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Dec 1963

Volume 6, Issue 12, pp. 1661-1782


Structure of Shock Fronts in Argon and Nitrogen

M. Linzer and D. F. Hornig

Phys. Fluids 6, 1661 (1963); http://dx.doi.org/10.1063/1.1711007 (8 pages) | Cited 39 times

Online Publication Date: 9 December 2004

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The optical reflectivity method was used to investigate the structure of shock fronts in argon from Mach 1.70 to Mach 4.85 and in nitrogen from Mach 2.01 to Mach 3.72. Experimental data were obtained at two wavelengths and over a wide range of initial pressures. The reflectivities, corrected empirically for shock curvature, were fitted to a bimodal profile to yield a maximum‐slope density thickness. The reciprocal of the thickness in argon (expressed in terms of the Maxwellian mean free path in the undisturbed gas) rises rapidly to a maximum of approximately 0.31 at about Mach 3.5 and decreases gradually thereafter. Above Mach 3 the thickness is about 50% greater than calculated from the Navier‐Stokes equations, using a realistic viscosity‐temperature relationship. There is excellent agreement, especially at the higher shock strengths, with recent bimodal calculations carried out by Muckenfuss, using realistic intermolecular potentials. In nitrogen, the shocks are thinner than in argon and appear to attain a minimum value of 2.5 initial mean free paths at about Mach 3.7. Rotational relaxation appears to be as rapid in the strong shocks as previously observed in weak shocks; it appears to be completed within the shock front. The experimental density thicknesses are approximately 50% greater than those calculated from the Navier‐Stokes equations, using the experimental shear viscosity μ and a bulk viscosity of 2μ∕3. The agreement with these Navier‐Stokes solutions is about as good as those in argon.

Navier‐Stokes Calculations of Argon Shock Wave Structure

L. M. Schwartz and D. F. Hornig

Phys. Fluids 6, 1669 (1963); http://dx.doi.org/10.1063/1.1711008 (7 pages) | Cited 11 times

Online Publication Date: 9 December 2004

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The classical Navier‐Stokes theory was used to calculate profiles of plane shock waves in argon. The viscosity‐temperature relationship employed in the calculation was based on a Lennard‐Jones 6–12 intermolecular potential function for which the parameters were derived from experimental viscosity measurements up to 1100°K. With this viscosity function, the maximum‐slope shock thicknesses obtained were smaller than previously calculated assuming viscosity proportional to T0.816. Also it was found that the maximum‐slope thickness based on the density profile was less than that based on the velocity profile. The density profile thicknesses calculated with the Lennard‐Jones viscosity function were the same order of magnitude as, but not in quantitative agreement with experimental density thicknesses obtained with the optical reflectivity technique. It was found that Navier‐Stokes profiles become asymmetric as the shock strength is increased. However, the calculated asymmetry would have a negligible effect on thickness measurements by the optical reflectivity method.

Relation between Thermal Conductivity and Viscosity for Nonpolar Gases. II. Rotational Relaxation of Polyatomic Molecules

Cleveland O'Neal and Richard S. Brokaw

Phys. Fluids 6, 1675 (1963); http://dx.doi.org/10.1063/1.1711009 (8 pages) | Cited 34 times

Online Publication Date: 9 December 2004

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The dimensionless ratio f = λM∕ηCv relating the thermal conductivity, molecular weight, viscosity, and constant volume molar heat capacity has been determined for several nonpolar polyatomic gases in the neighborhood of room temperature (270°–295° K). The experimental method, due to Eckert and Irvine, provides a direct determination of f by measurement of the subsonic temperature recovery factor. A recent theory of Mason and Monchick has been used to calculate collision numbers for rotational relaxation from the experimental data as follows: CH4, 9.4; CF4, 3.0; SF6, 2.5; C2H4, 2.4; C2H6, 4.0; O2, 12; N2, 7.3; CO2, 2.4; and C2H2, 1.8. Collision numbers for the near‐spherical molecules were in close accord with a classical theory for rough sphere molecules with attractive forces; ethylene, which deviates appreciably from spherical symmetry, exhibited a smaller collision number. The data on linear molecules were in qualitative agreement with a quantum treatment. In general, collision numbers for rotational relaxation are determined by the following factors: (1) The molecular mass distribution, (2) the strength of the intermolecular attractive forces, and (3) the molecular asymmetry.

Radiation Smoothing of Shocks with and without a Magnetic Field

M. Mitchner and M. Vinokur

Phys. Fluids 6, 1682 (1963); http://dx.doi.org/10.1063/1.1711010 (11 pages) | Cited 12 times

Online Publication Date: 9 December 2004

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A transverse magnetic field imposed on a radiating shock wave is shown to inhibit the smoothing tendency of radiation energy transfer, and to alter the conditions for the occurrence of a temperature overshoot. Necessary and sufficient conditions for the smoothing of shocks by the mechanism of radiation energy transfer acting alone are discussed and numerical results are derived for the case of no magnetic field. A possible experimental test is proposed.

Final Stage Decay of Grid‐Produced Turbulence

H. S. Tan and S. C. Ling

Phys. Fluids 6, 1693 (1963); http://dx.doi.org/10.1063/1.1711011 (7 pages) | Cited 14 times

Online Publication Date: 9 December 2004

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A kinetic model of the final‐stage decay of grid‐produced turbulence is presented. Theoretical analysis leads to an inverse‐square energy decay law. The prediction has been confirmed by measurements in a low‐speed water channel. A replot of the Dryden‐Schubauer and Batchelor‐Townsend wind‐tunnel data also indicates better agreement with the present inverse‐square, rather than themath‐power decay law proposed by earlier investigators.

Convergent Classical Kinetic Equation for a Plasma

E. A. Frieman and D. L. Book

Phys. Fluids 6, 1700 (1963); http://dx.doi.org/10.1063/1.1711012 (7 pages) | Cited 48 times

Online Publication Date: 9 December 2004

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A kinetic equation for a plasma of electrons and infinite mass ions is derived which exhibits no divergences for any impact parameter. The basic expansion used is in nλD3, the number of particles in a Debye sphere. The collision operator has Boltzmann, Fokker‐Planck, and Lenard‐Balescu behavior in the appropriate impact parameter regimes.

Time Dependence of the Two‐Particle Correlation Function in a One‐Component Plasma

George L. Lamb

Phys. Fluids 6, 1707 (1963); http://dx.doi.org/10.1063/1.1711013 (7 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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The linearized equations governing the time dependence of the one‐particle distribution function and the two‐particle correlation function in a one‐component plasma which is slightly removed from thermal equilibrium are investigated in the plasma limit. The integral equation for the two‐particle correlation function is solved by the Wiener‐Hopf method. It is shown that a self‐consistent evolution of the one‐particle distribution function and the two‐particle correlation function is not prescribed by the theory unless lengths on the order of the distance of closest approach in a two‐body encounter are retained. The relation of the analysis to the conjecture by Bogoliubov concerning the time dependence of multiparticle distribution functions is discussed. In particular, it is shown that although modes corresponding to distances larger than the Debye length are very slowly damped they do not make an appreciable contribution to the kinetic equations.

Kinetic Theory of Plasma and the Electromagnetic Field

Thomas H. Dupree

Phys. Fluids 6, 1714 (1963); http://dx.doi.org/10.1063/1.1711014 (16 pages) | Cited 73 times

Online Publication Date: 9 December 2004

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An exact kinetic equation for plasma and the electromagnetic field is derived. This equation describes the fluctuations of the fields and particle distributions. The solution is obtained by expanding in a parameter which characterizes the amplitude of these fluctuations. A systematic procedure is given for generating the solution to arbitrary order in the expansion. Some typical applications of the theory are presented. These include calculations of a collision integral, incoherent scattering, and bremsstrahlung emission and absorption.

Kinetic Treatment of the Stability of a Relativistic Particle Beam Passing through a Plasma

R. C. Mjolsness

Phys. Fluids 6, 1730 (1963); http://dx.doi.org/10.1063/1.1711015 (11 pages) | Cited 7 times

Online Publication Date: 9 December 2004

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The equilibrium configuration consists of a uniform particle beam of circular cross section and infinite extent streaming at highly relativistic velocity through a uniform, dense background plasma. The plasma is characterized by a scalar conductivity, and the beam is described by a collisionless Boltzmann equation in which a two mass approximation to the relativistic dynamics has been made. The stability problem for this configuration is formulated as a set of three linear, coupled integral equations for three field variables (certain Hankel transforms of the perturbed electric field), and a formal solution of the equations is obtained by iteration. The dispersion relation appears as a solvability condition. The treatment gives a full account of the betatron orbits of the beam particles. Asymptotic results are obtained for low‐frequency, long‐wavelength disturbances and for high‐frequency, highly localized disturbances.

Hose Instability for Relativistic Particle Beams in a Plasma Background

R. C. Mjolsness, J. Enoch, and C. L. Longmire

Phys. Fluids 6, 1741 (1963); http://dx.doi.org/10.1063/1.1711016 (9 pages) | Cited 4 times

Online Publication Date: 9 December 2004

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A macroscopic analysis is given of the low‐frequency, long‐wavelength instabilities of the relativistic beam‐plasma configuration. A two mass approximation is used for the particle dynamics. Plasma effects are accounted for by means of a tensor conductivity whose nondiagonal elements are due to the self‐magnetic field of the beam. The analysis is directed toward establishing the effect of the nondiagonal terms on growth rates. Three approximate methods of analysis are discussed. The conclusion is that the nondiagonal terms, even when large, contribute minor modifications to the dispersion law.

Plasma‐Beam Instability in the Hartree‐Appleton Approximation

Jacob Neufeld

Phys. Fluids 6, 1750 (1963); http://dx.doi.org/10.1063/1.1711017 (7 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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The interaction of a beam of protons of small intensity moving with velocity cβ (where c is the velocity of light) through a stationary plasma is investigated under the assumption that the beam is aligned along the direction of an impressed static magnetic field. Expressions are derived for frequencies and rates of growth characterizing the transverse waves excited by the beam and aligned along the direction parallel to that of the impressed field. It is assumed that the frequencies of the excited waves are large when compared to the proton gyrofrequency and are sufficiently high so that the motion of the plasma ions perturbed by these waves are neglected. It is shown that two waves are simultaneously excited by a beam having velocity cβ < cβmax and a relationship is obtained between βmax and the parameters charaterizing the stationary plasma.

Electric Field along a Magnetic Line of Force in a Low‐Density Plasma

Hans Persson

Phys. Fluids 6, 1756 (1963); http://dx.doi.org/10.1063/1.1711018 (4 pages) | Cited 24 times

Online Publication Date: 9 December 2004

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Stationary states of a collisionless plasma in a narrow axially symmetric magnetic mirror field are considered. It is shown that if the electric field vanishes identically along the magnetic field, then the angular distributions of ion and electron velocities must agree at each point. In a general case, when this condition on the distributions is not fulfilled, there is an electric field parallel with the magnetic field.

Laminar Steady State Electrohydrodynamic Flow in an Annular Channel

J. L. Shohet

Phys. Fluids 6, 1759 (1963); http://dx.doi.org/10.1063/1.1711019 (3 pages)

Online Publication Date: 9 December 2004

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An analytic solution is obtained for the condition of laminar electrohydrodynamic flow in an annular channel. It is assumed the charged dielectric liquid has a constant density and mobility of charge, and the current density is constant across the channel. Velocity profile curves are presented.
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Exact Solution of the Collisionless Plasma‐Sheath Equation

S. A. Self

Phys. Fluids 6, 1762 (1963); http://dx.doi.org/10.1063/1.1711020 (7 pages) | Cited 207 times

Online Publication Date: 9 December 2004

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The plasma‐sheath problem for the low‐pressure discharge in plane geometry is treated exactly, that is, with no arbitrary division into plasma and sheath regions. Numerical solutions are presented for various values of the parameter α, which is of the order of the ratio of the Debye length to the discharge width for 10−3 ≤ α ≤ 10−1; and for three assumptions regarding the ion generation rate, namely generation uniform, proportional to electron density, and proportional to the square of electron density.
For the higher values of α, corresponding to weak laboratory discharges, there is a smooth transition from a quasi‐neutral plasma region to a thick sheath. At the smaller values of α, the conventional model of a quasi‐neutral plasma region passing rather abruptly into a narrow sheath region is substantiated. In all cases, accurate values for the potential profile throughout the plasma and sheath regions are given and compared with the separate asymptotic plasma and sheath solutions for α = 0. The ion current density, wall potential, space‐charge density, mean ion energy, and sheath thickness are discussed.

Drift Instabilities in Cylindrical Discharges

John Wesson

Phys. Fluids 6, 1769 (1963); http://dx.doi.org/10.1063/1.1711021 (3 pages) | Cited 1 time

Online Publication Date: 9 December 2004

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Fluid equations are used to determine the drift stability of a general shearless cylindrical discharge. Arbitrary ion and electron temperatures are allowed. It is shown that a sufficiently large or small ratio of ion to electron temperature gives stability, and that, provided the azimuthal field is not too small, marginal magnetohydrodynamic stability implies drift stability.
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Magneto‐Acoustic Waves in a Plasma

J. Dé

Phys. Fluids 6, 1772 (1963); http://dx.doi.org/10.1063/1.1711022 (3 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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Abstract Unavailable

Morse Potential Parameters for Helium

O. P. Bahethi and S. C. Saxena

Phys. Fluids 6, 1774 (1963); http://dx.doi.org/10.1063/1.1711023 (2 pages) | Cited 5 times

Online Publication Date: 9 December 2004

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Abstract Unavailable

Spectral Distribution of Charged Particles in a Turbulent Plasma

Harold S. Rothman, Harold Guthart, and Tetsu Morita

Phys. Fluids 6, 1775 (1963); http://dx.doi.org/10.1063/1.1711024 (3 pages) | Cited 1 time

Online Publication Date: 9 December 2004

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Abstract Unavailable

Complete Current‐Voltage Characteristics of a Shock‐Heated Gas

Hugo K. Messerle and Donald W. George

Phys. Fluids 6, 1777 (1963); http://dx.doi.org/10.1063/1.1711025 (2 pages) | Cited 1 time

Online Publication Date: 9 December 2004

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Abstract Unavailable

Spectroscopic Observations on a Fully Ionized Barium Plasma

E. Hinnov, J. G. Hirschberg, F. W. Hofmann, and N. Rynn

Phys. Fluids 6, 1779 (1963); http://dx.doi.org/10.1063/1.1711026 (2 pages) | Cited 23 times

Online Publication Date: 9 December 2004

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Abstract Unavailable

Shock Waves in a Pinched Discharge

A. Folkierski and R. Latham

Phys. Fluids 6, 1780 (1963); http://dx.doi.org/10.1063/1.1711027 (3 pages) | Cited 3 times

Online Publication Date: 9 December 2004

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Abstract Unavailable
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