Volume 12, Issue 3, March 2005
 LETTERS


Reduced intermittency in the magnetic turbulence of reversed field pinch plasmas
View Description Hide DescriptionThe statistical temporal properties of broadband magnetic turbulence in the edge of reversed field pinch(RFP) plasmas are significantly altered when global magnetohydrodynamic tearing modes and magnetic relaxation are reduced. Standard RFP plasmas, having relatively large tearing fluctuations, exhibit broadband intermittent bursts of magnetic fluctuations in the bandwidth . When the global tearing is reduced via parallel current drive in the edge region, the magnetic turbulence is much less intermittent and has statistical behavior typical of selfsimilar turbulence (like that expected in selforganized criticality systems). A connection between intermittency and long wavelength plasma instabilities is therefore implied.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Effects of hot electrons on the stability of a closed field line plasma
View Description Hide DescriptionMotivated by the electron cyclotron heating being employed on dipole experiments, the effects of a hot species on stability in closed magnetic field line geometry are investigated by considering a Zpinchplasma. The interchange stability of a plasma of background electrons and ions with a small fraction of hot electrons is considered. The species diamagnetic drift and magnetic drift frequencies are assumed to be of the same order, and the wave frequency is assumed to be much larger than the background, but much less than the hot drift frequencies. An arbitrary total pressuredispersion relation is obtained, with the background plasmatreated as a single fluid, while a fully kinetic description is employed for the hot species. The analysis of the dispersion relation shows that two different kinds of resonanthot electron effects modify the simple magnetohydrodynamic interchange stability condition. When the azimuthal magnetic field increases with radius, there is a critical pitch angle above which the magnetic drift of the hot electrons reverses. The interaction of the wave with the hot electrons with pitch angles near this critical value always results in instability. When the magnetic field decreases with radius, magnetic drift reversal is not possible and only low speed hot electrons will interact with the wave. Destabilization by this weaker resonance effect can be avoided by carefully controlling the hot electron density and temperature profiles.

Lateral and transverse wakes due to moving charged particles
View Description Hide DescriptionThe wake structure of a charged particle moving in a dusty plasma is analyzed for the cases where the charge speed is greater or less than the dustacoustic speed. In the case of , where the Mach number is the ratio of the test particle speed to the dust acoustic speed, constructive interference of acoustic oscillations leads to both lateral and transverse wakes, while in the case of , only lateral wakes are obtained.

On the jets, kinks, and spheromaks formed by a planar magnetized coaxial gun
View Description Hide DescriptionMeasurements of the various plasma configurations produced by a planar magnetized coaxial gun provide insight into the magnetic topology evolution resulting from magnetic helicity injection. Important features of the experiments are a very simple coaxial gun design so that all observed geometrical complexity is due to the intrinsic physical dynamics rather than the source shape and use of a fast multipleframe digital camera which provides direct imaging of topologically complex shapes and dynamics. Three key experimental findings were obtained: (1) formation of an axial collimated jet [Hsu and Bellan, Mon. Not. R. Astron. Soc.334, 257 (2002)] that is consistent with a magnetohydrodynamic description of astrophysical jets, (2) identification of the kink instability when this jet satisfies the Kruskal–Shafranov limit, and (3) the nonlinear properties of the kink instability providing a conversion of toroidal to poloidal flux as required for spheromak formation by a coaxial magnetized source [Hsu and Bellan, Phys. Rev. Lett.90, 215002 (2003)]. An interpretation is proposed for how the central column instability provides flux amplification during spheromak formation and sustainment, and it is shown that jet collimation can occur within one rotation of the background poloidal field.

The frequency and damping of ion acoustic waves in collisional and collisionless twospecies plasma
View Description Hide DescriptionThe dispersion properties of ion acoustic waves are sensitive to the strength of ionion collisions in multispecies plasma in which the different species usually have differing chargetomass ratios. The modification of the frequency and damping of the fast and slow acoustic modes in a plasma composed of light (lowZ) and heavy (highZ) ions is considered. In the fluid limit where the light ion scattering mean free path is smaller than the acoustic wavelength, , the interspecies friction and heat flow carried by the light ions scattering from the heavy ions causes the damping. In the collisionless limit, , Landau damping by the light ions provides the dissipation. In the intermediate regime when , the damping is at least as large as the sum of the collisional and Landau damping.

Graphical analysis of electron inertia induced acoustic instability
View Description Hide DescriptionRecently, the practical significance of the asymptotic limit of for electron density distribution has been judged in a twocomponent plasma system with drifting ions. It is reported that in the presence of drifting ions with drift speed exceeding the ion acoustic wave speed, the electron inertial delay effect facilitates the resonance coupling of the usual fluid ion acoustic mode with the ionbeam mode. In this contribution the same instability is analyzed by graphical and numerical methods. This is to note that the obtained dispersion relation differs from those of the other known normal modes of low frequency ion plasma oscillations and waves. This is due to consideration of electron inertial delay in derivation of the dispersion relation of the ion acoustic wave fluctuations. Numerical calculations of the dispersion relation and wave energy are carried out to depict the graphical appearance of poles and positivenegative enegy modes. It is found that the electron inertia induced ion acoustic waveinstability arises out of linear resonance coupling between the negative and positive energy modes. Characterization of the resonance nature of the instability in Mach number space for different wave numbers of the ion acoustic mode is presented.

Ballooning mode stability in the Hallmagnetohydrodynamics model
View Description Hide DescriptionThe governing equations of the ballooning modes are derived within the Hallmagnetohydrodynamics (HMHD) model and given a standard Hamiltonian form, which is then used to derive sufficient conditions for stability. In most cases, ideal magnetohydrodynamics(MHD) stability implies HMHD stability, as is the case for tokamak configurations if the pressure is a monotone increasing function of density and the entropy is monotone decreasing. The same result holds for general MHD plasmas with constant entropy and for incompressible plasmas. However, in the case of (compressible) closedline systems such as the fieldreversed configuration, or in a typical magnetospheric magnetic field,MHD ballooning stability does not guarantee HMHD stability. For the explicitly solvable configuration of the pinch it is in fact shown that the plasma can be MHD stable but HMHD unstable.

Ideal magnetohydrodynamic interchanges in low density plasmas
View Description Hide DescriptionThe ideal magnetohydrodynamic equations are usually derived under the assumption , where is the Alfvén speed and is the speed of light. This system of equations is extended to low density plasmas wherein can be comparable to or greater than . This involves relaxation of the usual charge quasineutrality assumption and the inclusion of electromagnetic momentum on par with plasma momentum. The extended system is applied to interchange instabilities in “linetied” slab geometry as well as to centrifugally confined plasmas. It is found that interchange growth rates are reduced by a factor of , corresponding to a larger effective mass resulting from the extra electromagnetic momentum. Line tying is unaffected.
 Nonlinear Phenomena, Turbulence, Transport

Current singularities in planar magnetic points of finite compressibility
View Description Hide DescriptionThe formation of current singularities in nonresistive, linetied magnetic points is addressed. It is pointed out that, although gas pressure suppresses the current singularity development when strictly antiparallel, onedimensional magnetic fields implode, the pressure is likely to be less effective in the more realistic case of twodimensional magnetic fields. Detailed nonlinear relaxation computations at various levels of compressibility confirm that singularity is present even in the incompressible limit, but its strength, as determined by the amplitude and morphology of the current density, is considerably reduced. The singularity strength is quantified by computing the scalings of the peak current density with resolution. The scalings show that localized current structures can be expected only for negligible gas pressures. The numerical results imply that the inclusion of gas pressure effectively stalls fast magnetic reconnection in linetied point geometries.

Nonlinear saturated states of the magneticcurvaturedriven Rayleigh–Taylor instability in three dimensions
View Description Hide DescriptionThreedimensional electromagnetic fluid simulations of the magneticcurvaturedriven Rayleigh–Taylor instability are presented. Issues related to the existence of nonlinear saturated states and the nature of the temporal evolution to such states from random initial conditions are addressed. It is found that nonlinear saturated states arising from generation of zonal shear flows continue to exist in certain parametric domains but their spectrum and spatial characteristics have important differences from earlier twodimensional results reported in Phys. Plasmas4, 1018 (1997) and Phys. Plasmas8, 5104 (2001). In particular, the threedimensional nonlinear states possess a significant power level in short scales and the spatial structures of the potential and density fluctuations appear not to develop any functional correlations. Electromagnetic effects are found to inhibit the formation of zonal flows and thereby to considerably restrict the parametric domain of nonlinear stabilization. The role of finite and the contribution of the unstable drift wave branch are also discussed and delineated through a number of simulation studies carried out in special simplified limits.

Dynamics of turbulence spreading in magnetically confined plasmas
View Description Hide DescriptionA dynamical theory of turbulence spreading and nonlocal interaction phenomena is presented. The basic model is derived using Fokker–Planck theory, and supported by wavekinetic and type closures. In the absence of local growth, the model predicts subdiffusive spreading of turbulence. With local growth and saturation via nonlinear damping, ballistic propagation of turbulence intensity fronts is possible. The time asymptotic front speed is set by the geometric mean of local growth and turbulent diffusion. The leading edge of the front progresses as the turbulence comes to local saturation. Studies indicate that turbulence can jump gaps in the local growth rate profile and can penetrate locally marginal or stable regions. In particular, significant fluctuation energy from a turbulent edge can easily spread into the marginally stable core, thus creating an intermediate zone of strong turbulence. This suggests that the traditional distinction between core and edge should be reconsidered.

Oblique propagation of large amplitude electromagnetic solitons in pair plasmas
View Description Hide DescriptionWaves in pair plasmas have a fundamentally different dispersion due to the equal chargetomass ratios between negative and positive charges, which mix different time scales. In view of possible applications, e.g., to electronpositron and fullerene pair plasmas, stationary nonlinear structures are investigated for oblique or perpendicular propagation with respect to the static magnetic field. A generalized large amplitude extraordinary mode is found, having a linearly polarized electric field that is orthogonal to both the directions of wave propagation and of the static magnetic field. When the Alfvénic Mach number is in a suitably defined range, the pseudoenergy integral admits solutions with a negative waveelectric field, in a cone around parallel propagation, and solutions with a positive waveelectric field, at all angles of propagation. The exact analytical solution describing these solitary waves has also been obtained. At weakly nonlinear amplitudes, the solutions reduce to familiar solutions of the Korteweg–de Vries or modified Korteweg–de Vries equations.

Nonlinear dust phasespace vortices (holes) in chargevarying dusty plasmas
View Description Hide DescriptionThe recent analysis of dust voids [A. A. Mamun and P. K. Shukla, Phys. Plasmas11, 1757 (2004)] is extended to include selfconsistently the dust charge variation. Numerical solutions of highly nonlinear equations are carried out including dust charging and dust trapping. It is found that under certain conditions the effect of dust charge variation can be quite important. In particular, it may be noted that the dust charge variation leads to an additional enlargement of the nonlinear dust voids. The effects of ion/electron temperature, trapping parameter, and dust size on the properties of these nonlinear dust voids are briefly discussed.

Hall effect on relaxation process of flowing plasmas
View Description Hide DescriptionThe Hall effect on the nonlinear dynamics of a flowing plasma has been studied by comparing the magnetohydrodynamics(MHD)equations and the Hall MHDequations. Numerical simulations of both systems show that the turbulence brings about dissipation of the magnetic and kinetic (flow) energies, and selforganization of largescale structures occurs. However, the perpendicular flow to the magnetic field is generated more effectively and the kinetic energy dissipates much faster in the Hall MHD system. The enhanced energy dissipation is primarily due to the production of smallscale fluctuations, which proves the creation of scale hierarchy by the singular perturbation of the Hall effect.

Higherorder nonlinearity of electronacoustic solitary waves with vortexlike electron distribution and electron beam
View Description Hide DescriptionThe nonlinear wave structure of smallamplitude electronacoustic solitary waves (EASWs) is investigated in a fourcomponent plasma consisting of cold electron fluid, hot electrons obeying vortexlike distribution traversed by a warm electron beam and stationary ions. The streaming velocity of the beam, , plays the dominant role in determining the roots of the linear dispersion relation associated with the system. Using the reductive perturbation theory, the basic set of equations is reduced to a modified Korteweg–de Vries (mKdV) equation. With the inclusion of higherorder nonlinearity, a linear inhomogeneous mKdV type equation with fifthorder dispersion term is derived and the higherorder solution is obtained using a renormalization method. However, both mKdV and mKdVtype solutions present a positive potential, which corresponds to a hole (hump) in the cold (hot) electron number density. The mKdVtype solution has a smaller energy amplitude and a wider width than that of mKdV solution. The dependence of the energy amplitude, the width, and the velocity on the system parameters is investigated. The findings of this investigation are used to interpret the electrostatic solitary waves observed by the Geotail spacecraft in the plasma sheet boundary layer of the Earth’s magnetosphere.

Effect of electron collisions on transport coefficients induced by the inverse bremsstrahlung absorption in plasmas
View Description Hide DescriptionThe transport coefficients of fully ionized plasmas under the influence of a highfrequency electric field are derived solving numerically the electron Fokker–Planck equation using a perturbation method, parametrized as a function of the electron meanfreepath compared to the spatial scales . The isotropic and anisotropic contributions of the inverse bremsstrahlung heating are considered. Electronelectron collision terms are kept in the analysis, which allows us to consider with sufficient accuracy to describe plasmas with arbitrary atomic number . Practical numerical fits of the transport coefficients are proposed as functions of and the collisionality parameter .

Aspects of threedimensional magnetic reconnection
View Description Hide DescriptionThe nonlinear behavior of reconnecting modes in three spatial dimensions (3D) is investigated, on the basis of a collisionless fluid model in slab geometry, assuming a strong constant guide field in one direction. Unstable modes in the socalled large regime are considered. Single helicity modes, i.e., modes with the same orientation with respect to the guide field, depending on all three spatial coordinates correspond to “oblique” modes with, in general, mixed parity around the corresponding resonant magnetic surface, giving rise to a nonlinear drift of the magnetic island point. The nonlinear coupling of initial perturbations with different helicities introduces additional helicities that evolve in time in agreement with quasilinear estimates, as long as their amplitudes remain relatively small. Magnetic field lines become stochastic when islands with different helicities are present. Basic questions such as the proper definition of the reconnection rate in 3D are addressed.
 Magnetically Confined Plasmas, Heating, Confinement

Theoretical interpretation of frequency sweeping observations in the MegaAmp Spherical Tokamak
View Description Hide DescriptionFrequency sweeping (chirping) of high frequency magnetohydrodynamic modes is widely observed in tokamak plasmas. In this paper observations of chirping in neutralbeamheated plasmas in the MegaAmp Spherical Tokamak (MAST) [A. Sykes, R. J. Akers, L. C. Appel et al., Nucl. Fusion41, 1423 (2001)] are considered, and it is shown that these may be interpreted using the Berk–Breizman augmentation of the Vlasov–Maxwell equations. This model includes an energetic particle source: it leads not only to a single chirp but also to a series of bursting events. This repetitious behavior is characteristic of the chirping seen in experiments such as MAST. The similarity between features in velocity space and features in frequency space reinforces the theory that holeclump pair formation is responsible for the observed frequency sweeping.

A theory for the pressure pedestal in high (H) mode tokamak discharges
View Description Hide DescriptionWhen a tokamakplasma makes a transition into the good or the high confinement H mode, the edge density and pressure steepen and develop a very sharp pressure pedestal. Prediction of the height and width of this pressure profile has been actively pursued so as to provide a reliable extrapolation to future burning plasma devices. The doubleBeltrami twofluid equilibria of Mahajan and Yoshida [Phys. Plasmas7, 635 (2000)] are invoked and extended to derive scalings for the edge pedestal width and height with plasma parameters: these scalings come out in agreement with the established semiempirical scalings. The theory predictions are also compared with limited published Hmode data and the agreement is found to be very encouraging.

Generation and saturation of largescale flows in flute turbulence
View Description Hide DescriptionThe excitation and suppression of largescale anisotropic modes during the temporal evolution of a magneticcurvaturedriven electrostatic flute instability are numerically investigated. The formation of streamerlike structures is attributed to the linear development of the instability while the subsequent excitation of the zonal modes is the result of the nonlinear coupling between linearly grown flute modes. When the amplitudes of the zonal modes become of the same order as that of the streamer modes, the flute instabilities get suppressed and poloidal (zonal) flows dominate. In the saturated state that follows, the dominant largescale modes of the potential and the density are selforganized in different ways, depending on the value of the ion temperature.