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Feb 1988

Volume 31, Issue 2, pp. 225-421

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The onset of plume dynamics in the spectral space

Alain P. Vincent and David A. Yuen

Phys. Fluids 31, 225 (1988); http://dx.doi.org/10.1063/1.866850 (3 pages) | Cited 1 time

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Time‐dependent convection for infinite Prandtl number fluids has been investigated hitherto in the physical domain. Dynamics of plumelike structures resulting from boundary‐layer instabilities can be interpreted in the spectral domain as having both direct and inverse cascades of energy taking place. In the physical domain only a small part of the spectrum is discernible. But the rest of the spectrum is needed for properly describing the nonlinear process. Only a relatively few modes, fewer than ten, are actually required for describing the essential features associated with the onset of plume dynamics.
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47.27.T- Turbulent transport processes
47.27.N- Wall-bounded shear flow turbulence
91.45.Dh Plate tectonics
FREE

Contact line stability at edges: Comments on Gibbs’s inequalities

D. C. Dyson

Phys. Fluids 31, 229 (1988); http://dx.doi.org/10.1063/1.866851 (4 pages) | Cited 6 times

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In his discussion of contact line equilibrium for a system comprising two liquids and a solid, Gibbs [Scientific Papers (Dover, New York, 1961), Vol. 1, p. 326] used an argument that resulted in two inequalities he claimed to be applicable when the three‐phase contact line coincides with an edge on the solid surface. A simple counterexample is given that shows Gibbs’s inequalities lack universal applicability. A serious objection to Gibbs’s argument is noted and his discussion is altered to remove the objectionable feature. This leads to modified inequalities, which surprisingly are known and have been attributed to Gibbs by recent authors.
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64.10.+h General theory of equations of state and phase equilibria
47.10.-g General theory in fluid dynamics
68.08.Bc Wetting
68.03.Cd Surface tension and related phenomena

The drag coefficient for a spherical bubble in a uniform streaming flow

I. S. Kang and L. G. Leal

Phys. Fluids 31, 233 (1988); http://dx.doi.org/10.1063/1.866852 (5 pages) | Cited 21 times

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The drag coefficient CD=48/R for a spherical bubble in a uniform streaming flow at high Reynolds number, which was first obtained via a dissipation method by Levich [Zh. Eksp. Teor. Fiz. 19, 18 (1949)], is rederived here by direct integration of the normal stress over the bubble surface. The present study also shows that the drag coefficient up to O(R−1) depends only on the O(1) vorticity distribution right on the bubble surface, and is independent of the vorticity distribution in the fluid. Therefore the drag coefficient up to O(R−1) is completely determined by the irrotational flow solution, which is perfectly consistent with the dissipation method.
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47.55.Kf Particle-laden flows
47.15.Cb Laminar boundary layers

Perturbed motions of a bubble rising in a vertical tube

R. M. Fearn

Phys. Fluids 31, 238 (1988); http://dx.doi.org/10.1063/1.866853 (4 pages) | Cited 4 times

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Experiments are reported in which long air bubbles rising in liquid‐filled vertical tubes were perturbed by coaxial wires. Distinctly different flow regimes were found to arise as the thickness of the wire was varied. The breaking of axial symmetry observed in the experiments is discussed in the light of ideas from bifurcation theory.
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47.55.Kf Particle-laden flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Nonlinear unstable viscous fingers in Hele–Shaw flows. I. Experiments

Anne R. Kopf‐Sill and G. M. Homsy

Phys. Fluids 31, 242 (1988); http://dx.doi.org/10.1063/1.866854 (8 pages) | Cited 12 times

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Post‐instability viscous fingering in rectilinear flow in a Hele–Shaw cell has been studied experimentally. Of particular interest was the characterization of the range of length scales associated with tip splitting, over a reasonably wide range of parameters. A digital imaging system was used to record the patterns as a function of time, which allowed properties such as the tip velocity, finger width, perimeter, and area to be studied as functions of time and capillary number. The tip velocity was observed to be approximately constant regardless of the occurrence of splitting events, and the average finger width decreased as the degree of supercriticality increased. Quantitative measures of the fact that there is a limit to the complexity of viscous fingers are provided, and that over the range of parameters studied, no evidence for fractal fingering exists. A discussion of the dynamics of tip splitting explains why this is so.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.56.+r Flows through porous media

Experimental test of the perturbation expansion for the Taylor instability at various wavenumbers

Richard M. Heinrichs, David S. Cannell, Guenter Ahlers, and Michael Jefferson

Phys. Fluids 31, 250 (1988); http://dx.doi.org/10.1063/1.866855 (6 pages) | Cited 18 times

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Measurements of the Fourier components of the axial variation of the velocity component w in a Taylor–Couette apparatus containing ten pairs of vortices at various average wavenumbers q, as a function of ϵ≡R/Rc−1, are reported. For all values of q studied, excellent agreement with the perturbation expansion of Davey [J. Fluid Mech. 14, 336 (1962)] for the amplitudes of the Fourier components was obtained, provided the power law dependence on ϵ was taken as a function of ϵ≡ϵ−ϵm(q). Here ϵm(q) is the marginal stability curve, below which the laminar flow state is stable against perturbations of wavenumber q. The wavenumber dependence of the leading coefficients in the expansions for the fundamental and first harmonic was also measured, and it was found that while the coefficient for the fundamental was independent of q, the coefficient for the first harmonic monotonically decreased with increasing q, over the range studied.
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47.20.-k Flow instabilities
47.35.-i Hydrodynamic waves
47.15.G- Low-Reynolds-number (creeping) flows

A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment

Gregory J. Hartke, V. M. Canuto, and William P. Dannevik

Phys. Fluids 31, 256 (1988); http://dx.doi.org/10.1063/1.866856 (7 pages) | Cited 2 times

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Recently published experimental results [Int. J. Heat Mass Transfer, 23, 738 (1980)] on thermally driven high Rayleigh number turbulent convection have shown that the N∝R2/7 relation (where N is the Nusselt number and R is the Rayleigh number), which is valid up to R≊5×108, is superceded at this point by the relation N=AσR1/3 that holds at least up to R≊1011. For water (Prandtl number σ=6.6), the experimental value for Aσ was found to be Aσ=0.0556±0.001. In the present work, the equations for a turbulent fluid driven by thermal convection are solved using the two‐point closure prescription of the direct interaction approximation. The theoretical N vs R relation at high R is found to be of the form N=AσR1/3 and for σ=6.6, and the predicted value of the coefficient Aσ is computed to be Aσ≲0.08, in good agreement with the experimental value. Extension of the model to situations other than convection is discussed.
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47.27.-i Turbulent flows
44.25.+f Natural convection

Analysis and computer simulation of confined ring vortices driven by falling sprays

K. D. Marx

Phys. Fluids 31, 263 (1988); http://dx.doi.org/10.1063/1.866857 (15 pages)

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When a liquid spray is injected into the upper region of a closed container, it will entrain air as it falls to the bottom under the influence of gravity. In some cases, the resulting flow field assumes the form of one or more large ring vortices. In this paper, the droplet drag mechanism by which this systematic motion is sustained in steady state is studied theoretically and numerically. It is shown that the structure of the airflow is approximately that of a solution to the inviscid fluid equations. The airflow velocity is determined by the equilibrium of energy exchanged between the air and the spray in different regions of the flow. A simple formula for estimating the order of magnitude of the flow velocity is derived. Numerical calculations that solve for the coupled flow of the gas and the interacting spray are presented for cases of practical interest. The effect of varying the droplet diameter distribution and the mass flow rate of the spray is investigated.
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47.55.Kf Particle-laden flows
47.32.Ef Rotating and swirling flows

A covariant formalism for wave propagation applied to stimulated Raman scattering

C. J. McKinstrie and D. F. DuBois

Phys. Fluids 31, 278 (1988); http://dx.doi.org/10.1063/1.866858 (10 pages) | Cited 18 times

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The governing equations for stimulated Raman scattering are derived in a Lorentz frame moving with arbitrary velocity relative to the background plasma. These equations are fundamental to the study of relativistic beat‐wave solitary waves, which have recently been proposed for particle acceleration by Mima et al. [Phys. Rev. Lett. 57, 1421 (1986)]. An averaged Lagrangian density is constructed for this three‐wave interaction. This results in a natural definition for the action flux density four‐vector of each wave and the combined stress–energy tensor. It also follows from the Lagrangian structure of the system that the Manley–Rowe relations are satisfied. The covariant formalism presented here can also be used to study wave propagation in a multicomponent plasma, in which each plasma species moves with arbitrary velocity relative to the frame of observation. As a specific example, the dispersion relation for Langmuir‐wave propagation in two warm relativistic electron beams is derived for the first time.
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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.Sb Solitons; BGK modes
52.75.Di Ion and plasma propulsion
52.59.Px Hard X-ray sources

Relativistic solitary‐wave solutions of the beat‐wave equations

C. J. McKinstrie

Phys. Fluids 31, 288 (1988); http://dx.doi.org/10.1063/1.866859 (10 pages) | Cited 5 times

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In the beat‐wave accelerator [Phys. Rev. Lett. 43, 267 (1979)], a large‐amplitude Langmuir wave is produced by the beating of two laser beams whose frequencies differ by approximately the plasma frequency. The relativistic equations governing this three‐wave interaction are shown to admit two types of solitary‐wave solutions. Temporal solitary waves propagate at speeds greater than the speed of light and carry no information. Spatial solitary waves propagate at speeds less than the speed of light and do carry information. Analytic expressions are obtained for the envelopes of these waves and for the relationship between their speed and maximum amplitude. For the limit in which the propagation speed of the solitary wave is equal to the speed of light, there is no distinction between a temporal solitary wave and a spatial solitary wave. However, it can be shown that the solitary wave is unstable in this limit. The potential of the spatial solitary waves for particle acceleration [Phys. Rev. Lett. 57, 1421 (1986)] is studied. Although the spatial solitary waves are capable of accelerating particles to high energy, for typical beat‐wave parameters the laser–plasma coupling efficiency is too low for this scheme to be practical.
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52.75.Di Ion and plasma propulsion
52.35.Sb Solitons; BGK modes
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Linear mode conversion and the operator theory of wave mechanics

R. O. Dendy

Phys. Fluids 31, 298 (1988); http://dx.doi.org/10.1063/1.866860 (4 pages) | Cited 2 times

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The linear mode conversion regime for the approximate dispersion relation [ω−ω1(x,k)][ω−ω2(x,k)]=η occurs near x=xc, k=kc such that ω1(xc,kc)=ω2(xc, kc). Cairns and Lashmore‐Davies [Phys. Fluids 25, 1605 (1982); 26, 1268 (1983)] have recently expressed the associated energy flow in terms of a single parameter that involves η and the partial derivatives of ω1 and ω2. In this paper, a different, wave‐mechanical approach is used to obtain the same result. The process of linear mode conversion is discussed using the system mathΨ=i ∂Ψ/∂t, where math is a Hermitian operator. The degeneracy of plasma modes, and their coupling by warm plasma corrections in an inhomogeneous plasma, is dealt with using first‐order perturbation theory. Simple coupled first‐order differential equations for the wave amplitudes follow, which can be integrated directly. The calculated energy flow reproduces the expression that is obtained from the theory of Cairns and Lashmore‐Davies.
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52.25.Mq Dielectric properties
52.35.Tc Shock waves and discontinuities
41.20.Jb Electromagnetic wave propagation; radiowave propagation

Nonlinear evolution of longitudinal plasma waves

Young‐ping Pao

Phys. Fluids 31, 302 (1988); http://dx.doi.org/10.1063/1.866861 (9 pages) | Cited 4 times

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Long‐time nonlinear behavior of single‐mode longitudinal plasma waves is studied on the basis of the Vlasov equation with Fokker–Planck collision terms. The resonant layer, trapped island, collisional sublayers, and X‐point neighborhoods are analyzed. A nonlinear evolution equation is obtained and the wave‐generated current is also evaluated.
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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.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.50.Gj Plasma heating by particle beams

Ensemble‐mean modeling of two‐equation type in magnetohydrodynamic turbulent shear flows

Akira Yoshizawa

Phys. Fluids 31, 311 (1988); http://dx.doi.org/10.1063/1.866862 (7 pages) | Cited 8 times

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Ensemble‐mean two‐equation modeling is studied in magnetohydrodynamic turbulent shear flows. This model consists of a system of equations governing the mean velocity, the mean magnetic field, the total turbulent energy (the sum of turbulent kinetic and magnetic energy), and its dissipation rate. The turbulence effect in the Navier–Stokes equation is written in the form of an eddy‐viscosity representation, whereas the counterpart in the mean magnetic induction equation is expressed in the combination of alpha dynamo terms and an eddy‐magnetic diffusivity representation. The implication of the present model in reversed‐field pinches of plasma in controlled nuclear fusion is also discussed.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.27.T- Turbulent transport processes
52.30.-q Plasma dynamics and flow

Magnetohydrodynamic equations for systems with large Larmor radius

A. B. Hassam and J. D. Huba

Phys. Fluids 31, 318 (1988); http://dx.doi.org/10.1063/1.866863 (8 pages) | Cited 37 times

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A set of one‐fluid, modified magnetohydrodynamic (MHD) equations is developed that describes magnetized plasmas for which the relevant scale lengths are intermediate between the electron and ion Larmor radii, and the relevant time scales are intermediate between the electron and ion cyclotron frequencies. It is shown that the momentum equation is the same as that of conventional MHD but that the evolution of the magnetic field is strongly affected. The implications of the modified MHD system on the ‘‘frozen‐in’’ theorem, magnetosonic waves, Alfvén waves, and the interchange instability are examined.
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52.30.-q Plasma dynamics and flow
52.20.Dq Particle orbits

Modon formation in the nonlinear development of the collisional drift wave instability

Mitsuo Kono and Eiichi Miyashita

Phys. Fluids 31, 326 (1988); http://dx.doi.org/10.1063/1.866864 (6 pages) | Cited 36 times

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Nonlinear evolution of the collisional drift wave instability has been investigated by means of numerical simulations based on a model equation derived from a two‐fluid approximation. This approximation is reduced to the Hasegawa–Mima equation when the collision and viscosity are neglected. A crucial feature is that coherent structures are formed from a turbulent state. A scenario for a path to the self‐organized motion through the turbulent motion has been found as follows. The initial exponential growth of a linear instability is followed by a parametric instability that excites many modes. At the same time, the wave breaks up into small vortices. The inverse cascade of the wave energy then sets in and small vortices fuse into larger ones. A large modon is formed at the final stage of evolution.
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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.Kt Drift waves

Energetic particle stabilization of ballooning modes in finite‐aspect‐ratio tokamaks

X.‐H. Wang, A. Bhattacharjee, M. E. Mauel, and J. W. Van Dam

Phys. Fluids 31, 332 (1988); http://dx.doi.org/10.1063/1.866865 (8 pages) | Cited 4 times

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The theory of energetic particle stabilization of ballooning modes in tokamaks is revisited. When the energetic particles are drift‐reversed, a region of ballooning instability, akin to that which causes the Van Dam–Lee–Nelson limit [in Proceedings of the Workshop on EBT Ring Physics (Oak Ridge National Laboratory, Oak Ridge, TN, 1980), p. 471; Phys. Fluids 23, 1850 (1980)] in magnetic mirrors, is identified. At higher values of core poloidal beta a ‘‘third’’ region of stability is conjectured to occur. The inclusion of finite‐aspect‐ratio effects can eliminate ballooning instability completely when the energetic particles are non‐drift‐reversed, but the region of instability for drift‐reversed particles persists. Requirements for energetic particle stabilization in large‐ and small‐aspect‐ratio tokamak experiments and reactors 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.)
52.55.Fa Tokamaks, spherical tokamaks

Ponderomotive stabilization of external kink modes in tokamaks

D. A. D’Ippolito

Phys. Fluids 31, 340 (1988); http://dx.doi.org/10.1063/1.866866 (7 pages) | Cited 8 times

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It is shown that external kink modes in tokamaks can be stabilized by applied radio frequency (rf) waves in the ion cyclotron range of frequencies. This stabilization results from the work done by the plasma against the ponderomotive force exerted by the rf field. For a strongly evanescent surface field (such as the near field of an ion Bernstein wave coupler), the ponderomotive layer is confined to the vicinity of the plasma surface and, if sufficiently strong, influences kink stability in the same way as a close‐fitting conducting wall. This effect is illustrated by deriving an analytic condition for stabilizing a single (m,n) mode in the low‐beta straight tokamak model by means of a cylindrically symmetric E∥ rf field. The effects of poloidally or toroidally nonuniform rf fields are examined in a two‐mode coupling perturbation analysis. This stabilization mechanism may be useful in extending the beta limit of ion‐Bernstein‐wave‐heated tokamaks against both ideal and resistive modes.
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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.Fa Tokamaks, spherical tokamaks

Tokamak m=1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations

L. A. Charlton, B. A. Carreras, J. A. Holmes, and V. E. Lynch

Phys. Fluids 31, 347 (1988); http://dx.doi.org/10.1063/1.866867 (12 pages) | Cited 12 times

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The linear stability and nonlinear evolution of the resistive m=1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Fa Tokamaks, spherical tokamaks

A fully toroidal fluid analysis of the magnetohydrodynamic ballooning mode branch in tokamaks

P. Andersson and J. Weiland

Phys. Fluids 31, 359 (1988); http://dx.doi.org/10.1063/1.866868 (7 pages) | Cited 57 times

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A comparatively complete two fluid description of collisionless electromagnetic ballooning modes has been derived. Using an unexpanded ion density response, it has been shown for the first time using a fluid theory that a necessary and sufficient condition for an instability of the magnetohydrodynamic (MHD) branch below the MHD beta limit is the presence of an ion temperature gradient exceeding a threshold. The cause of this instability has been identified and an analytical dispersion relation is given.
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52.55.Fa Tokamaks, spherical tokamaks
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Averaged cold plasma equations for ion cyclotron waves in stellarators

K. S. Riedel

Phys. Fluids 31, 366 (1988); http://dx.doi.org/10.1063/1.866869 (6 pages)

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When the toroidally varying component of a stellarator equilibrium is much smaller (larger) than the helically varying component, the cold plasma equations can be averaged over the helical (toroidal) angle to yield a two‐dimensional description of ion cyclotron wave propagation. Higher order corrections may be computed iteratively; at each step only a two‐dimensional operator need be inverted. Since the cold plasma equations have a singularity at the cyclotron resonance, a special coordinate system is introduced that exactly represents the resonance surface.
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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

Raman backscattering and forward scattering thresholds in parabolic density profiles

Kent Estabrook, W. L. Kruer, and E. A. Williams

Phys. Fluids 31, 372 (1988); http://dx.doi.org/10.1063/1.866870 (3 pages) | Cited 12 times

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The growth of stimulated Raman backscattering (RBS) and forward scattering (RFS), as a function of density and temperature in a parabolic density profile, is examined and simulation results are compared to analytic theory. This work is relevant to the burnthrough foil experiments, in which Raman scattering is explored in spatial scale lengths long enough to be relevant to high gain targets.
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52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
52.38.Bv Rayleigh scattering; stimulated Brillouin and Raman scattering
52.38.-r Laser-plasma interactions

The effect of the time‐dependent self‐consistent electrostatic field on gyrotron operation

Robert G. Kleva, Thomas M. Antonsen, and Baruch Levush

Phys. Fluids 31, 375 (1988); http://dx.doi.org/10.1063/1.866871 (12 pages) | Cited 12 times

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The time‐dependent self‐consistent electrostatic field is shown to have a deleterious effect on gyrotron operation. As the electron beam density increases, the nonlinear efficiency is degraded seriously by the self‐electrostatic field. Time‐dependent multimode simulations demonstrate that at sufficiently large beam densities the electron cyclotron instability is quenched and the oscillation will not start. Contrary to previous investigations, electrostatic effects do not necessarily increase the linear growth rate of the electromagnetic cavity mode and, depending on the beam density, electrostatic effects can actually stabilize the mode. Typically, however, considerations of linear theory are not important in an overmoded, open resonator gyrotron because the system evolves nonlinearly into a state consisting of a single mode which is linearly stable, but nonlinearly the most efficient mode.
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84.40.Fe Microwave tubes (e.g., klystrons, magnetrons, traveling-wave, backward-wave tubes, etc.)

Three‐dimensional simulation of the Raman free‐electron laser

A. K. Ganguly and H. P. Freund

Phys. Fluids 31, 387 (1988); http://dx.doi.org/10.1063/1.866819 (7 pages) | Cited 11 times

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The nonlinear evolution of the free‐electron laser amplifier is investigated numerically in the collective Raman regime for a configuration in which a relativistic electron beam propagates through a loss‐free cylindrical waveguide in the presence of a helical wiggler and an axial guide magnetic field. A set of coupled nonlinear differential equations is derived that governs the evolution of the TE waveguide modes, the beam space‐charge mode, and the trajectories of an ensemble of electrons. Comparison with experiment shows good agreement for cases in which the intersection between the vacuum waveguide mode and the beam resonance line are near ‘‘grazing’’ (i.e., when the intersections are sufficiently close together to result in one broad gain bandwidth). For interactions in which two distinct gain bands occur, the numerical procedure tends to underestimate the beam–plasma frequency and results in a 15%–20% discrepancy with experiment.
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41.60.Cr Free-electron lasers
42.60.Da Resonators, cavities, amplifiers, arrays, and rings
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.65.-y Plasma simulation

Ion front and ablation in a freely expanding two‐ion, two‐temperature, noncollisional plasma

M. K. Srivastava, B. K. Sinha, and S. V. Lawande

Phys. Fluids 31, 394 (1988); http://dx.doi.org/10.1063/1.866820 (16 pages) | Cited 7 times

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The equations for the free expansion of a two‐ion, two‐temperature, noncollisional, isothermal, and quasineutral plasma are derived and solved using a self‐similar technique. The hydrodynamic variables are determined by four independent parameters, viz., α, the relative charge to mass ratio of the two ions; N10, the initial concentration of the main ion; τ, the temperature ratio of the hot and cold electrons; and ρ, the initial concentration ratio of the cold and hot electrons. The formation of an ion front in the numerically dominant species is predicted for the first time even under the quasineutral and isothermal assumptions. A necessary condition for the breakdown of the self‐similar solution is derived. The location of the ion front and the point where the solution breaks down are tabulated as a function of the four parameters and the results are discussed. The expression for the normalized ion current, taking into account the flux limitation under the free‐streaming limit, is derived. The expressions for the mass, momentum, and energy ablation are also derived and the relevant data are discussed with reference to laser–plasma interaction.
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52.30.-q Plasma dynamics and flow

Detailed measurements of anisotropic mirror plasma ion energy distributions during drift cyclotron loss‐cone instability

J. H. Booske, M. J. McCarrick, R. F. Ellis, and J. A. Paquette

Phys. Fluids 31, 410 (1988); http://dx.doi.org/10.1063/1.866821 (8 pages) | Cited 2 times

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Using improved computer filtering and a reconstruction analysis we have been able to extract additional details on a mirror plasma’s midplane ion energy distribution from the current–voltage (I–V) curve of a voltage‐swept electrostatic end loss analyzer (ELA). For the University of Maryland’s MIX‐1 plasma [Phys. Fluids 23, 3439 (1976)], the diagnostic technique has provided us with important information on the ‘‘loss‐cone region’’ of an anisotropic ion distribution during drift cyclotron loss‐cone (DCLC) instability experiments. Observations include convincing verification of ion distribution modification during DCLC evolution and an enhancement of the loss‐region boundary over that predicted by simplified trapping theory. The reconstruction analysis involves matching the differentiated I–V curves (i.e., dI/dV vs V) to theoretically predicted curves based on model midplane ion distribution functions. The theoretical curves are obtained from the model midplane distributions by a mapping transformation based on conservation of magnetic moment and total energy of each ion along lines of magnetic flux.
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52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.35.Kt Drift waves
28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium
52.70.Nc Particle measurements
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