Volume 7, Issue 9, September 2000
 LETTERS


Modifications to the edge current profile with auxiliary edge current drive and improved confinement in a reversedfield pinch
View Description Hide DescriptionAuxiliary edge current drive is routinely applied in the Madison Symmetric Torus [R. N. Dexter, D. W. Kerst, T. W. Lovell et al., Fusion Technol. 19, 131 (1991)] with the goal of modifying the parallel current profile to reduce currentdriven magnetic fluctuations and the associated particle and energy transport. Provided by an inductive electric field, the current drive successfully reduces fluctuations and transport. Firsttime measurements of the modified edge current profile reveal that, relative to discharges without auxiliary current drive, the edge current density decreases. This decrease is explicable in terms of newly measured reductions in the dynamo (fluctuationbased)electric field and the electrical conductivity. Induced by the current drive, these two changes to the edge plasma play as much of a role in determining the resultant edge current profile as does the current drive itself.

Interaction of Rayleigh–Taylor mode with shearflow and vortexflow in magnetized plasmas
View Description Hide DescriptionA twodimensional vortex subjected to shear flow is considered in Rayleigh–Taylor mode of magnetized plasmas. It is shown that, when vortexflow is almost absent, linear instability is suppressed due to shearflow. In the presence of a vortex, however, there is a possibility of secondary instability excitation. It is demonstrated that the efficiency of this secondary instability depends on the sense of rotation and strength of vortexflow and shearflow.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Electrostatic driftlike waves in a bounded dusty plasma
View Description Hide DescriptionA number of different types of obliquely propagating dustassociated electrostatic driftlike waves, namely, the Shukla–Varma mode, the lowerhybrid mode, coupled electron–drift–dust–ion–acoustic waves, coupled ion–drift–dust–electron–acoustic waves, coupled dust–drift–dust–acoustic waves, and coupled dust–drift–dust–cyclotron waves, in a nonuniform bounded dusty magnetoplasma are theoretically investigated. The last two are studied by considering the dynamics of the negatively charged dust grains, whereas the other ones are studied by considering the presence of the static dust grains. The dispersion properties of these driftlike waves, which are found to be significantly modified by the combined effects of plasma density inhomogeneity, finite boundary of the dusty plasma, obliqueness of the propagating mode, and external magnetic field, are examined. The relevance of this investigation to lowtemperature laboratory dusty magnetoplasmas is discussed.

A kinetic description for low frequency longitudinal waves in a dust plasma including charge fluctuations
View Description Hide DescriptionA kinetic description is presented here for the study of low frequency electrostatic waves in a dusty plasma including the effect of charge fluctuations on the dust grains. The kinetic description uses the charge on the grains as a dynamical variable as a generalization of the usual kinetic model to describe the charge fluctuationeffects. When properly carried out it leads to the appearance of a new term in the dispersion relation arising out of the kinetic treatment of charge fluctuations. This new term strongly modifies the known dust plasma modes such as the dust acoustic modes, dustCoulomb mode, etc., as well as leads to new modes of oscillation in the zero wave number limit both in the tenuous and dense plasma regimes (determined entirely by charging and discharging frequencies of the grain as a capacitance), which may be called as “grain capacitanceoscillations.” Because of the presence of such a frequency of oscillation, the possibility is also pointed out of a reflection of dustacoustic wave from the region of increasing plasma density very much analogous to the reflection of a plasma wave in a region of increasing plasma density. There is also found the existence in the tenuous plasma regime of a new purely oscillatory and purely damped “dust hybrid” mode with a frequency as a geometric mean of the new term—modified dust acoustic wave frequency and discharging frequency.

Nonstationary driven oscillations of a magnetic cavity
View Description Hide DescriptionThe problem of transition to the steady state of driven oscillations in a magnetic cavity in a cold resistive plasma is addressed. The foot point driving polarized in the inhomogeneous direction is considered, and it is assumed that the cavity length in the direction of the equilibrium magnetic field is much larger than the cavity width in the inhomogeneous direction. The latter assumption enables one to neglect the variation of the magnetic pressure in the inhomogeneous direction, which strongly simplifies the analysis. The explicit solution describing the nonstationary behavior of the magnetic pressure and the velocity is obtained. This solution is used to study the properties of the transition to the steady state of oscillation. The main conclusion is that, in general, there are two different characteristic transitional times. The first time is inversely proportional to the decrement of the global mode. It characterizes the transition to the steady state of the global motion, which is the coherent oscillation of the cavity in the inhomogeneous direction. The second time is the largest of the two times, the first transitional time and the phasemixing time, which is proportional to the magnetic Reynolds number in power. It characterizes the transition to the steady state of the local motion, which is oscillations at the local Alfvén frequencies, and the saturation of the energy damping rate. An example from solar physics shows that, in applications, the second transitional time can be much larger than the first one.

Magnetohydrodynamic waves in a homogeneous plasma convected uniformly at relativistic speed
View Description Hide DescriptionThe plasma in several physical situations such as movement of electrons along the geomagnetic field lines in the magnetosphere, the movement of the ionosphere, propagation of cosmic rays, etc., can be appropriately simulated by a drifting relativistic model. Keeping this in view, a general dispersion relation for magnetohydrodynamic(MHD)waves has been derived in a laboratory stationary coordinate system with respect to which plasma is drifting with a velocity which need not be small compared with the speed of light. This dispersion relation gives several earlier wellknown results for MHD waves supported by an ideal relativistic plasma. The characteristic equation for arbitrary direction of propagation with reference to the ambient magnetic field is quite unwieldy. So, the detailed discussion is confined to the special cases when the propagation vector is along or across the magnetic field. However, wherever feasible, approximate solutions for arbitrary direction of propagation have also been discussed.
 Nonlinear Phenomena, Turbulence, Transport

Turbulent steadystate configuration of an inductively driven, dissipative tokamak plasma
View Description Hide DescriptionBy taking Faraday’s equation into account and using a variational principle that optimizes dissipation, it is shown that the turbulent steadystate profile of current density of an inductively driven tokamak plasma is peaked at the axis and decreases monotonically to a finite value at the edge. It corresponds to a state of minimum rate of dissipation of poloidal magnetic field energy under the constraint that all tearing points on its rational surfaces are equally effective in reducing the slope of the current density across the surface. An alternative interpretation is that the configuration corresponds to a state of maximum poloidal magnetic field energy for the prescribed plasma current.

Magnetohydrodynamic flows sustaining stationary magnetic nulls
View Description Hide DescriptionExact solutions of the resistive magnetohydrodynamic equations are derived which describe a stationary incompressible flow near a generic null point of a threedimensional magnetic field. The properties of the solutions depend on the topological skeleton of the corresponding magnetic field. This skeleton is formed by onedimensional and twodimensional invariant manifolds (socalled spine line and fan plane) of the magnetic field. It is shown that configurations of generic null points may always be sustained by stationary fieldaligned flows of the stagnation type, where the null points of the magnetic and velocity fields have the same location. However, if the absolute value of the current density component parallel to the spine line exceeds a critical value the solution is not unique—there is a second nontrivial solution describing spiral flows with the stagnation point at the magnetic null. The characteristic feature of these new flows is that they cross magnetic field lines but they do not cross the corresponding spine and fan of the magnetic null. Therefore these are nonideal but nonreconnecting flows. The critical value coincides exactly with a threshold separating the topological distinct improper radial and spiral nulls. It is shown that this is not an accidental coincidence: the spiral fieldcrossing flows of the considered type are possible only due to the topological equivalence of the field lines forming the fan plane of the spiral magnetic null. The explicit expression for the pressure distribution of the solution is given and its isosurfaces are found to be always ellipsoidal for the fieldaligned flows, while for the fieldcrossing flows there are also cases with a hyperboloidal structure.

Stability of zonal flow in electron temperature gradient driven turbulence
View Description Hide DescriptionThe electron temperature gradient driven turbulence in a slab configuration modeling the negative shear tokamak is studied using a gyrokineticfinite elementparticleincell code. It is found that quasisteady zonal flows are generated in finite magnetic shear regions in both sides of the surface, where the electron thermal transport is reduced substantially compared with the surface region. Stability analyses of the electrostatic Kelvin–Helmholtz (KH) mode show that the quasisteady zonal flow pattern is closely related to the profile or the magnetic shear, which has a stabilizing effect on the KH mode. By changing the profile to reduce the magnetic shear, the KH mode becomes unstable for the quasisteady zonal flow, and the zonal flows disappear in the weak magnetic shear region. Numerical results show a possibility of controlling zonal flows with the magnetic shear, which depends on the stability of the KH mode.

Experimental analysis of mode coupling and plasma turbulence induced by magnetic fields
View Description Hide DescriptionWaveletspectrum and bispectrum techniques are applied to study the development of temporal turbulence induced by a confinement toroidalmagnetic field in a toroidal magnetoplasma created by radio frequencywaves. For low magnetic fields the plasma is roughly uniform and the analyzed electrostatic linear frequency spectra are essentially determined by the driven radio frequencies. However, by increasing the toroidalmagnetic field, gradients in the plasma radial profiles and broader frequency spectra are observed. Thus, spectral components with frequencies higher than those injected in the plasma are excited. Moreover, this variation of magnetic field also induces nonlinear phase coupling between low frequency coherent peaks and continuous high frequency spectral components.

Effects of phasebunching in strongly turbulent plasmas
View Description Hide DescriptionThe effects of phase bunching on the collisionless dissipation of nonlinear wave fields is explored, with emphasis on situations relevant to strong turbulence applications. It is argued that in a homogeneous, steadystate plasma, there is no preferred phase of the electric field experienced by particles as they enter a wave packet. However, an initially phaseuniform ensemble of particles will generally be phasebunched after interacting with a wave packet. This can lead to a dramatically intensified interaction with subsequent packets encountered by the particles. Numerical calculations reveal that the local wave dissipation can increase by orders of magnitude if the transiting particles have been phasebunched prior to entering a wave packet. The wave particle interactions, called transittime dissipation, comprise Landau damping and a nonresonant type of damping. The nonresonant damping causes a redistribution of field energy within a wave packet. This effect is particularly strong in phasebunched systems. These results may force modifications to previous treatments of strong turbulence which have assumed isotropy and homogeneity, and employed standard Landau damping.

The radio frequency magnetic field effect on electron heating in a low frequency inductively coupled plasma
View Description Hide DescriptionRadio frequency power with a low frequency of 4 MHz is delivered to a solenoidal inductively coupled plasma at a low pressure of 1 mTorr. The electron energy distribution functions(EEDFs) are measured by a rf compensated Langmuir probe at different rf powers. As the rf power increases, a MaxwellianEEDF evolves into a biMaxwellian EEDF with a low energy peak. This means that the electron heating in the plasma greatly changes. This EEDF transition can be understood by considering the rf magnetic fieldeffect, which is strong at low frequency.

Alfvén vortices and chaos in electron–positron dusty magnetoplasma with equilibrium flows
View Description Hide DescriptionA set of coupled nonlinear differential equations which govern the dynamics of lowfrequency shortwavelength electromagnetic waves in a nonuniform magnetized electron–positron (pair) plasma with dust has been derived. In the linear limit, a local dispersion relation has been derived and analyzed. It is shown that in the absence of density gradients and equilibrium sheared plasma flow, can make the dust shear Alfvén waves unstable. In the nonlinear case, the temporal behavior of nonlinear dissipative system can be expressed in the form of well known Lorenz and Stenflo type equations that admit chaotic trajectories. On the other hand, a quasistationary solution of the mode coupling equations can be represented in the form of dipolar and vortexchain solutions. The results of our present investigation should be helpful for understanding plasma transport and wave phenomena in the pulsars magnetosphere.

Nonlinear properties of small amplitude dust ion acoustic solitary waves
View Description Hide DescriptionIn this paper some nonlinear characteristics of small amplitude dust ion acoustic solitary wave in three component dusty plasma consisting of electrons, ions, and dust grains have been studied. Simultaneously, the charge fluctuation dynamics of the dust grains under the assumption that the dust charging time scale is much smaller than the dust hydrodynamic time scale has been considered here. The ion dust collision has also been incorporated. It has been seen that a damped Korteweg–de Vries (KdV) equation governs the nonlinear dust ion acoustic wave. The damping arises due to ion dust collision, under the assumption that the ion hydrodynamical time scale is much smaller than that of the ion dust collision. Numerical investigations reveal that the dust ion acoustic wave admits only a positive potential, i.e., compressive soliton.
 Magnetically Confined Plasmas, Heating, Confinement

Poloidal force generation by applied radio frequency waves
View Description Hide DescriptionA theoretical framework is developed for calculating the nonlinear rf forces that can drive sheared poloidal flow in a tokamak plasma. It is shown that the rfinduced flow drive can be calculated without first obtaining an explicit result for the nonlinear distribution function. Instead, for modes satisfying the eikonal approximation, the flow drive can be expressed entirely in terms of moments of the linearized plasma responses. The method is applied to obtain explicit results for poloidal force generation for sheared flow drive applications in a hot plasma slab that supports rf waves of arbitrary polarization. The theory is fully electromagnetic and retains (Bessel function) effects for the ion dynamics without approximation. An illustrative application to the ion Bernstein wave is presented.

Nonlinear dynamo mode dynamics in reversed field pinches
View Description Hide DescriptionThe nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant errorfield, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the wellknown equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a selfconsistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on errorfield locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the socalled “slinky mode” locks in some reversed field pinchdevices, but not in others. The locking of the slinky mode is currently an issue of outstanding importance in reversed field pinch research.

Taylor relaxation and λ decay of unbounded, freely expanding spheromaks
View Description Hide DescriptionA magnetized coaxial gun is discharged into a much larger vacuum chamber and the subsequent evolution of the plasma is observed using high speed cameras and a magnetic probe array. Photographic results indicate four distinct regimes of operation, labeled I–IV, each possessing qualitatively different dynamics, with the parameter determining the operative regime. Plasmas produced in Regime II are identified as detached spheromak configurations. Images depict a donutlike shape, while magnetic data demonstrate that a closed toroidal fluxsurface topology is present. Poloidal flux amplification shows that Taylor relaxation mechanisms are at work. The spatial and temporal variation of plasma indicate that the spheromak is decaying and expanding in a manner analogous to a selfsimilar expansion model proposed for interplanetary magnetic clouds. In Regime III, the plasma is unable to detach from the gun due to excess bias flux. Analysis of toroidal and poloidal flux as well as the profile shows that magnetic flux and helicity are confined within the gun for this regime.

Local poloidal and toroidal plasma rotation velocities and ion temperature in a tokamak plasma obtained with a matrix inversion method considering asymmetries
View Description Hide DescriptionAn inversion technique is presented for the local poloidal and toroidal rotation velocities and for the ion temperature from line integrated measurements performed on Tokamak de Varennes (TdeV) [R. Decoste and TdeV Team, Proceedings of the 15th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville, 1994 (International Atomic Energy Agency, Vienna, 1995) IAEACN60/A411]. The velocity is obtained using two matrix inversions; the first for the emissivity and the second with the velocity weighted emissivity. The temperature is obtained with three matrix inversions:emissivity,temperature weighted emissivity and rotation velocity squared. The effect of the rotation velocity represents up to 16% in the ion temperature for TdeV plasmas. The local values obtained using the lengths matrix with the magnetic flux lines from the equilibrium code are compared with those obtained by a standard Abel inversion with circular flux lines. Differences up to 20% are observed between the emissivities deduced with circular and real flux lines, whereas the rotation velocity and the ion temperature are very similar. The technique was applied for the poloidal and toroidal geometry to determine the poloidal and toroidal velocities and the emission asymmetries. Top poloidal and toroidalemissivities present strong asymmetries due to the divertor plates and the X point whereas bottom poloidal and toroidalemissivities show an inner–outer symmetry, making the inversion more reliable in this region. A first approach to model the strong asymmetry was made assuming that the emissivity has both a radial and a poloidal dependence. The best result was obtained using a radial dependence and a peaked function of the poloidal angle for the poloidal asymmetric part of the emissivity. Both emissivity and velocity asymmetries are present in the upper part of the plasma implying that the X point behaves as a source. Examples of emissivities, rotation velocities and ion temperatures observed in TdeV plasmas in H and L (high and low confinement) modes with different bottom plasma triangularity are shown.

Analytic spherical torus plasma equilibrium model
View Description Hide DescriptionAn analytic spherical torusplasma equilibrium model is developed from a general solution to the Grad–Shafranov equation. The analytic model allows the calculation of axisymmetric plasma equilibria with arbitrary aspect ratio, elongation, triangularity, and diamagnetism. Using a numerical method, examples of optimized analytic equilibria are presented with plasma profiles similar to those of bootstrapped spherical tokamaks. Numerical results obtained from analytic equilibrium solutions for plasmas with aspect ratios elongations κ=3.0, and Troyon factors suggest that spherical tori can achieve toroidal beta values as large as at poloidal beta values with stable magnetic wells,

Detailed comparison of simulated and measured plasma profiles in the scrapeoff layer and edge plasma of DIIID
View Description Hide DescriptionThe results of detailed comparisons between experimental measurements of the scrapeoff layer and divertorplasmas and simulations using the UEDGE code for a DIIID discharge [J. Luxon et al., Proceedings of the 11th International Conference on Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1986), Vol. I, p. 159] are reported. The simulations focus on understanding the flow of both fuel and impurity particles throughout the edge and scrapeoff layer (SOL)plasma. The core impurity content and the core hydrogen ionization rate can be explained by sputtering and recycling in the divertor region alone. The model reproduces most of the detailed experimental measurements. The simulations include the effect of intrinsic impurities, assumed to be carbon originating from sputtering of the plasma facing surfaces. The simulations accurately reproduce the total radiated power, although the spatial profile of radiation is somewhat narrower in the simulation. The measuredcarbon density on closed field lines is reproduced well with the simulation. Comparison of carbon emission lines indicates the total carbonsputtering yield is a factor of 2 to 4 less than expected, although the total radiated power and core carbon content are insensitive to the sputtering yield. The agreement between simulation and experiment permits more meaningful interpretation of the experimental measurements.