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Showing papers in "Physics of Fluids in 1958"


Journal ArticleDOI
TL;DR: In this article, an approximate formula for the thermal conductivity of multicomponent gas mixtures is derived from rigorous kinetic theory by well-defined approximations, and the form of the formula is quite similar to the earlier empirical Lindsay-Bromley equation.
Abstract: An approximate formula for the thermal conductivity of multicomponent gas mixtures is derived from rigorous kinetic theory by well‐defined approximations. Numerical calculations with the formula are relatively simple, and the only data needed are the molecular weights, thermal conductivities, and either viscosities or heat capacities of the pure components at the same temperature as the mixture. The form of the formula is quite similar to the earlier empirical Lindsay‐Bromley equation. The formula is tested by comparison with experimental results on a number of binary and ternary mixtures involving both monatomic and polyatomic nonpolar gases. Agreement is satisfactory, and is nearly as good as obtained with the full rigorous theory.

521 citations


Journal ArticleDOI
TL;DR: In this paper, a variety of properties are derived satisfied by any static equilibrium of a plasma governed by the well-known magnetostatic equations, and a variational principle for such equilibria is derived.
Abstract: A variety of properties are derived satisfied by any static equilibrium of a plasma governed by the well‐known magnetostatic equations. Some of these are local and quite trivial. Others involve integrals over surfaces of constant pressure, which are shown to be topologically toroidal under fairly general assumptions.A variational principle for such equilibria is derived. One of its consequences is to provide a characterization of equilibria by their values of certain invariants.Finally, conditions are obtained additional to the magnetostatic equations appropriate to the steady state of a plasma slowly diffusing across a magnetic field out of a topologically toroidal region.

419 citations


Journal ArticleDOI
TL;DR: In this article, the basic concepts of the controlled thermonuclear program at Project Matterhorn, Princeton University are discussed, the theory of confinement of a fully ionized gas in the magnetic configuration of the stellarator is given, the theories of heating are outlined, and the bearing of observational results on these theories is described.
Abstract: The basic concepts of the controlled thermonuclear program at Project Matterhorn, Princeton University are discussed. In particular, the theory of confinement of a fully ionized gas in the magnetic configuration of the stellarator is given, the theories of heating are outlined, and the bearing of observational results on these theories is described.Magnetic confinement in the stellarator is based on a strong magnetic field produced by solenoidal coils encircling a toroidal tube. The configuration is characterized by a ``rotational transform,'' such that a single line of magnetic force, followed around the system, intersects a cross‐sectional plane in points which successively rotate about the magnetic axis. A theorem by Kruskal is used to prove that each line of force in such a system generates a toroidal surface; ideally the wall is such a surface. A rotational transform may be generated either by a solenoidal field in a twisted, or figure‐eight shaped, tube, or by the use of an additional transverse multipolar helical field, with helical symmetry.Plasma confinement in a stellarator is analyzed from both the macroscopic and the microscopic points of view. The macroscopic equations, derived with certain simplifying assumptions, are used to show the existence of an equilibrium situation, and to discuss the limitations on material pressure in these solutions. The single‐particle, or microscopic, picture shows that particles moving along the lines of force remain inside the stellarator tube to the same approximation as do the lines of force. Other particles are presumably confined by the action of the radial electric field that may be anticipated.Theory predicts and observation confirms that initial breakdown, complete ionization, and heating of a hydrogen or helium gas to about 106 degrees K are possible by means of a current parallel to the magnetic field (ohmic heating). Flow of impurities from the tube walls into the heated gas, during the discharge, may be sharply reduced by use of an ultra‐high vacuum system; some improvement is also obtained with a divertor, which diverts the outer shell of magnetic flux away from the discharge. Experiments with ohmic heating verify the presence of a hydromagnetic instability predicted by Kruskal for plasma currents greater than a certain critical value and also indicate the presence of other cooperative phenomena. Heating to very much higher temperatures can be achieved by use of a pulsating magnetic field. Heating at the positive‐ion cyclotron resonance frequency has been proposed theoretically and confirmed observationally by Stix. In addition, an appreciable energy input to the positive ions should be possible, in principle, if the pulsation period is near the time between ion‐ion collisions or the time required for a positive ion to pass through the heating section (magnetic pumping).

381 citations


Journal ArticleDOI
TL;DR: In this article, the fundamental conservation equations governing fluid dynamics and including radiation were written down and the Rankine-Hugoniot conditions were derived for shock waves subjected to radiation flux.
Abstract: The fundamental conservation equations governing fluid dynamics and including radiation are written down. The Rankine‐Hugoniot conditions are derived for shock waves subjected to radiation flux. Similarity solutions are obtained for the constant density and constant pressure cases. Some results are stated for the combined radiation‐fluid dynamics corresponding to a power law dependence of the temperature on the time.

368 citations


Journal ArticleDOI
TL;DR: In this article, a statistical formalism for describing the behavior of sprays is presented, which includes the effects of droplet growth, the formation of new droplets, collisions, and aerodynamic forces.
Abstract: A statistical formalism for describing the behavior of sprays is presented, which includes the effects of droplet growth, the formation of new droplets, collisions, and aerodynamic forces. Criteria for the efficiency of impinging jet atomization are developed. It is shown that if the incident jets have a size distribution of a generalized Rosin‐Rammler type, then the resulting spray belongs to the same class of distributions. The size history of evaporating sprays is also obtained from the theory. A spray combustion analysis given by Probert is extended to include more general size distributions and the effects of droplet interactions and the relative motion of the droplets and the fluid. It is shown that the over‐all spray evaporation rate is largest for uniform sprays.

364 citations


Journal ArticleDOI
TL;DR: In this article, the stability of a system of charged particles in the Boltzmann equation in the small m/e limit has been investigated, and the results show that the first order variation of the energy vanishes trivially and the second order variation yields a quadratic form in the displacement variable ξ.
Abstract: Criteria useful for the investigation of the stability of a system of charged particles are derived from the Boltzmann equation in the small m/e limit. These criteria are obtained from the examination of the variation of the energy due to a perturbation, when subject to the general constraint that all regular, time‐independent constants of the motion (including the energy) have their equilibrium values.The first‐order variation of the energy vanishes trivially, and the second‐order variation yields a quadratic form in the displacement variable ξ (which may be introduced because of the well‐known properties of this limit). The positive‐definiteness of this form is a sufficient condition for stability.Several theorems are stated comparing stability under the present theory with that under conventional hydromagnetic fluid theories where heat flow along magnetic lines of force is neglected. Generalizations can be made to systems where the effect of collisions is included.

302 citations


Journal ArticleDOI
Abstract: An attempt is made to analyze the factors which determine the operation of the bubble chamber It is concluded that the majority of bubbles in conventional chambers are nucleated by moderately energetic free electrons produced by the incident particles in Coulomb encounters Nuclei are displaced too infrequently by Coulomb encounters to account for the observed densities of bubbles The electrons deposit their kinetic energy in highly localized regions which then are the source of explosions which produce bubbles of greater than critical size in a time of the order of 10−10 or 10−11 sec The bubbles grow subsequently by evaporation of the fluid The temperature of the fluid should be sufficiently close to the critical temperature that the energy required to produce the bubble of critical size can be provided by an electron with a range comparable to or less than the diameter of the bubble of critical size Otherwise the electron will be unable to localize its energy in a sufficiently small volume in any but highly improbable cases It is also concluded that the viscosity of the liquid plays a very important role in determining the threshold energy for forming a bubble of critical size when it has a value near 1 centipoise or larger

231 citations


Journal ArticleDOI
TL;DR: In this paper, the effect at Earth of the distortion of the outer boundary of the geomagnetic field is computed; no matter how unevenly and anisotropically the outer field is distorted.
Abstract: The dynamical properties of the solar wind blowing past the geomagnetic field are investigated by considering the effective viscosity and the resulting transition layer thickness. The collision of ions in the solar wind produces a negligible viscosity in the flow past the geomagnetic field, but such an inviscid flow is shown to be unstable. The resulting disordered interface between the field and the wind yields Fermi acceleration of ions and consequently a not insignificant effective viscosity. The Fermi acceleration results in suprathermal ions which may have an energy spectrum like that observed for primary auroral protons.The auroral zones and the agitated nature of the polar geomagnetic field are shown to follow from the depth of penetration of the solar wind into the geomagnetic field. The injection of gas into the geomagnetic field is studied. The effect at Earth of the distortion of the outer boundary of the geomagnetic field is computed; no matter how unevenly and anisotropically the outer field ...

222 citations


Journal ArticleDOI
TL;DR: In this paper, a chemically reactive species is emitted from the surface of a body located in a hydrodynamic flow field and diffuses into the fluid where it undergoes a simple isothermal, homogeneous transformation.
Abstract: A chemically reactive species is emitted from the surface of a body located in a hydrodynamic flow field. It diffuses into the fluid where it undergoes a simple isothermal, homogeneous transformation. The analysis given enables one to trace the reaction history of this component in a laminar boundary layer flow which develops over the surface of a body.For illustration the development of a first‐order reaction in the neighborhood of a flat plate is calculated. Two reaction types are considered. In one case the reactant is destroyed; in the other, it is generated. The reaction histories show a number of interesting features which are discussed in some detail.

214 citations


Journal ArticleDOI
TL;DR: In this article, known intermolecular force laws are used to calculate virial coefficients of the equation of state and the transport properties at very high temperatures for the rare gases and for molecular nitrogen.
Abstract: Known intermolecular force laws are used to calculate virial coefficients of the equation of state and the transport properties at very high temperatures for the rare gases and for molecular nitrogen. The crucial force laws which enable the calculations to be carried to high temperatures are those derived from molecular beam scattering measurements, which are valid at close distances of molecular approach. The calculations cover the temperature range from 1000° to 15 000°K, but take into account only the translational degrees of freedom and neglect the effects of excitation, dissociation, and ionization. The treatment of mixtures is outlined, and illustrated by calculations for the binary system helium‐argon. The methods which are used offer an approach to the problem of obtaining reasonably accurate estimates of gas properties at temperatures so high that direct experiments would be extremely difficult, if not impossible.

209 citations


Journal ArticleDOI
TL;DR: In this paper, a generalization of the Mayer cluster integral theory for quantum statistics of interacting particles has been developed, where the cluster integrals are integrals over propagators which are derived from the Green's function solution of the Bloch equation (which follows from the Schroedinger equation by replacing it/ℏ by β = 1/kT).
Abstract: A systematic generalization of the Mayer cluster integral theory has been developed to deal with the quantum statistics of interacting particles. The grand partition function appears in a natural way and the cluster integrals are integrals over propagators which are derived from the Green's function solution of the Bloch equation (which follows from the Schroedinger equation by replacing it/ℏ by β = 1/kT). Every cluster integral can be represented by a hybrid of a Mayer graph and a Feynman diagram in (β, r) space.The generalization of classical ring cluster integrals has been analyzed. It is shown that in the case of the electron gas the classical limit of the contribution of these integrals to the grand partition function yields the Debye‐Huckel theory while the low temperature limit leads to the Gell‐Mann—Brueckner equation for the correlation energy of the ground state.A prescription is given for the construction of the cluster integral associated with any given diagram.

Journal ArticleDOI
TL;DR: In this article, a variety of situations which differ little from that of a zero pressure uniform axial magnetic field are obtained by means of an energy principle, and criteria for ascertaining the stability of these equilibria are found.
Abstract: Hydromagnetic equilibria are obtained for a variety of situations which differ little from that of a zero pressure uniform axial magnetic field. Criteria for ascertaining the stability of these equilibria are found by means of an energy principle. In particular, if helically invariant fields are present, stable equilibria with nonzero pressure and net axial current can be found.

Journal ArticleDOI
TL;DR: Stability diagrams for hydromagnetic kink instabilities in a zero pressure plasma confined in a stellarator geometry with arbitrary mixtures of l = 2 and l = 3 multipolar helical fields and with various radial distributions of the current parallel to the confining magnetic field were calculated in this article.
Abstract: Stability diagrams are calculated for hydromagnetic kink instabilities in a zero‐pressure plasma confined in a stellarator geometry with arbitrary mixtures of l = 2 and l = 3 multipolar helical fields and with various radial distributions of the current parallel to the confining magnetic field. The introduction of small pressure gradients increases the size of the unstable regions. Modes with small azimuthal wavenumber grow more rapidly than those with large m. Experimental data, obtained with the model C Stellarator, show that the plasma is macroscopically stable except for certain intervals of rotational transform. These intervals agree qualitatively with those in which the theory predicts the plasma should be unstable against the kink instability.

Journal ArticleDOI
TL;DR: In this paper, the exact solution of the 6-order differential equation which governs the stability of a viscous fluid contained between two rigid walls and heated from below is briefly reviewed and extended to include detailed results on the curve of neutral stability and the cell pattern at the onset of instability.
Abstract: The exact solution of the sixth‐order differential equation which governs the stability of a viscous fluid contained between two rigid walls and heated from below is briefly reviewed and extended to include detailed results on the curve of neutral stability and the cell pattern at the onset of instability. Two approximate methods of solution are then discussed which employ a Fourier or Fourier‐type expansion and which require the solution of only a fourth‐ or a second‐order differential equation. A comparison of these approximate results with the exact solution gives some insight into the relative accuracy of these methods when applied to other more general problems for which an exact solution cannot be obtained.

Journal ArticleDOI
TL;DR: Plesset and Zwick as mentioned in this paper showed that the predicted bubble radius is asymptotically proportional to t 1/2 when R is large enough for surface tension to be negligible.
Abstract: Plesset and Zwick [M S Plesset and S A Zwick, J Appl Phys 23, 95–98 (1952); 25, 493–500 (1954); J Math Phys 33, 308–330 (1955)] have calculated the rate of growth of vapor bubbles in slightly superheated steam under constant external pressure Their calculation assumes that the temperature drop is localized in a thin ``boundary layer'' near the bubble wall; the predicted bubble radius R(t) is asymptotically proportional to t1/2 when R is large enough for surface tension to be negligible An analysis of this asymptotic phase is given, which avoids the above ``boundary layer'' assumption, and contains that part of the analysis of Plesset and Zwick dealing with this phase as a limiting case The analysis is shown to be (approximately) applicable also to gas bubbles in supersaturated liquids

Journal ArticleDOI
TL;DR: In this article, a simple theoretical analysis of the motion of a column of air in a long pipe, closed at one end and driven at the other by an oscillating piston, is presented.
Abstract: Several authors studied experimentally the motion of a column of air in a long pipe, closed at one end and driven at the other by an oscillating piston. At resonance, they observed shock waves traveling in the tube. The paper presents a simple theoretical analysis of the motion, based on discontinuous linearized solutions and a secular equation. This equation guarantees that the motion remains periodic in spite of the cumulative effects of the nonlinear terms. For an inviscid gas, the amplitude at resonance is found to be finite and to be determined by nonlinear effects. This differs from previous results of Frederiksen. Friction can be taken into account and is included in the final results, which are presented in the form of a chart.

Journal ArticleDOI
TL;DR: In this article, the authors considered the second case only and considered the electric field to be produced by an externally imposed oscillation of the axial field and found that as far as the heating of the plasma is concerned, there are four characteristic times which play a fundamental role.
Abstract: There are two ways of heating a plasma confined by a strong axial magnetic field. In the first of these the electric field is parallel to the magnetic field, the situation that obtains in ohmic heating. In the second of these, the electric field is perpendicular to the main axial magnetic field. In this paper we consider the second case only and consider the electric field to be produced by an externally imposed oscillation of the axial field. This method of heating is often called magnetic pumping.It is found that as far as the heating of the plasma is concerned, there are four characteristic times which play a fundamental role. These four times are: (1) the collision time, (2) the period of the oscillating field, (3) the time of transit of a typical ion through the heating region, and (4) the cyclotron period of an ion. If these four characteristic times are all of comparable order, the theoretical analysis is exceedingly complex. Therefore, four cases were considered in which these were taken to be of ...

Journal ArticleDOI
TL;DR: In this paper, a general method was developed for calculating the additional mechanical energy dissipation incurred by the presence of solid particles suspended in an incompressible viscous fluid in laminar flow.
Abstract: A general method is developed for calculating the additional mechanical energy dissipation incurred by the presence of solid particles suspended in an incompressible viscous fluid in laminar flow. The development is applicable to flow in any apparatus within which the steady motion of a homogeneous fluid can be described by omitting the inertial terms in the Navier‐Stokes equations or in which the motion occurs in concentric circles. The validity of the results obtained is limited to situations in which the particle dimensions are small compared to those of the apparatus in which the motion is occurring.The technique, based largely upon a reciprocal theorem for the inertialess flow of viscous fluids, is employed to calculate the permanent pressure drop accompanying the passage of liquid through a bed of fluidized solids. When the particles are uniformly distributed throughout the bed, this pressure diminution is equal to the bed weight (corrected for buoyancy) per unit area of duct—in agreement with exper...

Journal ArticleDOI
TL;DR: In this paper, the decay rates of mean concentration and fluctuations have been obtained in some limiting cases and with some simplifying assumptions, and the principal hypothesis introduced is that a first-order reaction has no effect on the size structure of the scalar field.
Abstract: Under the restrictions of (A) isotropy in turbulent velocity and concentration fluctuation fields, (B) negligible effect of reaction on fluid motion, and (C) negligible effect of heat of reaction on local reaction rate, equations have been deduced for some statistical functions of the concentration of reactant. For a first‐order reaction the simplest equations do not differ in general character from those of pure mixing without reaction, but the nonlinear nature of second‐order reactions introduces decided differences. Solutions for the decay rates of mean concentration and fluctuations have been obtained in some limiting cases and with some simplifying assumptions. The principal hypothesis introduced is that a first‐order reaction has no effect on the size structure of the scalar field.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the flow of a monatomic gas between two parallel plates kept at the same temperature and moving in opposite directions, and the deviation from the equilibrium distribution, φ(c, x), satisfies the linearized Boltzmann equation.
Abstract: The flow of a monatomic gas between two parallel plates kept at the same temperature and moving in opposite directions is studied. The relative velocity of the plates is much smaller than the speed of sound. The deviation from the equilibrium distribution, φ(c, x), satisfies the linearized Boltzmann equation. The customary boundary conditions are adopted in which a fraction of the molecules is specularly reflected and the rest emitted with a Maxwellian distribution characteristic of the plate. The method consists of setting φ = φ+ for cx > 0 and φ = φ− for cx < 0 so that positive and negative velocities are distinguished. We take φ± = a 0 ±(x)cz + a 1 ±(x)czcx . The space functions are determined by taking half‐range velocity moments of the Boltzmann equation. Explicit results for the distribution function, flow velocity and stress are given for a general law of force. Numerical results are worked out for hard sphere molecules. The method treats both microscopic boundary conditions and conservation laws exactly. Precise results are obtained both for the low‐pressure region and for the high‐pressure coefficient of viscosity. The region of slip flow is analyzed. Maxwell's slip condition is remarkably close to the condition obtained here from the kinetic theory. In this region of pressures, the deviations from the velocity profile of the hydrodynamic slip flow theory are everywhere very small, and are completely negligible at distances greater than ⅛ of a mean free path from a plate.

Journal ArticleDOI
TL;DR: In this paper, a kinetic theory of moderately dense gases is developed based on a modified Boltzmann equation, which takes into account the ''collisional transfer'' of momentum and energy.
Abstract: A kinetic theory of moderately dense gases is developed. The theory is based on a modified Boltzmann equation, which takes into account the ``collisional transfer'' of momentum and energy. The theory applies to pure gases made up of spherical molecules, and the effect of multiple collisions is neglected. The Boltzmann equation is solved by a perturbation method which is applicable near equilibrium. Expressions for the flux coefficients, i.e., the thermal conductivity, bulk, and shear viscosity are obtained from this solution and these are in turn evaluated for a rigid sphere potential.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the generation of hydromagnetic and ion cyclotron waves by an induction coil for a cylindrical plasma in a uniform confining magnetic field.
Abstract: Generation of hydromagnetic and ion cyclotron waves by an induction coil is considered for a cylindrical plasma in a uniform confining magnetic field. Resonance widths are calculated and power absorption is calculated and compared to ohmic losses in the induction coil. Rapid thermalization of transverse plasma waves occurs when appreciable numbers of ions stream through the periodic perturbation with velocities such that, in their own rest frames, these ions ``feel'' the perturbation at their own cyclotron frequency. This effect, termed cyclotron damping, makes possible an efficient plasma heating scheme for thermonuclear reactors. Radio‐frequency power can be transferred from an induction coil into ion cyclotron waves with an efficiency typically greater than 65%. The wave energy can be quickly transformed into energy of effectively random transverse ion motion by causing the ion cyclotron wave to travel along a magnetic field which decreases slowly with distance.

Journal ArticleDOI
TL;DR: In this article, a three-point correlation equation is used to obtain a relation for the triple correlations applicable at times before the final period, which is made determinate by neglecting the quadruple correlations.
Abstract: A three‐point correlation equation is used to obtain a relation for the triple correlations applicable at times before the final period. In this case the equation is made determinate by neglecting the quadruple correlations. Higher order approximations, valid at still earlier times, could be obtained by considering four‐ or five‐point correlation equations. In each case the set of equations is made determinate by neglecting the highest order correlation. Only two‐ and three‐point correlation equations are considered here. The correlation equations are converted to spectral form by taking their Fourier transforms. Expressions are obtained for the energy transfer function, which describes the transfer of energy from large to small eddies, and for the energy spectrum function which gives the contributions of the various eddy sizes to the total energy. By integrating the energy spectrum over all wave numbers (or eddy sizes), the following energy decay law is obtained: u2¯=A(t−t0)−5/2+B(t−t0)−7, where u2¯ is the mean square of the velocity fluctuation, t is the time, and A, B, and t0 are constants determined by the initial conditions. For large times the last term becomes negligible leaving the well‐known −5/2 power decay law for the final period. Comparison of the decay law with experimental data indicates good agreement for times considerably before, as well as during, the final period.

Journal ArticleDOI
TL;DR: The velocity and attenuation of ordinary sound in liquid helium have been measured at a frequency of 1 Mc/sec in the neighborhood of the λ point as discussed by the authors, and the results below Tλ can be described with good quantitative accuracy if this relaxation time is given by τ = 8.8 × 10−12(Tλ − T)−1.
Abstract: The velocity and attenuation of ordinary sound in liquid helium have been measured at a frequency of 1 Mc/sec in the neighborhood of the λ point. By using measuring techniques of high resolution, it was possible to observe the behavior in this region in considerable detail. The velocity passes through a minimum approximately 2 × 10−4 °K below the λ point; the maximum attenuation occurs about 8 × 10−5 °K below Tλ. Both velocity and attenuation behave in a manner characteristic of a relaxation process, with the relaxation time a rapid function of temperature near Tλ. The results below Tλ can be described with good quantitative accuracy if this relaxation time is given by τ = 8.8 × 10−12(Tλ − T)−1.Excess attenuation is also observed above the λ point; this cannot be explained by the above relaxation process. The experimental uncertainties are so large in helium I that no reliable conclusions can be reached, but there is some indication that the quantity α/ω2 is not independent of frequency in this region.The...

Journal ArticleDOI
TL;DR: Theoretical calculations have indicated that an attractive possibility for heating the ions of a plasma directly, swiftly, and efficiently is to feed energy into ion cyclotron waves and cause this wave energy to thermalize.
Abstract: Theoretical calculations have indicated that an attractive possibility for heating the ions of a plasma directly, swiftly, and efficiently is to feed energy into ion cyclotron waves and cause this wave energy to thermalize Experiments at the milliwatt power level verify the existence of a resonance in a helium plasma at the cyclotron frequency of the doubly charged helium ion The variation of the plasma loading with magnetic field strength is markedly asymmetrical, in agreement with the theory of ion cyclotron wave generation The observed plasma loading indicates an efficiency of power transfer between the induction coil and the plasma greater than 60%

Journal ArticleDOI
TL;DR: In this paper, the compressibility of a sample of very pure methane has been measured with high precision from 0°C to 150°C and over a pressure range of about 20 to 230 atmos.
Abstract: The compressibility of a sample of very pure methane has been measured with high precision from 0°C to 150°C and over a pressure range of about 20 to 230 atmos The precision attained is of the order of 1 part in 104 Small but consistent discrepancies exist between the present results and earlier measurements, and it is believed these discrepancies are the result of a small impurity of ethane in the methane used earlier The virial coefficients of methane are redetermined from the present measurements, and the intermolecular forces of methane are calculated from the second virial coefficient for several forms of force laws These force laws are then used to calculate the third virial coefficient, the crystal properties at 0°K, and the viscosity for comparison with experiment All the force laws fit the second virial coefficient very well, but some can be eliminated on the basis of the other properties

Journal ArticleDOI
TL;DR: In this article, the effect of the electric field due to the charge on the body in inducing collective motion leads to similar results both for high and low density gases, and formulas are obtained for the electrohydrodynamic drag and for increased ionization in the Mach cone behind the body.
Abstract: The electrohydrodynamic phenomena associated with the high‐velocity motion of a charged body in a plasma are investigated with a view to applications to satellite motion in the ionosphere. It is shown that the effect of the electric field due to the charge on the body in inducing collective motion leads to similar results both for high‐ and low‐density gases. By using a linearized theory, formulas are obtained for the electrohydrodynamic drag and for the increased ionization in the Mach cone behind the body.

Journal ArticleDOI
TL;DR: In this paper, the collective motions of a fully ionized cold plasma in a uniform external magnetic field are treated by standard small amplitude theory, and completeness theorems are presented with the aid of scalar potentials representing the electromagnetic field quantities.
Abstract: The collective motions of a fully ionized cold plasma in a uniform external magnetic field are treated by standard small amplitude theory. Finite temperature and collision effects are neglected. Specializing the analysis to a neutral plasma of uniform unperturbed density containing electrons and ions of one species, one obtains a dielectric tensor and dispersion relation which is a special example of results previously given by Astrom. A detailed discussion of the exact dispersion relation is given for the entire frequency spectrum, and completeness theorems are presented with the aid of scalar potentials representing the electromagnetic field quantities. It is found that when the Alfven dielectric constant α = 4πn(m + M)c2/B02 becomes comparable in magnitude to the ion‐to‐electron mass ratio, the plasma space charge may play an important role in determining the nature of collective oscillations. In particular, if the axial wavelength of the perturbation is sufficiently large, the singularities of the eff...

Journal ArticleDOI
TL;DR: The basic concepts of confinement and ohmic heating in a figure-eight stellarator are briefly reviewed and experimental data in these areas summarized in this paper, where the ionization level in a helium discharge, with an initial pressure of about 1 μ of Hg, becomes virtually complete during the heating pulse, and the electric resistivity corresponds to a kinetic temperature of about 100 volts, or 106 degrees.
Abstract: The basic concepts of confinement and ohmic heating in a figure‐eight stellarator are briefly reviewed and experimental data in these areas summarized. The production of energetic x‐rays by runaway electrons, up to ten milliseconds after the disappearance of the accelerating field, has indicated effective single‐particle confinement by magnetic fields of 20 000 to 30 000 gauss. However, the plasma confinement time during ohmic heating appears to be limited by unknown processes to approximately 100 microseconds for hydrogen, more than three orders of magnitude shorter than predicted from classical collisional diffusion. The ionization level in a helium discharge, with an initial pressure of about 1 μ of Hg, becomes virtually complete during the heating pulse, and the electric resistivity corresponds to a kinetic temperature of about 100 volts, or 106 degrees. After the heating pulse, the electron density decays with a time constant as great as 6 milliseconds under some conditions. The hydromagnetic kink instability predicted by Kruskal has been clearly observed.

Journal ArticleDOI
TL;DR: In this article, a small plane mirror is placed just behind the wire so as to be perpendicular to the axis of the optical system and the reflected image of the wire explosion coincides with the disturbance itself when seen through the slit by the camera lens.
Abstract: A simple technique has been found for rendering visible the shock wave formed by an exploding wire after the shock has separated from the luminous contact surface. A small, plane mirror is placed just behind the wire so as to be perpendicular to the axis of the optical system. Thus the reflected image of the wire explosion coincides with the disturbance itself when seen through the slit by the camera lens. Rotating mirror pictures taken under these conditions show very clear outlines of the parabolic shock wave as it propagates ahead of the luminous contact surface. The separation of the shock and contact surface is complete by about one μsec. Beyond this time the shock is clearly nonluminous and ordinarily would not be visible. Comparison of shock trajectories with predictions from the similarity solutions for strong shock waves obtained by S. C. Lin may be interpreted as showing that the shock is receiving additional energy while traversing the early part of its path. After this phase both shock and contact surface accurately obey a parabolic law over intervals of several microseconds.