bluuebunny/crossref_metadata_2025 huggingface dataset:
Rotational Instability in the Theta Pinch
Authors: Bodin H. A. B. , Newton A. A.
Published: December 2004

An experimental study of the rotation and associated instability was made in a theta pinch with a peak field of 85 kG reached in 2.3 μsec. The starting deuterium gas pressure was in the range 50–150 μ Hg, and for operation on the second half-cycle of the sinusoidal driving field the magnetic flux trapped within the plasma varied between ±100 kMx. In most conditions the circular cross section of the plasma became perturbed along its length by the growth of two flutes which rotated at an angular velocity of up to 6 × 107 rad/sec. It is deduced from measurements on the rotation that the plasma acquires its angular momentum at the start of the half-cycle, and the results are interpreted on the basis that the angular momentum is initially in a diamagnetic (azimuthal) ion current. A model is described for establishing this current as a consequence of contact between the plasma and the walls. Results on the time of onset of the instability, and on the growth rate of the flutes, point to the existence of some damping or stabilizing process; it is found that field diffusion, or a rapid axial contraction of the plasma (due to closed reversed field loops), can lead to instability, and when these are reduced the stable time is increased. The possible influence of finite Larmor radius stabilization is discussed. The stability condition, originally derived for low β but recently shown to have more general validity, is in qualitative agreement with the results.
Hydrodynamic Effects Produced by Pulse Microwave Discharges
Authors: Lin Shao-Chi , Theofilos George P.
Published: December 2004

An elementary theory is proposed for estimating the strength of pressure waves to be expected from sudden breakdown of a gas by high frequency electromagnetic waves in a one-dimensional geometry. It is shown that, for an uncontrolled breakdown where the local field strength is not carefully matched to the instantaneous plasma condition to avoid strong reflections, the heating effect will be self limiting and the resultant shock strength depends only on the incident wave frequency and on the initial gas density. A numerical example for microwave breakdown in air indicates that, at normal sea level density, the shock wave accompanying the breakdown is generally quite weak (of the order of Mach 1.1 at 100 Gc/sec frequency). However, for breakdown at lower air densities, stronger shock waves can be anticipated. Preliminary experimental observations of pressure waves generated in a one-dimensional channel by pulse microwave discharges tended to confirm the general features of the elementary theory but showed somewhat stronger effects than predicted.
Excitation of Waves in a Warm Plasma by a Current Source
Authors: Kuehl Hans H.
Published: December 2004

The general expression for the electromagnetic field due to an arbitrary monochromatic current source in an unbounded, homogeneous, warm, collisionless plasma in the absence of a magnetostatic field is derived. A hydrodynamic description is used in which ion and electron motion is included. The general results are specialized to the case of an electric dipole source. It is found that the field is generally composed of three parts which, in the radiation region, correspond to the well-known transverse, longitudinal electron, and longitudinal ion waves. The power flow in the radiation region is shown to be largest along the axis of the dipole for low frequencies whereas the maximum occurs perpendicular to the dipole at high frequencies.
Relation between Thermal Conductivity and Viscosity for Nonpolar Gases. II. Rotational Relaxation of Polyatomic Molecules
Authors: O'Neal Cleveland , Brokaw Richard S.
Published: December 2004

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.
Convergent Classical Kinetic Equation for a Plasma
Authors: Frieman E. A. , Book D. L.
Published: December 2004

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.
Stability of the Positive Column in a Time-Dependent Magnetic Field
Authors: Johnson Roy R. , Jerde David A.
Published: December 2004

The stability of a weakly ionized plasma column in a longitudinal magnetic field containing a small time varying component is investigated, using a macroscopic approach previously developed by the authors for a static field. The time dependence of the field is taken to be linear, and its influence on the column given by the presence of the induced azimuthal electric field. A dispersion relation is derived from the linearized equations of continuity and momentum conservation for the ions and electrons, from which a family of stability boundary curves in the Ez vs B plane are found for the case of a helical perturbation in helium. The condition of energy balance of the column including the azimuthal electric field is combined with the dispersion relation to yield a family of stability boundary curves in the Eθ vs B plane with gas pressure times column radius as a parameter. These curves indicate regions of stability which are absent in the case of a static magnetic field.
Thermodynamic Properties of He3 and He4 Solutions. II. Temperatures Above the Superfluid Transition in Solution
Authors: Chandra R. , Nanda V. S.
Published: December 2004

The thermodynamics of He3 and He4 solutions is considered for temperatures and concentrations for which the solution does not show superfluidity. Calculations of the excess chemical potentials from the experimental vapor pressure data have been carried out between 1°K and 2°K by Roberts and Swartz. It is found that while the behavior of the He3 component can be reasonably explained down to 1°K within the framework of the classical solution theories, no such agreement is obtainable for the He4 component. The discrepancy is explained by extending some general thermodynamical considerations of Gorter regarding pure He4 to the solution. Further it is found that with a suitable choice of the Gibbs free energy expression of pure He4 a satisfactory quantitative agreement is also obtainable along these lines.
Many-Body Functions of a One-Dimensional Gas
Authors: Baxter R. J.
Published: December 2004

Formal expressions are obtained for the thermodynamic behavior and many-body functions of a one-dimensional system of particles with an arbitrary interaction potential. These expressions are particularly simple when the potential function satisfies a linear differential equation with constant coefficients over the domain (0, ∞). Explicit, exact results are obtained for a Coulomb interaction and compared with the Kirkwood approximation.
Structure of Plasma Sheaths
Authors: Sestero Arrigo
Published: December 2004

A model is given to provide a microscopic description of plasma sheaths, using the Vlasov equation for ions and electrons coupled with Maxwell's equations for the fields. The sheaths considered connect two different constant states of a plasma in a magnetic field. In the charge-neutral approximation a solution is obtained in closed form in terms of quadratures. The solution depends essentially on three free parameters, related to the differences in density and electric potential between the two end states, and to the value of β, the ratio of the plasma pressure to the magnetic pressure, on one side of the sheath. The scaling law changes considerably from one solution to another. Solutions are obtained which scale according to some representative electron Larmor radius, or ion Larmor radius, or piece-wise according to both. As a limiting case, when the density is allowed to go to zero on one side of the sheath, one obtains the boundary layer between a plasma and a containing vacuum magnetic field. As a peculiar feature in this limiting situation, the curve for the electric potential appears to be very sensitive to the slightest changes in the distribution functions, in the asymptotic region where the plasma density becomes vanishingly small.
Gravitational Resistive Instabilities in Plasma with Finite Larmor Radius
Authors: Jukes J. D.
Published: December 2004

The linearized equations of a gravity driven, resistive instability of a plasma supported by a planar, sheared magnetic field are shown to be characterized by a variational principle from which an eigenvalue corresponding to a periodic growth is obtained. The effect of a finite ion Larmor radius is included through off-diagonal terms in the pressure tensor in the momentum fluid equation.

When the Larmor radius is zero a numerical solution for the growth rate is found using a one parameter trial function which indicates that the correct function maximizes this rate. When the Larmor radius becomes significant, viz., with decreasing wavelength, the instability becomes an overstability with a reduced growth rate becoming proportional to the square root of the ratio of the resistivity to the wavelength. Whilst numerical results are given beyond this transition, the Larmor radius has become comparable with the thickness of an internal resistive layer and the equations cease to be reliable.
Collapse and Rebound of a Spherical Bubble in Water
Authors: Hickling Robert , Plesset Milton S.
Published: December 2004

Some numerical solutions are presented which describe the flow in the vicinity of a collapsing spherical bubble in water. The bubble is assumed to contain a small amount of gas and the solutions are taken beyond the point where the bubble reaches its minimum radius up to the stage where a pressure wave forms which propagates outwards into the liquid. The motion during collapse, up to the point where the minimum radius is attained, is determined by solving the equations of motion both in the Lagrangian and in the characteristic form. These are found to be in good agreement with each other and also with the approximate theory of Gilmore which is shown to be accurate over a wide range of Mach number. The liquid flow during the rebound, which occurs after the minimum radius has been attained, is determined from a solution of the Lagrangian equations. It is shown that an acoustic approximation is valid even for fairly high pressures, and this fact is used to determine the peak intensity of the pressure wave as it moves outwards at a distance from the center of collapse. It is estimated in the case of typical cavitation bubbles that such intensities are sufficient to cause cavitation damage.
Two-Stream Instability in a Cold Inhomogeneous Plasma in a Strong Magnetic Field
Authors: Harris E. G.
Published: December 2004

The two-stream instability in a cold plasma in a very strong magnetic field is considered. The density distribution is assumed to be the same for all species and varies arbitrarily in directions perpendicular to the field. For a given wavenumber in the direction of streaming there is a discrete set of normal modes. The stability of the system is determined by the lowest eigenvalue of a differential equation. A variational principle is devised for this lowest eigenvalue. The variational principle is applied to Gaussian and exponential density distributions. It is indicated how the eigenvalues corresponding to higher modes may be found by a Wentzel-Kramers-Brillouin method.
Plasma Conductivity at Low Frequencies and Wavenumbers
Authors: Kivelson M. G. , DuBois D. F.
Published: December 2004

The low-frequency electromagnetic conductivity of high-temperature, low-density plasmas is examined starting from a linearized kinetic equation of the Balescu type. The equation is solved in the limits ω ≫ Γee and Γii ≫ ω, where Γee and Γii are the inverses of the equipartition times of electrons and ions, respectively. The conductivity is related in a well-known way to the properties of collective waves, and expressions are obtained for the phase velocity and damping of these waves. The results agree with experiment to just within experimental accuracy.
Nonsteady Response of Plasmas to Microwave Radiation
Authors: Yen K. T.
Published: December 2004

A theoretical study of some nonsteady aspects of microwave radiation on ionized gases is presented. For weakly ionized gases, the concept of ``stabilized'' electron temperature is introduced. It is shown that under certain conditions, ionizations due to microwave radiation may be assumed to take place with the electron temperature remaining at this stabilized value. A simple expression for the ionization rate can then be obtained. Several time scales pertinent to these nonsteady processes have been obtained, and their relative order of magnitude is seen to be crucial in determining the nature of the nonsteady response. One type of nonsteady solutions for the ionization front of the gas under microwave radiation has been considered in some detail. Three different modes of response are possible depending on the initial electron density distributions. In particular, when the initial distribution is of the form ba exp (aξ)/[1 + b exp (aξ)], for ξ ≤ 0, where a and b are constants, the ionization front will propagate in the negative ξ direction toward the source of microwave radiation at a constant speed and with the same profile of electron density. This nonsteady response characteristic has some similarity with those observed in shock tube experiments.
Structure of a Plasma Shock Wave
Authors: Jaffrin Michel Y. , Probstein Ronald F.
Published: December 2004

The one-dimensional, steady-state structure of a shock wave in a fully ionized plasma is investigated in the absence of external applied magnetic or electric fields. The structure is assumed to be described by the Navier-Stokes equations written for the electron and ion fluids, together with Poisson's equation for the self-induced electric field. When the Debye length downstream of the shock (λD2) is small compared to the ion-ion mean free path there (l2), the plasma remains essentially neutral and the equations governing the charge separation and electric field can be uncoupled from the system. The remaining equations are reduced by a boundary layer type analysis, which uses the fact that different dissipative mechanisms are important over different length scales, and an integration in phase space is carried out. It is found that when the free stream Mach number M1 is less than 1.12, the plasma behaves like a single fluid and there is only one shock layer whose thickness is proportional to l2/ε, where ε is the square root of the electron to ion mass ratio. When M1 > 1.12, an ion shock appears imbedded in a wider electron thermal layer and the respective thicknesses are of order l2 and l2/ε. Within the ion shock the electric field and charge separation each show a single damped oscillation with an amplitude proportional, respectively, to λD2/l2 and (λD2/l2)2. When the shock is strong, a precursor electric shock layer in which the electric field and the charge separation again show a single damped oscillation appears upstream at the beginning of the thermal layer. With λD2 and l2 of the same order, the electrical effects interact directly with the flow in the two electric shock layers. The equations are simplified by the fact that the electrical gradients are reduced by the increased tendency towards charge neutrality. Calculations for M1 = 10 show that in the imbedded electric shock layer there is a relative excess of electrons of approximately 50% locally and that there are damped vestiges of ion oscillations present.
Investigation of the High-Energy Acceleration Mode in the Coaxial Gun
Authors: Mather J. W.
Published: December 2004

The amount of deuterium gas admitted to a short center electrode (1 cm) coaxial plasma gun delineates two regions of operation, depending on whether the gas is localized near the inlet port or allowed to diffuse throughout the gun length. In the former, fast deuterium ions with energy in excess of the applied voltage (V0 = 15 kV) emerge from the gun muzzle whereas in the latter, the accelerated plasma which initially starts at the breech end reaches an axial velocity of ∼2.5 × 107 cm/sec at the muzzle end and forms a high-density plasma focus on the axis in front of the central electrode. Neutron measurements show that this dense plasma is not in contact with the electrode and is most probably stagnated by the high ambient gas pressure downstream. Particle momentum analysis of the fast ion (> V0) distribution and neutron measurements downstream of the gun suggest two accelerated groups of fast ions, (1) a group of ∼1016 particles which diverge from the gun muzzle and (2) a group of ∼1014 particles which stream primarily along the axis with a radial distribution of ∼3 cm width. Multiple probes (Bθ) show an asymmetric angular distribution of the discharge current that varies as a function of time during a given discharge. A sharp break in the total gas current is accompanied by large inductive voltages. In the high-energy mode, inductive voltages up to 7V0 have been recorded at the breech end.
Velocity Limitation of a Coaxial Plasma Gun
Authors: Thom K. , Norwood J. , Jalufka N.
Published: December 2004

Arguments are cited to establish that for reasonable acceleration to occur in a pulsed coaxial plasma gun a conduction current must be drawn between electrodes in contact with the plasma. Further, under assumptions deemed justifiable for the coaxial gun it is shown that the current must consist of equal parts of ion and electron current. A drag force on the plasma then results from momentum exchange between the ions and the cathode. The equation of motion for the plasma including this drag force is solved and the results are shown to be consistent with experimental experience.
Thermally Inhomogeneous Plasma Column
Authors: Ecker G. , Zöller O.
Published: December 2004

Theoretical investigations of the cylindrical collision dominated plasma column in general use Schottky's assumption of constant temperatures. This assumption definitely breaks down with increasing current. Our investigation accounts for the temperature inhomogenities. The balances for the first three momenta of the three particle components are reduced to a system of two coupled differential equations including all temperature effects. These equations reveal a similarity law. They are solved numerically with the help of a computer. The radial density and temperature distributions together with the characteristic of the plasma column are presented and compared with Schottky's relations. The results provide the basis of the ``thermal instability'' calculated in a subsequent paper.
Initial Ionization Rates in Shock-Heated Argon, Krypton, and Xenon
Authors: Harwell Kenneth E. , Jahn Robert G.
Published: December 2004

The rate of ionization behind strong shock waves in argon, krypton, and xenon, is observed by a transverse microwave probe, over a range of electron densities low enough that atom-atom inelastic collisions are the rate-determining mechanism. Shocks of Mach number 7.0 to 10.0 propagate down a 2-in. sq. aluminum shock tube into ambient gases at pressures of 3.0 to 17.0 mm. Hg., heating them abruptly to atomic temperatures of 5500°K to 9600°K. The subsequent relaxation toward ionization equilibrium is examined in its early stages by the reflection, transmission, and phase shifts of a 24.0 Gc/sec (1.25 cm) transverse microwave beam propagating between two rectangular horns abreast a glass test section. The data yield effective activation energies of 11.9 ± 0.5 eV for argon, 10.4 ± 0.5 eV for krypton, and 8.6 ± 0.5 eV for xenon. These coincide, within experimental error, with the first excitation potentials, rather than the ionization potentials of the gases, indicating that in this range ionization proceeds via a two-step process involving the first excited electronic states of which the excitation step is rate controlling.
Stability of a Continuum Plasma
Authors: Miles John W.
Published: December 2004

Weibel has considered the stability of a cylindrical column of plasma, regarded as a viscous compressible fluid, that is confined by a combination of dc and rf magnetic fields. The integral equation in which his analysis culminates is considered here. The normal modes are first determined for a dc magnetic field and found to be definitely stable for all finite wavelengths and neutrally stable for infinite wavelengths. It then is shown that the addition of an rf magnetic field renders a finite number of these modes unstable in certain spectral bands. This last result is based on the hypothesis that the strength of the rf magnetic field is small compared with that of the dc field (or small in some other appropriate sense), in consequence of which the modes of the plasma in the presence of the rf magnetic field may be regarded as approximately independent.
Bounds on Plasma Instability Growth Rates
Authors: Fowler T. K.
Published: December 2004

A method is presented for obtaining upper bounds on the growth rate of plasma instabilities predicted by the linearized Vlasov equation. The technique is applicable to spatially nonuniform equilibria not amenable to conventional analysis. As examples, radially confined arc columns and mirror machine configurations are discussed. The fastest growth in these systems corresponds to that of known electrostatic instabilities in uniform, infinite plasmas. For arbitrary equilibria, it is shown that growth is always slower than some exponential, the plasma frequency being a typical maximum growth constant. Growth is strongly limited for equilibria ``near'' a stable state. For example, the streaming instability growth rate vanishes at least linearly with the streaming speed.
Turbulence in Non-Newtonian Fluids
Authors: Lumley John L.
Published: December 2004

The dissipation of turbulent energy is examined in incompressible isotropic fluids in which deformation depends only on current values of strain rate (Reiner-Rivlin fluids). For isotropic, homogeneous, decaying turbulence, two special cases are examined exactly—the Gaussian process and the inertial subrange. Generalizing from these and from known properties of turbulence in Newtonian media, it is concluded that anomalous properties of turbulence observed in non-Newtonian media (the Toms effect) cannot be expected for a Reiner-Rivlin model (nor for a simple power-law fluid, which is a subclass) and that the explanation for these observations must therefore be sought in visco-elasticity (i.e., dependence on history of strain). It is shown in addition that the form of the probability density of the strain tensor is almost surely quite sensitive to the form of the stress-deformation relation.
Flow Development in the Hydrodynamic Entrance Region of Tubes and Ducts
Authors: Sparrow E. M. , Lin S. H. , Lundgren T. S.
Published: December 2004

A new method of analysis has been devised for determining the developing laminar flow and corresponding pressure drop in the entrance region of tubes and ducts. The method is formulated in a general manner which applies to ducts of any cross section. Specific application is made for flow in a circular tube and in a parallel-plate channel, and the velocity distribution and pressure-drop results are compared with experimental data and prior analyses. These comparisons lend strong support to the findings of the present analysis.
Approximations to the Pair Correlation Function for a Hard-Sphere Fluid
Authors: Klein Max
Published: December 2004

The equation of state for hard spheres as predicted by the chain, watermelon, convolution-hypernetted chain (CHNC), Percus-Yevick, and two new approximations to the pair correlation function are compared with each other and with a reference isotherm.

The equations of state of the chain and watermelon approximations have been found to be only slight improvements over the linear correction to the ideal gas law. The Percus-Yevick theory has been found to be an improvement over the CHNC approximation for hard spheres in agreement with the results of Hoover and Poirier for hard cubes and of Broyles for several densities of the Lennard-Jones (12,6) gas. The new approximations are designated n = 1 and n = 2. They make use of the solutions to the CHNC integral equation but do not include all the diagrams for the pressure. The approximation n = 2 was found to yield an equation of state in excellent quantitative agreement with the reference isotherm for densities up to 0.707 times the close packed density.

Both the nearest and next nearest neighbors were computed as a function of density in each approximation. Only the CHNC and Percus-Yevick results extrapolate to the proper value at the density of close packing. Both of these approximations, furthermore, indicate the existence of a singularity at densities less than or equal to that of close packing. The approximations considered seem to form part of a uniform approach to the reference isotherm. At the same time, the representations of the known virial coefficients associated with each do not approach the correct virial coefficients in a uniform fashion. Therefore, an understanding of this sequence of approximations cannot be had from the usual examination of virial coefficients.
Thermoelectric Effects in a Joule-Heated Plasma
Authors: Hall Laurence S.
Published: December 2004

The temperature and potential distributions in a fully ionized, Joule-heated plasma have been computed for a one-dimensional system in which the thermoelectric terms have been taken into account, and a comparison is made with the case in which the cross terms are neglected. It is found that the thermoelectric terms cause the temperature distribution to be significantly skewed. Moreover, if T0 is the maximum temperature, it is found that these terms cause the potential to drop sharply near the anode, in the sense opposing the current flow, by from 15 to 35% of kT0/e.
Superposition of Dressed Test Particles
Authors: Rostoker Norman
Published: December 2004

Kinetic theory for a spatially homogeneous plasma with Coulomb interaction is considered within the framework of the adiabatic approximation or secular perturbation theory. Time dependent solutions are obtained for the pair correlation function, multiple time distribution functions, etc. Auto correlation functions and spectral densities for fluctuating quantities are defined and obtained for a stable or unstable plasma. The results show that the plasma behaves as though it consisted of statistically independent quasiparticles. The relationship between test-particle problems and the more general kinetic theory is clarified. Physical interpretation of each term in the Fokker-Planck equation is provided in terms of spontaneous emission, induced emission, and absorption.
Ionization Rates and Power Loss from θ-Pinches by Impurity Radiation
Authors: Kolb Alan C. , McWhirter R. W. P.
Published: December 2004

Calculations are presented for the influence of small impurity concentrations on the energy balance and electron temperature during the magnetic compression of a deuterium plasma. The rate equations which describe the ionization are based on the Corona Plasma Model in much the same way as has been done earlier for a plasma assumed to be homogeneous.

Despite the comparatively high electron densities (≳1016 cm−3) in these plasmas, this model should be applicable because of the high ionic charge at temperatures over ∼10 eV. The radial temperature and density distributions were obtained numerically by coupling the Hain-Roberts two-fluid, hydromagnetic equations to the Corona equations. The ionization of up to four different impurities, i.e., C, N, O, Ne, can be taken into account. Radiation losses were included in the electron energy-balance equation, but the influence of impurity ionization on the electron density and electrical conductivity was neglected. Therefore, only small impurity concentrations can be considered. However, only a few percent impurities have a drastic effect on the electron temperature so that the present calculations may be meaningful in the interpretation of certain experiments.
Nonadiabatic Motion of a Charged Particle in an Axisymmetric Magnetic Barrier
Authors: Roth J. Reece
Published: December 2004

A study was made of the motion of a single charged particle in the magnetic induction generated by an axisymmetric current sheet, the current of which was sinusoidally modulated along the axis. Several adiabatically invariant quantities were investigated, and it was found that M4 = |v×B|2/|B|3 varied least along a given trajectory. A particle was considered to be adiabatic if M4 varied by less than 5% during a single interaction with the magnetic barrier. An averaging process was found which made it possible to predict the relations between particle mass and energy, and the magnetic induction strength and geometry, which cause M4 to vary by more than 5% during a single interaction with the magnetic barrier.

Experimental apparatus was constructed which made it possible to study a single interaction of a beam of charged particles with a magnetic barrier under steady-state conditions. An experimental procedure was developed which made it possible to detect the transition from adiabatic to nonadiabatic reflection of the ion beam, and the results were compared with the results of the numerical computation.
Microwave Attenuation by Shocked Heated Air
Authors: Dvir M. , Low W.
Published: December 2004

The microwave attenuation of air in Mach range 8–12 is investigated at initial pressures of 5 mm Hg. It is shown (a) that the experimental peak attenuation is larger than given by conventional theory; (b) that the time dependence of the attenuation curve gives important information regarding the build-up of the ionization as a function of time, the contact surface and the zone behind it.

It is found that the microwave attenuation rises approximately linearly as a function of time to its peak value. The testing time is shorter than that predicted from ideal shock theory but sufficient to establish equilibrium. The electron density changes abruptly upon arrival of the driver gas. However, an appreciable electron density exists over a large region behind the contact surface indicating strong interface mixing. It is also shown that the nature of the surface of the shock tube influences the peak attenuation and the time dependence of this attenuation.
Flow of a Hydrogen Plasma through a Transverse Magnetic Field
Authors: Beckner Everet H.
Published: December 2004

A study has been conducted of the phenomena occurring when a hydrogen plasma is caused to flow through a transverse magnetic field. Plasma polarization effects were studied as well as the deceleration processes which occurred when large currents were extracted from the plasma. Standing ``wedge-shaped'' shock waves were observed when sufficient current was extracted to permit the deceleration phenomena to be manifested. The effective plasma resistance between electrodes was determined, and a correlation made with plasma conductivity measurements, including boundary layer effects. Finally, a determination was made of the power and energy extracted from the plasma.
Hydraulic Jump in a Rotating Fluid
Authors: Yih Chia-Shun , Gascoigne H. E. , Debler W. R.
Published: December 2004

A hydraulic jump occurs in a layer of fluid flowing down the inner wall of a rotating cylinder when the downstream conditions are adequate. The theory of these jumps is presented, together with supporting experimental data. The results confirm the similarity between free-surface flows under general rotation (and hence centripetal acceleration) and free-surface flows in the presence of a gravitational field, and indicate that the hydraulic jump in a rotating fluid is just the counterpart of the ordinary hydraulic jump.
Some Properties of Shock Relaxation in Gas Flows Carrying Small Particles
Authors: Rudinger George
Published: December 2004

Shock waves passing through uniform suspensions of droplets or solid particles in a gas upset the velocity and temperature equilibrium between the two phases, and a relaxation zone is created in which the equilibrium is gradually re-established. The effects of varying the shock strength or the properties of the mixture are investigated theoretically, and it is noted that some flow variables do not always change monotonically throughout the relaxation zone but may go through a maximum or minimum. The behavior of individual variables is discussed in some detail. A particularly interesting finding is that, for weak shock waves, the maximum particle drag and heat transfer may appear at some distance from, rather than immediately behind, the shock front. The behavior of the variables changes at critical conditions which depend on the thermodynamic properties of the materials involved, on the shock strength, and sometimes also on the assumptions made for the drag coefficient or the Nusselt number. For the gas velocity, these critical conditions can be expressed in simple analytical forms.

In all calculations some assumptions must be made for particle drag and heat transfer. Calculations based on plausible variations of the customarily used formulas show that the results are significantly affected by the assumption made for particle drag, but only to a minor extent by that for heat transfer. It is concluded that experimental determination of the drag coefficient by shock-tube techniques appears feasible.
Pressure Wave Generated in a Fissionable Gas by Neutron Irradiation
Authors: Smith H. P. , Busch C. W. , Oppenheim A. K.
Published: December 2004

An experiment is proposed to study the nonsteady gasdynamic phenomena produced by neutron induced exothermic nuclear reactions in a gaseous medium. The problem is formulated in terms of a set of characteristic equations in a time dependent, spatially unidimensional system and solved by means of a simplified analysis leading to a system of two first order, nonlinear, ordinary differential equations that permit the attainment of a clearer understanding of the salient features of the problem than can be obtained from a more rigorous solution. The problem involves the generation of a pressure wave in a long tube filled with a boron trifluoride, fully enriched in the boron-10 isotope which undergoes the reaction: 10B(n, α) 7Li as a result of a 1000 MW neutron pulse of approximately 10 msec halfwidth directed along part of its length by irradiation from a TRIGA reactor. The analysis predicts that the gas residing initially in the core will be heated to approximately 3000°K and that a compression wave with a peak pressure ratio of approximately 3 will emanate from the reactor and coalesce into a shock of Mach number 1.8 at a distance of approximately 17 ft from the reactor core. Measurement of the pressure wave should provide information on the amount of reversible heating that can be obtained from a gaseous nuclear reaction. It should be considered therefore of particular value in gaining specific familiarity with fissionable gasdynamics.
Stability of Idealized One-Reaction Detonations
Authors: Erpenbeck Jerome J.
Published: December 2004

The hydrodynamic stability of steady, one-dimensional detonations in an ideal-gas medium, undergoing the irreversible, unimolecular reaction A → B, having Arrhenius rate constant, is obtained in numerical form by application of the general theory of detonation stability. Stability results, as well as the pressure and progress variable profiles for the steady detonations, are presented for a (constant) heat capacity ratio γ of 1.2, a heat of reaction Q, relative to thermal energy in the cold reactants, of 50, activation energies Q‡ (in the same units) of 10 and 50, and at several detonation velocities, D. The neutral stability curves, consisting of the values of the disturbance wavelength transverse to the steady flow for which the steady detonation of given velocity changes stability (as functions of detonation velocity), are investigated. One-dimensional disturbances are found to be unstable at low detonation velocities (i.e., near the CJ point), for the larger activation energy (but not the smaller) but are stabilized by sufficient overdrive. At fixed detonation velocity, a range of wave lengths are unstable and for Q‡ = 50, this instability appears to persist for all detonation velocities. For decreasing heat of reaction (at fixed Q‡, γ, and D/DCJ) the detonation is found to become stable although for Q‡ = 50 the instability persists to very small values of the heat of reaction. Thus, the system Q = 0.3, Q‡ = 50, γ = 1.2 is found to be unstable when f = (D/DCJ)2 ≤ 1.1. The phenomenon of one-dimensional instability and its dependence on Q is also investigated.
Linearized Hyperbolic Steady Magnetohydrodynamic Flow Past Nonconducting Walls
Authors: Chu C. K.
Published: December 2004

Linearized steady hyperbolic flows of an ideally-conducting fluid past infinite insulating walls are considered. Because of the interaction between the magnetic fields in the fluid and in the solid wall, the fluid is everywhere disturbed and there are no regions of uniform flow. The flow cannot be constructed from shocks and simple waves as in ordinary supersonic gas dynamics, but must be found together with the field in the solid. Essentially, the linearized problem consists of a wave equation in the upper half-plane, and a Laplace equation in the lower half-plane, with appropriate boundary conditions on the interface and at infinity. A general procedure which yields the unique solution is given. Several specific examples are calculated, including the flow past a wavy wall, and the flow past a wall with two corners. It is shown that the flow past a single corner is not a meaningful problem, since the perturbations become infinite far away from the corner.
Kinetic Theory of an Electron-Photon Gas
Authors: Dreicer H.
Published: December 2004

An extension of the Boltzmann equation for plasmas is presented, including interactions between the electrons and the photons which populate the radiation field. This development results in those electron-photon collision integrals which are required to describe relaxation towards equilibrium of both particles and radiation field as a result of radiative interactions alone. Single-photon emission and absorption as well as Compton scattering are treated. The equation derived is specialized to the case of electrons orbiting in a steady magnetic field, and is used to follow the relaxation of a test electron which is interacting with a thermal radiation field via the emission and absorption of cyclotron radiation. It is also used to study the saturation properties of the cyclotron radiation maser. In the case of Compton scattering by free electrons a clear separation between these electron-photon collision terms and the usual electric field term in the Boltzmann equation is shown to exist. Collision terms are also derived for the photon transport equation, with particular attention paid to the effect of enhanced scattering when more than one mode of the radiation field is simultaneously occupied. This equation is then used to evaluate a new type of light scattering experiment, one which involves the enhanced Compton scattering by free electrons traversing an intense radiation field excited in two of its modes. The entire treatment is based upon independent particle behavior. Many-body collective effects are ignored.
Solitary Waves in a Collision-Free Plasma with an Isotropic Pressure
Authors: Cordey J. G.
Published: December 2004

The effect of an isotropic pressure on longitudinal nonlinear plasma waves is investigated. Two distinct types of solitary wave solutions are found, one similar to the nonlinear zero pressure wave and a new type which is best described as a solitary wave within a solitary wave. The order of magnitude of the width of the first type of wave and the outer part of the second is the geometric mean of the gyroradii of the ions and electrons when moving with the Alfvén speed. It is found that the isotropic pressure shortens the width of the first type of wave. Both cases of unequal and equal ion and electron temperatures are investigated for the two types of waves.
Kinetic Theory of the Classical Electron Gas in a Positive Background. I. Equilibrium Theory
Authors: Guernsey Ralph L.
Published: December 2004

An approximation scheme is developed for calculating the equilibrium properties of a system containing both short-range and weak long-range interactions. The results are applied to the calculation of the pair correlation and equation of state for an electron gas in a neutralizing background. Although the starting point is the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, the short-range divergence usually encountered in the ``dynamic'' approach is avoided, and the results (calculated through second order in the plasma parameter) are found to be in agreement with previous calculations by diagrammatic methods.
Propagation of a Reflected Shock Wave in a Transverse Magnetic Field
Authors: Boublil Yolande , Earnshaw Kenneth B.
Published: December 2004

Shock waves are reflected from a wall in the presence of a transverse magnetic field. The gas is highly ionized and therefore the lines of force can be considered ``frozen in.'' In such a case the magnetic field is compressed and the Rankine-Hugoniot relations, including magnetic pressure and magnetic energy as given by de Hoffmann and Teller, are used. The magnetic probes show an increase of the magnetic field behind the reflected shock, and the velocity of the reflected shock waves (measured from streak camera photographs) increases with increasing fields. For a constant incident velocity, the dependence of the reflected shock velocity on the magnetic field is given by a linear function: Ur2 = a + bB2 where a and b are constant in a first approximation. This law has been verified by experimental results.
Measurement of Ion Energies in a θ-Pinch
Authors: Goldman L. M. , Kilb R. W. , Pollock H. C.
Published: December 2004

The energy of the deuterons in a θ-pinch device has been determined by comparing the rate of production of neutrons and 14.7 MeV protons when a plasma of D and 3He is compressed. The different energy dependence of the fusion cross sections for D + D → 3He + n and D + 3He → 4He + p allows a determination of the deuteron energy if the velocity distribution function is properly chosen. Using a monoenergetic velocity distribution, the energy of the deuterons undergoing fusion is found to be in the range of 10 keV for the conditions of the experiment.
Virial Coefficients of Carbon Monoxide-Hydrocarbon Mixtures
Authors: Connolly J. F.
Published: December 2004

Virial coefficients have been obtained for mixtures of carbon monoxide with benzene and n-octane. Gas compressibilities and liquid solubilities were measured in order to cover the temperature range 50° to 300°C. The Kihara intermolecular potential-energy function is somewhat more effective in predicting the experimental mixed second virial coefficients than is the Lennard-Jones function.
Kinetic Equations for a Plasma Including Radiation in the Presence of an External Magnetic Field
Authors: Fante Ronald
Published: December 2004

The solutions of the Simon-Harris hierarchy of equations for a spatially homogeneous plasma in an external magnetic field are obtained by an operator technique. These solutions are then used to formally derive a Fokker-Planck equation and what may be interpreted as a radiative transfer equation. Finally the solutions for the limiting case of zero magnetic field are obtained and examined.
Instabilities due to Resistivity Gradients in a Low-Pressure Plasma
Authors: Hoh F. C.
Published: December 2004

Instabilities due to resistivity gradients in a low-pressure plasma are reconsidered using the electrostatic approximation. The fastest growth rate is proportional to η∥⅓, where η∥ is the resistivity component parallel to the magnetic field. Contrary to earlier belief, heat conductivity along the field lines does not reduce the growth rate appreciably for Stellarator type of data. This mode is strongly localized in a thin layer inside the plasma, and hence may not produce much anomalous diffusion. Comparison is made with the much slower Kadomtsev mode, proportional to η∥, which is not localized. The effects of finite Larmor radius and Hall current acting in the plane perpendicular to the magnetic field are deduced. The corresponding actions parallel to the magnetic field, which seems to be more important when the plasma pressure is not too low, is not considered.
The Natural Time of a Viscoelastic Fluid: Its Significance and Measurement
Authors: Truesdell C.
Published: December 2004

A ``natural time'' is defined in terms of the viscometric functions of a simple fluid. Its magnitude is a measure of the relative importance of normal-stress effects. Such a time is shown to be an ordering parameter for departures from the theory of linear viscosity in fluids with fading memory. The frequency dependence of the absorption and phase shift in the diffusion of forced sinusoidal shearing at the boundary of a semi-infinite mass of fluid are shown to depend critically upon the natural time.
Measure of the Intricacy of Turbulence
Authors: Betchov R.
Published: December 2004

A quantity is defined which measures the degree of complication of a turbulent flow. It indicates the amount of information necessary per unit volume to describe the turbulence with an accuracy comparable to thermal agitation. It represents a small supplement to the entropy of the fluid. It is also found that maximum intricacy corresponds to a maximum rate of energy dissipation.
Estimates of Shock-Tube Precursor Infrared Excitation
Authors: Lapp M.
Published: December 2004

A simple analysis is given for pre-excitation of molecular species in shock-tube flows by precursor infrared radiation. Estimates of rough magnitudes are given under shocked-gas temperature and pressure conditions corresponding to a Mach 5.5 shock propagating into 200 Torr of a 5% test gas, 95% argon mixture. It is found that the effect is slight for species of moderate infrared emission, such as CO, while it may be of some significance for species of high infrared emission, such as CO2.
Visible Continuum Emission from Shocked Noble Gases
Authors: Alpher R. A. , White D. R.
Published: December 2004

Relative intensities have been measured at maximum luminosity in the visible continuum emitted by shock-ionized argon, krypton, and xenon. The attendant physical conditions at local thermodynamic equilibrium were 0.5 eV ⪝ temp. ⪝ 1.5 eV, 0.5 ⪝ press. ⪝ 2 atm and 10−2 ⪝ degree of ionization ⪝ 0.25. The dependence of the data on electron concentration and temperature correlates well with the Kramers-Unsöld theory, indicating that free-bound electron transitions are the primary source of the continuum.