Index of content:
Volume 28, Issue 2, February 1985

The stability of solutions of the classical unsteady boundary‐layer equation
View Description Hide DescriptionAn aspect of the stability of boundary‐layer profiles containing a point of zero shear away from the wall is examined. Analysis of a viscous critical layer at the point of zero shear shows that the classical unsteady boundary‐layer equation contains a short‐wavelength unstable solution. The presence of this instability has consequences for the numerical solution of the classical boundary‐layer equation, and may be connected with the initiation process of Van Dommelen and Shen’s nonlinear unsteady separation singularity.

Low‐frequency plasma‐waveguide cutoff
View Description Hide DescriptionA new low‐frequency cutoff for the m=−1 fast wave in a cold cylindrical plasma in the ion‐cyclotron frequency range is reported for the completely‐filled plasma waveguide. The presence of a vacuum gap between the plasma and the conducting wall enables the wave to propagate to arbitrarily small frequencies. For ω∼ω_{ c i }, this mode is a surface wave and undergoes a resonance at the ion‐cyclotron frequency.

Formation of a nearly spherical field‐reversed configuration
View Description Hide DescriptionBy utilizing a laser‐produced plasma technique, the possibility of realizing a field‐reversed configuration (FRC) with a nearly spherical plasma cross section is examined experimentally on the basis of a double‐cusp bias magnetic field. Plasma measurements by magnetic probes and x‐ray pinhole camera confirm the formation of a nearly spherical FRC.

Experiments on impulsive spin‐down to rest
View Description Hide DescriptionExperiments were performed to determine the stability characteristics of impulsive spin‐down to rest in a circular cylinder of moderate aspect ratio. The characteristics measured include the onset time, onset wavelength, and time history of the wavelength for the Taylor–Görtler instability, as well as the global stability limit of the apparatus. Results compare favorably with earlier theoretical, numerical, and experimental investigations.

Experiments on convection at very high Rayleigh numbers
View Description Hide DescriptionExperiments in which a thick layer of fluid was heated from below at a constant rate were conducted at flux Rayleigh numbers in the range of 10^{9} to 10^{1} ^{2}. The resulting convection was investigated by statistical analysis of the temperature signals from a pair of thermistor probes at different horizontal spacings. Power spectra showed that the temperature variance was distributed over a broad band of periods but that the centroid of this band, the characteristic period, depended very nearly on the − (1)/(2) power of the heat flux. Measurements of the coherency between the probe signals at varying distances were interpreted as defining a characteristic horizontal length scale that depended approximately upon the − (1)/(4) power of the heat flux. These results tend to substantiate the boundary layer instability model of convection at very high Rayleigh numbers.

Geometric interpretation of the possible velocity vectors obtained with multiple‐sensor probes
View Description Hide DescriptionA geometric interpretation for the operation of probes that use multiple sensors is presented. This interpretation provides a method for visualizing how the individual sensor reponse and the geometrical arrangement of the sensors are related to the measurements made with a given probe. The interpretation also provides a simple explanation for the occurrence of multiple solutions of the nonlinear equations for a probe. It is shown that a measured set of three cooling velocities, using a three‐sensor hot‐wire probe, can be produced by as many as eight different velocity vectors, only one of which is the correct velocity vector.

Diffusivities of transferable quantities in turbulent flow with mean velocity distribution
View Description Hide DescriptionThe relation between turbulent diffusivities for transferable quantities and the Lagrangian displacement of fluid particles in a flow field with a mean velocity distribution is derived on the assumption of a gradient transport. The turbulent diffusivities in a plane jet and in two interacting plane parallel jets are calculated by using Lagrangian trajectories that have been computed based on a simple model. The results indicate that the mean velocity distribution affects the turbulent transport, and that neglect of this factor can give a fivefold overestimation of the diffusivity in interacting jets.

Conditional Reynolds stress in a strongly heated turbulent boundary layer with premixed combustion
View Description Hide DescriptionA two‐color laser Doppler anemometry technique has been used to measure velocity statistics and Reynolds stress in a turbulent boundary layer over a strongly heated wall (T _{ w }=1100 K) with premixed ethylene–air combustion. Measurements in the isothermal and nonreacting heated wall turbulent boundary layers were also made for comparison. Conditional velocity covariance −∼(u v) are deduced using the quadrant and ‘‘hole’’ analysis methods. The conditional data obtained in the isothermal layer are in exellent agreement with those deduced by others based on hot‐wire data. The results obtained in the heated and reacting layers indicate that the decrease in mean Reynolds stress can be attributed to a reduction in the −∼(u v) contributions associated with a burst of low momentum fluid form the wall. The reduction is much more significant in the reacting layer than in the heated layer. Comparison with previous density shows that the changes in conditional −∼(u v) contributions occur mostly within the constant density sublayer of combustion products adjacent to the wall. In the region where combustion reaction takes place, no significant change in the turbulence intensities or Reynolds stress is found.

The interaction of plane and axisymmetric jets with a rarefied background gas
View Description Hide DescriptionThe interaction of a supersonic plane or axially symmetric jet with a background gas of equal or different species is investigated in the transition regime between continuum and free‐molecule flow by solving a set of Boltzmann equations with simplified collision terms. In the solution, the discrete ordinate method is applied and extended to axially symmetric flow by introducing an approximation to the curvature terms. The rate of convergence of the solution is increased by using the deviations of the distribution functions from the equilibrium solutions as dependent variables. The results show that three flow regions characterized by the ratio of cross to self‐collisions can be identified in the jet structure. The penetration of the jet by background molecules is studied with regard to isotope separation. The influence of various assumptions for the boundary conditions on the solution is discussed. Density profiles computed for axially symmetric flow are compared with recent experimental data.

Thermal excitation of waves on quantized vortices
View Description Hide DescriptionWe consider the problem of the thermal excitation of vortex waves on quantized vortex lines and rings. We discover that this problem, which has been largely neglected in the past, apparently presents a ‘‘free energy catastrophe’’ above about 1.85 K; that is, if one naively proceeds to compute the thermally induced vortex waves on rings or lines, the entropy of the waves becomes so large that the free energy of vortices is driven negative, and superfluidity could not exist. Various mechanisms for eliminating this problem are considered; it appears to be necessary to consider the relevant system to be the vortex plus the bath in order to avoid double counting of states. We comment on the relevance of this calculation to the problem of thermally induced nucleation of vortices.

Guiding‐center autonomy theorem
View Description Hide DescriptionA study is made of the guiding‐center motion of charged particles in a collisionless magnetoplasma in the standard paraxial limit, with finite‐orbit ordering. As a preliminary, a simple one‐fluid representation of the macroscopic plasma motion is set up, and the guiding‐center equations are then referred to a Lagrangian coordinate network comoving with the representative fluid. They are then found to split themselves off from the fluid equations as an autonomous subsystem. It is concluded that the fluid motion (or the network motion) has no effect on the guiding‐center trajectories relative to the network.

The effect of hydrodynamic turbulence on Langmuir waves in a slightly ionized plasma
View Description Hide DescriptionTwo‐dimensional, hydrodynamic turbulence, and the transport of enstrophy by this turbulence from large spatial scales to small spatial scales, is considered. This fluid is taken as slightly ionized, with a small number of ions in equilibrium with it. These ions produce a fluctuating magnetic field that induces a fluctuating electric field, either or both of which alter the distribution function of the electrons present. Considering a cold‐electron plasma, it is found that turbulence can heat the electrons, increase their Langmuir frequency and decrease the Landau damping.

Steady‐state solution of a two‐dimensional Fokker–Planck equation with strong quasilinear diffusion for lower‐hybrid current drive
View Description Hide DescriptionThe two‐dimensional Fokker–Planck equation with strong quasilinear diffusion on the tail of the electron distribution function is solved analytically and numerically. The quasilinear diffusion is taken to be parallel to the confining magnetic field of the plasma, as is appropriate for lower‐hybrid current drive. The radio frequency fields that produce this quasilinear diffusion are assumed to be imposed by external sources. It is found that an appreciable broadening of the resonant plateau in the direction perpendicular to the toroidal magnetic field leads to more particles carrying the current. As a result both the current (J) and the power dissipated (P _{ d }) are substantially enhanced, compared with the predictions of one‐dimensional theory. The figure of merit J/P _{ d } is three times larger than the one found from the one‐dimensional theory.

Particle simulation of drift waves in a sheared magnetic field
View Description Hide DescriptionElectrostatic properties of density gradient drift waves (the universal mode) in a sheared magnetic field are studied using a two‐and‐one‐half dimensional (2 1/2 ‐D) particle code. For the case of a single rational surface, the drift waves are found to be stable with an eigenmode structure that matches the linear theoretical prediction as long as the ion resonance layer is well within the system. This applies to both even and odd parity modes with respect to the rational surface. The dependence on various parameters such as the shear length is examined.

Wave‐induced plasma transport in the magnetic drift frequency range
View Description Hide DescriptionA calculation of the quasilinear transport and heating of plasma particles and diffusion of particle energy is presented, emphasizing the resonant interaction of plasma particles with waves in the magnetic drift frequency range. Substantial transport can occur for relatively small wave field amplitudes in a number of applications involving tandem mirrors and ELMO Bumpy Toruses (EBT), e.g., pumping of thermal barriers in tandems and profile control in EBT’s. The diffusion is selective and can cause preferential transport of a particular charge or energy component, and can even be inward in some cases.

Analytic theory of resistive ballooning modes
View Description Hide DescriptionThe linearized resistive magnetohydrodynamic (MHD) equations have been solved analytically in a large‐aspect‐ratio toroidal plasma to obtain a dispersion relation for resistive ballooning modes. The calculation is limited to values of β=8πn T/B ^{2} below the threshold for ideal ballooning modes. The dispersion relation yields a universal curve which can be used to determine mode stability as a function of the plasma parameters. Because of the strong stabilizing influence of plasma compressibility, resistive‐ballooning modes are only unstable in tokamaks which are either quite cold or are very close to the ideal threshold.

Density fluctuations and current penetration on a magnetized plasma column
View Description Hide DescriptionAn experiment is described where an anomalously rapid current penetration is correlated with the appearance of strong fluctuations measured with a forward laser scattering technique. In this experiment, the current of a magnetized plasma column (5 eV, 10^{2} ^{1} m^{−} ^{3}) is reversed linearly on a time scale (μsec) much shorter than the classical time for current penetration toward the center of the column. Strong skin currents are observed to develop followed by a rapid current transport phase. The anomaly level of the current penetration is inferred from a comparison with numerical simulations. Simultaneously with the appearance of strong skin currents, we observe the onset of a large fluctuation level (ñ_{ e }/n _{ e }∼1%) which persists for the duration of the anomalous current transport phase. The main contribution is from broadband fluctuations at low frequencies (a few MHz) and long wavelengths (a few mm). The nature of the fluctuations is not clear although a low level of ion‐acoustic turbulence appears to be involved.

Error magnetic fields in a cylindrical plasma: Stability with zero pressure
View Description Hide DescriptionThe importance of error magnetic fields is that, if large enough, they cause the destruction of magnetic surfaces. In this paper error fields in a cylindrical plasma are described by nonlinear tearing mode theory, which deals with plasma equilibria having concentrated currents flowing along closed magnetic field lines. Because of the small spatial scale of the current distribution, resistive diffusion is significant even for small resistivity and, in certain cases, causes instability. An energy principle exists and is discussed. This conceptual framework is used in a study of the stability of zero pressure equilibria toward spontaneous generation of error fields, relevant for the reversed field pinch program. Cylindrical Ohmic states are shown to be extremely unstable. Relaxed states (having flattened current profiles) have much better stability. Both completely relaxed states of the Taylor type and partially relaxed Robinson‐type states are studied. A new class of metal–liner stabilized profiles is found, which offers one explanation for the apparent stability observed in experiments with distant conducting shells. The possibility that relaxed states have weakly stochastic magnetic field lines is discussed.

Neutral particle density transients in gaseous discharges
View Description Hide DescriptionA model is presented which describes the neutral density transients in gaseous discharges. It is shown that the duration of the initial density transient is governed by the speed of sound in the gas in which the discharge is produced. The development of the gas‐flow velocity pattern in the discharge tube is a consequence of the interplay between three competing volume forces: (a) the driving volume force, which is generated by the interaction of the charged particles with the neutral particles, (b) the viscosity force, and (c) the neutral pressure gradient force. The influence of the geometry of the discharge tube on the neutral particle density transients is also discussed. The initial neutral particle density transient is believed to be the origin of acoustic resonances observed in rf‐excited gaseous discharges.

Numerical simulation of electromagnetic turbulence in tokamaks
View Description Hide DescriptionNonlinear two‐ and three‐fluid equations are written for the time evolution of the perturbed electrostatic potential, densities, vector potential, and parallel ion motion of collisional and trapped electron plasmas in tokamak geometry. The nonlinear terms arise from the Ẽ×B _{0} convection (d̃/d t=∂/∂t+ṽ_{ E } ⋅ ∇_{⊥}) and magnetic flutter [∇̃_{∥}=∇_{∥}+(B _{⊥}/B _{0}) ⋅ ∇_{⊥}]. Simplified two‐dimensional (k _{⊥}) mode coupling simulations with a fixed average parallel wavenumber (k _{∥}=1/R q) and curvature drift [ω_{ g }=(L _{ n }/R)ω_{ * } ] characteristic of outward ballooning are performed. Homogeneous stationary turbulent states of the dissipative drift and interchange modes from 0≤β<β_{crit} for both the collisional and trapped electron plasmas are obtained. Transport coefficients associated with E×B and magnetic motions are calculated. The problem of simulating plasmas with high viscous Reynolds number is treated with an absorbing mantle at the largest wavenumbers. The results are summarized by comparison to simple mixing length rules: ñ/n _{0}∼1/k _{⊥} L _{ n }, B̃/B _{0} ∼(β/2) ⋅ q ⋅ ñ/n _{0}, D _{ E }∼γ/k ^{2} _{⊥}.