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Dec 1978

Volume 21, Issue 12, pp. 2129-2371

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Small Reynolds number nearly isotropic turbulence in a straight duct and a contraction

J. C. Bennett and S. Corrsin

Phys. Fluids 21, 2129 (1978); http://dx.doi.org/10.1063/1.862168 (12 pages) | Cited 33 times

Online Publication Date: 8 August 2008

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Measurements have been made of nearly isotropic, low Reynolds number, grid‐generated turbulence. The decay results agree with the predictions for ’’final period’’ isotropic turbulence decay (in time) by the linear approximation of von Kármán and Howarth, and Batchelor and Townsend. This agreement occurs in spite of the fact that at the smallest turbulence Reynolds number attained, Rλ≈4, the inertial (triple velocity correlation) term in the double velocity correlation equation is not negligible as assumed in the theoretical estimates. As in experiments of Batchelor and Stewart, the turbulence shows appreciable departure from isotropy, indicated by component energy inequality growth downstream. It is also shown by nonzero velocity skewness, not reported heretofore at small Rλ. Measurement of the effect of a secondary contraction on small Reynolds number turbulence indicates that the contraction has less effect than at larger Reynolds numbers.
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47.27.Gs Isotropic turbulence; homogeneous turbulence

Combined effects of pressure gradient and heating on the stability of freon‐114 boundary layer

A. R. Wazzan, H. Taghavi, W.‐C. Hsu, and Carl Gazley

Phys. Fluids 21, 2141 (1978); http://dx.doi.org/10.1063/1.862169 (7 pages) | Cited 2 times

Online Publication Date: 8 August 2008

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Numerical computations have been made for the laminar boundary‐layer development and stability of a series of similar Falkner–Skan wedge flows in freon‐114 with surface heating. The variation in physical properties (primarily viscosity) of the fluid alters the thickness and velocity profile of the boundary layers and consequently, their stability characteristics. Heating of the surface, with an accompanying reduction of viscosity close to the wall, has the qualitative effect as a more negative (i.e., more favorable) pressure gradient. The effects of various combinations of pressure gradient and heat transfer on the characteristics of these variable‐property laminar boundary layers, on their neutral stability, and on the growth of disturbances by the linear stability theory are described. The minimum critical Reynolds number is presented as a function of pressure gradient, temperature difference, and free‐stream temperature. The latter has an appreciable effect because of the rapid change in the temperature derivative of the viscosity with temperature level.
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47.15.Cb Laminar boundary layers
47.15.Fe Stability of laminar flows
51.20.+d Viscosity, diffusion, and thermal conductivity

Fluctuating flow due to a rotating disk

R. Purushothaman

Phys. Fluids 21, 2148 (1978); http://dx.doi.org/10.1063/1.862170 (6 pages) | Cited 1 time

Online Publication Date: 8 August 2008

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The flow due to super‐imposed torsional oscillations on a rotating disk in a semi‐infinite expanse of viscous fluid is studied for the large and small frequencies separately. Analytical‐numerical solutions are obtained for the oscillatory and time mean flows. Expressions for the skin friction on the disk and the axial flow in the far field are given.
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47.32.Ef Rotating and swirling flows

Transition of the axisymmetric starting plume cap

D. J. Shlien

Phys. Fluids 21, 2154 (1978); http://dx.doi.org/10.1063/1.862171 (5 pages) | Cited 4 times

Online Publication Date: 8 August 2008

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The beginning of a continuous buoyancy (heat) injection into a stationary fluid results in a cap of buoyant fluid followed by a steady plume. This cap undergoes a transition in which a breakup is observed at a height from the source which increases with decreasing buoyancy injection rates. Sequences of cine film frames are presented illustrating this transition. A numerical criterion for the transition was found, namely, that the product of the power injected times the time at which transition occurs is a constant (19 cal). This can be related to an effective Rayleigh or Reynolds number, but the transition mechanism remains unknown. A critical effective Rayleigh number for the thermal may be estimated from these results to be 105 which in this case represents an injected heat of 10 cal.
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44.90.+c Other topics in heat transfer (restricted to new topics in section 44)
47.27.-i Turbulent flows

On inertial motion

Alan J. Faller

Phys. Fluids 21, 2159 (1978); http://dx.doi.org/10.1063/1.862172 (3 pages)

Online Publication Date: 8 August 2008

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For a medium whose motion is described by v+B×v=0, where B is perpendicular to the two‐dimensional velocity v, the trajectory of each element of the medium is a circle that is determined by the initial value of v. Through a transformation of coordinates the differential equation for the (transformed) velocity derivative matrix is U+U2=−I, a special Ricatti equation for which the solution is known. This allows the determination of ∇⋅v, ∇×v, and other functions of the velocity derivatives until the time of formation of a shock.
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47.10.-g General theory in fluid dynamics

Theory of the classical electron gas

Ralph L. Guernsey

Phys. Fluids 21, 2162 (1978); http://dx.doi.org/10.1063/1.862173 (5 pages) | Cited 5 times

Online Publication Date: 8 August 2008

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It is shown that the apparent divergences in the Meeron expansion for the properties of the classical equilibrium electron gas, suggested by Cohen and Murphy, can be resolved by a more careful treatment of the region of small particle separation. Explicit expressions are given for the ϵ4 (lnϵ)2 and ϵ4 lnϵ corrections to the equation of state.
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05.20.-y Classical statistical mechanics

Cylindrical, axisymmetric magnetohydrodynamic turbulence

George Vahala

Phys. Fluids 21, 2167 (1978); http://dx.doi.org/10.1063/1.862174 (7 pages) | Cited 3 times

Online Publication Date: 8 August 2008

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Incompressible magnetohydrodynamic turbulence is considered for an axisymmetric plasma in cylindrical geometry. The equilibrium statistical states to which the plasma evolves are examined by imposing an external constraint of constant toroidal current on the equilibrium Gibbs ensemble. Only the state with maximal magnetic helicity to energy ratio has zero‐mean kinetic energy for intially quiescent systems. There is an upper bound on the toroidal current to toroidal flux ratio below which this unique stable force free state can exist and whose magnetic flux surfaces are basically concentric circles. Above this critical value, the plasma is unstable with islands present in the flux surfaces. This stability result is in sharp contrast with both the results of a linearized δW analysis as well as considering the stability of the linearized spectral coefficient evolution equations for nonforce‐free states.
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52.35.Ra Plasma turbulence
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.30.-q Plasma dynamics and flow

Effect of induced pressure and impulse on cw laser penetration of solids

Ven H. Shui

Phys. Fluids 21, 2174 (1978); http://dx.doi.org/10.1063/1.862175 (5 pages) | Cited 1 time

Online Publication Date: 8 August 2008

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The transient behavior of the cw laser produced melt layer when subjected to an over‐pressure/impulse has been analyzed. Results show that the over‐pressure and impulse required for significant melt removal by individual microsecond laser pulses are very high (≳103 atm and ≳104 dyn sec/cm2, respectively) and melt removal by such pulses is unlikely to be achieved in practice. The quasi‐steady‐state melt removal resulting from long‐duration over‐pressure produced either by single long‐duration pulses (≳100 μsec), by high repetition rate pulses or by the cw laser itself has also been analyzed, with results indicating the possible practical operating regimes for such a mechanism.
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79.20.Ds Laser-beam impact phenomena
FREE

Existence of rarefaction shocks in a laser‐plasma corona

B. Bezzerides, D. W. Forslund, and E. L. Lindman

Phys. Fluids 21, 2179 (1978); http://dx.doi.org/10.1063/1.862176 (7 pages) | Cited 112 times

Online Publication Date: 8 August 2008

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General conditions under which rarefaction shocks can exist in the expanding corona of a plasma heated by a laser are derived. In particular, for the case of a two‐electron temperature isothermal plasma with temperatures Th and Tc, such a shock is shown to occur if Th/Tc≳5+√24. The case of rarefaction shocks induced by the ponderomotive force is also briefly discussed.
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52.35.Tc Shock waves and discontinuities
52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
52.25.Kn Thermodynamics of plasmas

Quantum plasmas I: The convergence formalism

Roger D. Jones

Phys. Fluids 21, 2186 (1978); http://dx.doi.org/10.1063/1.862177 (5 pages) | Cited 2 times

Online Publication Date: 8 August 2008

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It is shown from first principles, using the formalism of Wigner distributions, that the divergences in the plasma kinetic equation due to the long range nature of the Coulomb interaction can be eliminated even if the plasma is rapidly varying, inhomogeneous, and immersed in external fields. This is due to the fact that for plasmas which have a screening length much larger than either the electron thermal wavelength or the classical distance of closest approach there is a large region in impact parameter space in which collision terms based on binary collisions and collision terms based on small momentum transfer give the same result.
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52.25.Dg Plasma kinetic equations

Quantum plasmas. II: The high frequency conductivity of a magnetized plasma

Roger D. Jones

Phys. Fluids 21, 2191 (1978); http://dx.doi.org/10.1063/1.862178 (4 pages) | Cited 1 time

Online Publication Date: 8 August 2008

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The high frequency conductivity of a magnetoplasma is calculated from a fully convergent quantum mechanical kinetic equation. The frequency of the perturbing field is not restricted to frequencies low in comparison with the plasma frequency nor is the temperature of the unperturbed plasma restricted to values low in comparison with a Rydberg.
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52.25.Fi Transport properties
52.25.Dg Plasma kinetic equations

Boundary value problems for three‐dimensional plasmas

Ralph L. Guernsey

Phys. Fluids 21, 2195 (1978); http://dx.doi.org/10.1063/1.862155 (7 pages) | Cited 1 time

Online Publication Date: 8 August 2008

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The full three‐dimensional Maxwell–Vlasov system is solved as a boundary value problem for systems contained by plane, perfectly reflecting boundaries. The spatial behavior of the fields seems to contradict some commonly made assumptions. In particular, for low frequency, ω≪ωp, and typical plasma densities, all components of the electric and magnetic fields decay to zero on a scale which is no larger and 0.05 cm.
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52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.25.Mq Dielectric properties

Kinetic theory of neutral hydrogen atoms in a bounded hydrogen plasma slab

Keith H. Burrell

Phys. Fluids 21, 2202 (1978); http://dx.doi.org/10.1063/1.862156 (6 pages) | Cited 13 times

Online Publication Date: 8 August 2008

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The transport of neutral hydrogen atoms in a hydrogen plasma slab is considered. After making a reasonable approximation for the charge exchange rate, analytic solutions for the neutral distribution function are obtained which depend on one spatial and three velocity variables. To obtain these, a condition must be imposed that implies uniform electron and ion temperatures. Specular reflection of the neutrals at the boundaries is considered. Solutions associated with the diffusion approximation are also given and the condition for its validity is discussed. The solutions are evaluated for the case of Maxwellian ion distribution functions.
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52.25.Fi Transport properties
52.25.Dg Plasma kinetic equations

Ion fluctuations and velocity distribution in the presence of ion cyclotron waves

H. Böhmer, S. Fornaca, N. Rynn, and M. Wickham

Phys. Fluids 21, 2208 (1978); http://dx.doi.org/10.1063/1.862157 (3 pages) | Cited 14 times

Online Publication Date: 8 August 2008

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Ion density fluctuations and the ion velocity distribution function in the presence of the current‐driven electrostatic ion cyclotron instability are determined using resonance fluorescence of the ions. The optical line intensity modulation shows that the ion density modulation can be as large as 90%. From the Doppler broadening of the lines it is found that the distribution function of ions heated by the unstable ion cyclotron waves is Maxwellian with an uncertainty of 5%.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.50.Gj Plasma heating by particle beams
52.25.Gj Fluctuation and chaos phenomena
52.25.Os Emission, absorption, and scattering of electromagnetic radiation

Reflection and absorption of ion‐acoustic waves in a density gradient

Osamu Ishihara, Igor Alexeff, H. J. Doucet, and W. D. Jones

Phys. Fluids 21, 2211 (1978); http://dx.doi.org/10.1063/1.862158 (7 pages) | Cited 24 times

Online Publication Date: 8 August 2008

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One problem with ion‐acoustic waves is that sometimes they are observed to be reflected from discharge tube walls, and sometimes to be absorbed. Theoretical computation reveals that a velocity gradient produced by a density gradient plays a significant role in the reflection. The velocity gradient produces a subsonic−supersonic transition and long wavelength waves are reflected before reaching the transition while short wavelength waves penetrate over the transition and are absorbed in the supersonic flow plasma.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Nonlinear saturation of the dissipative trapped electron instability

Stefano Migliuolo and Albert Simon

Phys. Fluids 21, 2218 (1978); http://dx.doi.org/10.1063/1.862159 (8 pages) | Cited 5 times

Online Publication Date: 8 August 2008

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The nonlinear saturation amplitude of the dissipative trapped electron instability is calculated. Comparison is made with an experiment carried out in linear mirror geometry and near threshold, with only a single mode predominating. A model in which the untrapped electrons respond in a Boltzmann fashion yields good agreement. A model in which Landau damping is included predicts saturation amplitudes much smaller than observed. The first model seems appropriate for linear geometries while the second may apply to closed devices.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Jd Magnetic mirrors, gas dynamic traps

Bernstein waves, parametric instabilities, and magnetic shear

J. L. Sperling

Phys. Fluids 21, 2226 (1978); http://dx.doi.org/10.1063/1.862160 (4 pages) | Cited 2 times

Online Publication Date: 8 August 2008

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The effect of magnetic shear on electrostatic Bernstein waves is investigated. It is shown that shear leads to nonlocal eigensolutions and the convective damping of the Bernstein waves. The threshold for the parametric instability of a magnetosonic wave into two Bernstein waves in a multispecies plasma is increased by shear. For a magnetosonic heating experiment conducted on a tokamak comparable to the Doublet III device at General Atomic, the parametric instability may still be excited despite the plasma inhomogeneities provided the pump wave amplitude exceeds a critical value to be estimated in this paper.
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52.35.Dm Sound waves
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Stochastic acceleration by an obliquely propagating wave‐An example of overlapping resonances

Gary R. Smith and Allan N. Kaufman

Phys. Fluids 21, 2230 (1978); http://dx.doi.org/10.1063/1.862161 (12 pages) | Cited 73 times

Online Publication Date: 8 August 2008

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A simple problem exhibiting intrinsic stochasticity is treated: the motion of a charged particle in a uniform magnetic field and a single plane wave. Detailed studies of this wave‐particle interaction show the following features. An electrostatic wave propagating obliquely to the magnetic field causes stochastic motion if the wave amplitude exceeds a certain threshold. The overlap of cyclotron resonances then destroys a constant of the motion, allowing appreciable momentum transfer to the particles. A wave of large enough amplitude would thus suffer severe damping and lead to rapid heating of a particle distribution. The stochastic motion resembles a diffusion process even though the wave spectrum is monochromatic. The methods of this paper should be useful for other problems showing stochasticity such as superadiabaticity in mirror machines, destruction of magnetic surfaces in toroidal systems, and lower hybrid heating.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)

Experiment on sideband dispersion

T. P. Starke and J. H. Malmberg

Phys. Fluids 21, 2242 (1978); http://dx.doi.org/10.1063/1.862162 (11 pages) | Cited 4 times

Online Publication Date: 8 August 2008

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The dispersion of the sidebands of a large amplitude plasma wave has been measured. Sidebands propagate according to a beam‐plasma type dispersion. Sideband dispersion is calculated with a quasi‐linear theory using the locally measured time‐averaged electron velocity distribution. This model assumes that the large wave and the sidebands interact primarily through the time average of the perturbation the large wave causes in the velocity distribution. The measured sideband dispersion agrees with the predictions of this model.
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52.35.-g Waves, oscillations, and instabilities in plasmas and intense beams

Phase‐locked particle motion in a large‐amplitude plasma wave

Gary R. Smith and N. R. Pereira

Phys. Fluids 21, 2253 (1978); http://dx.doi.org/10.1063/1.862163 (10 pages) | Cited 24 times

Online Publication Date: 8 August 2008

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A plasma wave with an oscillating amplitude and phase occurs in two commonly studied situations, the beam‐plasma interaction and the launching of a large‐amplitude wave in a Maxwellian plasma. Electron motion in such a wave is either regular or stochastic. Theoretical study shows that regular motion can exhibit a phase‐locking effect, which explains the persistence of amplitude oscillations observed in simulations and experiments. An additional (’’test’’) wave of moderate amplitude can prevent phase‐locking, causing stochastic motion instead, and thereby destroy the amplitude oscillations. The effects studied are also relevant to the theory of sideband instability.
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52.35.-g Waves, oscillations, and instabilities in plasmas and intense beams
52.40.Mj Particle beam interactions in plasmas

Ergodic behavior of lower hybrid decay wave ray trajectories in toroidal geometry

Jean‐Marie Wersinger, Edward Ott, and John M. Finn

Phys. Fluids 21, 2263 (1978); http://dx.doi.org/10.1063/1.862164 (5 pages) | Cited 32 times

Online Publication Date: 8 August 2008

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In cylindrical geometry, as a result of both magnetic shear and density gradient there exist radially trapped lower hybrid decay waves bouncing back and forth in the low density region of the plasma. If this situation persists in toroidal geometry, it could have a severely destabilizing effect on the nonresonant parametric decay of an externally launched lower hybrid heating wave. However, it is shown here that weak toroidicity causes some of these waves to follow ergodic ray trajectories, and hence to be detrapped and to reach their lower hybrid resonance. The fraction of waves which shows ergodic behavior increases as the aspect ratio R0/a decreases. For realistic aspect ratios, i.e., R0/a≲5, nearly all the rays are ergodic and energy flows toward the resonance. The consequences for lower hybrid wave heating are discussed.
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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.Gj Plasma heating by particle beams

Universal drift instability from single‐particle approach

V. S. Chan and Seung Kai Wong

Phys. Fluids 21, 2268 (1978); http://dx.doi.org/10.1063/1.862165 (3 pages)

Online Publication Date: 8 August 2008

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An exact evaluation of the universal drift instability growth rate in a magnetic field with zero shear is presented. It is based on an asymptotic expansion of the energy equation for large time, in which the change in the kinetic energy of the plasma due to interaction with the wave is obtained from a single particle approach.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Kt Drift waves

Time evolution of mass flows in a collisional tokamak

Adil B. Hassam and Russell M. Kulsrud

Phys. Fluids 21, 2271 (1978); http://dx.doi.org/10.1063/1.862166 (9 pages) | Cited 72 times

Online Publication Date: 8 August 2008

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The time evolution, due to dissipative processes, of an initial pattern of poloidal and toroidal mass flows in a tokamak is considered. The calculation is applicable to a collisional, low β, axisymmetric tokamak of arbitrary minor cross section. Time rates of change of poloidal flows which are subsonic but larger than the diamagnetic speed are given according to the magnitude of the flow and the collisionality of the plasma. Over most of parameter space for typical tokamaks, the poloidal rotation is strongly damped by magnetic pumping at the rate (l/qR)2νii, where l is the mean free path, qR is the ’’connection length,’’ and νii is the ion‐ion collision frequency. At higher speeds, even stronger damping is effected by electron thermal conduction. The toroidal rotation is determined largely by the conservation of toroidal angular momentum. A heuristic explanation of the damping due to magnetic pumping is given.
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52.30.-q Plasma dynamics and flow
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices

Analytic, high β, flux conserving equilibria for cylindrical tokamaks

D. J. Sigmar and George Vahala

Phys. Fluids 21, 2280 (1978); http://dx.doi.org/10.1063/1.862167 (7 pages) | Cited 4 times

Online Publication Date: 8 August 2008

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Using Grad’s theory of generalized differential equations, the temporal evolution from low to high β due to ’’adiabatic’’ and nonadiabatic (i.e., neutral beam injection) heating of a cylindrical tokamak plasma with circular cross section and peaked current profiles is calculated analytically. The influence of shaping the initial safety factor profile and the beam deposition profile and the effect of minor radius compression on the equilibrium is analyzed.
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52.50.Gj Plasma heating by particle beams
52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
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

l=1,2 high‐beta stellarator

R. R. Bartsch, E. L. Cantrell, R. F. Gribble, K. A. Klare, K. J. Kutac, G. Miller, and R. E. Siemon

Phys. Fluids 21, 2287 (1978); http://dx.doi.org/10.1063/1.862179 (8 pages) | Cited 4 times

Online Publication Date: 8 August 2008

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The final scyllac experiments are described. These experiments utilized a feedback‐stabilized, l=1,2 high‐beta stellarator configuration and like the previous feedback‐stabilization experiments were carried out in a toroidal sector, rather than a complete torus. The energy confinement time, obtained from excluded flux measurements, agrees with a two‐dimensional calculation of particle end loss from a straight theta pinch. Because simple end loss was dominant, the energy confinement time was independent of whether equilibrium adjustment or feedback stabilization fields were applied. The dynamical characteristics of the toroidal equilibrium were improved by elimination of the l=0 field used previously, as expected from theory. A modal rather than local feedback control algorithm was used. Although feedback clearly decreased the m=1 motion of the plasma, the experimental test of modal feedback, which is expected from theory to be superior to local feedback, is considered inconclusive because of the limitations imposed by the sector configuration.
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52.55.Fa Tokamaks, spherical tokamaks
52.55.Hc Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices
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