Volume 7, Issue 3, March 2000
 LETTERS


Betadependent upper bound on ion temperature anisotropy in a laboratory plasma
View Description Hide DescriptionLaser induced fluorescencemeasurements of ion temperatures, parallel and perpendicular to the local magnetic field, in the Large Experiment on Instabilities and Anisotropies space simulation chamber (a steadystate, high beta, argon plasma) display an inverse correlation between the upper bound on the ion temperature anisotropy and the parallel ion beta These observations are consistent with in situspacecraftmeasurements in the Earth’s magnetosheath and with a theoretical/computational model that predicts that such an upper bound is imposed by scattering from enhanced fluctuations due to growth of the ion cyclotron anisotropy instability (the Alfvén ion cyclotron instability).
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Kinetic simulation on ion acoustic wave in gas discharge plasma with convective scheme
View Description Hide DescriptionIn a onedimensional plasmasheath system representing a concave quasistationary electric potential typical of a negatively charged system, oscillations of ion are simulated by the aid of a convective scheme useful for weakly ionized plasma, and are theoretically investigated. The frequency spectra of the ion current through a cathode reveal to us that two modes of ion acoustic waves are dominant; a high and a low frequency mode. By deriving a linear differential equation with a dissipation and an ion flow, and taking for granted the sheath width and the distribution of ion flow velocity, the dispersion relation for a finite length system can be calculated. The simulation results, such as the reinforcement of the low frequency mode and the suppression of the high frequency mode, are satisfactorily corroborated by the linear theory. The instabilities of the waves are caused by the asymmetry of boundary conditions and by the dissipative effect.

DustCoulomb and dustacoustic wave propagation in dense dusty plasmas with high fugacity
View Description Hide DescriptionA detailed investigation of electrostatic dust wave modes in unmagnetized dusty plasmas consisting of electrons, ions and dust grains has been carried out over a wide range of dust fugacity and wave frequency by using fluid as well as kinetic (Vlasov) theories. The dust fugacity parameter is defined by where and R are respectively the dust number density, the plasma Debye length and the grain size (radius), and is the dust plasma parameter. Dusty plasmas are considered to be tenuous, dilute or dense according as or In particular, attention is focused on the “dust–acoustic waves” (DAWs) and the “dust–Coulomb waves” (DCWs) which exist in the tenuous (low fugacity) and the dense (high fugacity) regimes, respectively, when the wave frequency is much smaller than the grain charging frequency. Unlike the DAWs, which exist even with constant grain charge, the DCWs [N. N. Rao, Phys. Plasmas6, 4414 (1999)] are the normal modes associated with grain charge fluctuations, and exist in dense dusty plasmas. In the long wavelength limit, the DCW phase speed scales as where is the DAW phase speed. In the dilute (medium fugacity) regime, the two modes merge into a single mode, which may be called the “dust charge–density wave” (DCDW) since the latter involves contributions arising from both the DAW and the DCW. On the other hand, for frequencies much larger than the charging frequency, DAWs are shown to exist also in the dilute regime. The real frequency as well as the damping rate in each case are explicitly calculated from both the fluid as well the kinetic theories, and a comparison between the two has been carried out. In the allowed fugacity regimes (tenuous, dilute or dense), all the three waves are weakly damped and, hence, can propagate as normal modes. The present analysis of wave propagation in dusty plasmas over different fugacity regimes suggests the introduction of a new length scale defined by where is the Wigner–Seitz radius and is a parameter related to the charging frequencies. This length scale which governs the dispersive properties of the DCW modes is most useful in the dense regime, and plays a role which is very similar to that of the Debye length in the tenuous regime. The ratio of to is a measure of the dust fugacity, and is given through The very recent experimental observation [S. Nunomura et al., Phys. Rev. Lett. 83, 1970 (1999)] on a selfexcited instability associated with grain charge fluctuations may be an indication of DCWs in the strong coupling regime. The possibility of the existence of a dust thermal wave (DTW) in the superdense regime has been pointed out. A heuristic, but simple, derivation of DCWs based on grain dynamics but supplemented by physical inputs from the plasma response has also been presented.

On the existence of small amplitude double layers in an electron–positron–ion plasma
View Description Hide DescriptionA theoretical model is presented to investigate the double layers, associated with the kinetic Alfvén waves, in a magnetized electron–positron–ion plasma with a small but finite value of β, and smallamplitude double layer solutions are obtained. The existence of smallamplitude double layers requires that the density of ions is appreciably larger than that of positrons at equilibrium. The properties of the double layers are determined by the ratio between the number densities of positrons and ions at equilibrium, the direction cosines defining the moving frame, as well as the electron to positrontemperature ratio.

Dust lattice waves in a plasma crystal
View Description Hide DescriptionThe dust lattice wave in dusty plasma crystals is reexamined, taking into account the dependence of the dust grain charge on the grain potential. The Poisson equation for small grain potentials then assumes the form of the Schrödinger equation. The spatial distribution of the potential in the lattice includes the effect of the whole system of dust particles. Such a selfconsistent description gives the dispersion relation for the dust lattice wave, which is different from the expression found earlier. The case of large grain charge is also considered. The frequency of the lattice oscillation increases considerably for large grain charges. Furthermore, it is noted that an ideal lattice can only exist if the dusty plasma parameters satisfy a definite relation between the dusty plasma Debye radius, the intergrain separation, and the grain size.

Plasma screening effects on inelastic Compton scattering of photons by hydrogenic ions in strongly coupled classical plasmas
View Description Hide DescriptionPlasma screening effects on inelastic Compton scattering of photons by hydrogenic ions in uniformly distributed strongly coupled classical plasmas are investigated. The interaction potential in strongly coupled plasmas is given by the ion–sphere model. The screened radial atomic wave functions and energy eigenvalues for the and states of the hydrogenic target ion in strongly coupled plasmas are obtained by the Ritz variational and perturbational calculations. The expression for the lowestorder transition matrix element is obtained by a two photon process associated with terms quadratic in the vector potential A. The inelastic Compton scattering cross section from the ground state to the excited state is obtained as a function of the incident photon energy including the plasma screening effects through the ion–sphere radius. In strongly coupled plasmas, the plasma screening effect on the inelastic Compton scattering cross section is found to be stronger than that on the photoionization cross section.

Interaction of a shear Alfvén wave with a filamentary density perturbation in a lowβ plasma
View Description Hide DescriptionThis analytic study investigates the interaction between a largescale shear Alfvén wave propagating through a lowβ plasma and a preexisting density perturbation of small transverse scale. The interaction forms an in situantenna that selfconsistently generates two fieldaligned current channels of opposite polarity. The expansion of the current channels across the confining field is bounded by the cone trajectories of smallscale inertial Alfvén waves. The spatial patterns of the radiated fields are obtained, and the magnitude of the parallel electric field and its effective phase velocity are assessed. An effective cross section that varies with the parallel and transverse scale lengths of the density perturbation summarizes the efficiency of the direct conversion process.

Effects of background gas pressure on the dynamics of a nonneutral electron plasma confined in a Malmberg–Penning trap
View Description Hide DescriptionThe effects of electron–neutral collisions on plasma expansionproperties and the evolution of the diocotron mode are investigated in the Electron Diffusion Gauge (EDG) experiment, a Malmberg–Penning trap with plasma length cm, plasma radius cm, and characteristic electron density Essential features of the diocotron modedynamics in the absence of electron–neutral collisions are verified to behave as expected. The mode frequency, the growth rate of the resistivewall instability, and the frequency shift at nonlinearly large amplitudes are all in good agreement with theoretical predictions. When helium gas is injected into the trap, the evolution of the mode amplitude is found to be very sensitive to the background gas pressure down to pressures of Torr, the lowest base pressure achieved in the EDG device. The characteristic time scale τ for nonlinear damping of the diocotron mode is observed to scale as over two ordersofmagnitude variation in the background gas pressureP. The evolution of the plasma density profile has also been monitored in order to examine the shape of the evolving density profile and to measure the expansion rate. The density profile is observed to expand radially while maintaining a thermal equilibrium profile shape, as predicted theoretically. While the expansion rate is sensitive to background gas pressure at pressures exceeding Torr, at lower pressures the crossfield transport appears to be dominated by other processes, e.g., asymmetryinduced transport. Finally, the expansion rate is observed to scale approximately as for confining fields ranging from 100 to 600 G.

Kinetic and fluid calculations for the periodically oscillating plasma sphere
View Description Hide DescriptionPrevious work [D. C. Barnes and R. A. Nebel, Phys. Plasmas 5, 2498 (1998)] has demonstrated the existence of a onedimensional selfsimilar oscillating ion solution which remains in local thermodynamic equilibrium at all times during an oscillation in a harmonic oscillator potential. Here it is shown that all spherically symmetric distributions, in which x, y, and z are independent, are of this form. However, in a real device the density profile will be truncated due to the presence of a wall or conductor. Particle simulations of these truncated profiles are presented and compared with the idealized solutions in the proper limits. Results are also interpreted in terms of rigid rotor rotation in phase space as is appropriate for a harmonic oscillator. Next, it is demonstrated that the deviations from Maxwellian velocity distributions that are observed when the plasma contracts will be quickly rethermalized during the expansion phase. Energy throughput resulting from this rethermalization is discussed.

Theories of relativistic ion cyclotron instabilities
View Description Hide DescriptionA perturbation theory and a kinetic theory are developed to investigate the novel physics of relativistic ion cyclotron instabilities. The existence of the instabilities is determined by the normalized mass deficits per nucleon of fast and slow ions and respectively), and by their Lorentz factors and respectively); while the ion bunching is caused by the relativistic variation of ion mass. If only a quadratic instability can occur at high cyclotron harmonics of the fast ion in the lowerhybrid frequency regime and above; the threshold on the harmonic number is determined by the dielectric constant of the slow ion. The peak growth rate is higher at the harmonics just above the threshold. If it is negative, both a cubic instability (or instead a coupled quadratic instability if the resonant slow ion cyclotron harmonic is the first harmonic) and the high harmonic quadratic instability can be driven. The cubic instability is due to the harmonic interaction of fast and slow ion cyclotron motions with the wave frequency in between. This introduces a novel instability concept, namely, a twostreaming process in gyrospace. Thus, the cubic instability is also called a twogyrostream instability even without beams in real space in contrast to conventional twostream instability. Both theories show that, as compared to the conventional axial phase bunching mechanism, the importance of the inclusion of the relativistic mass variation effect (and the gyrobunching mechanism) depends on the phase velocity of the wave along the external magnetic field, and is not related to the Lorentz factors (or kinetic energies); that is, if (e.g., the relativistic gyrobunching mechanism always dominates. While the importance of this study in fundamental plasma physics is emphasized here, some issues (e.g., nonlinear saturation, wave polarization, and nonuniform magnetic field) related to its application are also discussed.

Numerical studies of relativistic ion cyclotron instabilities
View Description Hide DescriptionThe novel physics of relativistic ion cyclotron instabilities is numerically investigated. The growth rate spectrums and the possibility being absolute instability of two fast ion cases (that the fast ions are energetic proton and alpha particle, respectively) are numerically studied and compared with the analytical theory. The fundamental difference in the characteristics of the instabilities due to a slight change in fast ion mass per nucleon is emphasized; it is determined by the relative normalized mass deficit per nucleon of fast and slow ions, and by the difference of their Lorentz factors. For the energetic proton case, both a cubic instability and a high harmonic quadratic instability can be driven; while, for the energetic alpha particle case, only the quadratic instability can occur at the high alpha cyclotron harmonics in the lower hybrid frequency regime and above; the threshold is determined by the dielectric constant of the slow ion. The peak growth rate is highest at the harmonics just over the threshold. Many new physics discovered by the numerical results are explained. A numerical polynomial expansion method with curve fitting is developed to conclude that the instabilities studied are absolute, because the analytical results cannot be used to address this important issue.
 Nonlinear Phenomena, Turbulence, Transport

Computer simulations of asymmetric spontaneous fast reconnection
View Description Hide DescriptionThe spontaneous fast reconnectionmodel is extended to the general asymmetric situations, where magnetic reconnection may take place between the field lines that are anchored in different magnetic dipole sources. It is demonstrated for a wide variety of parameters that the asymmetric fast reconnection mechanism can evolve as a nonlinear instability, so that an asymmetric plasmoid swells predominantly in the region of a weaker magnetic field and propagates along the field lines. In the central diffusion region, the secondary tearing is likely to take place and significant erosion of the stronger magnetic field occurs; accordingly, the X neutral point moves with time, where the (currentdriven) anomalous resistivity is found to be always locally enhanced, allowing the fast reconnection mechanism to be sustained quasisteadily and extended outwards further. The associated shock structure standing at the boundary of the stronger magnetic field is identified with the ordinary slow shock, in general, combined with an intermediate wave in the presence of sheared field. On the other hand, the shock standing at the boundary of the weaker magnetic field has an intermediate shocklike structure near the diffusion region, which propagates along the shock layer to finally become the ordinary combination of a slow shock and a finiteamplitude rotational intermediate wave at the plasmoid boundary.

Improved boundary layer analysis of forced magnetic reconnection due to a boundary perturbation
View Description Hide DescriptionLinear boundary layer analysis of forced magnetic reconnection due to an externally imposed boundary perturbation has been reworked. This improved analysis introduces correct asymptotic matching to take into account the effect of inertia in the inner layer precisely, and adopts a time dependent boundary perturbation which is suitable for this analysis. The improved analysis demonstrates a new reconnection process and clarifies the role of stability against the tearing modes in the process. The initial evolution of this new reconnection process is characterized by some significant features which affect the subsequent evolution toward a fully reconnected state. One is that the reconnected flux increases on the same time scale as the boundary perturbation, which excludes the Sweet–Parker time scale obtained by use of the constant asymptotic matching. Another is that an induced surface current on a resonant surface is in such a direction as to oppose the progress of the reconnection, because the equilibrium is stable against tearing modes in the absence of the boundary perturbation.

Ionacoustic solitons and double layers in a twoelectron temperature plasma with hot isothermal electrons and cold ions
View Description Hide DescriptionIt is found that a twoelectron temperatureplasma with isothermal electrons and cold ions admits both compressive and rarefactive solitons, as well as compressive and rarefactive double layers (depending on the concentration of lowtemperature electrons). In this paper, a Korteweg–de Vries (KdV) equation and a KdVtype equation with cubic and fourthorder nonlinearity at the critical density of the lowtemperature isothermal electrons are derived to discuss the properties of ionacoustic solitons in a twoelectron temperatureplasma. In the vicinity of the critical electron density of lowtemperature isothermal electrons, we have derived a KdVtype equation with mixed nonlinearity, and the solution of this equation will have both compressive and rarefactive double layers for those values of critical electron density of lowtemperature electrons for which ionacoustic solitons do not exist. By using quasipotential analysis, critical Mach numbers and are obtained such that compressive ionacoustic solitons exist when and rarefactive ionacoustic solitons exist when

Twodimensional electronmagnetohydrodynamic nonlinear structures
View Description Hide DescriptionTwodimensional coherent electromagnetic structures involving the dynamics of the electron population in a quasineutral plasma with immobile ions are described. These structures consist of small scale magnetic vortices that propagate at a constant velocity. The dispersion relations of dipolar and tripolar vortices and of dipolar vortices and of vortex chains are given. The magnetic field of these vortices is threedimensional. In addition, stationary quadrupolar vortices are described that are formed in the neighborhood of an Xpoint of the background configuration.

Nonlinear time evolution of thermal structures
View Description Hide DescriptionThe nonlinear stability and time evolution of thermal structures constituted by optically thin plasmas are analyzed. The structure has been assumed to be heated at a rate cooled by the standard cooling function for plasmas with solar abundances and with an anisotropicthermal conduction coefficient. Secondorder analytical results are obtained for the thermal equilibrium solutions. For nonhomogeneous solutions and strong disturbances, a numerical analysis is carried out. The angle between the temperature gradient and the magnetic field is a crucial parameter in determining the stability of structures close to the marginal state. A central overheating may occur for large enough amplitudes of the initial disturbance imposed on stable steadystate thermal structures. Implications of the above results in the formation of cool structures in the solar atmosphere and in the interstellar medium are outlined.

On the exact amplitude, speed and shape of ionacoustic waves
View Description Hide DescriptionNonlinear ionacoustic solitary waves in cold collisionless plasma are investigated by a direct analysis of the field equations. The exact amplitude is obtained by simply solving an algebraic equation. The results are compared to those of a thirdorder perturbation approach and the error associated with using the perturbation technique is determined.
 Magnetically Confined Plasmas, Heating, Confinement

Coupled fullwave and raytracing numerical treatment of mode conversion in a tokamak plasma
View Description Hide DescriptionA new approach for the numerical description of tokamakplasma waves in the ion cyclotron range of frequencies is discussed. It implies coupling of the fullwave and raytracing codes and is capable of unified treatment of waves of completely different scale and behavior. The method is applied for simulations of the electron heating scenario, based on fast wave (FW)–ion Bernstein wave (IBW) mode conversion near the ion–ion hybrid resonance in Tore Supra [B. Saoutic et al., Phys. Rev. Lett. 76, 1647 (1996)]. The twodimensional fullwave “ALCYON” code [D. J. Gambier and A. Samain, Nucl. Fus. 25, 283 (1985)] is used to describe the global FW field pattern in the plasma volume. A smallscalewaves filter, introduced into the code, artificially damps the modeconverted power, which is further prescribed to IBW rays. Remnant smallscale fields are extracted from the global pattern to provide information necessary for IBW rays to start. Threedimensional evolution of IBW rays is simulated by the “RAYS” raytracing code [Yu. Petrov, Nucl. Fus. 34, 63 (1994)], being unrestricted by finite mesh size and finite Larmor radius effects.

Stabilization of the internal kink mode in a tokamak by toroidal plasma rotation
View Description Hide DescriptionThe stability of the internal kink mode is analyzed for a tokamak with a toroidally rotating plasma, by a large aspect ratio expansion of the compressible magnetohydrodynamic equations. Assuming that the central poloidal beta is of order unity, it is found that the internal kink mode is stabilized by rotational frequencies of order where is the Alfvén frequency and ε is the inverse aspect ratio. The internal kink then turns into a stable oscillation with a Dopplershifted frequency where Γ is the adiabatic index and M is the sonic Mach number. The stabilization comes from the centrifugal force which gives a stable density (or entropy) distribution within each magnetic surface. The parallel motion associated with the internal kink mode then behaves as the Brunt–Väisälä oscillations of a stably stratified fluid in a gravitational field. At lower rotational frequencies, the only effect of the rotation is a corotation of the usual (nonrotating) instability, whereas the ordering represents a transition regime where the stabilizing effect of the rotation competes with the drive from the internal kink instability. Kinetic behavior along the field lines is expected to influence this stabilization mechanism, as it depends on the adiabatic index Γ.

Tilt mode stability scaling in fieldreversed configurations with finite Larmor radius effect
View Description Hide DescriptionThe marginal stability of a static plasma with finiteLarmorradius (FLR) effects depends on a combination of the FLR effect and the ideal magnetohydrodynamic(MHD) potential energy. For the tilt mode in a fieldreversed configuration (FRC) previous computations of these two factors led to a prediction of stability for where is the macroscale parameter (separatrix radius/ion skin depth) and E is the elongation (separatrix half length/separatrix radius). This prediction explained the observed stability of most experiments. However, recent computations of actual MHD eigenfunctions indicate that the MHD growth rate has a much weaker scaling with elongation than previously believed. As a consequence, most of the longlived, stable FRC experiments lie in the region predicted to be unstable. It appears then that the stability of FRC experiments is not explained by FLR effects in a static equilibrium.