Volume 5, Issue 9, September 1998
 ARTICLES


Waves and instabilities in streaming magnetized plasma
View Description Hide DescriptionThe evolution of electrostatic waves and excitation of instabilities in twocomponent streaming plasmas in a magnetic field are analytically studied. The modified spectrum and growth term of instability are derived to explain the physical situations like cold plasma, warm plasma, ion fusion aspect along with the uncoupled mode. The striking features of the analysis are displayed in the form of profiles of the refractive index (η) varying with particle thermal energy in different streaming regimes The effect of streaming enhances the frequency propagation of waves or dispersion, including phase velocity and refractive indices. However, the damping or growth term of instability is diminished, appreciably owing to the streaming. The findings may have important implications to space and magnetospheric settings where a beam–plasma interaction exists.

Collisionless reconnection using Alfvén wave radiation resistance
View Description Hide DescriptionPatchy magnetic reconnection involves transient fieldaligned current filaments. The spatial localization, transient timedependence, and orientation of these current filaments means they must radiate torsional Alfvén waves. Radiation of wave energy does not come for free—it must load the current which acts as the radiative source. This loading (radiation resistance) is proposed as the energy sink required for collisionless magnetic reconnection to proceed. Radiation resistance for both inertial and kinetic Alfvén waves is calculated and, for highly collisionless plasmas, is shown to exceed by a substantial factor both Spitzer resistivity and the effective resistance due to the direct acceleration of electrons (inertial loading). The radiation resistivity is shown to provide the magnetic field diffusivity required for magnetic fields to diffuse across the assumed width of the current filament on the time scale of the reconnection. It is also shown that Landau damping of the radiated waves results in the generation of energetic, fieldaligned particles: in the regime the energetic particles are electrons while in the regime, the energetic particles are ions.

On the radial structure of toroidal drift modes in the presence of background flows
View Description Hide DescriptionThe influence of flow shear and curvature on toroidal drift modes has been studied for the case of strong inhomogeneity where the ballooning mode formalism does not apply. It has been found that flow curvature is often as important as the flow shear and may lead to complete cancellation of magnetic shear damping. The limit of validity of the ballooning mode formalism is explored.

Solutions of the plasma equilibrium within the magnetic field of a point dipole
View Description Hide DescriptionFor axial symmetry, in this study we report on analytical solutions of the magnetohydrodynamics(MHD) equilibrium of a plasma within the magnetic environment of a point dipole. Inside the plasma domain, the magnetic flux function is calculated for a given shape of the pressure profile. Another magnetic flux function is derived outside the plasma domain, where the pressure vanishes. Both functions and their normal derivatives are continuous through the boundary between the two domains; together they constitute the solution of our problem. A pressure profile that is a quadratic function of the magnetic flux function is used. It leads to an exact solution which is a simple function of the spherical coordinates. It is shown that, in this situation, the plasma energy is distributed over the entire plasma domain. This solution is well suited as a magnetospheric model. The magnetic flux function determined outside the plasma domain is expressed by a very general formula that is valid for wide classes of both the pressure profiles and the shape of a plasma exterior boundary. Far away from this boundary, as near the coordinate center, the magnetic field tends to be dipolar.

Static local field correction description of acoustic waves in strongly coupling dusty plasmas
View Description Hide DescriptionThe kinetic equations for an interacting dust system with external timedependent forces is considered from the Born–Bogolyubov–Green–Kirkwood–Yvon equations. A kinetic equation is obtained by writing the twoparticle distribution function as a product of two oneparticle distribution functions and the equilibrium radial distribution function. It is shown that a Vlasovlike equation is recovered with a collision term which is a functional of the pair correlation function.Wave behavior from the corresponding fluid equations is considered for a dusty plasma. The results are in qualitative agreement with previously obtained dispersion relations based on generalized hydrodynamics and the quasilocalized charge approximation.

Plasma oscillons in spherically bounded magnetized plasmas
View Description Hide DescriptionOscillatingpatterns of nonlinear waves in a cold nonneutral magnetized plasma bounded by a spherical dielectric are obtained. These patterns, or oscillons, are composed of bulk and surface waves that are strongly but not resonantly coupled.

Surface waves in a magnetized plasma with mobile dust grains
View Description Hide DescriptionWave propagation in a dusty, magnetized, strongly inhomogeneous plasma at frequencies below the ion–cyclotron frequency, and near the dust cyclotron frequency, is considered. The dust grains are assumed to carry a proportion of the negative charge of the plasma.Waveresonances and cutoffs in a homogeneous plasma are discussed. The dispersion relation for surface waves propagating on an interface between a dusty plasma and a vacuum is derived and studied, and their connection to surface waves in general twoionspecies plasmas is analyzed. The damping of the waves due to Alfvén resonance absorption in a narrow but nonzero width interface is derived, and it is shown that for a range of frequencies above the dust cyclotron frequency the surface wave can propagate undamped by resonance absorption.

Azimuthally symmetric pseudosurface and helicon wave propagation in an inductively coupled plasma at low magnetic field
View Description Hide DescriptionThe mode transition from a capacitively coupled mode (E mode) to an inductively coupled mode (H mode) was observed in an inductive Ar plasma source by applying an axially uniform low B field. The applied fundamental rf was 13.56 MHz and many harmonic components were observed. A beat and standing wave patterns of azimuthally symmetric mode) first and second harmonic pseudosurfaces and helicon waves were measured at various densities and B fields (12–28 G). Wave propagation mode changes, from pseudosurface to helicon waves and from helicon to pseudosurface waves, were observed at critical conditions, and

Once more: The continuous spectrum of ideal magnetohydrodynamics
View Description Hide DescriptionA controversy on the existence of continuous spectra of ideal magnetohydrodynamics in addition to the wellknown Alfvén and slow continua, dating back to a conjecture by Grad [Proc. Natl. Acad. Sci. USA 70, 3377 (1973)] and revived by LashmoreDavies, Thyagaraja, and Cairns [Phys. Plasmas 4, 3243 (1997)], is once more resolved by demonstrating that the resolvent operator is bounded in the relevant domain: There are no additional continua. In addition, the solution of the initial value problem is constructed in terms of the threedimensional Green's dyadic, which is free of apparent singularities and clearly exhibits the classical continua as δ functions on the diagonal. This construction provides the connection with the proper and improper normal modes and shows that the local dynamics on the magnetic surfaces is described by the classical continua.

Dusty plasma ionization instability with ion drag
View Description Hide DescriptionThe effect of ion drag on negatively charged dust grains is considered as a possible mechanism of excitation of the dustacoustic (DA) ionizationinstability. It is found that DA waves are more and more damped as the coefficient for ion drag, μ, increases from zero to a critical value, For a zerofrequency (nonpropagating) perturbation grows when the drag of the ions on the dust grains overcomes the effect of the perturbation electric field.

Excitation of lower hybrid waves by a densitymodulated electron beam in a plasma cylinder
View Description Hide DescriptionA densitymodulated electron beam propagating through a plasma cylinder drives electrostatic lower hybrid waves to instability via Cerenkov interaction. The lower hybrid waveinstability has the largest growth rate γ when the frequency and wave number of the modulation are comparable to that of the unstable wave. The growth rate of the instability increases with the modulation index Δ and is maximized for For γ turns out to be The growth rate scales as the onethird power of the beam density. The real frequency of the unstable wave increases as almost the square root of the beam voltage. The results of the theory are applied to explain some of the experimental observations of Chang [Phys. Rev. Lett. 35, 285 (1975)].

On the origin of the ion acoustic soliton
View Description Hide DescriptionThe excitation of ion acoustic solitons by a grid modulated near the ion plasma frequency is studied computationally in a plasma of kinetic ions and Boltzmann electrons. It is found that a largeamplitude, pulselike, ion acoustic wave is launched from the grid and then amplified via inverse Landau damping. This wave is unstable and decays nonlinearly into an ion acoustic soliton and an ion acoustic wave packet. The model reproduces features observed in the experiment of Yi et al. [Phys. Plasmas 4, 2436 (1997)], confirming its essential correctness. The results are also consistent with Korteweg–de Vries theory.

Parametric decays of a circularly polarized electromagnetic wave in an electron–positron plasma
View Description Hide DescriptionParametric decays of a circularly polarized electromagnetic wave in an electron–positron unmagnetized plasma are studied. Like in the case of a plane polarized wave, there are two distinctive situations. One in which ( is the electroacoustic speed, the speed of light, and is the phase velocity of the electromagnetic wave), and the other situation when In the first case, there is an ordinary decay instability and two modulational instabilities. One of the modulational instabilities is a resonant instability, and the other is a nonresonant, essentially electromagnetic instability in which the pump wave decays into two sideband waves. In the second situation there are two modulational instabilities similar to the previous situation, but as the intensity of the pump wave increases, the resonant modulational instability disappears and only the nonresonant electromagnetic instability remains. The effect of Landau damping on the electroacoustic modes is also studied. This effect is simulated through a collisional term in the fluid equations.

Fast reconnection due to localized anomalous resistivity
View Description Hide DescriptionA threedimensional resistive magnetohydrodynamic code has been used to model the reconnection process at the surface, in periodic cylindrical geometry. Large current densities are expected at this reconnection layer and an enhancement of the transport properties is expected if the local drift speed exceeds a critical velocity, such as some multiple of the local sound speed. This effect is modeled in these simulations by the local enhancement of the resistivity coefficient where the criterion for microturbulence is satisfied. It is found that the reconnection times for this type of simulation are comparable to the reconnection times for a plasma where the resistivity is enhanced everywhere, implying that the reconnection is dominated by the local resistivity value and not its gradient. An analytic scaling law of the reconnection rate for the case when the local electron drift velocity is limited to a multiple of the sound speed is presented. This model predicts that when this multiple is reconnection times are close to experimental values in large tokamaks. Under these conditions, electron inertia and electron viscosity can be shown to be unimportant. The onset of microturbulence acts as a trigger for the reconnection process, and partial reconnection can occur if the conditions for microturbulence cease.

Controlling chaotic states of a Pierce diode
View Description Hide DescriptionA recently developed nonlinear approach to control chaos is applied to the Pierce diode. In the latter, both (kinetic) virtual cathodeoscillations and (hydrodynamic)plasma oscillations appear. Via the period doubling route, the plasma oscillations can become chaotic. They are, however, usually superimposed by virtual cathodeoscillations. Here it is shown that in the hydrodynamic, as well as in the kinetic regime, unstable periodic orbits can be stabilized. The results can be applied to bring the Pierce diode into a welldefined state of microwaveoscillations.

The morphological evolution and internal convection of drifting plasma clouds: Theory, dielectricincell simulations, and body dielectric simulations
View Description Hide DescriptionThe evolution of drifting plasma clouds is investigated with the aid of a computational technique denoted here as “dielectricincell.” Many of the familiar phenomena associated with clouds of collisionless plasma are seen and explained and lesswellknown phenomena associated with convection patterns, with the stripping of cloud material, and with the evolution of plasma clouds composed of differing ion species are investigated. The effects of spatially uniform diffusion are studied with the dielectricincell technique and with another computational technique denoted as “Nbody dielectric;” the suppression of convection, the suppression of structure growth, the increase in material stripping, and the evolution of cloud anisotropy are examined.

Ion dynamics in multiple electrostatic waves in a magnetized plasma. I. Coherent acceleration
View Description Hide DescriptionA new phenomenon of coherent acceleration of ions by a discrete spectrum of electrostatic waves propagating perpendicularly to a uniform magnetic field is described. It allows the energization of ions whose initial energies correspond to a region of phase space that is below the chaotic domain. The ion orbits below the chaotic domain are described very accurately using a perturbation analysis to second order in the wave amplitudes. This analysis shows that the coherent acceleration takes place only when the wave spectrum contains at least two waves whose frequencies are separated by an amount close to an integer multiple of the cyclotron frequency. The way the ion energization depends on the wave numbers and wave amplitudes is also presented in detail using the results of the perturbation analysis.

Ion dynamics in multiple electrostatic waves in a magnetized plasma. II. Enhancement of the acceleration
View Description Hide DescriptionThe maximal energy an ion can gain from a discrete spectrum of electrostatic waves propagating perpendicularly to a uniform magnetic field is investigated. In the case when the wave spectrum contains at least two onresonance waves, the ion is shown to reach energies which are much higher than in the case of one wave. When the ion energization is enhanced, even when the ion motion is not coherent, the ion orbit remains close to orbits found from a first order perturbation analysis. This implies that, unlike in the case of a single wave, the ion can reach high energies regardless of how small the wave amplitudes are. The dependence of the ion energization on the wave spectrum characteristics is described in great detail by deriving the extent, in action, of the first order orbits, and the way these orbits may connect.

Effect of a snow plow in bursty magnetic reconnection
View Description Hide DescriptionThis paper concentrates on aspects of magnetic fieldreconnection for a timevarying reconnection rate. There are a number of aspects of timedependent reconnection that have no analogous behavior with the steadystate case. The localization of such timevarying features is of particular interest due to the fact that modeling is generally based on the steadystate case. In order to get optimal physical and mathematical insight, the most simple model is used: identical plasma and magnetic field behavior (except for the field orientation) on either side of the reconnection layer; furthermore the plasma is assumed to be incompressible. The primary interest is the distribution of different energy modes as a result of reconnection. Following a pulse of reconnection, propagating field reversal regions (FRRs) form. Inside these FRRs, the magnetic field energy is decreased, leading to accelerated plasmajets. As a result of the fast motion of the FRRs, there is an accumulation of magnetic energy external to their leading fronts (analogous to the snow accumulation in front of a moving snow plow), and a corresponding energy rarefaction in their wake regions.

On the viscous boundary layer near the center of the resistive reconnection region
View Description Hide DescriptionThis paper studies the behavior of the magnetic field near the center of the reconnection layer in the framework of twodimensional incompressible resistive magnetohydrodynamics with uniform resistivity in a steady state. Priest and Cowley [J. Plasma Phys. 14, 271 (1975)] have presented an argument showing that when the viscosity ν is zero, the magnetic separatrices do not cross at a finite angle but osculate at the Xpoint. In the present paper it is shown that this conclusion is in fact not correct. First, some results of numerical simulations of the reconnection layer are presented. These results contradict the conclusions of Priest and Cowley. To explain this contradiction, an analytical theory for the neighborhood of the Xpoint is developed. When viscosity ν is small, a narrow boundary layer develops near the neutral point. Some of the higher derivatives of the stream function Φ become very large near the Xpoint, leading to a nonzero angle between the separatrices. As the boundary layer shrinks and nonanalytic logarithmic terms emerge in the expansion of Φ in the outer region. This makes the Taylor expansion of Priest and Cowley invalid in the case The results of our boundary layer analysis are in good agreement with the numerical simulations.
