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Volume 3, Issue 4, April 1996

Fast ion orbits in spherical tokamaks
View Description Hide DescriptionIn a spherical tokamak, the 1/R variation of the toroidal field is extreme, and for a given value of the safety factor a relatively low average toroidal field can be used, together with large plasma current and large plasma minor radius and elongation. The poloidal and toroidal fields are then of similar size. In consequence, the orbits of fast ions depart considerably from the guiding center orbits because of gyromotion in the small magnetic fields on the low‐field side.

On a kinetic theory for strongly coupled dusty plasmas
View Description Hide DescriptionA kinetic theory for strongly coupled dusty plasmas is developed from the Bogolyubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy. In these plasmas, interparticle distances are typically much smaller than the Debye length, and the coupling parameter Γ_{ d }≡q ^{2} _{ d }/d _{ dT } _{ d } is much larger than unity. (Here q _{ d } is the dust charge,T _{ d } is the temperature, and d _{ d }≡[3/(4πn _{ d })]^{1/3} is the inter‐dust‐particle distance.) For such quasi‐steady‐state plasmas, a theoretical argument is given for the validity of the Vlasov equation in the regimes Γ_{ d }≪1 and Γ_{ c }≫Γ_{ d }≫1, where Γ_{ c } designates the coupling parameter when Coulomb crystallization occurs.

Influence of trapped electrons on the time‐independent states of a negatively biased single‐ended Q machine
View Description Hide DescriptionMeasurements of basic plasma parameters in a low‐density single‐ended Q machine with a negatively biased cold plate are compared with pertinent predictions of time‐independent collisionless plane‐diode theory. As was also found in particle simulations [Phys. Fluids B 3, 244 (1991)] and previous experiments, theory and experiment agree well if space‐charge conditions near the hot‐plate surface are electron rich, in which case the potential distributions are monotonically decreasing. For ion‐rich conditions, however, where the potential distributions exhibit a single maximum located in front of the hot plate, the plasma properties are found to depend very sensitively on the amount and distribution of the electrons trapped in the region of positive potential. In this regime, the experimental findings agree very well with a theoretical model in which a certain amount of trapped electrons is assumed.

Electrostatic ion cyclotron instabilities in negative ion plasmas
View Description Hide DescriptionThe effect of negative ions on the collisionless electrostaticion cyclotron instability (EICI) is investigated analytically and numerically. The singly ionized negative ion species has mass greater than or equal to the mass of the singly ionized positive ion species. Standard linear Vlasov theory is used to estimate the critical electron drift velocity. It is shown that the critical drifts for the excitation of both the light and heavy ion EIC modes decrease as the relative density of negative ions increases. Our results are compared with available negative ion plasma experiments concerning the EICI, and possible applications to experiments in the ionosphere are briefly discussed.

Experimental observation of very low‐frequency macroscopic modes in a dusty plasma
View Description Hide DescriptionImages of a cloud of grains in a dusty plasma reveal a pair of very low‐frequency modes, termed here the filamentary and great void modes. The plasma was a radio‐frequency discharge formed between parallel‐plate graphiteelectrodes. A cloud of 100 nm carbon particles was produced by accretion of carbon atoms produced by sputtering the graphite. The cloud was illuminated with a laser sheet and imaged with a video camera. The great void mode was a spoke‐shaped region of the cloud that was free of dust and rotated azimuthally in the discharge. The filamentary mode had the appearance of turbulent striations, with a smaller amplitude than the great void. The filamentary mode sometimes appeared as a distinctive vortex, curling in the poloidal direction. Both modes had a very low frequency, on the order of 10 Hz. Two possible causes of the modes are discussed. The low phase velocity of the modes may be consistent with a dust‐acoustic wave. Alternatively, the great void may be an ionizationwave that moved the dust about, since a modulation in the glow was seen moving at the same speed as the void. It is argued that existing theories of waves in dusty plasmas assume weakly collisional plasmas, which may be unsuitable for explaining experimental results in laboratory dusty plasmas, since they are often strongly coupled.

Theoretical analysis of driven magnetic reconnection experiments
View Description Hide DescriptionIn this paper we present a theoretical framework for the Magnetic Reconnection Experiment (MRX) [M. Yamada et al., Bull. Am. Phys. Soc. 40, 1877 (1995)] in order to understand the basic physics of the experiment, including the effect of the external driving force, and the difference between co‐ and counterhelicity cases of the experiment. The problem is reduced to a one‐dimensional (1‐D) resistive magnetohydrodynamic(MHD) model. A special class of holonomicboundary conditions is defined, under which a unique sequence of global equilibria can be obtained, independent of the rate of reconnection. This enables one to break the whole problem into two parts: a global problem for the ideal region, and a local problem for the resistive reconnection layer. The calculations are then carried out and the global solution for the ideal region is obtained in one particular case of holonomic constraints, the so called ‘‘constant force’’ regime, for both the co‐ and counterhelicity cases. After the sequence of equilibria in the ideal region is found, the problem of the rate of reconnection in the resistive reconnection region is considered. This rate tells how fast the plasma proceeds through the sequence of global equilibria but does not affect the sequence itself. Based on a modified Sweet–Parker model for the reconnection layer, the reconnection rate is calculated, and the difference between the co‐ and counterhelicity cases, as well as the role of the external forces is demonstrated. The results from the present analysis are qualitatively consistent with the experimental data, predicting faster reconnection rate for the counterhelicity merging and yielding a positive correlation with external forcing.

Quasi‐thermal fluctuations in a beam‐plasma system
View Description Hide DescriptionThe quasi‐thermal electrostatic field fluctuations of a stable unmagnetized electron beam‐plasma system is considered. Both the beam and the background plasma are modeled as isotropic Maxwellians. Both the normal modes of the plasma and the contributions from other modes are considered. The dependence of these fluctuations on beam velocity, density, and temperature are examined. The implications of these waves for real beam‐plasma systems are also discussed.

Two‐temperature relaxation in nonideal partially ionized plasmas
View Description Hide DescriptionEvolution equations for the coupled relaxation of densities and temperatures for the components in nonideal partially ionized plasmas are given. In these equations many‐body effects, such as screening, self‐energy, and lowering of the binding energy, are included. The coupled equations are solved numerically for a hydrogen plasma consisting of electrons, protons, and atoms. Impact ionization, three‐body recombination, and elastic processes are taken into account. Thermal relaxation times are determined and the results are compared with those from the literature. The influence of many‐body effects on the evolution process are discussed. In some cases, a significantly increased lifetime of the two‐temperature regime is found.

Temperature and anisotropic‐temperature relaxation measurements in cold, pure‐electron plasmas
View Description Hide DescriptionPlasma temperatures in the range 25 to 2×10^{6} K have been measured using a cryogenic, ultra‐high vacuum, pure‐electron plasma trap. The rate ν at which the temperatures parallel and perpendicular to the applied magnetic field relax to a common value has been measured over the temperature range 28 to 3.8×10^{5} K and the magnetic field range 20 to 60 kG. This rate ν is closely related to the plasma collision frequency. When the cyclotron radius r _{c} is large compared to the classical distance of closest approach b (r _{c}/b≫1), the measured values of ν are in agreement with conventional collision theory. When the cyclotron radius is small compared to the classical distance of closest approach (r _{c}/b≪1), ν drops precipitously as r _{c}/b is decreased, in agreement with the many‐electron adiabatic invariant theory of O’Neil and Hjorth.

Nonlinear evolution of a narrow stratified velocity‐shear layer
View Description Hide DescriptionThe nonlinear evolution of the Kelvin–Helmholtz instability in a narrow stratified velocity‐shear layer has been computed using numerical and analytical techniques. It is found that the Kelvin–Helmholtz instability develops, in the nonlinear regime, in a distinctly different manner in configuration and k space when finite temperature effects are included in the fluid approximation. Vortex generation is inhibited with the vortices becoming striated and anisotropic. In addition, large density and electric field fluctuations are produced in the nonlinear regime.

Local transit‐time damping in a magnetic field, and the arrest of lower‐hybrid wave collapse
View Description Hide DescriptionThe transit‐time power dissipated locally within a coherent wave packet in the presence of ambient and induced magnetic fields is calculated analytically as a function of position via a perturbed‐orbit approach, generalizing earlier results for unmagnetized interactions. The theory is used to investigate local damping in a nonlinearly‐collapsing lower‐hybrid (LH) wave packet, and hence to estimate the arrest scale of LH wave collapse in a thermal electron‐ion plasma. It is shown that either electrons or ions can dominate damping, depending on the strength of the magnetic field and the electron and ion temperatures.

Nonlocal electron transport in spherical plasmas
View Description Hide DescriptionThe influence of spherical geometry on nonlocal radial electron heat transport has been studied using perturbation analysis . The nonlocal expression for the radial heat flux is obtained in the limit of large ion charge. The deviation of the spherical nonlocal heat transport from the planar theory has been investigated and it has been found that the space curvature can significantly modify the heat flux compared to the planar result when the delocalization length (that associated with the faster electrons which dominate energy transport) is comparable to the radius.

A physical mechanism for the onset of radial electric fields in magnetically confined plasmas
View Description Hide DescriptionA simple physical mechanism is described, which could trigger the Low‐mode to High‐mode (L–H) transition. The instantaneous ion density profile is significantly modified by a sudden temperature increase, because Larmor radii and banana orbit widths are proportional to thermal velocity. The electric fields that are observed in H‐mode plasmas could be produced in the radial region where a large second derivative of the density profile exists, either by strong additional heating or by the heat pulse associated to a sawtooth crash. The L–H transition threshold for the time derivative of the ion temperature is of the order of magnitude of the values that are measured in the outer part of the plasma by electron temperature fast diagnostics at sawtooth crashes. This model agrees with the experimental evidence that L–H transitions are often triggered by a sawtooth crash, and the predicted dependence of the threshold on plasma parameters is fairly consistent with available data.

Theory of self‐organized critical transport in tokamak plasmas
View Description Hide DescriptionA theoretical and computational study of the ion temperature gradient(ITG) and η_{ i }instabilities in tokamakplasmas has been carried out. In a toroidal geometry the modes have a radially extended structure and their eigenfrequencies are constant over many rational surfaces that are coupled through toroidicity. These nonlocal properties of the ITG modes impose a strong constraint on the drift mode fluctuations and the associated transport, showing self‐organized criticality. As any significant deviation away from marginal stability causes rapid temperature relaxation and intermittent bursts, the modes hover near marginality and exhibit strong kinetic characteristics. As a result of this, the temperature relaxation is self‐similar and nonlocal, leading to radially increasing heat diffusivity. The nonlocal transport leads to Bohm‐like diffusion scaling. Heat input regulates the deviation of the temperature gradient away from marginality. We present a critical gradient transport model that describes such a self‐organized relaxed state. Some of the important aspects in tokamaktransport like Bohm diffusion, near marginal stability, radially increasing fluctuation energy and heat diffusivity, intermittency of the wave excitation, and resilient tendency of the plasma profile can be described by this model, and these prominent features are found to belong to one physical category that originates from the radially extended nonlocal drift modes. The obtained transport properties and scalings are globally consistent with experimental observations of low confinement mode (L‐mode) discharges. The nonlocal modes can be disintegrated into smaller radial islands by a poloidal shear flow, suggesting that the transport changes from Bohm‐like to near gyro‐Bohm.

Role of edge turbulence in detached divertor plasmas
View Description Hide DescriptionThe role of edge turbulence in detached divertor plasmas is investigated. It is shown that the edge turbulence, through poloidal transport of parallel momentum, can produce a significant plasma pressure drop along the magnetic field lines toward the divertor plate, a feature that characterizes the detached divertor plasma regime.

Instability heating of a solid fiber Z‐pinch
View Description Hide DescriptionA dense Z‐pinch formed by the electrical breakdown of solid CD_{2} fibers in an 800 kA, 100 ns risetime pulse generator has been studied with optical and radiationdiagnostics. It has been found that, contrary to calculations based on classical joule heating of the plasma that predict approximate dynamic equilibrium, the pinch always expands explosively while displaying intense m=0 hydromagnetic instability activity. Excellent agreement with the observed expansion rate as well as with measured electron temperatures and neutron yield has been obtained by including in a simulation code the direct heating of ions by turbulence arising from instability growth.

Transport of impurity ions along the field lines in magnetized plasma
View Description Hide DescriptionA simple one‐dimensional model describing the spread of laser blow‐off injected ions along the magnetic field lines is presented. The model is based on the kinetic theory. A closed set of kinetic equations that contain a Coulomb collision term is solved numerically. For impurity density less than the plasma density, the effect of the ambipolar electric field is negligible, as shown. The results of the model calculation are compared with experimental results obtained on the TokamakExperiment for Technically Oriented Research (TEXTOR) [H. Soltwisch et al., Plasma Phys. Controlled Fusion 26, 23 (1984)] tokamak by the use of injection of lithium atoms, and the agreement is satisfactory. The results of the model and possible applications for diagnostic purposes are discussed in detail.

Alfvén ion–ion hybrid wave heating in the Phaedrus‐T tokamak
View Description Hide DescriptionIn the Phaedrus‐T tokamak [R. A. Breun et al., Fusion Technol. 19, 1327 (1991)], Alfvén waves are indirectly driven by a fast waveantenna array. Small fractions of minority ions are shown to have a large effect on the Alfvén spectrum, as measured at the edge. An ion–ion hybrid Alfvén mode has been identified by measuring dispersion properties. Landau damping is predicted to be large and spatially localized. These Alfvénic waves are experimentally shown to generate correlated electron heating and changes in density near the core of the tokamak plasma. Fast waveantenna fields can mode convert at a hybrid Alfvén resonance and provide a promising route to spatially localized tokamakheating and current drive, even for low effective ionic chargeZ _{eff}≊1.3–2.

Numerical study on the dynamics of Z‐pinch carbon plasma
View Description Hide DescriptionThe dynamics of Z‐pinch carbon plasma has been investigated using one‐dimensional Lagrangian code. This code calculates the single‐fluid, two‐temperature magnetohydrodynamic(MHD)equations coupled with an ionization balance equation. The motion of plasma column and shock front is studied in comparison with the analytical models such as the snowplow and the slug model. The energy flow during the pinch is also studied. During the pinch phase, the temperature increases due to shock heating and adiabatic heating. After the pinch the plasma is cooled down rapidly due to adiabatic expansion which can lead to an adequate condition for recombination Extreme‐Ultra‐Violet (XUV) lasers. The effect of the radiative trapping of resonance line on hydrodynamics and population kinetics is also investigated. The calculation shows that there can exist a high gain on hydrogen‐like C VI Balmer‐α line (18.2 nm).

Confinement and the safety factor profile
View Description Hide DescriptionThe conjecture that the safety factor profile, q(r), controls the improvement in tokamakplasmas from poor confinement in the Low‐ (L‐) mode regime to improved confinement in the supershot regime has been tested in two experiments on the TokamakFusion Test Reactor (TFTR) [Plasma Phys. Controlled Nucl. Fusion Res. 1, 51 (1987)]. First, helium was puffed into the beam‐heated phase of a supershot discharge, which induced a degradation from supershot to L‐mode confinement in about 100 ms, far less than the current relaxation time. The q and shear profiles measured by a motional Stark effectpolarimeter showed little change during the confinement degradation. Second, rapid current ramps in supershot plasmas altered the q profile, but were observed not to change significantly the energy confinement. Thus, enhanced confinement in supershot plasmas is not due to a particular q profile, which has enhanced stability or transport properties. The discharges making a continuous transition between supershot and L‐mode confinement were also used to test the critical‐electron‐temperature‐gradient transport model. It was found that this model could not reproduce the large changes in electron and ion temperature caused by the change in confinement.