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Dec 1962

Volume 5, Issue 12, pp. 1489-1666

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Poiseuille Plasma Experiment

H. W. Emmons and R. I. Land

Phys. Fluids 5, 1489 (1962); http://dx.doi.org/10.1063/1.1706556 (12 pages) | Cited 40 times

Online Publication Date: 9 December 2004

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The flow of gas and electric current simultaneously through a tube provides an experimental arrangement for the study of the flow of high‐temperature gases capable of precision measurements and a precise mathematical theory. The precision experimental technique and some initial experimental results together with a simplified theory are presented in this paper. Mean electrical conductivities and kinematic viscosities are given for a number of gases. The arc performance is shown to be predictable with fair precision by a very simple discontinuous model of the plasma properties which is capable of wide exploitation in magnetohydrodynamics.

Instabilities of a Liquid Conductor

Uno Ingard and David S. Wiley

Phys. Fluids 5, 1500 (1962); http://dx.doi.org/10.1063/1.1706557 (3 pages) | Cited 4 times

Online Publication Date: 9 December 2004

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Observations of pinch and spiral instabilities of a liquid conductor falling in an axial magnetic field are reported. Measured rates of change of the stream diameter and the spiral radius are given, and a stream ``bifurcation'' phenomenon that was induced by spiral instability is described.

Plasmoid Dipole Rotation in a Theta Pinch

G. L. Clark and R. F. Wuerker

Phys. Fluids 5, 1503 (1962); http://dx.doi.org/10.1063/1.1706558 (4 pages) | Cited 12 times

Online Publication Date: 9 December 2004

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The behavior of the toroidal plasmoid formed in a theta pinch due to trapping of magnetic field lines has been photographed with an ultra‐high‐speed image‐converter camera. Photographs show the plasma ring rotating about an axis perpendicular to the applied magnetic field. This rotation is seen not only as a possible explanation for the sudden disappearance of the trapped magnetic field, but as a mechanism for accelerating the ions caught in the plasmoid. A preliminary analysis provides an upper bound to the ion energies obtainable through such a mechanism.
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Anomalous Diffusion Arising from Microinstabilities in a Plasma

William E. Drummond and Marshall N. Rosenbluth

Phys. Fluids 5, 1507 (1962); http://dx.doi.org/10.1063/1.1706559 (7 pages) | Cited 267 times

Online Publication Date: 9 December 2004

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A plasma is considered in which a Maxwellian distribution of electrons with thermal velocity ve and drift velocity vD is drifting relative to a Maxwellian distribution of ions with thermal velocity vi. For vD ≲ ve the usual ion acoustic waves are stable, however, electrostatic ion cyclotron waves with ω ≅ Ωi are unstable for vD ≳ 5vi. In the case when 5vi ≲ vD ≲ ve, and Te∕Ti < 2 the electrostatic ion cyclotron waves grow to a nonlinear equilibrium spectrum. This spectrum of waves leads to a diffusion of electrons across the field lines with a diffusion coefficient D = αρ2eΩe, where ρe is the electron Larmor radius and Ωe is the electron Larmor frequency. α, the ratio of the resulting diffusion coefficient to the Bohm diffusion coefficient, is given by a constant × (vD∕ve)5(Te∕Ti)2.

High‐Frequency Conductivity of a Fully Ionized Plasma

Carl Oberman, Amiram Ron, and John Dawson

Phys. Fluids 5, 1514 (1962); http://dx.doi.org/10.1063/1.1706560 (9 pages) | Cited 80 times

Online Publication Date: 9 December 2004

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A complete classical derivation of the frequency‐dependent conductivity is presented which properly takes into account collective dynamics. This treatment rests on the joint solution of the first two members of the BBGKY hierarchy, in the plasma limit, when both are able to change on the same time scale. For arbitrary frequencies this leads to an integral equation for the one‐particle distribution function which can be solved by conventional variational and∕or numerical procedures. For frequencies high compared to the collision frequency, an explicit statement of the conductivity is possible. This high‐frequency limit is further examined in the limit of small electron to ion mass ratio and these limiting results are compared with those of other authors.

Close Collisions in a Plasma

David E. Baldwin

Phys. Fluids 5, 1523 (1962); http://dx.doi.org/10.1063/1.1706561 (8 pages) | Cited 19 times

Online Publication Date: 9 December 2004

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A two‐body distribution function in a plasma is developed for use in a kinetic equation for the one‐body distribution function. The kinetic equation is obtained for a uniform plasma for circumstances in which the time dependence of higher‐order distribution functions can be assumed to occur within a functional dependence on the one‐particle distribution function. The resulting interaction term is new, in the sense that it contains no divergent integrals, and is considered accurate to first order in (e2∕KTλD). The interaction term is composed of two parts. The first is a Boltzmann collision integral with a Debye‐shielded interaction. The second term is due to the deviation of the shielding cloud from a Debye shield and is of the Fokker‐Planck form, the coefficients of which are finite and well behaved. Because of its form, with a convergent collision integral and convergent Fokker‐Planck coefficients, the solution may be considered a joining of the previous solutions to the problem.

Formation of Drift Instabilities by Collisional Relaxation of High‐Energy Particles

H. Dreicer and R. Mjolsness

Phys. Fluids 5, 1531 (1962); http://dx.doi.org/10.1063/1.1706562 (14 pages) | Cited 5 times

Online Publication Date: 9 December 2004

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The relaxation of a small group of fast test electrons as a result of two‐body Coulomb encounters with slow field electrons and ions orbiting in a magnetic field is investigated. The analysis is based upon an asymptotic form of the Fokker‐Planck equation which includes the slowing down in speed as well as the angular scattering of the test electrons. The derivation as well as the analytic solution of this equation is presented, and is used to illustrate a case where collisional relaxation of the test electrons alone is responsible for the formation of a second peak in the one‐dimensional electron velocity distribution. The maximum growth rate for the resulting electrostatic drift instability is calculated in the limit when the second peak is much smaller than the main peak, and is found to be proportional to the ratio of test to field particle density. The results are used to suggest an explanation of the several unstable current steps observed in the stellarator during its crowbarred relaxation phase.

Interaction between Cold Plasmas and Guided Electromagnetic Waves. II

Lyman Mower and S. J. Buchsbaum

Phys. Fluids 5, 1545 (1962); http://dx.doi.org/10.1063/1.1706563 (7 pages) | Cited 3 times

Online Publication Date: 9 December 2004

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The interaction between cylindrically symmetric anisotropic plasma column and bounded electro‐magnetic waves is analyzed theoretically. The properties of a cylindrical cavity coaxial with a cold plasma column and a coaxial with a static magnetic field are determined. The shift in the resonant frequency of the cavity‐plasma system is calculated in the high‐electron‐density limit and compared with the numerical solution presented earlier.

Interaction between a Radio Wave and a High‐Temperature Plasma

Toyoki Koga

Phys. Fluids 5, 1552 (1962); http://dx.doi.org/10.1063/1.1706564 (6 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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The effect of the temperature of a fully ionized plasma on its conductivity to a radio wave is investigated, taking into consideration the finite wavelength of the radio wave. The order of the effect is kT∕(ma2), where T is the temperature of the gas, m the mass of an electron, k the Boltzmann constant, a the phase velocity of the wave. The relativistic effect is not considered.

Bremsstrahlung from a Plasma

David B. Chang

Phys. Fluids 5, 1558 (1962); http://dx.doi.org/10.1063/1.1706565 (6 pages) | Cited 13 times

Online Publication Date: 9 December 2004

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The effect of correlations on bremsstrahlung from a plasma is studied by using in Kirchhoff's law an absorption coefficient obtained from a Boltzmann‐Fokker‐Planck equation. A simple derivation of the Fokker‐Planck coefficients is given by relating them to familiar dc coefficients. A dispersion formula giving the principal behavior of the absorption coefficient is obtained from a first iterate solution of the Fokker‐Planck equation, treating the scattering of electrons by ions as a perturbation. The absorption coefficient reduces to the incoherent radiation result at frequencies much higher than the plasma frequency. At the plasma frequency it is greater than the incoherent absorption coefficient by a factor of O[(nλD3)½], where n is the electron density and λD is the Debye length. The effect of surface reflections on the net emission is discussed.

Plasma Correction to Single‐Particle Cyclotron Radiation

David B. Chang

Phys. Fluids 5, 1564 (1962); http://dx.doi.org/10.1063/1.1706566 (7 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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The saddle‐point evaluation used by Trubnikov and Kudryavtsev and Drummond and Rosenbluth to obtain the O (ωp2∕ωωH) absorption coefficient for single particle cyclotron radiation from a mildly relativistic plasma, is extended to include terms of O(ωp4 ∕ ω2ω2H) describing collective plasma effects—where ωp, ωH, and ω are the plasma frequency, electron cyclotron frequency, and observed frequency, respectively. The O(ωp4 ∕ ω2ωH2) correction modifies the O(ωp2 ∕ ωωH) calculation through the introduction of an additional steepest descent path; through the inclusion of additional terms in the expansion of the dispersion formula; by changing the location of the saddle points; and by altering the expressions evaluated at the saddle points. For a typical thermonuclear plasma, the fractional O(ωp4 ∕ ω2ω2H) correction to the absorption coefficient for propagation perpendicular to the magnetic field is found to be approximately — ωp2∕ωωH.

Interaction between a Plasma and the External Current and Flux

T. H. Jensen and H. G. Voorhies

Phys. Fluids 5, 1571 (1962); http://dx.doi.org/10.1063/1.1706567 (6 pages)

Online Publication Date: 9 December 2004

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The external current and flux in plasma devices are studied in order to obtain information on the plasma by the observation of these quantities. Two devices have been investigated, namely the long mirror and the cusp. The result of the investigations is that one can obtain approximately the following quantities: total kinetic energy of the plasma, energy exchange between plasma and field, and energy exchange between the plasma and the surroundings.

Diffusion of Electrons in a Scattering Medium

E. Blue, J. H. Ingold, and W. J. Ozeroff

Phys. Fluids 5, 1576 (1962); http://dx.doi.org/10.1063/1.1706568 (4 pages) | Cited 6 times

Online Publication Date: 9 December 2004

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The diffusion approximation to the more exact transport theory of charged‐particle flow in a scattering gas is described and used to calculate the potential and electron density distributions for a simple case. In this simple case, electrons are emitted from a plane source and flow to a plane collector through the scattering gas under the influence of a density gradient and of electric fields due to a combination of space charged fields and externally applied fields. The resultant current‐voltage relationship is complicated; however, a plot of ln J vs ln Va, where J is the electric current density and Va the applied voltage, has a slope which varies from one to two, according to whether the major component of the electric current is the density gradient or the electric field, respectively. These results are compared to those reported earlier in the literature.

Moment Equations and Boundary Conditions for Magneto‐Gas Dynamics

H. T. Yang

Phys. Fluids 5, 1580 (1962); http://dx.doi.org/10.1063/1.1706569 (10 pages) | Cited 3 times

Online Publication Date: 9 December 2004

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Based on the work of Burgers and particularly of Kolodner, moment equations are obtained from the Boltzmann equation for a conducting gas in electric and magnetic fields. Relatively simple stress and heat‐flux equations yielding one‐fluid description of a slightly ionized gas mixture have been obtained. The associated boundary conditions are obtained by applying conservation laws near the wall. These moment equations and boundary conditions together with Maxwell's electromagnetic equations and their boundary conditions form a determinate system to describe the dynamics of a rarefied conducting gas in electric and magnetic fields. This system includes, as limiting cases, both the Grad thirteen‐moment equations for rarefied gases and the usual continuum magneto‐gas‐dynamic equations.

Structure of Strong Plasma Shock Waves in a Transverse Magnetic Field

G. G. Comisar

Phys. Fluids 5, 1590 (1962); http://dx.doi.org/10.1063/1.1706570 (7 pages)

Online Publication Date: 9 December 2004

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The structure of a plane stationary shock wave in a plasma with a transverse magnetic field is explored by using the restricted variational principle of Rosen to evaluate the adjustable factors of Mott‐Smith's bimodal representation for the ion and electron distribution functions. The resulting solutions, in the strong shock limit, indicate that the particle number densities are essentially those of the nonmagnetic case, and that the transverse magnetic field departs considerably from the usual frozen‐in field profile, due to local dissipative effects of electrical conductivity.

Similarity Solution for Cylindrical Magnetohydrodynamic Blast Waves

Carl Greifinger and Julian D. Cole

Phys. Fluids 5, 1597 (1962); http://dx.doi.org/10.1063/1.1706571 (11 pages) | Cited 18 times

Online Publication Date: 9 December 2004

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A similarity solution is obtained for the flow behind a very strong (in the hydrodynamic sense) cylindrical magnetohydrodynamic shock wave produced by the sudden release of energy along a line of infinite extent in a plasma. The plasma is assumed to be an ideal gas with infinite electrical conductivity, and to be permeated by the azimuthal magnetic field of a line current. It is shown that it is of critical importance to take into account the ambient magnetic pressure, no matter how small. It is found that, to preserve similarity, the external circuit is required to maintain a constant axial current; this result also appears in the related problem, treated by Greenspan, where the ambient plasma is nonconducting. This boundary condition is shown to have some interesting consequences, especially with regard to the energy content of the system. The dependence of the shock speed on the explosive energy is determined as a function of the ambient magnetic field both for the present case and for Greenspan's case, and interesting differences are noted. Other differences between the two cases are also discussed.

Propagation of Sound in a Gas of Rigid Spheres

C. L. Pekeris, Z. Alterman, L. Finkelstein, and K. Frankowski

Phys. Fluids 5, 1608 (1962); http://dx.doi.org/10.1063/1.1706572 (9 pages) | Cited 36 times

Online Publication Date: 9 December 2004

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The linearized Boltzmann integral equation for the problem of propagation of sound in a rigidsphere gas was solved by first determining the eigenfunctions of the collision operator and then solving the propagation matrix. Determinants up to order n = 105 were solved, and the results are illustrated. With the maximum order 105 of the matrix solved, the values of the propagation parameters obtained show convergence to within 2% for R > 1.8, where R = 2fc∕3πf. The theoretical results are in fairly good agreement with Greenspan's measurements of the speed and attenuation of sound in rarefied helium.

Momentum Transfer between Gas Molecules and Metallic Surfaces in Free Molecule Flow

Robert E. Stickney

Phys. Fluids 5, 1617 (1962); http://dx.doi.org/10.1063/1.1706573 (8 pages) | Cited 7 times

Online Publication Date: 9 December 2004

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Measurements of the normal momentum transfer between gases and metallic surfaces were obtained under conditions of free molecule flow with a torsion balance and molecular beam apparatus. Helium, hydrogen, neon, nitrogen, carbon dioxide, and argon were investigated on tungsten, platinum‐blackened‐tungsten, platinum, and aluminum surfaces which were contaminated to an undetermined degree with oxides and adsorbed gases. A thermal beam of gas molecules was directed against the test surface at normal incidence, and momentum transfer measurements were obtained with the surface at various temperatures over the range 25° to 550° C.
The experimental results indicate that the efficiency of the momentum transfer process increases with the molecular weight of the test gas and the roughness of the test surface, but is relatively independent of the substrate material under the present conditions. The momentum transfer rates for helium and hydrogen are significantly less than those measured for the heavier gases at the same surface temperature. The accommodation of the test gases to the surface temperature appears to be incomplete except, possibly, for argon and carbon dioxide. The results cannot be explained successfully by means of the classical model which assumes that the re‐emitted gas consists of two components, one experiencing specular reflection and the other complete accommodation at the surface. A modified model and a corresponding momentum accommodation coefficient are introduced and employed in the discussion of the experimental data.

Inertia‐Controlled Ambipolar Diffusion

Karl‐Birger Persson

Phys. Fluids 5, 1625 (1962); http://dx.doi.org/10.1063/1.1706574 (8 pages) | Cited 70 times

Online Publication Date: 9 December 2004

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The general nonlinear ambipolar‐flow equations are derived and discussed. The important non‐linearities are caused by the inertia of the ions and by the heat‐conduction mechanism. It is shown that all essential effects associated with these nonlinearities can be demonstrated in the plane‐parallel case. The influence of the nonlinearity caused by the inertia is discussed in detail for the plane‐parallel case and it is shown that this flow is analogous to the flow of a fluid with friction through a contracting nozzle. The limiting velocity—the isothermal or the adiabatic sound velocity—which is found in the exit of a nozzle is also found at the boundary in the case of inertia‐controlled diffusion, provided this boundary acts like a perfect sink. Bohm's criterion—the ion drift velocity less than or equal to the sound velocity of the electron‐ion gas in front of the boundary or the wall sheath—appears as an integral part of the inertia‐controlled‐diffusion theory. In the inertia‐controlled‐diffusion theory are incorporated, as integral parts, all the assumptions that necessarily must be added to the linear‐diffusion theory in order to make it realistic. The isothermal and inertia‐controlled diffusion leads always to wall‐stabilized plasma configurations which directly correspond to the fundamental mode solution in the linear‐diffusion theory.

Rate of Ionization behind Shock Waves in Air. I. Experimental Results

Shao‐Chi Lin, Richard A. Neal, and Walter I. Fyfe

Phys. Fluids 5, 1633 (1962); http://dx.doi.org/10.1063/1.1706575 (16 pages) | Cited 30 times

Online Publication Date: 9 December 2004

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The electron density profile behind normal shock waves in air at initial pressures 0.02 ≤ p1 ≤ 0.2 mm Hg and in the shock‐Mach‐number range 14 ≤ Ms ≤ 20 has been measured, using microwave‐reflection and magnetic‐induction probes in a 24‐in.‐diameter shock tube. It was found that the electron density generally rises rapidly behind the shock front without much incubation to a transient peak value which is considerably higher (i.e., by a factor of between 2 and 3) than that corresponding to the final equilibrium value. At a fixed shock Mach number, the maximum electron density gradient behind the shock appears to vary with the square of the initial air density, indicating that all the important rate‐governing steps are due to binary collisions. Thus, at Ms = 20, the distance behind the shock required to reach 90% of the transient peak electron density was found to be about 10 times the viscosity mean free path of the undisturbed gas ahead of the shock. At Ms = 14, the corresponding distance was found to be approximately 40 times the initial mean free path.

Correspondence between Normal‐Shock and Blunt‐Body Flows

W. E. Gibson and P. V. Marrone

Phys. Fluids 5, 1649 (1962); http://dx.doi.org/10.1063/1.1706576 (8 pages) | Cited 7 times

Online Publication Date: 9 December 2004

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An approximate solution for coupled, nonequilibrium chemistry along streamlines of inviscid, blunt‐body airflows is described. The solution is derived from a correspondence between the chemical relaxation zone along a streamline and that behind a normal shock. This correspondence applies in general for Newtonian flows with binary kinetics. Along the stagnation streamline, binary kinetics are not required. The approximate solution is compared with exact numerical solutions of the blunt‐body problem and is found to be accurate for the high enthalpies corresponding to hypersonic flight.

Thermal and Radiative Properties of Recombining Atomic Nitrogen

Thomas Marshall and R. A. Kawcyn

Phys. Fluids 5, 1657 (1962); http://dx.doi.org/10.1063/1.1706577 (4 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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A series of experiments on phenomena associated with the atomic recombination of nitrogen atoms is briefly discussed. The temperature dependence of the three‐body rate coefficient has been found to fit a power law k(T) ∝ T−0.6 over the temperature range of 200°–400°K. The absolute photon production rate accompanying the atomic recombination in the Rayleigh afterglow has been measured and found to be about one photon per 200 recombinations. The experiments rely on an electron spin resonance technique to measure the absolute atomic nitrogen density, and permit a rough determination of the dissociation energy of nitrogen.
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Further Studies of Cr 1 Emission from the Shock Tube

G. Charatis and T. D. Wilkerson

Phys. Fluids 5, 1661 (1962); http://dx.doi.org/10.1063/1.1706578 (2 pages) | Cited 10 times

Online Publication Date: 9 December 2004

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Stability of Electrically Charged Conducting Droplets

John W. Cahn

Phys. Fluids 5, 1662 (1962); http://dx.doi.org/10.1063/1.1706579 (2 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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Comment on ``Flow of an Incompressible Fluid in a Hydromagnetic Capacitor''

W. S. Lewellen

Phys. Fluids 5, 1663 (1962); http://dx.doi.org/10.1063/1.1706580 (2 pages) | Cited 1 time

Online Publication Date: 9 December 2004

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