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Dec 1974

Volume 17, Issue 12, pp. 2155-2299

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Electronic nonequilibrium in a supersonic expansion of ionized gas

D. D. McGregor and M. Mitchner

Phys. Fluids 17, 2155 (1974); http://dx.doi.org/10.1063/1.1694684 (12 pages) | Cited 2 times

Online Publication Date: 11 August 2003

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An experimental and analytical study of nonequilibrium among the populations of the excited levels of potassium vapor passing through a supersonic nozzle is presented. In the experiment a small amount of potassium vapor was injected into a flow of a mixture of argon and helium, heated by an arc jet electric discharge to a temperature of approximately 2500°K at a pressure of 3 atm. The resulting plasma was passed through a supersonic nozzle (attaining Mach 2.2 at nozzle exit); the gas temperature dropped from 2500° to 1000°K in a time scale of 3 × 10−5sec. The electron temperature (though somewhat independent of the gas temperature) also decreased rapidly, causing the free electrons to recombine with ions of potassium. The recombined electrons passing through the energy level structure of potassium formed the basis of the electronic nonequilibrium. Spectrometric measurements (line intensity and line reversal) of the gas were performed upstream of the nozzle and at the nozzle exit. The electronic populations of expanded potassium vapor were observed to depart from equilibrium in qualitative accordance with theoretical predictions. Larger electron excitation cross sections (than the present theoretical ones) in the energy region near threshold would bring theoretical calculations of excited level populations and electron density at the nozzle exit into better agreement with measured values for these quantities.

Shock wave structures in weakly ionized gases using the Krook kinetic model

M. Masuda, T. Ikui, and T. Murakami

Phys. Fluids 17, 2167 (1974); http://dx.doi.org/10.1063/1.1694685 (2 pages)

Online Publication Date: 11 August 2003

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The structures of the normal shock waves in weakly ionized nonequilibrium flows have been analyzed by the Krook kinetic models using the Maxwellian or the ellipsoidal distribution functions, and the calculated results were compared with those obtained from the bimodal approximations.

Temperature measurements behind shock waves using a line radiation technique

H. Semerjian and R. A. Dobbins

Phys. Fluids 17, 2169 (1974); http://dx.doi.org/10.1063/1.1694686 (7 pages)

Online Publication Date: 11 August 2003

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A method of determining the temperature of hot gases is described that is based on the measurement of the intensity of radiation on the center of an emission line. The line is selected on the basis that it possesses blackbody intensity at the central frequency and that its width is large compared with the available spectral resolution of the optical equipment. With these conditions fulfilled, no information on the specific properties of the spectral line is required to recover temperature. The method is applied to determine the temperature behind a shock‐wave propagating into xenon gas. The temperature of the shock‐heated gas is calculated by Rankine‐Hugoniot conditions based on the measured shock velocity. A comparison between measured and theoretical temperatures is presented, and it shows improved agreement at higher temperatures and pressures. The most serious limitation on the accuracy of our implementation of this experiment is considered to be the uncertainty of the shock velocity in the presence of moderate shock attenuation.

Stagnation‐point flow in a rotating cylinder

R. W. Davis and G. S. S. Ludford

Phys. Fluids 17, 2176 (1974); http://dx.doi.org/10.1063/1.1694687 (5 pages)

Online Publication Date: 11 August 2003

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Linear theory is used to study the pure stagnation‐point flow created inside a rotating cylinder by introducing fluid uniformly through the top surface and removing it uniformly through the side wall. Of main interest is the completely new role played by the E1/2 layer at the side wall, although the (unsteady) E1/4 and E1/3 layers also have novel features.

Spatial stability of some Falkner—Skan profiles with reversed flow

H. Taghavi and A. R. Wazzan

Phys. Fluids 17, 2181 (1974); http://dx.doi.org/10.1063/1.1694688 (3 pages) | Cited 6 times

Online Publication Date: 11 August 2003

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The Orr‐Sommerfeld equation is solved numerically for the boundary layer profiles which are the solutions to Stewartson's branch of the Falkner‐Skan equation. These profiles are of significance in describing post‐separation flows with negative skin friction. The cases considered are for the Hartree pressure gradient parameter β  =  −0.18, −0.15, −0.10, and −0.05. The profiles become more stable as β decreases from ‐0.05 to ‐0.18 in contrast to the results of the Falkner‐Skan similarity profiles with positive skin friction.

Unsteady magnetic boundary layer flow of power‐law fluids

Djordje S. Djukic

Phys. Fluids 17, 2184 (1974); http://dx.doi.org/10.1063/1.1694689 (3 pages) | Cited 1 time

Online Publication Date: 11 August 2003

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The Galerkin approximation technique is used to solve the flow problem of an infinite plate immersed in a non‐Newtonian power law fluid in the presence of a constant transverse magnetic field. The velocity outside the boundary layer depends exponentially on time.

Experimental study of an aligned magneto‐fluid dynamic flow

P. A. Pincosy and Harlow G. Ahlstrom

Phys. Fluids 17, 2187 (1974); http://dx.doi.org/10.1063/1.1694690 (5 pages)

Online Publication Date: 11 August 2003

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A magneto‐fluid dynamic flow interaction in the shock tube flow of an electrically conducting test gas over a cone aligned with an applied magnetic field was experimentally observed, where RM  =  0.25. For the variable applied field up to 0.9 W/m2, the maximum Ia  =  0.50, and A varied from greater than to less than unity. Gas dynamic flow changes were not observed, but the measured unsteady induced magnetic field data effectively illustrated the role of diffusion in the propagation of the fast and slow magnetoacoustic waves. In addition, the direct observation of the fast magnetoacoustic wave was a very significant result.

Collisional parameters of a test particle and a streaming plasma

J. G. Siambis and S. N. Stitzer

Phys. Fluids 17, 2192 (1974); http://dx.doi.org/10.1063/1.1694691 (9 pages) | Cited 2 times

Online Publication Date: 11 August 2003

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The collisional interaction of a test‐charged particle with a streaming Maxwellian distribution of field particles is considered analytically. Values are found for the collisional parameters of dynamical friction force, diffusion tensor, and rate of energy change for a wide range of field particle densities, temperatures, and streaming velocities. Retention of the velocity dependence of the Coulomb logarithm leads to substantial differences in the values of the parallel component of the diffusion tensor and the rate of energy change for the test particle as compared with the Spitzer values. Collision frequencies for momentum transfer, π/2 angular deflection, and energy change for the test particle and the test plasma are defined, simply related to each other, compared with the Spitzer definitions and evaluated for a simple case. The new definitions for the collision frequencies place in evidence the enhancement of collisional momentum and energy transfer in the absence of stationary thermal equilibrium.

Magnetic field dependence of plasma relaxation times

David Montgomery, Glenn Joyce, and Leaf Turner

Phys. Fluids 17, 2201 (1974); http://dx.doi.org/10.1063/1.1694692 (4 pages) | Cited 31 times

Online Publication Date: 11 August 2003

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A previously derived Fokker‐Planck collision integral for an electron plasma in a dc magnetic field is examined in the limit in which the Debye length is greater than the thermal gyroradius, which is in turn greater than the mean distance of closest approach. It is demonstrated that the collision integral can be satisfactorily approximated by the classical Landau value (which ignores the presence of a dc magnetic field) if the following replacement is made: In the Coulomb logarithm, the Debye length is replaced by the gyroradius. This induces a fundamental logarithmic dependence on magnetic field in the relaxation times. Numerical comparison of the asymptotic approximations with the previously derived exact results is made, and good agreement is found. The simplification this introduces into the description of collision processes in magnetized plasmas is considerable.

Nonlinear excitation of ion acoustic waves

P. Michelsen and J. L. Hirshfield

Phys. Fluids 17, 2205 (1974); http://dx.doi.org/10.1063/1.1694693 (3 pages) | Cited 2 times

Online Publication Date: 11 August 2003

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The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.

Absolute and convective ion beam instability studied through Green's function

V. O. Jensen, P. Michelsen, and Hulbert C. S. Hsuan

Phys. Fluids 17, 2208 (1974); http://dx.doi.org/10.1063/1.1694694 (7 pages) | Cited 4 times

Online Publication Date: 11 August 2003

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See Also: Erratum

Show Abstract
A Vlasov plasma with a double‐humped, unstable ion velocity distribution function is considered. A δ function in space is assumed as the initial perturbation and the plasma response to this perturbation is calculated, i.e., the Green's function for the problem is found. The response can be divided into two parts: a self‐similar, damped part of the form t−1h(x/t), and an unstable, exponentially growing part. The conditions for absolute and convective growth of the latter are discussed.

Nonlinear evolution of parallel‐propagating hydromagnetic waves

Ronald H. Cohen and Russell M. Kulsrud

Phys. Fluids 17, 2215 (1974); http://dx.doi.org/10.1063/1.1694695 (11 pages) | Cited 77 times

Online Publication Date: 11 August 2003

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The nonlinear evolution of plane hydromagnetic fluctuations propagating along the unperturbed magnetic field direction is considered. From an expansion of the ideal magnetohydrodynamic equations and the hydromagnetic shock jump conditions, it is shown that a wave in which the magnitude of the magnetic field is nonconstant steepens into a shock and subsequently evolves toward a purely Alfvénic fluctuations of lower mean energy density. Explicit expressions are derived for the asymptotic state and for the characteristic lines which describe the evolution toward that state. A class of fluctuations which includes linearly polarized waves is shown to evolve into rotational discontinuities. The results are applied to observations of hydromagnetic fluctuations in the solar wind.

Observations of the stable equilibrium and classical diffusion of field reversing relativistic electron coils

D. A. Phelps, A. C. Smith, D. M. Woodall, R. A. Meger, and H. H. Fleischmann

Phys. Fluids 17, 2226 (1974); http://dx.doi.org/10.1063/1.1694696 (10 pages) | Cited 21 times

Online Publication Date: 11 August 2003

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Observations of high current relativistic electron coils are presented and interpreted theoretically. Electron coil self‐magnetic field strengths up to almost twice that of the external magnetic field at the mirror center are observed. Lifetimes up to 30 μsec are related to the classical diffusion of electron coils in a stable equilibrium state. The diffusion mechanism is verified as inelastic small angle scattering of the relativistic electrons from a neutral gas background.

Kinetic theory of plasma scrape‐off in a divertor tokamak

F. L. Hinton and R. D. Hazeltine

Phys. Fluids 17, 2236 (1974); http://dx.doi.org/10.1063/1.1694697 (5 pages) | Cited 29 times

Online Publication Date: 11 August 2003

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The structure of the plasma boundary, in a tokamak with a poloidal divertor, is considered. The assumption, of hot, collisionless ions, and cold, collisional electrons is shown to be self‐consistent. The density gradient length is shown to be of the order of ρpi, the ion poloidal gyroradius, at typical poloidal angles. Plasma diffusion across the separatrix, and particle motion along the field lines to the collector plates, are described by a kinetic equation. From the solution of the boundary‐layer problem, the ion flux and ion energy flux, to the plates, are calculated. The ratio of these fluxes, and the corresponding ratio for the electrons, complete the specification of divertor boundary conditions, to be used in tokamak transport codes.

Ion cyclotron waves and fast waves in a toroidal cavity

D. G. Swanson

Phys. Fluids 17, 2241 (1974); http://dx.doi.org/10.1063/1.1694698 (8 pages) | Cited 8 times

Online Publication Date: 11 August 2003

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The propagation of ion cyclotron waves and fast waves in a toroidal cavity with a spatially varying static magnetic field as in a tokamak or stellarator is examined. Using a cold plasma model in a square cross section conducting toroidal cavity and neglecting effects of electron inertia, the wave equation is reduced to an ordinary differential equation which is numerically integrated subject to boundary conditions to find eigenmodes which represent cavity resonances. For the fast wave, only very small perturbations from the corresponding uniform plasma guide problem are found, and it is concluded that effects of toroidicity on the fast wave are not significant. For the ion cyclotron wave it is found that the region of propagation is generally confined to the high magnetic field side of the cyclotron resonance and for low order modes vertically and azimuthally, the region of propagation does not extend to the resonance location. A new type of wave behavior appears due to toroidicity which is similar to the ion cyclotron wave but depends differently on wavelength and may be important for fusion plasma heating because of its possibly greater accessibility. On the basis of the wave profiles, optimum antenna designs will be profoundly affected by toroidicity.

Probability distribution for Fourier components of the electric field in weak plasma turbulence theory

T. M. O'Neil

Phys. Fluids 17, 2249 (1974); http://dx.doi.org/10.1063/1.1694699 (6 pages) | Cited 13 times

Online Publication Date: 11 August 2003

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Probability distributions for Fourier components of the electric field, including joint distributions for various Fourier components and multiple time distributions for the same component, are determined using the central limit theorem of probability theory and two assumptions within the spirit of weak turbulence theory. The distributions are all Gaussians or simple integrals of Gaussians. This statistical framework is applied to the special case where the turbulence is dominated by the wave‐particle interaction. In this case, quantities appearing in the distributions as parameters, such as the mean and standard deviation, are determined by quasilinear theory and Dupree's recent theory of phase space granulation, or clumps.

Numerical simulation studies of a turbulent heating experiment

D. W. A. Whitfield and H. M. Skarsgard

Phys. Fluids 17, 2255 (1974); http://dx.doi.org/10.1063/1.1694700 (6 pages) | Cited 4 times

Online Publication Date: 11 August 2003

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Electrostatic, one‐dimensional, numerical plasma simulations have been used to study results from the University of Saskatchewan turbulent heating experiment. In a simulation plasma with an initial sinusoidal density perturbation (approximating the effect of a bumpy magnetic field parallel to the plasma current in the experiment), the application of a constant external‐electric field can cause the electrons to split into two groups, one freely accelerating and the other trapped near zero velocity in a potential well resulting from the inhomogeneous ion density. The ensuing electron‐electron instability can cause reduced acceleration and heating of the electrons, even when the ions are infinitely massive. This process appears to have a role in the experiment although close quantitative agreement cannot be claimed. A common and important feature of the simulations was the tendency of all observed instabilities to heat the electrons at a rate which maintained the ratio of electron drift to thermal velocity near unity. This heating rate has been observed in the experiment.

Observation of anomalous soft x‐ray emission from a turbulently heated high voltage θ‐pinch

Erol Oktay

Phys. Fluids 17, 2261 (1974); http://dx.doi.org/10.1063/1.1694701 (6 pages) | Cited 8 times

Online Publication Date: 11 August 2003

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Soft x‐ray emission from the Maryland high voltage θ‐pinch is measured as a function of two experimental parameters which in effect determines the electron density in the initial plasma. The x‐ray intensity increases rapidly as the electron density is lowered; however, the electron temperature deduced from thin foil absorption of these x rays does not vary significantly. The absolute intensity of these about 3‐keV x rays is orders of magnitude larger than the calculated intensity of bremsstrahlung radiation. To enhance x‐ray emission, we put a small Cu target in the plasma, and measure absorption characteristics and intensity of these target x rays also. The time of x‐ray emission correlates with those of neutron emission and implosion of magnetic field on the axis.

Synchrotron radiation spectrum for an intense relativistic E layer

Ronald C. Davidson and S. M. Mahajan

Phys. Fluids 17, 2267 (1974); http://dx.doi.org/10.1063/1.1694702 (8 pages) | Cited 3 times

Online Publication Date: 11 August 2003

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The synchrotron radiation spectrum is calculated for an intense relativistic nonneutral E layer including self‐field effects. The analysis is carried out for the class of thin E‐layer equilibria described self‐consistently by equilibrium distribution functions of the form fe0 (x, p)  =  R0F(H)δ(Pθ − P0), where H is the energy, is the canonical angular momentum, and R0 and p0 are constants. Since individual electrons execute radial betatron oscillations about a helix with mean radius R0, the single‐particle emission spectrum is modified from the conventional Schott‐Trubnikov result. To determine the spectrum of radiation emitted by all electrons in the E layer, the single‐particle emission spectrum is averaged over the distribution function fe0 (x, p) that self‐consistently generates the E layer equilibrium.

Electromagnetic wavefunctions for parabolic plasma density profiles

Alfredo Bauos and Daniel L. Kelly

Phys. Fluids 17, 2275 (1974); http://dx.doi.org/10.1063/1.1694703 (7 pages)

Online Publication Date: 11 August 2003

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The one‐dimensional Helmholtz equation w″ + k02g(z)w(z)  =  , k0  =  2π/λ0 , is solved making use of an extension of Langer's method. The function g(z) is restricted to the class of Epstein profiles, g(z)  =  g(0) + [1 − g(0)] tanh2(z/2λ) , where λ is the scale length, corresponding to no turning points, a quadratic turning point at z  =  0, or a pair of turning points, depending on whether g(0) is positive, zero, or negative. This method yields uniformly valid solutions in terms of confluent hypergeometric functions. First, a solution w+(z) is obtained for 0  ≤  z which, as z → ∞, becomes the transmitted plane wave. Then, applying the method of analytic continuation, a linear combination is obtained w−(z)  =  wi(z) + wr(z) valid for z  ≤  0 which, as z → − ∞, yields the superposition of the incident and reflected plane waves. As an illustration of this method and as an application to parabolic density profiles, the mean energy density of the electric field is obtained numerically, in the vicinity of z  =  0, when the parameter ratio λ/λ0  ≥  100, and for the case of a single quadratic turning point and also for the case in which there are two neighboring turning points. With this choice of parameters, the results yield useful information on the tuning criterion for parametric excitation of the ionosphere.

Wavenumber surfaces of magnetoatmospheric waves

Tyan Yeh

Phys. Fluids 17, 2282 (1974); http://dx.doi.org/10.1063/1.1694704 (8 pages) | Cited 6 times

Online Publication Date: 11 August 2003

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Small‐amplitude wave motion in a gravitationally stratified atmosphere permeated by a magnetic field consists, for each Fourier component with a certain frequency and horizontal wavenumber, of six quasiplane waves. Their mixture varies with height due to the continual interaction among these quasiplane waves. The simultaneous effects of compressibility, gravity, and a horizontal or a vertical magnetic field are shown by various wavenumber surfaces for decoupled plane waves.
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Randomization of the gyration phase through binary collisions

Hiromu Momota and Tomonori Takizuka

Phys. Fluids 17, 2290 (1974); http://dx.doi.org/10.1063/1.1694705 (2 pages) | Cited 3 times

Online Publication Date: 11 August 2003

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A criterion for the gyration phase being well randomized through binary collisions for a bounce motion of a charged particle in a magnetic mirror is investigated theoretically. The resultant criterion is seen to be easily satisfied even for the case of very rare collisions.

Kinetic theory of the resistive torque on a rotating cylinder

A. Gervois and Y. Pomeau

Phys. Fluids 17, 2292 (1974); http://dx.doi.org/10.1063/1.1694706 (2 pages)

Online Publication Date: 11 August 2003

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The resistive torque exerted upon a rotating cylinder by a rarefied gas may be computed by an expansion in powers of the inverse Knudsen number. The first correction diverges logarithmically, and the renormalized theory should replace the argument of the divergent logarithm by the Knudsen number.

Induced magnetic field for the Rayleigh motion of an insulated plate

Graham Wilks

Phys. Fluids 17, 2294 (1974); http://dx.doi.org/10.1063/1.1694707 (2 pages)

Online Publication Date: 11 August 2003

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The impulsive motion of an insulated plate in a transverse magnetic field is examined for fluids of small magnetic Prandtl number.
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Microscopic plasma Hamiltonian

Y‐K. M. Peng

Phys. Fluids 17, 2296 (1974); http://dx.doi.org/10.1063/1.1694708 (2 pages) | Cited 2 times

Online Publication Date: 11 August 2003

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A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler‐Lagrange equations of the Low Lagrangian.
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