Index of content:
Volume 3, Issue 7, July 1996

Stellarators with the magnetic symmetry of a tokamak
View Description Hide DescriptionTo meet the requirements of the U.S. Stellarator Power Plant Study, a Modular Helias‐like Heliac (MHH) configuration was developed that has features in common with a quasihelically symmetric experiment proposed at the University of Wisconsin [D. Anderson and P. Garabedian, Nucl. Fusion34, 881 (1994)]. Improvements have been made in the design of the MHH that raise the β limit, increase the confinement time, and simplify the geometry of the coils. In particular, specifications have been found for a stellarator with just two field periods that has a magnetic field spectrum B _{ mn } close to axial symmetry. This configuration has physical properties that make it an interesting candidate for a follow‐on experiment to assess the equilibrium, stability and transport of advanced stellarators.

Theory of the collisional presheath in a magnetic field parallel to the wall
View Description Hide DescriptionIn the limit of a small Debye length (λ_{D}→0) the plasma boundary layer in front of a negative absorbing wall is split up into a collision‐free planar space charge sheath and a quasineutral presheath, where the ions are accelerated to fulfill the Bohm criterion. Apart from ion inertia, the mechanism of the presheath depends on an additional effect controlling the ion field acceleration. The present paper considers a stationary presheath dominated by the deflection of the ion orbits in a magnetic field parallel to the wall. The ion transport is provided by charge exchange collisions with cold neutrals. The potential profiles and ion distributions resulting from the self‐consistent kinetic analysis are compared with expectations based on a previous hydrodynamic model. The transition from ‘‘closed’’ to ‘‘open’’ ion orbits results in typical deviations near the sheath edge. The kinetic Bohm criterion is found to be fulfilled marginally.

Evaluation of the modified plasma dispersion function for half‐integral indices
View Description Hide DescriptionSpace and astrophysical plasmas typically possess particle distribution functions with a power‐law tail (in energy) that are well modeled by generalized Lorentzian distributions with an associated spectral index κ. Dispersionequations for linear waves of any mode in a plasma described by a Lorentzian‐type particle distribution involve the modified plasmadispersion function Z _{κ} ^{*}, a special function analogous to the plasmadispersion function Z that arises when the particle distribution is Maxwellian. The function Z _{κ} ^{*}, originally defined by Summers and Thorne [Phys. Fluids B 3, 1835 (1991)] for integral values of κ, was recently generalized to real values of κ by Mace and Hellberg [Phys. Plasmas2, 2098 (1995)]. In the present paper, a general formula is derived for the modified plasmadispersion function Z _{κ} ^{*} corresponding to half‐integral values of κ, and simple, explicit closed‐form expressions are given for the functions Z _{3/2} ^{*}, Z _{5/2} ^{*}, Z _{7/2} ^{*}, Z _{9/2} ^{*}, and Z _{11/2} ^{*}. These results complement the simple, closed‐form expressions for the functions Z _{κ} ^{*}, for κ=1, 2, 3,..., that already exist in the literature.

Properties of an argon plasma free jet generated from a continuous optical discharge
View Description Hide DescriptionThe expansion of a supersonic free jet generated from a laser‐sustained argon plasma is studied experimentally by using two techniques: (i) the time‐of‐flight analysis of velocity distributions of the atom beam skimmed from the free jet, leading to the conclusion that the translational relaxation of the heavy particles (neutral atoms and ions) follows very accurately the classical isentropic laws; (ii) the fluorescence technique for studying the internal state relaxation process by local analysis of the radiation emitted spontaneously from the plasma free jet. Only the electronic states excited above 14.5 eV are found to be in a Boltzmann equilibrium, defining a local temperature T _{excit} in the structure of the free jet. The axial electronic temperature, calculated using a simple one‐dimension thermodynamic model, follows fairly well the experimental values of T _{excit}, while the translational temperature of the heavy particles decreases much lower, in agreement with the asymptotic value deduced from the velocity distributions of the atom beam. Thus appears the uncoupling between the electronic excitation process, governed by the electronic collisions, and the translational cooling of the heavy particles, governed by the collisions between the heavy particles. A more detailed analysis of the excitation process is obtained through the calculation of the state population densities with a collisional‐radiative model. The agreement with the experimental measurements is rather good for most of the states investigated.

Effects of static magnetic fields on rf‐driven plasma sheaths
View Description Hide DescriptionThe physics of sheath formation during rf capacitordischarges in magnetized plasmas is examined, for arbitrary angle between the dcmagnetic field and the oscillating rf electric field. Observations from particle simulations show that the induced dcsheath potential under given rf drive increases with increasing angle between the electric and magnetic fields, reaching a maximum nearly twice the unmagnetized dc potential for nearly perpendicular E and B. Analytic study of the ion dynamics in the time‐averaged sheath field reveals that the ion motion is unstable, yielding unbound ion transport across the magnetic lines. The effective ion mass m*, employed for the acceleration along the electric field, is obtained as a function of the magnetic angle and the relative magnetic strength. The magnetized presheath ions are partially demagnetized inside the sheath. The ratio of the effective masses m _{ B }/m*, where m _{ B } stands for fully magnetized ions, parametrizes the sheath potential and sheath thickness. The sheaths behave as unmagnetized in the limit of parallel E and B.

Finite Larmor radius magnetohydrodynamics of the Rayleigh–Taylor instability
View Description Hide DescriptionThe evolution of the Rayleigh–Taylor instability is studied using finite Larmor radius (FLR) magnetohydrodynamic (MHD) theory. Finite Larmor radius effects are introduced in the momentum equation through an anisotropic ion stress tensor. Roberts and Taylor [Phys. Rev. Lett. 3, 197 (1962)], using fluid theory, demonstrated that FLR effects can stabilize the Rayleigh–Taylor instability in the short‐wavelength limit (kL _{ n }≫1, where k is the wave number and L _{ n } is the density gradient scale length). In this paper a linear mode equation is derived that is valid for arbitrary kL _{ n }. Analytic solutions are presented in both the short‐wavelength (kL _{ n }≫1) and long‐wavelength (kL _{ n }≪1) regimes, and numerical solutions are presented for the intermediate regime (kL _{ n }∼1). The long‐wavelength modes are shown to be the most difficult to stabilize. More important, the nonlinear evolution of the Rayleigh–Taylor instability is studied using a newly developed two‐dimensional (2‐D) FLR MHD code. The FLR effects are shown to be a stabilizing influence on the Rayleigh–Taylor instability; the short‐wavelength modes are the easiest to stabilize, consistent with linear theory. In the nonlinear regime, the FLR effects cause the ‘‘bubbles and spikes’’ that develop because of the Rayleigh–Taylor instability to convect along the density gradient and to tilt. Applications of this model to space and laboratory plasma phenomena are discussed.

Transport in a toroidally confined pure electron plasma
View Description Hide DescriptionO’Neil and Smith [T.M. O’Neil and R.A. Smith, Phys. Plasmas1, 8 (1994)] have argued that a pure electron plasma can be confined stably in a toroidalmagnetic field configuration. This paper shows that the toroidal curvature of the magnetic field of necessity causes slow cross‐field transport. The transport mechanism is similar to magnetic pumping and may be understood by considering a single flux tube of plasma. As the flux tube of plasma undergoes poloidal E × B drift rotation about the center of the plasma, the length of the flux tube and the magnetic field strength within the flux tube oscillate, and this produces corresponding oscillations in T _{∥} and T _{⊥}. The collisional relaxation of T _{∥} toward T _{⊥} produces a slow dissipation of electrostatic energy into heat and a consequent expansion (cross‐field transport) of the plasma. In the limit where the cross section of the plasma is nearly circular the radial particle flux is given by Γ_{ r }=1/2ν_{⊥,∥} T(r/ρ_{0})^{2} n/(−e∂Φ/∂r), where ν_{⊥,∥} is the collisional equipartition rate, ρ_{0} is the major radius at the center of the plasma, and r is the minor radius measured from the center of the plasma. The transport flux is first calculated using this simple physical picture and then is calculated by solving the drift‐kinetic Boltzmann equation. This latter calculation is not limited to a plasma with a circular cross section.

Computer experiments on dynamical cloud and space time fluctuations in one‐dimensional meta‐equilibrium plasmas
View Description Hide DescriptionThe test particle picture is a central theory of weakly correlated plasma. While experiments and computer experiments have confirmed the validity of this theory at thermal equilibrium, the extension to meta‐equilibrium distributions presents interesting and intriguing points connected to the under or over‐population of the tail of these distributions (high velocity) which have not yet been tested. Moreover, the general dynamical Debye cloud (which is a generalization of the static Debye cloud supposing a plasma at thermal equilibrium and a test particle of zero velocity) for any test particle velocity and three typical velocity distributions (equilibrium plus two meta‐equilibriums) are presented. The simulations deal with a one‐dimensional two‐component plasma and, moreover, the relevance of the check for real three‐dimensional plasma is outlined. Two kinds of results are presented: the dynamical cloud itself and the more usual density (or energy) fluctuation spectrums. Special attention is paid to the behavior of long wavelengths which needs long systems with very small graininess effects and, consequently, sizable computation efforts. Finally, the divergence or absence of energy in the small wave numbers connected to the excess or lack of fast particles of the two above mentioned meta‐equilibrium is exhibited.

Unified kinetic singular layer equation for converting the magnetohydrodynamic stability condition to a fully kinetic one
View Description Hide DescriptionConversion of the magnetohydrodynamic(MHD) stability conditions to fully kinetic ones is required, since the primary assumption for MHD description that particles move collectively as fluid cells is violated for nearly collisionless fusion plasmas. A unified kinetic singular layer equation is derived in this paper for implementing this conversion. The scheme outlined in the paper makes the conversion able to be realized in a rather simple way for both low and high n modes (n the mode number). Moreover, the equation covers a wide parameter domain. The frequency ranges from the ion transit frequency to that to be much lower than the ion bounce frequency. In particular, the case with mode frequency comparable to the magnetic drift one can also be treated; and the large aspect ratio assumption is not required. The application to investigate the energetic particle effect on the MHD modes is also outlined in the paper. The results are discussed, with the importance of the q (safety factor) value on the stability reiterated.

Measurement of the full polarimetric transition matrix of a magnetized plasma
View Description Hide DescriptionIt is shown that the full polarimetric transition matrix of a magnetized plasma can be determined with a good time resolution (down to 100 ns) and, furthermore, it is possible to make use mainly of phase measurements, which are less sensitive to noise than amplitude measurements. The simultaneous measurement of the nine elements of the absolute transition matrix (or of the eight elements of the normalized transition matrix) allows a significant enhancement of the information obtained for each probing beam.

Rapid generation of Langmuir wave packets during electron beam–plasma instabilities
View Description Hide DescriptionA new mechanism for Langmuir wave localization is investigated. Typical computer simulation of weak electron beam–plasma instabilities proceeds as follows: As Langmuir waves grow out of the noise, they react back on the beam particles by trapping. The subsequent phase shift puts the electrons out of phase with the waves. Then the instability is locally quenched, resulting in strong wave modulation, even before saturation of the instabilities. The typical size of wave packets is given by 2πv _{ p }/ω̄_{ t }, where v _{ p } and ω̄_{ t } denote the phase speed of the dominant wave and the average bounce frequency, respectively. The time scale for this process is considerably shorter than that of parametric instabilities.

Quasi‐two‐dimensional fast kinematic dynamo instabilities of chaotic fluid flows
View Description Hide DescriptionThis paper tests previous heuristically derived general theoretical results for the fast kinematic dynamo instability of a smooth, chaotic flow by comparison of the theoretical results with numerical computations on a particular class of modelflows. The class of chaotic flows studied allows very efficient high resolution computation. It is shown that an initial spatially uniform magnetic field undergoes two phases of growth, one before and one after the diffusion scale has been reached. Fast dynamo action is obtained for large magnetic Reynolds numberR _{ m }. The initial exponential growth rate of moments of the magnetic field, the long time dynamo growth rate, and multifractal dimension spectra of the magnetic fields are calculated from theory using the numerically determined finite time Lyapunov exponent probability distribution of the flow and the cancellation exponent. All these results are numerically tested by generating a quasi‐two‐dimensional dynamo at magnetic Reynolds numberR _{ m } of order up to 10^{5}.

On the efficiency of energy transfer by nonlinear magnetohydrodynamic waves propagating along magnetic slabs
View Description Hide DescriptionA finite‐difference numerical code is utilized to study the behavior of magnetohydrodynamic(MHD) body and surface waves on magnetic slabs. The waves are excited by finite amplitude velocity perturbations, imposed either inside the slab or in field‐free or magnetized surroundings. The paper investigates the efficiency of energy leakage from the slab to the surroundings and vice versa. In the former, waves are converted to acoustic waves or MHD fast waves depending upon the surroundings and, in the latter, to body and surface waves propagating along the slab. The dependence of the former case on the perturbations and physical parameters, such as plasma β and the slab thickness, has been studied in detail. It is found that energy leakage to the surroundings is of the order of 50%. The dependence of the latter case on β and external magnetic field is also studied.

Pulsed currents carried by whistlers. VI. Nonlinear effects
View Description Hide DescriptionIn a large magnetized laboratory plasma (n≂10^{11} cm^{−3}, kT _{ e }≥1 eV, B _{0}≥10 G, 1 m × 2.5 m), current pulses in excess of the Langmuir limit (150 A, 0.2 μs) are drawn to electrodes in a parameter regime characterized by electron magnetohydrodynamics (ω_{ ci }≪ω≪ω_{ ce }). The transient plasma current is transported by low‐frequency whistlers forming wave packets with topologies of three‐dimensional vortices. The generalized vorticity,Ω, is shown to be frozen into the electron fluid drifting with velocity v, satisfying ∂Ω/∂t≂∇×(v×Ω). The nonlinearity in v×Ω is negligible since v and Ω(r,t) are found to be nearly parallel. However, large currents associated with v≥(2kT _{ e }/m _{ e })^{1/2} lead to strong electron heating which modifies the damping of whistlers in collisional plasmas. Heating in a flux tube provides a filament of high Spitzer conductivity, which permits a nearly collisionless propagation of whistler pulses. This filamentation effect is not associated with density modifications as in modulational instabilities, but arises from conductivity modifications. The companion paper [Stenzel and Urrutia, Phys. Plasmas3, 2599 (1996)] shows that, after the decay of the transient wave magnetic field, magnetic helicity remains in the plasma due to temperature‐gradient driven currents.

Pulsed currents carried by whistlers. VII. Helicity and transport in heat pulses
View Description Hide DescriptionIn a uniform magnetoplasma (n≂10^{11} cm^{−3}, kT _{ e }≥0.5 eV, B _{0}≥15 G, 1 m × 2.5 m), electrons are heated locally and temporally by applying a short current pulse to a loop antenna or disk electrode. Electron magnetohydrodynamics characterize the experimental conditions. After the end of the applied current pulse and whistler wave transients, a current system driven by temperature gradients remains embedded in the plasma. The current system exhibits helicity. The associated electron drifts convect heat out of the flux tube. From diamagnetic field measurements, the decay of the electron temperature is obtained with high sensitivity (ΔkT _{ e }≂0.001 eV). The heat transport is inferred from the space–time dependence of the electron temperature. The temperature enhancement is confined to a channel whose length depends on heat input since the transport coefficients are temperature‐dependent.

Effects of vortex‐like and non‐thermal ion distributions on non‐linear dust‐acoustic waves
View Description Hide DescriptionThe effects of vortex‐like and non‐thermal ion distributions are incorporated in the study of nonlinear dust‐acoustic waves in an unmagnetized dusty plasma. It is found that owing to the departure from the Boltzmann ion distribution to a vortex‐like phase space distribution, the dynamics of small but finite amplitude dust‐acoustic waves is governed by a modified Kortweg–de Vries equation. The latter admits a stationary dust‐acoustic solitary wave solution, which has larger amplitude, smaller width, and higher propagation velocity than that involving adiabatic ions. On the other hand, consideration of a non‐thermal ion distribution provides the possibility of coexistence of large amplitude rarefactive as well as compressive dust‐acoustic solitary waves, whereas these structures appear independently when the wave amplitudes become infinitely small. The present investigation should help us to understand the salient features of the non‐linear dust‐acoustic waves that have been observed in a recent numerical simulation study.

Nonlinear expansion and heating of a nonneutral electron plasma due to elastic collisions with background neutral gas
View Description Hide DescriptionThis paper investigates theoretically the heating and nonlinear expansion of a nonneutral electron plasma due to elastic collisions with constant collision frequency ν_{ en } between the plasma electrons and a background neutral gas. The model treats the electrons as a strongly magnetized fluid (ω_{ pe } ^{2}/ω_{ ce } ^{2}≪1) immersed in a uniform magnetic fieldB _{0} e ̂ _{ z }. The model also assumes an axisymmetric plasma column (∂/∂θ=0) with negligible axial variation (∂/∂z=0), and that the process of heat conduction is sufficiently fast that the electrons have relaxed through electron‐electron collisions to a quasi‐equilibrium state with scalar pressure P(r,t)=n(r,t)T, and isothermal temperatureT. Assuming that the electrons undergo elastic collisions with infinitely massive background gas atoms, global energy conservation is used to calculate the electron heating rate, dT(t)/dt, as the plasma column expands on a time scale τ_{ diff }∼(ω_{ pe } ^{2}ν_{ en }/ω_{ ce } ^{2} )^{−1}, and the electrostatic potential energy decreases. Coupled dynamical equations that describe the nonlinear evolution of the mean‐square column radius r ^{2} _{0}(t) and electron temperatureT(t) are derived and solved numerically.

Ballooning instability precursors to high β disruptions on the Tokamak Fusion Test Reactor
View Description Hide DescriptionToroidally localized ballooning modes have been found as precursors to high β disruptions in many regimes on the TokamakFusion Test Reactor (TFTR) [D. Meade et al., Proceedings of the International Conference on Plasma Physics and Controlled Nuclear Fusion, Washington, DC, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, pp. 9–24]. Lower frequency, global magnetohydrodynamic(MHD) activity, typically an ideal n=1 kink mode, causes the toroidal localization. Larger‐amplitude n=1 modes result in stronger toroidal localization of the ballooning modes. The modes are typically localized to a region spanning about 90°–120° in the toroidal direction.

Radial profile of plasma potential with various biased electrode ring configurations in a toroidal plasma
View Description Hide DescriptionAn experimental study on behavior of radial profile of the floating potential with different biased electrode ring configurations has been carried out in a currentless magnetized toroidalplasma. Radial profile of the floating potential has been measured by biasing single ring of various sizes and two rings. It is observed that floating potential profile of a well shaped with controllable depth, hill‐cum‐well shaped, and almost flat positive potential can be obtained. Results on parameter dependence studies of floating potential on the bias voltage, magnetic field, and gas pressure are presented.

Tomography of (2, 1) and (3, 2) magnetic island structures on Tokamak Fusion Test Reactor
View Description Hide DescriptionHigh‐resolution electron cyclotron emission (ECE) image reconstruction has been used to observe (m,n)=(2,1) and (3, 2) island structures on TokamakFusion Test Reactor [Plasma Phys. Controlled. Fusion33, 1509 (1991)], where m and n are the poloidal and the toroidal mode number, respectively. The observed island structure is compared with other diagnostics, such as soft x‐ray tomography and magnetic measurements. A cold elliptic island is observed after lithium pellet injection. Evidence for the enhancement of the heat transfer due to the island is observed. A relaxation phenomenon due to the m=2 mode is newly observed in Ohmic plasmas.