Volume 5, Issue 7, July 1998
 LETTERS


The Kelvin–Helmholtz instability in the presence of dust charge fluctuations
View Description Hide DescriptionKelvin–Helmholtz instability is examined by considering the dust charge fluctuations in a dusty plasma. Electrons and ions are assumed to be in Boltzmann equilibria and the dust grains to follow the fluid equations with a full adiabatic equation of state. The transverse shear in the flow parallel to the magnetic field is considered. The instability is found to grow for limiting wave numbers for a particular value of shear velocity. The effect of adiabatic dust plasma pressure is to enhance the growth rate of the instability. For dense plasma, growth of the instability is affected by the presence of dust charge fluctuations.
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 ARTICLES


Dynamic plasma screening effects on electron–ion collisional excitations in a generalized Lorenzian (kappa) distribution plasma
View Description Hide DescriptionDynamic plasma screening effects are investigated on dipole transition probabilities for electronimpact excitation of hydrogenic ions in a generalized Lorenzian (kappa) velocity distribution plasmas. The electron–ion interaction potential is obtained by introduction of the plasma dielectric function. A semiclassical straightline trajectory method is applied to the path of the projectile electron in order to visualize the dynamic plasma screening effects on the semiclassical transition probabilities as a function of the impact parameter and the collision energy. The transition probability including the dynamic plasma screening effect is found to be always greater than that including the static plasma screening effects. It is also found that the dynamic plasma screening effects on the electron–ion collisional excitations in the Lorenzian velocity distribution plasmas are more effective than those in the Maxwellian velocity distribution plasmas.

Instability of a magnetized plasma jet
View Description Hide DescriptionThe stability characteristics of a plasma jet embedded in a parallel magnetic field are investigated. The Kelvin–Helmholtz kink mode, which dominates at small is stabilized at while the pinch mode remains unstable up to Contrary to a nonmagnetized jet, for finite the kink mode saturates quasilinearly by broadening the jet, such that becomes larger than the marginal value 0.46. Including finite resistivity the nonlinear behavior is eventually governed by the tearing mode for all values of consisting of a single plasmoid moving along the jet. Hence the shear flow cannot stabilize the tearing mode, so that the apparent tearing stability of resistive current sheets observed in numerical simulations of magnetic reconnection is only due to finitelength effects.

Instability of electromagnetic Rmode waves in a relativistic plasma
View Description Hide DescriptionAn explicit mathematical formalism is developed to evaluate the growth rate of fieldaligned electromagnetic Rmode waves in a relativistic plasma. The methodology is valid for weak wave growth or damping when the resonant relativistic electrons comprise a small portion of the total plasma population. Numerical results are obtained for realistic plasma parameters using three distinct distribution functions for the relativistic electron population. Wave growth rates obtained by numerical integration along the resonant relativistic ellipse are shown to be substantially smaller than calculations performed under the nonrelativistic approximation. The relativistic corrections are primarily due to a reduction in the resonant electron anisotropy. Changes from the standard nonrelativistic treatment are noticeable at relatively small electron thermal energies (a few keV), and they become very significant for thermal energies above 100 keV, especially in low density regions where the plasma frequency is comparable to or lower than the electron gyrofrequency. The results have applications to waveinstability in the outer radiation belts of the Earth, the inner Jovian magnetosphere, and other space plasmas where relativistic electrons are present.

Stable, thermal equilibrium, largeamplitude, spherical plasma oscillations in electrostatic confinement devices
View Description Hide DescriptionThe problem of largeamplitude spherical oscillations of an ion cloud in an Inertial Electrostatic Confinement (IEC) device is examined. It is shown that ion fluctuations of a Gaussian profile in a spherical, harmonic well are stable to all hydrodynamic modes, and stable oscillations about the oscillating equilibrium state may be damped by continuum damping. It is also shown that the ion state forms a thermal equilibrium, in spite of the orders of magnitude, density, and temperature changes during the oscillation cycle. Finally, a brief discussion of how to experimentally realize the required electron distributions for these oscillations is presented.

Ion Bernstein waves driven by two transverse flow layers
View Description Hide DescriptionThe interaction between two narrow layers of flow is investigated, along with their stability properties. The mode frequencies, growth rates, and eigenfunctions are calculated. It is found that the instability due to a single layer is robust to the inclusion of a second layer. Specifically, when the separation between the layers is on the order of the ioncyclotron radius, there is strong coupling between the two layers and the second layer is destabilizing. In addition, when the flow velocities are in opposite directions a wide variety of modes is possible, including nearzerofrequency modes, resulting in broadband structure in both the frequency spectrum and the wave number spectrum. These results may have implications for the understanding of the auroral ionosphere, where such spatial structure in the transverse electric field is often observed.

Description of contained mode solutions to the relevant magnetosonicwhistler wave equations
View Description Hide DescriptionThe generalization of magnetosonicwhistler modes having a dispersion relation of the form , where is the Alfvén velocity and , to the case of an inhomogeneous plasma leads to localized eigenmode solutions. These solutions, which are referred to as contained modes, are tightly confined in the direction of inhomogeneity. In this paper, the contained modes are analyzed for frequencies and for In a cylindrical or toroidal configuration, these modes propagate mostly in the poloidal direction and are localized within a narrow radial shell. Contained modes have been proposed as an underlying mechanism for anomalous ion cyclotron emission (ICE) in plasmas with an energetic ion population. Analytic expressions for the characteristics of these modes are obtained using an expansion in high poloidal mode number and are found to agree with numerical results. For typical plasma profiles, the contained modes are localized towards the edge of the plasma column. It is found that the key parameter which regulates the behavior of the mode is . This quantity is related to the Hall term which is kept as the first significant correction to Ohm’s law for the frequencies being considered. The Hall term introduces to the eigenmode equation a dependence on the sign of the poloidal phase velocity, and when is sufficiently large contained solutions only exist for modes whose poloidal phase velocity has the same orientation as the ion cyclotron motion. The dependence of the mode characteristics on finite is examined in detail. In particular, the quantity determines the poloidal mode number above which effects, such as a shift in the region of localization of the mode, become significant.

Predictions of finite Larmor radius reduced magnetohydrodynamics for Rayleigh–Taylor unstable plasmas
View Description Hide DescriptionFinite Larmor radius magnetohydrodynamics (FLR MHD), being valid when the ion Larmor radius is of the order of the characteristic length scale, predicts a Rayleigh–Taylor instability in an inhomogeneous plasma with unfavorable field line curvature. It is shown that the FLR MHDequations can be reduced to a set of two scalar fieldequations for the pressure and the electrostatic potential in the flute approximation and the large aspect ratio limit. Using a Galerkin approximation with a few dominating modes, the simple model reproduces previous numerical simulations based on the full FLR MHDequations.

Initial condition sensitivity of global quantities in magnetohydrodynamic turbulence
View Description Hide DescriptionThe effect of subtle changes in initial conditions on the evolution of global quantities in twodimensional magnetohydrodynamic(MHD)turbulence is studied. It is found that a change in the initial phases of complex Fourier modes of the Elsässer variables, while keeping the initial values of total energy, cross helicity, and Alfvén ratio unchanged, has a significant effect on the evolution of cross helicity. On the contrary, the total energy and Alfvén ratio are insensitive to the initial phases. The simulations are based on direct numerical simulation using the pseudospectral method.

Collisional amplification of test electromagnetic waves in a plasma subject to an intense highfrequency laser field
View Description Hide DescriptionRecently, calculations based on Fokker–Planck and Landau collision operators have been used to demonstrate that test waves with electric fields in the plane of polarization of external superintense laser fields can get amplified by nonlinear collisional processes. The calculations are similar in spirit to parametric instability calculations and make use of an averaging process for the collision operator whose range of validity is not clear. The Dawson–Oberman model of highfrequency plasma conductivity is used to reinvestigate this problem. It is shown that in the limit of small test wave frequency, no amplification is possible. This result contradicts the one obtained by earlier workers with averaged collision operators. At higher test wave frequencies earlier results are recovered.

Geometry of singular structures in magnetohydrodynamic flows
View Description Hide DescriptionThe flattening of current sheets is investigated by means of numerical simulations of the ideal incompressible magnetohydrodynamic equations in two dimensions. The use of adaptive mesh refinement techniques allows one to resolve the more and more singular structures and to follow the exponential growth of current density. The numerical results are in good agreement with a scaling ansatz proposed by Sulem et al. [J. Plasma Phys. 33, 191 (1985)]. The geometry of the current sheets is characterized by the alignment properties of the deformation matrices.

Generation of hot spots by fast electrons in lower hybrid grills
View Description Hide DescriptionGeneration of hot spots on plasma facing components magnetically connected to the grill is a main limiting factor in highpower operation of a lower hybrid system. A possible explanation for the hot spots is the sputtering caused by fast electrons generated by parasitic absorption of lower hybrid power near the grill mouth. The behavior of the edge plasma near the grill mouth is investigated with a new tool in this context: the selfconsistent particleincell(PIC) code XPDP2 [V. Vahedi et al., Phys. Fluids B 5, 2719 (1993)]. The PIC simulations provide the key parameters of the problem: the absorbed power, the radial deposition profiles, and the energy spectrum of the accelerated particles close to the grill.

Nonlinear electromagnetic gyrokinetic equation for plasmas with large mean flows
View Description Hide DescriptionA new nonlinear electromagneticgyrokinetic equation is derived for plasmas with large flow velocities on the order of the ion thermal speed. The gyrokinetic equation derived here retains a collision term and is given in the form which is valid for general magnetic geometries including the slab, cylindrical and toroidal configurations. The source term for the anomalous viscosity arising through the Reynolds stress is identified in the gyrokinetic equation. For the toroidally rotating plasma, particle, energy and momentum balance equations as well as the detailed definitions of the anomalous transport fluxes and the anomalous entropy production are shown. The quasilinear anomalous transport matrix connecting the conjugate pairs of the anomalous fluxes and the forces satisfies the Onsager symmetry.

Nonlinear tearing mode study using the “almost ideal magnetohydrodynamics (MHD)” constraint
View Description Hide DescriptionTearing modes of finite amplitude are studied numerically using the “almost ideal magnetohydrodynamics (MHD)” constraint, which is a modification of the ideal MHD constraints that allows reconnection of the magnetic field lines. For the onedimensional initial equilibria studied here, the stability criterion is found to be the same as that of the linear tearing mode theory, namely . The nonlinear saturation level of the mode can also be determined; it is found to be smaller than that estimated from [R. B. White et al., Phys. Fluids 20, 800 (1977)].

Amplitude modulation of dustlattice waves in a plasma crystal
View Description Hide DescriptionIt is found that the nonlinear dynamics of amplitudemodulated dispersive dust lattice waves (DLW) is governed by a nonlinear Schrödinger equation. The latter exhibits that a constant amplitude carrier dust lattice wave is modulationally stable, and that the modulated DLW packet propagates in the form of either an envelope dark soliton or an envelope shock. The relevance of our theoretical investigation to simulation studies as well as to a laboratory dusty plasmaexperiment is pointed out.

Nonlinear dynamics of magnetic buoyancy instabilities in a sheared magnetic field
View Description Hide DescriptionNonlinear dynamics of magnetic buoyancy instabilities for the Parkertype and interchangetype modes are numerically investigated with the aim of understanding the emerging mechanism of solar coronal magnetic loops. Twodimensional nonlinear magnetohydrodynamic(MHD) simulations of the magnetic buoyancy instabilities are performed in a highly stratified domain consisting of two temperature regions corresponding to the corona and the chromosphere, respectively. First, it is revealed that the angle between the wave vector and the magnetic field at the top interface of the magnetic layer is a crucial parameter controlling the basic properties of the instability. Second, it is found that the magnetic buoyancy instability in the sheared field grows nonlinearly larger than in the shearless field, although the magnetic shear reduces the linear growth rate. This is due to the Parkertype mode being destabilized by the nonlinear effect of the interchangetype instabilities. Third, it is shown that the magnetic buoyancy instability can drive magnetic reconnections which create isolated flux regions.

On the higherorder nonlinear corrections to the theory of plasma emission by a nonlinear beam instability
View Description Hide DescriptionA recent alternative theory of electromagnetic radiation with frequency in the vicinity of plasma frequency and/or its harmonic, put forth by the present author, invokes a new type of nonlinear beamplasma instability. The new theory was originally formulated by retaining the secondorder nonlinear response of the plasma only. However, in a general nonlinear instability theory it is well known that the thirdorder correction can have a contribution of the same order of magnitude as the secondorder nonlinearity. This article examines the validity of the original formulation of the nonlinear beam instability by reformulating the problem, keeping the full second and thirdorder nonlinear responses of the plasma. In the final analysis, however, it is found that the thirdorder nonlinear correction can indeed be neglected, and that the original formulation of the problem is justified.

Nonevolutionary discontinuous magnetohydrodynamic flows in a dissipative medium
View Description Hide DescriptionMagnetohydrodynamic discontinuities in a dissipative medium are considered from the view point of the principle of evolutionarity. For a nonevolutionary discontinuity, the problem of time evolution of a small perturbation does not have a unique solution. This means that an infinitesimal perturbation results in finite variation of the initial flow. Such a discontinuity cannot exist as a stationary configuration and it must disintegrate or transform to some other nonsteady flow. Using the kinematic properties of weakly damping highfrequency perturbations of a dissipative medium, the sufficient conditions of nonevolutionarity of the dissipative discontinuities are obtained. These conditions are shown to strengthen the known criterion of a discontinuous profile of inviscid shocks. It is suggested that time evolution of the nonevolutionary shock that contains the nonevolutionary internal discontinuity is a superposition of two oscillation processes with different characteristic times corresponding to internal disintegration and disintegration of the shock as a whole.

Optimization of power density by decreasing the length of tungsten wire array Z pinches
View Description Hide DescriptionReducing the length of 30 mm diam tungsten wire arrays on the 20 MA Z pulsed power accelerator [R. B. Spielman, S. F. Breeze, C. Deeney et al., Proceedings of the 11th International Conference on Particle Beams, Prague, Czech Republic, edited by K. Junwirth and J. Ullschmied (Czech Academy of Sciences, Prague, 1996), p. 150] from 2 to 0.75 cm has shown that the radiated powers are energies that remain constant at and The lengthindependent nature of the power and energy results in the radiated power per unit length increasing from to These highpower densities should result in approximately a 20% increase in radiation temperatures produced by a Zpinchdriven vacuum or internal hohlarums. Twodimensional radiation magnetohydrodynamic calculations indicate that the constant radiated energies with varying pinch lengths is consistent with the energy input being due to the work done by the Lorentz forces during the radial collapse, resulting in kinetic energy and during the onaxis pinch phase, resulting in pdV or compressional heating.

Relaxation of a twospecies magnetofluid and application to finiteβ flowing plasmas
View Description Hide DescriptionThe relaxation theory of a twospecies magnetofluid is presented. This generalizes the familiar magnetohydrodynamic (singlefluid) theory. The twofluid invariants are the selfhelicities, one for each species. Their “local” invariance follows from the helicity transport equations, which are derived. The global forms of the selfhelicities are examined in a weakly dissipative system. They are shown to pass three tests of ruggedness (“relative” invariance compared with the magnetofluid energy): the cascade test; the selective decay test; and the stability to resistive modes test. Once ruggedness is established, relaxed states can be found by minimizing the magnetofluid energy subject to constrained selfhelicities. The Euler equations are found by a variational procedure. Example equilibria are presented that resemble fieldreversed configurations (FRCs) and tokamaks. These states are characterized by finite pressure and significant sheared flows. Throughout the analysis it is shown how this more general theory reduces to the magnetohydrodynamic (singlefluid) theory for suitable reducing assumptions.
