Index of content:
Volume 3, Issue 9, September 1996

Properties of thermal flare plasmas (3×10^{6}–3×10^{7} K): Observational results
View Description Hide DescriptionOne of the most violent while best observed phenomena occurring in the solar upper atmosphere is flare emission in the 3×10^{6} to 3×10^{7} K temperature range. This emission, commonly called thermal flare emission, can vary in intensity by more than five orders of magnitude, and exhibits regular and predictable properties. A wealth of observational data regarding thermal solar flares has been collected. Through these data the morphological properties of thermal flares have been determined. Plasma properties such as electron temperatures, electron densities, mass motions, and variations in elemental abundances during the course of the flare are well established. Observational data have also been used to determine relationships between peak fluxes and maximum flare temperatures as well as general properties of the light curve of flares.

Measurements of the hole boring velocity from Doppler shifted harmonic emission from solid targets
View Description Hide DescriptionThe fast ignitor scheme for inertial confinement fusion requires forward driving of the critical density surface by light pressure (hole boring) to allow energy deposition close to the dense fuel. The recession velocity of the critical density surface has been observed to be v/c=0.015 at an irradiance of 1.0×10^{19} W cm^{−2} at a wavelength of 1.05 micron, in quantitative agreement with modeling.

Observation of beam‐enhanced sheath instability in a double plasma device
View Description Hide DescriptionThe effects of ion beams on sheathproperties are experimentally investigated in a double plasma device. The dispersion relations of the ion beam plasmas are measured by interferometer method. The low‐frequency instability due to sheath around the negatively biased grid is found to be controlled by two parameters, namely the grid biasing voltage and source anode biasing voltage. The instability is caused by the resonant coupling of the three ion beams that arise due to asymmetry of the sheath potential. The sheath structure follows the Child–Langmuir law and the frequency of the instability is also found to be inversely proportional to the sheath thickness. Therefore, the transit time model is considered to explain the observed phenomena. The coupling between the beam and the oscillating component of the ions through the sheath enhances the instability growth which occurs mainly in the presheath region. The excitation of the instability occurs within certain range of velocity ratio of different beam modes.

Perpendicular ion acceleration by localized high frequency electric fields in magnetized plasmas
View Description Hide DescriptionA basic process capable of explaining observations of fast perpendicular ions in a wide range of plasma environments is described. Spatial symmetry breaking perpendicular to the confining magnetic field is shown to cause irreversible energy gain for ions gyrating through an electric field having a nonuniform amplitude. The efficiency depends on the ratio of the ion Larmor radius to the scale length of the amplitude gradient, and on the scaled frequency ν≡ω/Ω_{ i }. A Landau resonance is not required, and there is no lower threshold on the electric field, because the mechanism is active in the linear regime. Theory, numerics, and particle‐in‐cell simulations are used to illustrate the interaction for electrostatic fields in the lower‐hybrid range of frequencies, but the process does not depend on a particular type of mode.

Evolution of a Maxwellian plasma driven by ion‐beam‐induced ionization of a gas
View Description Hide DescriptionThe ionization of gas by intense (MeV, kA/cm^{2}) ion beams is investigated for the purpose of obtaining scaling relations for the rate of rise of the electron density, temperature, and conductivity of the resulting plasma. Various gases including He, N, and Ar at pressures of order 1 torr have been studied. The model is local and assumes a drifting Maxwellian electron distribution. In the limit that the beam to gas density ratio is small, the initial stage of ionization occurs on the beam impact ionization time and lasts on the order of a few nanoseconds. Thereafter, ionization of neutrals by the thermal electrons dominates electron production. The electron density does not grow exponentially, but proceeds linearly on a fast time scale t _{th}=U/(v _{ b }ρ dE/dx) associated with the time taken for the beam to lose energyU via collisional stopping in the gas, where U is the ionization potential of the gas, v _{ b } is the beam velocity, ρ is the gas mass density, and dE/dx is the mass stopping power in units of eV cm^{2}/g. This results in a temperature with a slow time dependence and a conductivity with a linear rise time proportional to t _{th}.

l=1 electrostatic instability induced by electron‐neutral collisions in a nonneutral electron plasma interacting with background neutral gas
View Description Hide DescriptionThis paper investigates theoretically the electrostatic stability properties of a nonneutral electron plasma interacting with background neutral gas through elastic collisions with constant collision frequency ν_{ en }. The model treats the electrons as a strongly magnetized fluid (ω_{ pe } ^{2}/ω_{ ce } ^{2}≪1) immersed in a uniform magnetic field B _{0} ê _{ z }, and assumes small‐amplitude perturbations with azimuthal mode number l=1 and negligible axial variation (∂/∂z=0). The analysis also assumes weak electron collisions with ν_{ en }/ω_{ ce }=ε≪1, and that the process of heat conduction is sufficiently fast that the electrons have relaxed through electron‐electron collisions to a quasiequilibrium state with scalar pressure P(r,θ,t)=n(r,θ,t)T, and isothermal temperature T. Assuming that perturbed quantities vary with time according to exp(−iωt), the detailed stability analysis carried out to first order in ν_{ en }/ω_{ ce }≪1 shows that the real oscillation frequency and growth rate for the l=1 diocotron mode are given, respectively, by the simple expressions Re ω=ω_{0} and Im ω=(ν_{ en }/ω_{ ce })ω_{0}. Here, ω_{0}=Nec/r ^{2} _{ wB } _{0}, where r _{ w } is the perfectly conducting wall radius, and N=∫d ^{2} x n is the number of electrons per unit axial length. This analysis suggests that a measurement of the oscillation frequency and growth rate for the l=1 diocotron mode can be used to infer ν_{ en }, and thereby serve as a sensor for the background neutral pressure.

Instability of stagnation points in magnetohydrodynamic equilibria
View Description Hide DescriptionInstabilities associated with streamlines connecting stagnation points in an equilibrium with plane incompressible flow are studied. It is shown that they belong to two different types: If the velocity of fluid absorption at the endpoint is greater than the velocity of fluid emission at the initial point, only a discrete spectrum of unstable standing waves is possible; otherwise, Alfvénic waves accumulate to form a continuum of unstable frequencies. These are present no matter how small the equilibrium field or the mode number of the magnetic oscillations.

Spherical versus nonspherical plasma‐screening effects on semiclassical electron–ion collisional excitations in weakly coupled plasmas
View Description Hide DescriptionSpherical and nonspherical plasma‐screening effects are investigated on electron‐impact excitation of hydrogenic ions in weakly coupled plasmas. Semiclassical straight‐line trajectory method is used to describe the behavior of the projectile electron. Scaled 1s→2p _{−1} semiclassical excitation probabilities are obtained by the spherical and nonspherical Debye–Hückel interaction potentials. The plasma‐screening effect of the bound atomic wave functions in the transition probability obtained by the spherical Debye–Hückel model is found to be more effective than that in the transition probability obtained by the nonspherical Debye–Hückel model. The maximum position of the transition probability obtained by the nonspherical Debye–Hückel potential is more receded from the nucleus than that of transition probability obtained by the spherical Debye–Hückel potential.

The relativistic drift Hamiltonian
View Description Hide DescriptionThe relativistic Hamiltonian for the guiding center motion of particles in electric and magnetic fields is given in its canonical form. This drift Hamiltonian is valid if the particle gyroradius is sufficiently small compared to the spatial scale, and the cyclotron frequency is sufficiently large compared to the temporal scale, of the magnetic and electric fields. A method for determining the required magnetic coordinates for an earth‐like magnetic field is also given.

Electron heating in inductively coupled discharges
View Description Hide DescriptionAn analytic expression for the surface impedance for electron heating in inductively coupled discharges is derived from the kinetic equation with the optimum ordering that ν∼ω. Here, ν is the electron collision frequency, and ω is the frequency of the driven current inside the antenna coil. The expression is valid for both collisional and collisionless discharges, and can be employed in the modeling of the source.

Structure of homogeneous nonhelical magnetohydrodynamic turbulence
View Description Hide DescriptionResults are presented for three‐dimensional direct numerical simulations of nonhelical magnetohydrodynamic(MHD)turbulence for both stationary isotropic and homogeneous shear flow configurations with zero mean induction and unity magnetic Prandtl number. Small scale dynamo action is observed in both flows, and stationary values for the ratio of magnetic to kinetic energy are shown to scale nearly linearly with the Taylor microscale Reynolds numbers above a critical value of Re_{λ}≊30. The presence of the magnetic field has the effect of decreasing the kinetic energy of the flow, while simultaneously increasing the Taylor microscale Reynolds number due to enlargement of the hydrodynamic length scales. For shear flows, both the velocity and the magnetic fields become increasingly anisotropic with increasing initial magnetic field strength. The kinetic energy spectra show a relative increase in high wave‐number energy in the presence of a magnetic field. The magnetic field is found to portray an intermittent behavior, with peak values of the flatness near the critical Reynolds number. The magnetic field of both flows is organized in the form of ‘‘flux tubes’’ and magnetic ‘‘sheets.’’ These regions of large magnetic field strength show a small correlation with moderate vorticity regions, while the electric current structures are correlated with large amplitude strain regions of the turbulence. Some of the characteristics of small scale MHDturbulence are explained via the ‘‘structural’’ description of turbulence.

Electron cyclotron resonance heating near the turning point in inhomogeneous magnetic field
View Description Hide DescriptionCyclotron resonanceheating of electrons in a magnetic beach is studied by rigorous numerical analysis of the electron trajectories. It is confirmed that a heating response function [Y. Kiwamoto et al., Phys. Plasmas 1 834 (1994)] connecting the velocity distributions in both sides of the resonance layer can be applied over a wider range of electron velocities than originally expected. For electrons mirror‐reflected close to the resonance layer, however, the electron velocity distribution after heating substantially deviates from the prediction of the response function. The deviation is quantitatively evaluated to obtain a criterion of applicability of the response function.

The nonlinear diocotron mode in a pure electron plasma
View Description Hide DescriptionThe nonlinear diocotron mode, discussed by Fine, Driscoll, and Malmberg [Phys. Rev. Lett. 63, 2232 (1989)] is characterized by two equations, one describing the frequency of orbiting, the other giving the quadrupole moment, as functions of size and offset. A new analysis, based on the method of moments, which yields equations more general in their content, is presented here. For example, the new equations describe columns whose shapes are not elliptical and whose densities are not constant.

Analysis of the self‐oscillations instability due to the plasma coupling with an emissive hot cathode sheath
View Description Hide DescriptionExperimental results are reported showing that plasma self‐oscillations appear when the ion flux arriving at the hot emissive cathode double sheath boundary from a continuous plasma discharge is not high enough to sustain the discharge. Using the stability criterion of a double sheath and the particle balance equations, different conditions for the plasma stability are stated, in good qualitative agreement with experimental results. A nonlinear analysis giving the noninteger correlation dimension in a chaotic self‐oscillations regime is also reported, showing that a complete understanding of this instability may be reached by a finite set of nonlinear equations.

Even and odd modes driven by the trapped ion temperature gradient over the secular scale
View Description Hide DescriptionIn the long wavelength limit, the trapped ion temperature gradient driven modes on the secular scale are investigated by considering the lowest order effects of the finite banana orbit width and using the two‐scale expansion. Attention is focused on the effects of the wave–particle interaction over the secular scale. Also, the effects of the collisionless trapped electron dynamics are considered. The eigenmode equation derived is in the form of a modified Bessel equation. The even modes are almost not influenced by the effects of the wave–particle interaction. But for odd modes, the wave–particle interaction can give rise to instabilities of the ion branches. These odd modes are similar to the trapped ion scatteringmodes pointed out first by Coppi and Rewoldt [Advances in Plasma Physics, edited by A. Simon and W. Thompson (Wiley, New York, 1976), Vol. 6, p. 421]. The dependence of the growth rates on the ion temperature gradient is analyzed numerically. The typical eigenfunction curves of both the even and odd modes driven by the trapped ion temperature gradient over the secular scale are displayed.

Theory‐based transport modeling of the gyro‐radius experiments
View Description Hide DescriptionSelf‐consistent predictive transport simulations of temperature and density profiles have been carried out for ten dimensionally similar low (L) mode discharges from the TokamakFusion Test Reactor (TFTR) [D. Grove and D. M. Meade, Nucl. Fusion25, 1167 (1985)], Doublet III‐D Tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)], and the Joint European Torus [P. H. Rebut, R. J. Bickerton, and B. E. Keen, Nucl. Fusion25, 1011 (1985)], where only the normalized Larmor radius was allowed to vary. It is found that a purely gyro‐Bohm transport model predicts temperature and density profiles that match the experimental data from these ρ_{*} scans very well. In particular, a combination of theoretically derived transport models is used in these simulations, including the Weiland model for transport due to drift waves(ion temperature gradient and trapped electron modes) and the Guzdar–Drake model for transport due to resistive ballooningmodes. These gyro‐Bohm transport models depend very sensitively on the shapes as well as the magnitudes of the profiles. As the magnetic field, density and temperature are changed in each dimensionally similar series of discharges, the penetration length of neutrals from the edge varies considerably. This effect causes the shape of the density profiles to change near the edge of the plasma, which causes the scaling of our transport model diffusivities to differ significantly from their fundamentally gyro‐Bohm scaling.

Characterization of a partially‐ionized, detached, divertor plasma
View Description Hide DescriptionA combined edge plasma/Navier–Stokes neutral transportmodel is used to characterize divertorplasma detachment, in the collisional limit for neutrals, on a simplified two‐dimensional slab geometry with Alcator‐C‐MOD‐like plasma conditions [I. H. Hutchinson et al., Phys. Plasmas1, 1511 (1994)]. The neutral model contains three momentum equations which are coupled to the plasma through ionization, recombination, and ion–neutral elastic collisions. The neutral transport coefficients are evaluated including both ion–neutral and neutral–neutral collisions. Detachment is brought about via impurity radiation using a fixed fraction impurity model. The transportmodel is shown to reproduce all salient features of experimentally observed detachment, such as large drops in ion saturation current and plasma heat flux at the divertor plate. The solutions are also shown to be sensitive to volume recombination. A region of relatively high toroidal neutral Mach number is observed upon detachment. Due to the high neutral densities, 75% of the Lyman α radiation is assumed trapped in the problem. A total edge radiative loss (neutrals and impurities) of approximately 75% of the power crossing the separatrix is needed to observe strong detachment on Alcator‐C‐MOD‐like plasmas using the described model.

An analytic study of the magnetohydrodynamic stability of inverse shear profiles
View Description Hide DescriptionThis paper reports on the ideal magnetohydrodynamic(MHD) stability of tokamak field profiles that have a non‐monotonic safety factor q(r). An analytic criterion is obtained for these ‘‘inverse shear’’ profiles by expanding in inverse aspect ratio and assuming that the minimum in q is slightly less than the m/n value of the mode under examination (m and n being the principal poloidal and toroidal mode numbers of the instability). Three terms are identified as controlling the stability of this ‘‘double kink’’; two of them are stabilizing and due, respectively, to field line bending and the interaction of average favorable curvature with the pressure gradient. The possibility of instability comes from the third term which is due to toroidal coupling and is ballooning in character. The analytic results are compared with those from a fully toroidal stability code.

Reduction of transport in stellarators by self‐shielding
View Description Hide DescriptionIn neoclassical transport theory the parallel viscosity causes the plasma pressure orthogonal to the magnetic field to depend on the poloidal and toroidal angles. If the Fourier components of the perpendicular pressure and the field strength are p _{ MN } and ε_{ MN } B _{0}, then one obtains strong shielding of a Fourier component of the field when p _{ MN }/ε_{ MN }>B ^{2} _{0}/μ_{0}. Estimates imply shielding becomes important in a stellarator for ε_{ MN } smaller than a few tenths of a percent.

A threshold for excitation of neoclassical tearing modes
View Description Hide DescriptionStability criterion for neoclassical tearing modes is obtained from the drift kinetic equation. A finite amplitude of a magnetic island is required for mode excitation. The threshold is determined by the ratio of the transversal and the parallel transport near the island when the flattening of the pressure profile eliminates the bootstrap current. A number of supershots from the database of the TokamakFusion Test Reactor (TFTR) [D. J. Grove and D. M. Meade, Nucl. Fusion25, 1167 (1985)] are compared with the theory. In cases where the modes were observed in experiment the stability criterion was violated.