnetic trap in diamagnetic regime. The hybrid particle-in-cell model we develop allows to perform numerical experiments for the high ratio of Larmor radius of the ions and the one of the electrons due to the combining of the kinetic description for the ions and MHD description for the electron plasma component. The disadvantage of the model is the stability condition and the corresponding requirements for the time step. In practice a doubling of the grid nodes in each direction leads to the decrease of the time step x6 times. For the characteristic times of the plasma processes 102 reciprocal ion cyclotron frequencies the computations required few days for grids 100x500. The processing of the particle data takes more than 85% of the total computation time, thus its effective realization yields significant gain in performing. In our algorithm we combine the dynamic load balance and vectorized computations of densities and current densities. We present the results of numerical experiments on its basis including the highly non-uniform particle distribution in the domain and the increasing of the particle number due to the beam injection.

The plasma-wall transition with collisions and an oblique magnetic field: Reversal of potential drops at grazing incidences

The plasma-wall transition is studied by using 1d3V particle-in-cell simulations in the case of a one dimensional plasma bounded by two absorbing walls separated by 200 Debye lengths (λd). A constant and oblique magnetic field is applied to the system, with an amplitude such that r < λd < R, where r and R are the electron and ion Larmor radii, respectively. Collisions with neutrals are taken into account and modelled by an energy conservative operator, which randomly reorients ion and electron velocities. The plasma-wall transition (PWT) is shown to depend on both the angle of incidence of the magnetic field with respect to the wall, θ, and on the ion mean-free-path to Larmor radius ratio, λci/R. In the very low collisionality regime (λci≫R) and for a large angle of incidence, the PWT consists of the classical tri-layer structure (Debye sheath/Chodura sheath/pre-sheath) from the wall towards the center of the plasma. The drops of potential within different regions are well consistent with already published models. However, when sin θ≤R/λci or with the ordering λci<R, collisions cannot be neglected, leading to the disappearance of the Chodura sheath. In this case, a collisional model yields analytic expressions for the potential drop in the quasi-neutral region and explains, in qualitative and quantitative agreement with the simulation results, its reversal below a critical angle derived in this paper, a regime possibly met in the scrape-off layers of tokamaks. It is further shown that the potential drop in the Debye sheath slightly varies with the collisionality for λci≫R. However, it tends to decrease with λci in the high collisionality regime, until the Debye sheath finally vanishes.

Charged Particle Diffusion in Isotropic Random Magnetic Fields

Abstract The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider the diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of Larmor radius to the characteristic outer length scale of turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical results are compared to those from computer simulations, showing good agreement.

Geodesic acoustic mode in tokamaks: local consideration and eigenvalue analysis

A set of magnetohydrodynamic equations describing the geodesic acoustic mode (GAM) in tokamak plasmas is derived. The obtained equations take into account the presence of the energetic ions and allow to study energetic-ion-driven GAM instability perturbatively or non-perturbatively (EGAM mode). They are applicable to plasmas with , where , , cs is the sound velocity, vA is the Alfvén velocity, q is the tokamak safety factor. Using these equations, GAM/EGAM instability is studied in a local approach and by means of the eigenvalue analysis. It is shown that β-coupling (the coupling of Fourier harmonics of the perturbation due to finite β—ratio of the plasma pressure to the magnetic field pressure—and the curvature of the field lines) can be responsible for the radial structure of the GAM-mode. A conclusion is drawn that conditions for the GAM/EGAM instability to arise are mildest in the case of counter-injection of energetic ions with pitch angles χ2 < 0.6 and large ratio of Larmor radius of the energetic ions to a characteristic length of inhomogeneity of these ions. A numerical code solving the derived equations is developed. Specific calculations are carried out for tokamaks with a non-monotonic safety factor. On the other hand, it is found that due to the presence of the energetic ions the GAM/EGAM continuum can have an extremum even when the safety factor q(r) is monotonic, which indicates that global modes can exist also in this case.

Magnetic Measurements at the GDT Facility

Plasma generated electromagnetic oscillations at the frequency an order ion-cyclotron have been investigated in the high energy content regimes of GDT operation. That waves are found to be an Alfvén ion-cyclotron instability. The microinstability threshold scaling law has been defined: with increase of the plasma column radius to Larmor radius ratio the threshold value of the diamagnetism in the midplane decreases. It qualitatively matches the theoretical calculations.

Electron collection by a negatively charged sphere in a collisionless magnetoplasma

Easy-to-evaluate approximate formulas are presented for the repelled-species current collected by a spherical body in a collisionless, magnetized plasma, valid over the full range of ratio of Larmor radius to sphere radius. The form is an appropriate average of the lower and upper bounds obtained by prior analytic arguments. This formulation enables rapid evaluation of the floating potential in hybrid Boltzmann-particle-in-cell (PIC) codes with a background magnetic field. The treatment is validated by comparison of hybrid PIC (ion particle) code with full PIC (electron and ion particle) code calculations. It is found that typically for no value of magnetic field is it valid to approximate the electrons as fully magnetized but the ions as unmagnetized in the absence of plasma drift.

Dynamics of charged particles in bifurcated current sheets: The κ ≈ 1 regime

We examine the nonlinear dynamics of charged particles in the double‐hump current sheets that develop during the late growth phase of substorms. We focus on particles for which the adiabaticity parameter κ (defined as the square root of the minimum curvature radius to maximum Larmor radius ratio) is of the order of unity. We show that as in the case of a simple parabolic field reversal, the magnetic moment scattering experienced by these particles may be described as the result of perturbation of the gyromotion by an impulsive centrifugal force. Here however the double‐hump structure of the current sheet leads to two successive centrifugal perturbations, which has a significant impact on the net change of magnetic moment. In a single‐hump current sheet, three distinct regimes of magnetic moment variations are obtained for a given value of κ, namely, systematic enhancement at small pitch angles, negligible change at large pitch angles, and in between either damping or enhancement depending upon gyration phase. In contrast, in a double‐hump current sheet, repeated application of this three‐branch pattern can lead to magnetic moment damping for particles that previously experience magnetic moment enhancement and vice versa. The gyrophase gain both during and between the centrifugal impulses is found to play an essential role in the net magnetic moment change. In particular, in contrast to single‐hump current sheets, the κ ≈ 1 limit may be characterized by quasi‐adiabatic behavior with negligible variations of the magnetic moment.

Cross field diffusion of cosmic rays in a two-dimensional magnetic field turbulence

Cross field diffusion of energetic particles (cosmic rays) in a two-dimensional static magnetic field turbulence is studied performing test particle simulations. Qualitatively different diffusion processes are observed depending on the ratio of Larmor radius (ρ) to the correlation length (λ) of the magnetic field fluctuations. The diffusion is found to be composed of several regimes with distinct statistical properties, which can be characterized using Levy statistics.

On the use of photometer data to map dynamics of the magnetotail current sheet during substorm growth phase

The Canadian Auroral Network for the OPEN Program Unified Study (CANOPUS) is a large‐scale ground‐based instrument array of remote sensing equipment monitoring the high‐latitude ionosphere from the north central to the northwest portion of North America. It provides realtime coverage of auroral events such as magnetospheric substorms. In this paper the variation of magnetotail thickness is estimated during substorm growth phase by using a simple magnetic field model and data from the meridian scanning photometers in the CANOPUS array. An important parameter in the modeling process is the κ parameter, defined as the square root of the minimum curvature radius to maximum Larmor radius ratio. Through use of this parameter we are able to grossly determine the expected proton precipitation regions in the ionosphere. Two examples presented (February 9, 1995, and March 9, 1995) show that crosstail current sheet thinning from 2–0.1 RE can occur during the course of a growth phase. Within the framework of our model it is demonstrated that the magnetotail field line stretching, associated with thinning of the current sheet, is correlated with the equatorward motion of Hβ auroral emissions. Also demonstrated is the Earthward movement of the inner edge of the plasma sheet to within 6 RE.

A mechanism for ion acceleration near the anode of a magnetically insulated ion diode

We propose a theoretical model for the ion acceleration near the anode in the anode plasma of a magnetically insulated ion diode (MID). The applied diode voltage is screened by the anode plasma. We assume that as a result of the strong magnetization of the electrons and nonmagnetization of the ions in the anode plasma, a narrow space charge sheath is formed near the anode, of a width close to the electron Larmor radius. The potential drop that is formed across the sheath accelerates the ions born inside the sheath into the plasma. We solve a system of equations for the sheath and derive an approximate expression for the potential drop across the sheath. This expression exhibits the dependence of the ion energy on the magnetic field intensity and on the electron temperature and density. We also discuss an influence of the sheath width to the electron Larmor radius ratio as a parameter. The theoretical results are found to be in good agreement with the experimental measurements.

Sheath and presheath structure in the plasma–wall transition layer in an oblique magnetic field

In this paper we present a hydrodynamic study of a current carrying transition layer that separates the plasma from electrically conducting or insulating walls. The plasma is placed in a magnetic field that could be parallel to, or intersects obliquely with the walls. The self-consistent model of the smooth presheath–sheath transition of the near-wall plasma layer developed here for a finite Debye radius to ion Larmor radius ratio (Ψ) is based on a previously developed model of the quasineutral plasma presheath [Phys. Plasmas 4, 3461 (1997)]. The potential distribution in the presheath is found to have a positive maximum with respect to the plasma–presheath interface. In the case of a wall with a floating potential, the value of the maximum decreases with the incidence angle θ of the magnetic line force, and approaches zero when θ=2°. The presheath thickness generally increases with the incidence angle, from about the electron Larmor radius up to the ion Larmor radius, and depends on the electron to ion current ratio, ion velocity at the plasma–presheath interface, and Hall parameter. Analysis of presheath-sheath transition when Ψ is in the range of 10−2 to 10−4 shows that (1) the electric field at the presheath–sheath interface is finite, (2) the critical ion velocity at the sheath edge is about (0.6–0.9) of ion sound speed, depending on the plasma parameters, and generally increases with the ion to electron current ratio. The current–voltage characteristic of the transition layer does not depend on θ, the magnetic field incidence angle, for θ⩾5°.

On the nonadiabatic precipitation of ions from the near‐Earth plasma sheet

We examine the precipitation of ions which result from nonadiabatic pitch angle scattering in the near‐Earth magnetotail. We focus on dynamical situations between the adiabatic limit where the particle magnetic moment is conserved and the current sheet limit where particles experience meandering motion about the midplane. Defining the κ parameter as the square root of the minimum curvature‐radius‐to‐maximum Larmor radius ratio, the situations we consider correspond to κ between 1 and 3. We demonstrate that throughout this range of κ values, magnetic moment variations are systematically organized into three categories: (1) at small (a few degrees) equatorial pitch angles, large magnetic moment enhancements regardless of gyration phase; (2) at large equatorial pitch angles (typically, above 30°), negligible magnetic moment changes; and (3) in between, a prominent dependence upon gyration phase with either magnetic moment enhancement or damping. We show that these three distinct regimes can be understood in terms of relative magnitude of the centrifugal force experienced by the particles with regard to that of the Lorentz force. In agreement with previous studies, we show that detrapping of plasma sheet ions due to nonadiabatic pitch angle scattering is effective throughout the 1‐ to 3‐κ range. However, the degree of loss cone filling critically depends upon the angular characteristics of the incident population. It is significantly greater for initially isotropic populations than for initially field‐aligned ones, because only particles away from the magnetic field direction experience strong damping of magnetic moment.

The centrifugal impulse model of nonadiabatic behavior in a field reversal

We examine the possibility of describing the magnetic moment change experienced by particles traveling through a field reversal by the action of an impulsive centrifugal force on the time scale of their cyclotron turn. It is shown that such a centrifugal impulse model applies to situations where the ϰ parameter (defined as the square root of the minimum curvature radius-to-maximum Larmor radius ratio) is of the order of 1. It is demonstrated that the particle behavior can be organized by another parameter (referred to as ϰ α ) which is proportional to ϰ but involves the pitch angle, namely, one obtains: systematic magnetic moment enhancements for ϰ α ⪡ 1, large gyrophase effects with possible damping of the magnetic moment for ϰ α ∼ 1, and nearly constant magnetic moment for ϰ α ⪢ 1. When applied to ion transport in the near-Earth magnetotail, the model predictions are in agreement with numerical results, revealing enhanced trapping or detrapping of plasma sheet ions depending upon their pitch and phase angles.

Gyrophase effects in the centrifugal impulse model of particle motion in the magnetotail

We investigate the dynamics of charged particles in a magnetic field reversal in the particular case where the Larmor radius is comparable to the magnetic field line curvature radius. In the current interpretation framework based upon the parameter κ (defined as the square root of the minimum curvature radius‐to‐maximum Larmor radius ratio), this situation corresponds to κ of the order of 1. We show that this nonadiabatic regime, which lies at the transition between adiabatic motion (κ ≫ 1) and the nonadiabatic one characterized by oscillations about the field minimum (κ &lt; 1), results from prominent centrifugal effects in the field reversal. To model these effects, we develop a simple analytical description which is based upon an impulsive centrifugal force perturbing the particle gyromotion on the time scale of the cyclotron turn. Comparisons with numerical calculations of ion trajectories demonstrate that this centrifugal impulse model adequately describes both the magnetic moment variations and the gyrophase variations experienced by the particles. As for the magnetic moment, three distinct behaviors (negligible change, strong phase dependence with possible damping, and systematic enhancement) are identified depending upon pitch angle. As for the gyration phase, important bunching effects are obtained which are interpreted as being due to the action of the impulsive centrifugal force. These phase bunching effects are enhanced as the κ parameter approaches unity. In the limit κ ∼ 1, a strong imbalance is obtained between the two phase sectors corresponding to duskward and dawnward motions. This imbalance, which extends over a few tenths of an Earth radius in the Z direction, leads to the formation of a thin current sheet in the vicinity of the magnetotail midplane.

Application of the centrifugal impulse model to particle motion in the near‐Earth magnetotail

Particles traveling in the geomagnetic tail do not conserve their magnetic moment (first adiabatic invariant) due to significant field variations on the length scale of their Larmor radius. We examine the possibility of describing these magnetic moment changes by the action of an impulsive centrifugal force on the timescale of the particle cyclotron turn. Trajectory calculations demonstrate that such a centrifugal impulse model adequately describes the nonadiabatic particle behavior for situations where the κ parameter (defined as the square root of the minimum curvature radius‐to‐maximum Larmor radius ratio) is of the order of 1 to 2. In particular, it is shown that this behavior can be organized by another parameter (referred to as κα), which is proportional to κ but depends upon the particle pitch angle, namely, one obtains: systematic magnetic moment enhancements for κα ≪ 1, large gyrophase effects with possibly prominent damping of the magnetic moment for κα ∼ 1, and nearly constant magnetic moment for κα ≫ 1. More generally, we show that the centrifugal impulse approximation applies to an intermediate orbit regime at the transition between the fully adiabatic (magnetic moment conserving) regime and that regime where particles experience meandering motions about the field minimum. It applies to ion transport in the near‐Earth magnetotail where the magnetic field lines evolve from dipolar to taillike configurations and where the κ parameter nears unity. In this region of space the model predictions are in agreement with numerical results, revealing both enhanced trapping (due to magnetic moment enhancement) and possible precipitation (due to magnetic moment damping) of plasma sheet ions depending upon their pitch and phase angles.

Profile stabilization of tilt mode in a field-reversed configuration

The possibility of stabilizing the tilt mode in field-reversed configurations without resorting to explicit kinetic effects such as large ion orbits is investigated. Various pressure profiles, P(Ψ), are chosen, including ‘‘hollow’’ profiles, where current is strongly peaked near the separatrix. Numerical equilibria are used as input for an initial value simulation, which uses an extended magnetohydrodynamic (MHD) model that includes viscous and Hall terms. Tilt stability is found for specific hollow profiles when accompanied by high values of separatrix beta, βsep. The stable profiles also have moderate to large elongation, racetrack separatrix shape, and lower values of s̄, average ratio of Larmor radius to device radius. The stability is unaffected by changes in viscosity, but the neglect of the Hall term does cause stable results to become marginal or unstable. Implications for interpretation of recent experiments are discussed.

Cyclotron resonance phenomena in a pure electron plasma

An experiment designed to elucidate the features of cyclotron resonance in a rotating cylindrical pure electron plasma column is described. The density is well below the Brillouin limit and varies with radius, as does the rotational angular velocity. Thus the steady state is not the rigid-rotor equilibrium which is frequently studied theoretically. The readily observed modes are found to have kz≊0 and m=1,2,3,4... (eikzz+im θ) with frequencies which are within a few percent of the cyclotron frequency (140 MHz). A single m=1 mode is found that is downshifted from the cyclotron frequency by an amount equal to the m=1 diocotron frequency. For each of the higher m values, bands of closely spaced discrete modes are found which are upshifted from the cyclotron frequency by the Doppler effect of rotation. The bands of discrete modes are explained as radially trapped azimuthally propagating Bernstein modes in a rotating plasma and approximate theories for these modes are outlined. By comparing the results with experiments, plasma parameters such as the ratio of Larmor radius to plasma scale length, the central rotation frequency, and the ratio of peak to average density can be inferred.

Wave propagation near a cyclotron resonance in a nonuniform equilibrium magnetic field

The inclusion of the variation of the equilibrium magnetic field across the Larmor orbits of the resonant particles is crucial for a self-consistent treatment of cyclotron resonance in plasmas. Two contrasting nonrelativistic self-consistent calculations [T. M. Antonsen and W. M. Manheimer, Phys. Fluids 21, 2295 (1978); C. N. Lashmore-Davies and R. O. Dendy, Phys. Fluids B 1, 1565 (1989)] which analyze perpendicular propagation in the same nonuniform magnetic field are compared. It is shown that the first of these, which is a full wave calculation, makes an approximation that eliminates the damping found in the second, which calculates optical depth via a Wentzel–Kramers–Brillouin (WKB) approximation. A new expansion of the exact integral equation describing the problem is given, producing full wave equations which incorporate the perpendicular damping. The equations are of the correct form to ensure energy conservation and can easily be obtained to any order in an expansion in terms of the ratio of Larmor radius to perpendicular wavelength.

Finite Larmor radius wave equations in Tokamak plasmas in the ion cyclotron frequency range

The constitutive relation of a non-homogeneous plasma for h.f. waves in the ion cyclotron frequency domain is derived by integrating the Vlasov equation along the unperturbed particle orbits in the drift approximation. The integro-differential wave equations and the corresponding power balance equation in Tokamak geometry are obtained by expanding the h.f. current to second order in the ratio of the ion Larmor radius to the typical perpendicular wavelength; terms proportional to the much smaller ratio of Larmor radius to the length characterizing equilibrium gradients are neglected. This allows the author to cast the FLR wave equations into an explicitly vector form, and to identify clearly the physical meaning of each term. By specializing to a plane stratified model of the Tokamak, the author compared the complete set of FLR wave equations with a considerably simpler set previously derived by Swanson (1981) and by Colestock and Kashuba (1983), which has been extensively used for analytic and numerical studies of ICR heating. The author concludes that at least in the important scenario of a hydrogen minority in a deuterium plasma (and of pure first harmonic heating as a particular case), the use of the reduced set of equations is well justified, provided that finite Larmor radius contributions to electron absorption are taken into account.