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Aug 1981

Volume 24, Issue 8, pp. 1405-1592

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Görtler instability

S. A. Ragab and A. H. Nayfeh

Phys. Fluids 24, 1405 (1981); http://dx.doi.org/10.1063/1.863557 (13 pages) | Cited 12 times

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Görtler instability for boundary‐layer flows over generally curved walls is considered. The full‐linearized disturbance equations are obtained in an orthogonal curvilinear coordinate system. A perturbation procedure to account for second‐order effects is used to determine the effects of the displacement thickness and the variation of the streamline curvature on the neutral stability of the Blasius flow. The streamwise pressure gradient in the mean flow is accounted for by solving the nonsimilar boundary‐layer equations. Growth rates are obtained for the actual mean flow and compared with those for the Blasius flow and the Falkner–Skan flows. The results demonstrate the strong influence of the streamwise pressure gradient and the nonsimilarity of the basic flow on the stability characteristics.
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47.15.Fe Stability of laminar flows
47.10.-g General theory in fluid dynamics

Generalized scalar potentials for linearized three‐dimensional flows with vorticity

R. W. Hart

Phys. Fluids 24, 1418 (1981); http://dx.doi.org/10.1063/1.863558 (3 pages) | Cited 2 times

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The three‐dimensional time‐dependence velocity of incompressible fluids satisfying linearized incompressible Navier–Stokes equations can often be expressed in terms of a single h by v = A∇h+B(l×∇h)+Cl×(l×∇h), where l is a constant vector and A,B,C are scalar operators. For B,C≠0,curl v≠0.
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47.32.Ef Rotating and swirling flows

Instabilities of a compressible stratified fluid in horizontal sheared motion

P. L. Sachdev and A. Satya Narayanan

Phys. Fluids 24, 1421 (1981); http://dx.doi.org/10.1063/1.863559 (4 pages) | Cited 4 times

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The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible atmosphere in the presence of a lower boundary are studied. A jump in the Brunt–Väisälä frequency is introduced and the level at which this jump occurs is assumed to be different from the shear zone, to simulate sharp temperature discontinuities in the atmosphere. The results are compared with those of Pellacani, Tebaldi, and Tosi and Lindzen and Rosenthal. In the present configuration, new unstable modes with larger growth rates are found. The wavelengths of the most unstable gravity waves for the parameters pertaining to observed cases of clear air turbulence agree quite closely with the experimental values.
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47.20.-k Flow instabilities
47.55.Hd Stratified flows
92.60.hh Acoustic gravity waves, tides, and compressional waves

Some interesting properties of two‐dimensional turbulence

Charles G. Speziale

Phys. Fluids 24, 1425 (1981); http://dx.doi.org/10.1063/1.863560 (3 pages) | Cited 15 times

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The effect of superimposed rigid body motions on the structure of two‐dimensional turbulence is examined. It is found that with regard to the fluctuation dynamics of the flow, the rotational behavior of two‐dimensional turbulence is quite different from its three‐dimensional counterpart. The implications that this has on turbulence modeling are discussed briefly.
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47.27.-i Turbulent flows

Spectral transfer and velocity derivative skewness equation for a turbulent velocity field

Richard J. Driscoll and Lawrence A. Kennedy

Phys. Fluids 24, 1428 (1981); http://dx.doi.org/10.1063/1.863561 (3 pages) | Cited 1 time

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A derivation of the high wavenumber spectral transfer equation is given which indicates the wavenumber range of validity for this equation in terms of Reλ. A similar treatment is given for the commonly used spectral approximation for the velocity derivative skewness and the analogous scalar spectral quantities.
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47.27.-i Turbulent flows
47.27.Gs Isotropic turbulence; homogeneous turbulence

Variational moment solutions to the Grad–Shafranov equation

L. L. Lao, S. P. Hirshman, and R. M. Wieland

Phys. Fluids 24, 1431 (1981); http://dx.doi.org/10.1063/1.863562 (10 pages) | Cited 83 times

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A variational method is developed to find approximate solutions to the Grad–Shafranov equation. The surfaces of the constant poloidal magnetic flux ψ(R, Z) are obtained by solving a few ordinary differential equations, which are moments of the Grad–Shafranov equation, for the Fourier amplitudes of the inverse mapping R(ψ, ϑ) and Z(ψ, ϑ). Analytic properties and solutions of the moment equations are considered. Specific calculations using the Impurity Study Experiment (ISX‐B) and the Engineering Test Facility (ETF)/International Tokamak Reactor (INTOR) geometries are performed numerically, and the results agree well with those calculated using standard two‐dimensional equilibrium codes. The main advantage of the variational moment method is that it significantly reduces the computational time required to determine two‐dimensional equilibria without sacrificing accuracy.
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52.25.Fi Transport properties

Appendix: Variational moment solutions to the Grad–Shafranov equation [Phys. Fluids 24, 1431 (1981)]

Harold Weitzner

Phys. Fluids 24, 1440 (1981); http://dx.doi.org/10.1063/1.863563 (2 pages)

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Appendix to  Variational moment solutions to the Grad–Shafranov equation  (AIP)
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52.25.Fi Transport properties

Thermal heat flux in a plasma for arbitrary collisionality

S. A. Khan and T. D. Rognlien

Phys. Fluids 24, 1442 (1981); http://dx.doi.org/10.1063/1.863564 (5 pages) | Cited 40 times

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The thermal heat flux along a uniform magnetic field due to a temperature gradient is calculated using a Monte Carlo solution to the Fokker–Planck equation. This numerical solution, which is computed for a particular electron temperature profile, is valid for arbitrary mean‐free‐path, λmfp. The calculated heat flux makes a smooth transition between the analytic expressions for the short and long λmfp limits.
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52.25.Fi Transport properties

Centrifugal separation of a multispecies pure ion plasma

T. M. O’Neil

Phys. Fluids 24, 1447 (1981); http://dx.doi.org/10.1063/1.863565 (5 pages) | Cited 52 times

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Consider an unneutralized column of ions (a pure ion plasma) confined by an axial magnetic field. Because of space charge, there is a large radial electric field and a consequent rotation of the plasma column. For a multispecies ion plasma, the rotation tends to produce centrifugal separation of the plasma into its component species. Self‐consistent thermal equilibrium states which exhibit various degrees of separation are discussed.
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52.25.Fi Transport properties

Excitation of multiple ion‐acoustic shocks

Chung Chan, Mehyar Khazei, Karl E. Lonngren, and Noah Hershkowitz

Phys. Fluids 24, 1452 (1981); http://dx.doi.org/10.1063/1.863566 (4 pages) | Cited 11 times

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Multiple electrostatic ion‐acoustic shock‐like density perturbations are observed experimentally to be launched from a large plate in a quiescent collisionless plasma. The formation of the fastest shock is due to ions expelled from the edge of the ’’transient sheath’’ surrounding the plate. The second shock then evolves as a result of the surrounding ions filling in the region of density depression created by the first shock. Reflected ions and turbulent ion‐acoustic noise at the shock front and amplitude modulation in the trailing dispersing oscillations are only observed for the leading shock.
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52.35.Tc Shock waves and discontinuities
52.40.Kh Plasma sheaths

Parametric instabilities in an electron beam plasma system

R. Nakach, S. Cuperman, Y. Gell, and B. Levush

Phys. Fluids 24, 1456 (1981); http://dx.doi.org/10.1063/1.863549 (9 pages) | Cited 5 times

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The excitation of low‐frequency parametric instabilities by a finite wavelength pump in a system consisting of a warm electron plasma traversed by a warm electron beam is investigated in a fluid dissipationless model. The dispersion relation for the three‐dimensional problem in a magnetized plasma with arbitrary directions for the waves is derived, and the one‐dimensional case is analyzed numerically. For the one‐dimensional back‐scattering decay process, it is found that when the plasma‐electron Debye length (λDp) is larger than the beam‐electron Debye length (λDb), two low‐frequency electrostatic instability branches with different growth rates may exist simultaneously. When λDp≃λDb, the large growth rate instability found in the analysis depends strongly on the amplitude of the pump field. For the case λDp<λDb, only one low‐frequency instability branch is generally excited.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.40.Mj Particle beam interactions in plasmas

Variational principle for low‐frequency stability of collisionless plasmas

Thomas M. Antonsen, Barton Lane, and Jesús J. Ramos

Phys. Fluids 24, 1465 (1981); http://dx.doi.org/10.1063/1.863550 (9 pages) | Cited 35 times

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An analysis of the stability of an arbitrary β collisionless plasma to modes with wavelengths greater than the ion gyroradius is presented. The stability of such a plasma to perturbations that grow on the hydrodynamic time scale is determined by the Kruskal–Oberman energy principle. However, a configuration which is predicted to be stable on the basis of this kinetic energy principle may still be unstable to modes that grow with a frequency comparable to the diamagnetic or curvature drift frequency. A new variational principle that gives sufficient conditions for instability of these low‐ frequency modes is derived. The new principle indicates that two types of instabilities are possible; the first corresponds to the low‐frequency electrostatic, trapped particles mode, and the second is the low‐frequency limit of magnetohydrodynamic (interchange and ballooning) modes. The kinetic modifications to the interchange (Mercier) criterion are evaluated and the effect of the kinetic terms on ballooning modes is estimated.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Theory and simulation of stimulated Brillouin scatter excited by nonabsorbed light in laser fusion systems

C. J. Randall, James R. Albritton, and J. J. Thomson

Phys. Fluids 24, 1474 (1981); http://dx.doi.org/10.1063/1.863551 (11 pages) | Cited 25 times

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The noise spectrum from which stimulated Brillouin scatter grows has two sources in laser fusion plasmas; a broadband source due to ion‐acoustic fluctuations, and a line source, usually much larger, which is the nonabsorbed light returning from the plasma critical surface. We give a theoretical description of stimulated Brillouin backscatter when the fluctuation source may be neglected and the scatter grows exclusively from the nonabsorbed light. Gradients of background density, velocity, and temperature are allowed. Theoretical predictions are compared to numerical simulations of scatter for parameters of recent experiments. It is found that stimulated Brillouin scatter can be greatly enhanced by the presence of a critical surface and that it can become an important part of the total energy balance.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)

Integral‐equation formulation for drift eigenmodes in cylindrically symmetric systems

Ralph Linsker

Phys. Fluids 24, 1485 (1981); http://dx.doi.org/10.1063/1.863552 (7 pages) | Cited 27 times

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A method for solving the integral eigenmode equation for drift waves in cylindrical (or slab) geometry is presented. A leading‐order kinematic effect that has been noted in the past, but incorrectly ignored in recent integral‐equation calculations, is incorporated. The present method also allows electrons to be treated with a physical mass ratio (unlike earlier work that is restricted to artificially small mi/me owing to resolution limitations). Results for the universal mode and for the ion‐temperature‐gradient driven mode are presented. The kinematic effect qualitatively changes the spectrum of the ion mode, and a new ’’second region of instability’’ for k⊥ ρi≳1 is found.
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52.35.Kt Drift waves
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Temperature effects on harmonic generation in laser‐irradiated plasmas

N. E. Andreev, G. Auer, K. Baumgärtel, and K. Sauer

Phys. Fluids 24, 1492 (1981); http://dx.doi.org/10.1063/1.863553 (7 pages) | Cited 5 times

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The generation of second and third harmonics at the oblique incidence of a p‐polarized wave on an inhomogeneous plasma (resonance absorption) is studied. The relevant wave equations are solved numerically. First, the dependence of the emitted harmonics on the temperature, the density scale length, and the angle of incidence is investigated for a linear density profile. The strong oscillations of the harmonic emission in a certain temperature range are attributed to the position of the point where the condition for phase matching is fulfilled. In the second part a modified density profile with a caviton is considered, and it is shown that a large enhancement of harmonic emission is possible because of the formation of electrostatic resonant structures. This effect will become important under experimental nonstationary conditions when the density profile is deformed by the ponderomotive force.
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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.)
52.25.Kn Thermodynamics of plasmas
52.25.Os Emission, absorption, and scattering of electromagnetic radiation

Collisional shear Alfvén waves in sheared magnetic fields

J. F. Drake and Robert G. Kleva

Phys. Fluids 24, 1499 (1981); http://dx.doi.org/10.1063/1.863554 (9 pages) | Cited 13 times

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The structure of the shear Alfvén waves is investigated in a collisional plasma with shear. The fourth‐order equation obtained by combining Ampere’s law and the quasi‐neutrality condition is solved by the method of matched asymptotic expansions for k⊥ ρs≫≪1 to obtain the dispersion relation. A hierarchy of damped, localized modes are found which can have either even or odd parity. The solutions basically have the structure of kinetic Alfvén modes trapped between the two Alfvén cutoffs on either side of the rational surface. The mode damping arises from Ohmic dissipation by electrons near the rational surface. The relation between these modes, microtearing modes, and the Alfvén continuum is discussed.
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52.35.-g Waves, oscillations, and instabilities in plasmas and intense beams

Destabilitization of low mode number Alfvén modes in a tokamak by energetic or alpha particles

K. T. Tsang, D. J. Sigmar, and J. C. Whitson

Phys. Fluids 24, 1508 (1981); http://dx.doi.org/10.1063/1.863555 (9 pages) | Cited 34 times

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With the inclusion of finite Larmor radius effects in the shear Alfvén eigenmode equation, the continuous Alfvén spectrum, which has been extensively discussed in ideal magnetohydrodnamics, is removed. Neutrally stable, discrete radial eignmodes appear in the absence of sources of free energy dand dissipation. Alpha (or energetic) particle toroidal drifts destabilize these modes, provided the particles are faster than the Alfvén speed. Although the electron Landau resonance contributes to damping, a stability study of the parametric variation of the energy and the density scale length of the energetic particles shows that modes with low radial mode numbers remain unstable in most cases. Since the alpha particles are concentrated in the center of the plasma, this drift‐type instability suggests anomalous helium ash diffusion. Indeed, it is shown that stochasticity of alpha orbits due to the overlapping of radially neighboring Alfvén resonances is induced at low amplitudes, eiϕ/Ti≳0.05, implying a diffusion coefficient Drα≳4.4×103 cm2/sec.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Interpretation of the fine structure of electrostatic waves excited in space

R. Pottelette, M. Hamelin, J. M. Illiano, and B. Lembège

Phys. Fluids 24, 1517 (1981); http://dx.doi.org/10.1063/1.863556 (10 pages) | Cited 8 times

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Preliminary results are presented from an active wave experiment performed with a double‐dipole probe aboard the F4 rocket launched during the PORCUPINE campaign. They show that electrostatic cyclotron waves can be excited linearly around the half‐harmonics of the electron gyrofrequency. The most striking fact is that, under certain plasma conditions, the amplitude of waves excited at these peculiar frequencies can be even stronger than those observed at the characteristic resonances of the magnetoplasma. The fine structure of the signals received is also observed and interpreted. Theoretical numerical calculations of the potential created by a dipole antenna in a Maxwellian plasma are presented; good agreement is obtained with the complicated pattern of the various experimental results.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)

Proton beam‐target interaction at pellet fusion power densities

E. Peleg and Z. Zinamon

Phys. Fluids 24, 1527 (1981); http://dx.doi.org/10.1063/1.863567 (5 pages) | Cited 4 times

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The interaction of proton beams at pellet fusion power densities (∼100 TW/cm2) with initially solid targets is calculated. Radiation losses and conduction are shown to have important effects at these power densities.
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52.40.Mj Particle beam interactions in plasmas

Stability of colliding ion beams

E. A. Foote and R. M. Kulsrud

Phys. Fluids 24, 1532 (1981); http://dx.doi.org/10.1063/1.863568 (9 pages) | Cited 13 times

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Conditions are determined for the stability of two identical colliding ion beams in the presence of neutralizing electrons, but no background ions. Such a situation is envisioned for the Counterstreaming Ion Torus. The ion beams are taken to be Maxwellian in their frames of reference. The approximation of decoupled electrostatic and electromagnetic modes is made. The stability of the electrostatic modes depends on the relation between the ion‐electron temperature ratio and the relative beam velocities. The stability of the electromagnetic mode depends on the relation between the ion plasma β and the relative beam velocities.
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52.40.Mj Particle beam interactions in plasmas
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices

Theory of free electron laser instability in a relativistic annular electron beam

Han S. Uhm and R. C. Davidson

Phys. Fluids 24, 1541 (1981); http://dx.doi.org/10.1063/1.863569 (12 pages) | Cited 38 times

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A self‐consistent theory of the free electron laser instability is developed for a hollow electron beam propagating through an undulator (multiple mirror) magnetic field. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations. It is assumed that the beam is thin, with radial thickness much smaller than the mean beam radius, and that ν/γb≪1, where ν is Budker’s parameter and γbmc2 is the characteristic energy of the electron beam. The dispersion relation describing the free electron laser instability in a hollow relativistic electron beam is obtained for an equilibrium distribution function in which all electrons have the same value of transverse energy and the same value of canonical angular momentum, and a Lorentzian distribution in axial momentum. It is shown that the influence of finite radial geometry plays a critical role in determining the detailed stability behavior. Moreover, the growth rate and bandwidth of the instability can be expressed in terms of Budker’s parameter ν, instead of the plasma frequency as in the case of a uniform density beam. Furthermore, it is found that free electron laser stability properties exhibit a sensitive dependence on axial momentum spread.
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42.55.Ah General laser theory

Stability properties of azimuthally symmetric perturbations in an intense electron beam

Han S. Uhm and Martin Lampe

Phys. Fluids 24, 1553 (1981); http://dx.doi.org/10.1063/1.863570 (12 pages) | Cited 19 times

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The Vlasov–Maxwell equations are used to investigate the stability of azimuthally symmetric perturbations (e.g., sausage and hollowing modes) of an electron or ion beam immersed in a resistive plasma. The perturbed space charge and plasma current are treated self‐consistently for any value of the plasma conductivity. A similar analysis of the hose instability is also carried out. It is assumed that ν/γb≪1, where ν is Budker’s parameters and γbmc2 is the characteristic beam electron energy. The analysis is carried out for the ’’loss‐cone’’ distribution function in which all of the beam electrons have the same value of energy (in a frame of reference rotating with angular velocity ωb) and the same value of axial canonical momentum. In the high conductivity regime, the system is shown to be strongly destabilized by a sufficiently large value of the fractional current neutralization.
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52.40.Mj Particle beam interactions in plasmas
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.65.-y Plasma simulation

Anomalous absorption of ordinary electromagnetic waves in magnetized plasmas

A. T. Lin and C. ‐C. Lin

Phys. Fluids 24, 1565 (1981); http://dx.doi.org/10.1063/1.863571 (5 pages) | Cited 4 times

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Ordinary electromagnetic waves can be employed to heat electrons in magnetized plasmas through parametric instabilities if the power level exceeds a certain threshold. Around the electron cyclotron second harmonic frequency band, ordinary waves can decay into upper hybrid waves and other ordinary waves with lower frequency and wavenumber. Depending on the pump wavelength and power, both forward and backward scattering processes can take place. The decay waves ultimately fed energy into electrons through turbulent heating. Only bulk heating has been observed in the simulation.
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52.50.Gj Plasma heating by particle beams
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.25.Os Emission, absorption, and scattering of electromagnetic radiation
52.65.-y Plasma simulation

Stochastic instability induced in toroidal plasma by pulsed radio frequency

Giulio Casati and Enzo Lazzaro

Phys. Fluids 24, 1570 (1981); http://dx.doi.org/10.1063/1.863572 (5 pages) | Cited 4 times

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It is shown that the interaction of pulse modulated radio frequency waves of suitable amplitude, with the population of trapped particles in a tokamak may develop the features of the so‐called stochastic instability, eventually leading to a systematic increase in the energy of the particles and to their detrapping.
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52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Ion cyclotron modes in tokamaks

R. E. Waltz and R. R. Dominguez

Phys. Fluids 24, 1575 (1981); http://dx.doi.org/10.1063/1.863573 (7 pages) | Cited 3 times

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A linear theory of electrostatic ion cyclotron normal modes with moderate wavenumber (k⊥ ρi≲1) which can exist in a sheared magnetic field is given. Such modes have been seen in a scattering experiment on the TFR tokamak. A novel mode with fluid electron behavior is found, and the Drummond and Rosenbluth current‐driven mode with kinetic electron behavior is recovered. Toroidal effects are considered. The kinetic modes offer the most natural explanation for the experimental frequency spectrum. However, numerical solutions of the dispersion relations predict that current drifts three to ten times larger than those in TFR are needed for instability.
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52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
52.25.Gj Fluctuation and chaos phenomena
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