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Nov 1988

Volume 31, Issue 11, pp. 3165-3451

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The existence of two stages in the transition to three‐dimensionality of a cylinder wake

C. H. K. Williamson

Phys. Fluids 31, 3165 (1988); http://dx.doi.org/10.1063/1.866925 (4 pages) | Cited 135 times

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The transition to three‐dimensionality in the near wake of a circular cylinder involves two successive transitions, each of which corresponds with a discontinuity in the Strouhal–Reynolds number relationship. The first discontinuity [between Reynolds numbers (Re) of 170 to 180] is associated with the inception of vortex loops, and it is hysteretic. The second discontinuity (between Re=230 to 260) corresponds with a change to a finer‐scale streamwise vortex structure. At this discontinuity there is no hysteresis, and it is suggested that two modes of vortex shedding alternate in time.
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47.27.W- Boundary-free shear flow turbulence
47.27.Cn Transition to turbulence

Direct solution for the power spectrum of the Lorenz attractor

P. L. Andrews and R. E. Waltz

Phys. Fluids 31, 3168 (1988); http://dx.doi.org/10.1063/1.866926 (3 pages)

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A novel method is applied to the Lorenz system that deals directly with the power spectrum of the turbulent solutions. Analytic predictions are produced as to the level of turbulence and the spread in frequency space of the solution that are in good agreement with numerical computations. The method involves manipulation of the Fourier transformed Lorenz equations and their tempered distribution solutions.
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52.35.Ra Plasma turbulence
05.45.-a Nonlinear dynamics and chaos
47.52.+j Chaos in fluid dynamics

Radiation focusing in the cyclotron autoresonance maser

Robert G. Kleva, Baruch Levush, and P. Sprangle

Phys. Fluids 31, 3171 (1988); http://dx.doi.org/10.1063/1.866927 (3 pages) | Cited 2 times

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In the cyclotron autoresonance maser, an electromagnetic wave is amplified by interaction with an electron beam. Because of the copropagating electron beam, the refractive index seen by the wave is modified from the vacuum index and the dielectric properties of the electron beam can alter the propagation of the radiation beam. This phenomenon is studied through the use of a source‐dependent modal expansion of the fully three‐dimensional radiation field. In the exponential gain regime, the natural tendency of the radiation beam to spread diffractively is overcome and the beam is focused. The nature of the focusing is found to depend on the relative magnitude of the Doppler‐shifted wave frequency and the gyrofrequency.
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84.40.Ik Masers; gyrotrons (cyclotron-resonance masers)
42.65.Jx Beam trapping, self-focusing and defocusing; self-phase modulation

Periodic solutions for three sedimenting spheres

Russel E. Caflisch, Chjan Lim, Jonathan H. C. Luke, and Ashok S. Sangani

Phys. Fluids 31, 3175 (1988); http://dx.doi.org/10.1063/1.866928 (5 pages) | Cited 21 times

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Exact periodic solutions are found for the relative motion of three spheres sedimenting in a Stokes fluid. Nearby solutions are found to be nearly periodic for a long time. Existence of the exact periodic solutions is proved using the point‐particle approximation and symmetry properties of Stokes equations. Numerical simulations for finite‐sized particles are performed using a method of multipole expansions.
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47.55.Kf Particle-laden flows
82.70.-y Disperse systems; complex fluids
02.60.Cb Numerical simulation; solution of equations

Leakage losses from a hydraulic fracture and fracture propagation

Robert E. Johnson and Craig W. Gustafson

Phys. Fluids 31, 3180 (1988); http://dx.doi.org/10.1063/1.866929 (8 pages) | Cited 2 times

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The fluid mechanics of viscous fluid injection into a fracture embedded in a permeable rock formation is studied. Coupling between flow in the fracture and flow in the rock is retained. The analysis is based on a perturbation scheme that assumes the depth of penetration of the fluid into the rock is small compared to the characteristic length w30/k, where w0 is the characteristic crack width and k is the permeability. This restriction, however, is shown to be minor. The spatial dependence of the leakage rate per unit length from the fracture is found to be linear, decreasing from the well bore to the fracture tip where it vanishes. The magnitude of the leakage rate per unit length is found to decay in time as t−1/3 if the injection rate at the well bore is constant, and as t−1/2 if the well bore pressure is held constant. The results cast considerable doubt on the validity of Carter’s well‐known leakage formula (Drilling Prod. Prac. API 1957, 261) derived from a one‐dimensional theory. Using the simple fracture propagation model made popular by Carter, the present work also predicts that the fracture grows at a rate proportional to t1/3 for a fixed well bore injection rate and a rate proportional to t1/4 for a fixed well bore pressure.
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47.56.+r Flows through porous media
47.60.-i Flow phenomena in quasi-one-dimensional systems
83.10.Ff Continuum mechanics

The effect of nonzero viscosity ratio on the stability of fingers and bubbles in a Hele–Shaw cell

S. Tanveer and P. G. Saffman

Phys. Fluids 31, 3188 (1988); http://dx.doi.org/10.1063/1.866930 (11 pages) | Cited 6 times

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The linear stability of a steadily moving bubble or a finger in a Hele–Shaw cell is considered in the case when gravity and the ratio between the viscosities of the less and more viscous fluids are nonzero. The effect of gravity is easily incorporated by a transformation of parameters introduced previously by Saffman and Taylor [Proc. R. Soc. London Ser. A 245, 312 (1958)] for the steady flow, which makes the time‐dependent flows with and without gravity equivalent. For the nonzero viscosity ratio, the transformation of parameters introduced by Saffman and Taylor also makes steady finger and bubble flows with nonzero and zero viscosity ratios equivalent. However, for the unsteady case, there is no such equivalence and so a complete calculation is carried out to investigate the effect of the nonzero viscosity ratio on the stability of fingers and bubbles. The incorporation of the finite viscosity ratio is found not to qualitatively alter the linear stability features obtained in earlier work for the zero viscosity ratio, although there are quantitative differences in the growth or decay rate of various modes. For any surface tension, numerical calculation suggests that the McLean–Saffman branch of bubbles [Phys. Fluids 30, 651 (1987)] of arbitrary size is stable, whereas all the other branches are unstable. For a small bubble that is circular, the eigenvalues of the stability operator are found explicitly. The previous analytic theory for the stability of the finger in the limit of zero surface tension is extended to include the case of the finite viscosity ratio. It is found that, as in the case of bubbles, the finite viscosity ratio does not alter qualitatively any of the features obtained previously for the zero viscosity ratio.
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47.20.-k Flow instabilities
51.10.+y Kinetic and transport theory of gases

Vortex‐in‐cell simulation of bubble competition in a Rayleigh–Taylor instability

Juan A. Zufiria

Phys. Fluids 31, 3199 (1988); http://dx.doi.org/10.1063/1.866931 (14 pages) | Cited 21 times

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The penetration of a front of light fluid into a heavy fluid in a Rayleigh–Taylor unstable flow is studied by using a vortex‐in‐cell numerical algorithm. The algorithm is used to simulate the competition among the bubbles that are formed in the interface when the density ratio of the two fluids is very large. Several multifrequency initial conditions and the effect of surface tension have been considered. It is found that the front moves with constant acceleration. The values obtained for the acceleration of the front are in very good agreement with experimental results obtained by Read [Phys. D 12, 45 (1984)] and with the results obtained by using Zufiria’s [Phys. Fluids 31, 440 (1988)] model.
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47.15.ki Inviscid flows with vorticity
47.20.-k Flow instabilities
47.55.Kf Particle-laden flows
47.20.Dr Surface-tension-driven instability

The decay of a viscous vortex pair

Brian Cantwell and Nicholas Rott

Phys. Fluids 31, 3213 (1988); http://dx.doi.org/10.1063/1.866932 (12 pages) | Cited 18 times

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The evolution of a viscous vortex pair is investigated through the use of a heuristic model. The model is based on the linear superposition of two Oseen vortices of opposite circulation spaced a distance 2b apart. The vortices are allowed to evolve through viscous diffusion and their mutual induction. The motion is unforced and as a consequence the total hydrodynamic impulse is exactly conserved for all time. In the model the total circulation in the upper half plane is assumed to remain initially constant. This constraint is applied up to a finite time when the model solution reaches its asymptotic form corresponding to a drifting Stokes dipole dominated by interdiffusion of vorticity across the plane of symmetry. The drift velocity of the vortex pair is determined by the condition that the integrated pressure force vanishes on the line of symmetry at all times. At large time this leads to an asymptotic value of the drift velocity which scales with the similarity properties of the Stokes solution. To provide a more rigorous foundation for the drift, the asymptotic behavior of the flow for large time is investigated through an expansion of the solution in inverse powers of the time. First the second‐order pressure is determined as a solution of a Poisson equation with the source term generated by the first‐order flow field. Surprisingly, the solution turns out to be independent of the drift. Nevertheless, an exact condition for the drift is found by considering the limiting form of the second‐order pressure at infinity where the flow is irrotational and the pressure can be computed directly from the first‐order velocity field using Bernoulli’s equation. In this latter approach the far field pressure is determined up to an unknown function of time which upon comparison with the Poisson solution is identified as the drift. The exact drift obtained in this fashion differs by only 10% from the value obtained using the pressure field of the heuristic model. Finally, it is shown that the existence of the complete second‐order asymptotic solution of the Navier–Stokes equations requires the inclusion of the same drift in the first‐order solution that was found from the examination of the pressure. The second‐order vorticity and streamfunction are determined; the latter contains a
free constant to accommodate conditions at earlier times. Prospects for the existence of higher‐order asymptotic terms are discussed.
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47.27.T- Turbulent transport processes
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.27.Cn Transition to turbulence

Linear stability of plane Poiseuille flow of two superposed fluids

Stergios G. Yiantsios and Brian G. Higgins

Phys. Fluids 31, 3225 (1988); http://dx.doi.org/10.1063/1.866933 (14 pages) | Cited 100 times

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Stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically. Conditions for the growth of an interfacial wave are identified. The analysis extends Yih’s results [J. Fluid Mech. 27, 337 (1967)] for small wavenumbers to large wavenumbers and accounts for differences in density and thickness ratios, as well as the effects of interfacial tension and gravity. Neutral stability diagrams for the interfacial mode are reported for a wide range of the physical parameters describing the flow. The analysis shows also that the flow is linearly unstable to a shear mode instability. The dependence of the critical Reynolds number for the shear mode on the viscosity ratio is reported. Theoretical predictions of critical Reynolds numbers for both modes of instability are compared with available experimental data.
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47.20.Dr Surface-tension-driven instability
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)

Linear stability analysis of nonhomentropic, inviscid compressible flows

V. D. Djordjevic and L. G. Redekopp

Phys. Fluids 31, 3239 (1988); http://dx.doi.org/10.1063/1.866934 (7 pages) | Cited 7 times

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The linear stability of inviscid, compressible shear flows is studied. Some previous results for homentropic flows are extended to include adiabatic flows with variable temperature. Specific neutral solutions are obtained for both a shear layer and a wake in the subsonic regime that are stability boundaries. Unstable solutions are calculated for both streamwise and oblique disturbances in the shear layer flow. Other neutrally stable solutions are presented, which do not correspond to stability boundaries, describing stationary oscillations of supersonic shear flows.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.40.Dc General subsonic flows

Effects of excitation level on the stability of an axisymmetric mixing layer

M. M. Samet and R. A. Petersen

Phys. Fluids 31, 3246 (1988); http://dx.doi.org/10.1063/1.866935 (7 pages) | Cited 3 times

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The effect of various levels of excitation on the stability and development of an axisymmetric mixing layer was studied experimentally. The flow was excited axisymmetrically by a single speaker placed at the base of the plenum chamber. Measurements of mean and phase‐averaged velocity profiles were made using an array of hot‐wire probes. The measured profiles were compared to eigenfunctions calculated from linear, viscous stability theory. It is shown that the theoretical predictions, based on measured profiles of mean velocity, compare very well with the phase‐averaged measurements, even when the local disturbance reaches levels as high as 24% of the jet speed. The cumulative effect of excitation on the mean flow is examined as a function of local Strouhal number as well as excitation level.
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47.27.W- Boundary-free shear flow turbulence
47.60.Kz Flows and jets through nozzles
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
43.28.Py Interaction of fluid motion and sound, Doppler effect, and sound in flow ducts

Relative velocity fluctuations in turbulent flows at moderate Reynolds number. II. Model calculation

P. Tong and W. I. Goldburg

Phys. Fluids 31, 3253 (1988); http://dx.doi.org/10.1063/1.866936 (7 pages) | Cited 5 times

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A model calculation is presented to study turbulence at moderate Reynolds number, Re. In conformity with recent measurements, it is proposed that in the energy cascade the fractional volume occupied by eddies of various sizes depends on Re. By introducing a Re‐dependent parameter in the random beta model, it is shown that the scaling behavior of the small‐velocity fluctuations at moderate Re can be characterized by a single Re‐dependent scaling exponent α0. The calculated Re dependence of α0 is consistent with the experimental data. Corrections to this scaling are calculated using the multifractal concept. The Reynolds number dependence of other multifractal properties in turbulent flows is also calculated.
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47.27.Cn Transition to turbulence
05.45.-a Nonlinear dynamics and chaos

Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation

H. J. Kim and P. A. Durbin

Phys. Fluids 31, 3260 (1988); http://dx.doi.org/10.1063/1.866937 (6 pages) | Cited 58 times

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Vortex shedding and instability wave frequencies have been measured in the wakes of spheres in the Reynolds number range 500<Re<60 000. The effect of acoustic excitation was examined and an interaction between the two frequency modes was found at the lower Reynolds numbers; through this interaction, external forcing at the instability frequency could change the vortex shedding frequency. The development of the mean wake was manipulated by forcing near to the dominant shear layer instability frequency. With this forcing, the separated shear layer moved closer to the surface of the sphere and the reversed flow region of the wake was shortened. Concomitantly, the base pressure decreased and drag increased.
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47.27.W- Boundary-free shear flow turbulence
43.28.Py Interaction of fluid motion and sound, Doppler effect, and sound in flow ducts

The influence of electron trapping on stationary Langmuir waves

A. Bergmann and H. Schnabl

Phys. Fluids 31, 3266 (1988); http://dx.doi.org/10.1063/1.866938 (5 pages) | Cited 4 times

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The excitation of high‐amplitude Langmuir waves in a warm plasma is investigated in the framework of the hydrodynamic model. An integral expression is found describing the maximum possible amplitude in the limit of stationary waves. The steep increase of compression energy in the density peaks is shown to be the reason for this limitation of amplitude. If electron trapping in the potential of the Langmuir wave is taken into consideration, two consequences occur: The limit for the density peaks in the stationary wave is lowered, and the dispersion relation is modified. Because of the trapped electrons, allowed frequency bands appear below the original plasma frequency. Thus plasma waves containing trapped electrons are able to propagate in the overdense region.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.38.-r Laser-plasma interactions

Evolution of nonlinear polarization in localized and finite amplitude Alfvén waves

M. Hoshino

Phys. Fluids 31, 3271 (1988); http://dx.doi.org/10.1063/1.866939 (9 pages) | Cited 4 times

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Theoretical and computational study for a polarization change of localized and finite amplitude Alfvén waves propagating parallel to an applied magnetic field is presented using both reductive perturbation theory and numerical simulations. In the magnetohydrodynamic limit (ω≪Ωi) where right‐ and left‐hand circularly polarized waves are degenerate, one of the transverse components of the circularly polarized Alfvén wave is stable as it propagates, but the other component is unstable to either self‐focusing or diffraction effects. Consequently, the wave changes its polarization from circular to linear. In the high frequency regime (ω≳Ωi), where two circularly polarized waves (right‐ and left‐hand circularly polarized waves) are not degenerate, two transverse components of the circularly polarized Alfvén wave are strongly coupled to each other, and there is almost no polarization change.
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52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.65.-y Plasma simulation

Generalized parallel heat transport equations in collisional to weakly collisional plasmas

Emad Zawaideh, N. S. Kim, and Farrokh Najmabadi

Phys. Fluids 31, 3280 (1988); http://dx.doi.org/10.1063/1.866940 (6 pages) | Cited 13 times

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A new set of two‐fluid heat transport equations that is valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates, a set of moment equations describing plasma energy transport along the field lines of a space‐ and time‐dependent magnetic field is derived. No restrictions on the anisotropy of the ion distribution function or collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation (e.g., Spitzer and Härm or Braginskii), while in the weakly collisional limit, they describe a saturated heat flux (flux limited). Numerical examples comparing these equations with conventional heat transport equations show that in the limit where the ratio of the mean free path λ to the scale length of the temperature gradient LT approaches zero, there is no significant difference between the solutions of the new and conventional heat transport equations. As λ/LT→1, the conventional heat conduction equation contains a significantly larger error than (λ/LT)2. The error is found to be O(λ/L)2, where L is the smallest of the scale lengths of the gradient in the magnetic field, or the macroscopic plasma parameters (e.g., velocity scale length, temperature scale length, and density scale length). The accuracy of the flux‐limited model depends significantly on the value of the flux limit parameter which, in general, is not known. The new set of equations shows that the flux‐limited parameter is a function of the magnetic field and plasma parameter profiles.
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51.10.+y Kinetic and transport theory of gases
52.25.Dg Plasma kinetic equations
52.25.Fi Transport properties
52.65.-y Plasma simulation

The nonlinear three‐wave interaction with a finite spectral width

A. M. Martins and J. T. Mendonça

Phys. Fluids 31, 3286 (1988); http://dx.doi.org/10.1063/1.866941 (9 pages) | Cited 14 times

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The nonlinear interaction of three waves propagating in an infinite plasma with a finite spectral bandwidth is studied. A Hamiltonian formulation of the interaction is used and, with the help of a projection operator method, generalized Langevin equations are derived for the wave field amplitudes. A simple form of the evolution equations, more complete than the usual fixed‐phase equations, is obtained when the ballistic term and higher‐order corrections of the memory effects in the Langevin equations are neglected. Approximate analytical solutions are derived using a multiple time scale method. These are compared with the results of numerical integration. A number of new qualitative features related to the finite spectral bandwidth are discussed in detail.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Ra Plasma turbulence
63.10.+a General theory
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Parametric decay of a fast wave to two electromagnetic slow waves at half the pump frequency

S. C. Chiu

Phys. Fluids 31, 3295 (1988); http://dx.doi.org/10.1063/1.866942 (4 pages) | Cited 7 times

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The parametric decay process of a fast wave at the ion‐cyclotron range of frequencies (ICRF) into two electromagnetic slow (or ordinary) waves is considered. It is shown that in the dipole approximation of the pump wave, the decay process is possible at around half the frequency of the pump. Plasmas of interest that are susceptible to this decay process include deuterium–hydrogen (D–H), deuterium–helium 3 (D–He3), and deuterium–tritium (D–T) plasmas. It is shown that the growth rate may approach a few percent of the pump frequency at the edge, and may thus lead to edge electron heating.
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52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.50.Gj Plasma heating by particle beams

The effect of magnetized ions on the lower hybrid drift instability in field reversed configurations

R. Farengo, P. N. Guzdar, and Y. C. Lee

Phys. Fluids 31, 3299 (1988); http://dx.doi.org/10.1063/1.866943 (6 pages) | Cited 7 times

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The high beta regime of the lower hybrid drift instability is studied using a fully electromagnetic dispersion relation in the local approximation. The electrons are described using a kinetic model that includes the effect of finite beta orbit modifications and three different models (unmagnetized, magnetized without ∇B drifts, and magnetized with ∇B drifts) are used for the ions. It is found that when magnetized ions without ∇B drifts are considered, the modes remain unstable for larger values of beta and the spectrum is very different from the unmagnetized ion case. When ∇B drift effects are included, the results became very similar to the unmagnetized ion case and some arguments are provided to explain this behavior.
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52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.55.Jd Magnetic mirrors, gas dynamic traps

Quasilinear and toroidal effects on current drive by electron cyclotron waves

G. Giruzzi

Phys. Fluids 31, 3305 (1988); http://dx.doi.org/10.1063/1.866944 (7 pages) | Cited 28 times

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Current drive by electron cyclotron waves in toroidal geometry is investigated by means of a bounce‐averaged Fokker–Planck code. The case of the extraordinary mode at a frequency lower than the electron gyrofrequency is studied in detail for a wave packet of finite width, carrying a power in the megawatt range, which is absorbed away from the plasma center. It is shown that in this case, because of the interplay of quasilinear and trapping effects (i) the current drive efficiency is strongly power dependent and (ii) wave absorption at the inboard part of the magnetic surfaces does not maximize the efficiency, in contrast to the results of linear theory.
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52.50.Gj Plasma heating by particle beams
52.25.Dg Plasma kinetic equations
52.55.Fa Tokamaks, spherical tokamaks

Neutral beam injection and plasma convection in a magnetic field

H. Okuda and S. Hiroe

Phys. Fluids 31, 3312 (1988); http://dx.doi.org/10.1063/1.866945 (10 pages)

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Injection of a neutral beam into a plasma in a magnetic field has been studied by means of numerical plasma simulations. It is found that, in the absence of a rotational transform, the convection electric field arising from the polarization charges at the edges of the beam is dissipated by turbulent plasma convection, leading to anomalous plasma diffusion across the magnetic field. The convection electric field increases with the beam density and beam energy. In the presence of a rotational transform, polarization charges can be neutralized by the electron motion along the magnetic field. Even in the presence of a rotational transform, a steady‐state convection electric field and hence anomalous plasma diffusion can develop when a neutral beam is constantly injected into a plasma. Theoretical investigations of the convection electric field are described for a plasma in the presence of a rotational transform.
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52.25.Fi Transport properties
52.40.Mj Particle beam interactions in plasmas
52.35.Ra Plasma turbulence
52.65.-y Plasma simulation

Reversed‐field pinch Ohmic equilibria during current decay and termination

E. J. Caramana and R. A. Nebel

Phys. Fluids 31, 3322 (1988); http://dx.doi.org/10.1063/1.866946 (8 pages) | Cited 2 times

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The possible current decay and termination of reversed‐field pinch discharges via stable, Ohmic, self‐similar states that do not require any instabilities or dynamo effect for their maintenance are investigated. The equations that describe such states are derived; numerical solutions that are functions of the form of the resistivity profile, the current decay rate, and the pinch parameter are presented. Relevant constraints on stable termination are discussed.
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52.55.Ez Theta pinch
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)

Modeling of reversed‐field‐pinch magnetic probe measurements

Guthrie Miller

Phys. Fluids 31, 3330 (1988); http://dx.doi.org/10.1063/1.866947 (8 pages) | Cited 3 times

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Magnetic probe measurements carried out on the ZT‐40M reversed field pinch [Fusion Technol. 8, 1571 (1985)] for low current (50 kA) discharges with and without F‐Θ pumping are described. The internal probe measurements are used to determine the evolution of the axisymmetric equilibrium profiles. Of particular interest is the profile response to the large‐amplitude, oscillatory, toroidal, and poloidal driving voltages applied during F‐Θ pumping. The results are compared with a two‐field‐line stochastic magnetic field model.
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52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Ez Theta pinch

Oscillating field current drive in spheromaks

Allen H. Boozer

Phys. Fluids 31, 3338 (1988); http://dx.doi.org/10.1063/1.866948 (3 pages)

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If a spheromak plasma with a flux hole relaxes sufficiently rapidly to the flat current profile of a Taylor state, then the plasma current can be maintained, or increased, by varying certain geometric ratios of the plasma. The theory of this type of current drive is developed in terms of the internal and external inductances of a spheromak.
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52.55.Jd Magnetic mirrors, gas dynamic traps
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)

Entropy gradient‐driven electron inertial instabilities

Peter Amendt, H. U. Rahman, and M. Strauss

Phys. Fluids 31, 3341 (1988); http://dx.doi.org/10.1063/1.867021 (5 pages) | Cited 3 times

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In the vicinity of a density transition region or surface, electron temperature fluctuations are known to drive low frequency electromagnetic surface waves which may be connected with the self‐generation of magnetic fields in the laser–plasma interaction. Two methods of destabilization are considered. In the first approach an accelerating plasma surface is considered and this leads to instability only when an accompanying temperature gradient scale length is at most as large as the density gradient scale length. In the second approach the introduction of current is also found to cause instability near the plasma surface provided an identical temperature gradient threshold is exceeded. In both cases the growth rates for each instability are enhanced by the square root of the ion to electron mass ratio over the associated growth rates for ion‐inertial‐type instability.
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52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Tc Shock waves and discontinuities
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