摘要:

Starting from the Liouville equation, a chain of equations is obtained by integrating out the coordinates of all but one, two, etc., particles. One ``test'' particle is singled out initially. All other ``field'' particles are assumed to be initially in thermal equilibrium. In the absence of external fields, the chain of equations is solved by expanding in terms of the parameterg= 1/nLD3. For the time evolution of the distribution function of the test particle, an equation is obtained whose asymptotic form is of the usual Fokker‐Planck type. It is characterized by a frictional‐drag force that decelerates the particle, and a fluctuation tensor that produces acceleration and diffusion in velocity space. The expressions for these quantities contain contributions from Coulomb collisions and the emission and absorption of plasma waves. By consideration of a Maxwell distribution of test particles, the total plasma‐wave emission is determined. It is related to Landau's damping by Kirchoff's law. When there is a constant external magnetic field, the problem is characterized by the parameterg, and also the parameter &lgr; = &ohgr;c/&ohgr;p. The calculation is made by expanding in terms ofg, but all orders of &lgr; are retained. To the lowest order ing, the frictional drag and fluctuation tensor are slowly varying functions of &lgr;.When &lgr; ≪ 1, the modification of the collisional‐drag force due to the magnetic field, is negligible. There is a significant change in the properties of plasma waves of wavelength greater than the Larmor radius which modifies the force due to plasma‐wave emission. When &lgr; ≫ 1, the force due to plasma‐wave emission disappears. The collisional force is altered to the extent that the maximum impact parameter is sometimes the Larmor radius instead of the Debye length, or something in between. In the case of a slow ion moving perpendicular to the field, the collisional force is of a qualitatively different form. In addition to the drag force antiparallel to the velocity of the particle, there is a collisional force antiparallel to the Lorentz force. The force arises because the particle and its shield cloud are spiralling about field lines. The force on the particle is equal and opposite to the centripetal force acting on the ``shield cloud.'' It is much smaller than the Lorentz force.

ISSN:0031-9171    

DOI:10.1063/1.1705998

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

Alfve´n hydromagnetic waves are propagated through a cylindrical plasma. The wave velocity, attenuation, impedance, and energy transfer are studied. The theoretical equations predict correctly the functional dependence of the velocity and attenuation, and from these quantities accurate measurements of plasma density and temperature can be obtained. A qualitative agreement between theory and experiment is obtained for the hydromagnetic coaxial waveguide impedance, and the energy transferred from an oscillating circuit to the hydromagnetic wave is measured to be 43 ± 10&percent;.

ISSN:0031-9171    

DOI:10.1063/1.1705996

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The propagation of waves through a plasma, wherein the density and/or magnetic field strength are slowly varying functions of position is discussed. If the local propagation constant,kx, is a slowly varying function ofx, the adiabatic approximation will be valid. However,kx2may pass through zero as a function ofx. Using the WKB linear turning point connection formulas, examination shows that an incoming plasma wave is totally reflected in the region wherekx2≈ 0. A similar analysis for the case wherekx2is a singular function ofxshows that absorption of an incoming wave occurs in the vicinity of the singularity. Such singular behavior inkx2can occur for propagation along the magnetic field when the wave frequency is equal to the local ion or electron cyclotron frequency. For propagation transverse to the magnetic field, an apparent singularity occurs at a frequency somewhat below the ion cyclotron frequency, and at the two hybrid frequencies of Auer, Hurwitz, and Miller. A detailed examination, including higher order effects in electron mass ÷ ion mass, finite electron and ion temperatures, and ion‐ion and ion‐electron collisions shows that the absorption will take place at the apparent singularity only if the physical damping processes are strong enough to swamp the reactive effects of the higher order corrections. Otherwise the higher order reactive effects introduce a new propagation mode into the dispersion equation with a root which, in the vicinity of the apparent singularity, is conjugate to the root of the original mode. Partial or total reflection now occurs at the apparent singularity instead of absorption. It is, however, conjectured that some of the original mode energy may be reflected into the new mode. As the new mode recedes from the region of the apparent singularity, its wavelength can become comparable to the particle Larmor radius. Energy in this mode may then be absorbed by phase‐mixing processes which are of high order in the quantity (Larmor radius ÷ wavelength). Wave reflection from the apparent singularities will then heat ions in the case of the transverse ion cyclotron mode, and electrons in the case of the upper hybrid frequency.

ISSN:0031-9171    

DOI:10.1063/1.1705997

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

An electric discharge which is compressed by its own magnetic field, and ``stabilized'' by means of an axial magnetic field, can have transverse wave motions which cause its periodic compression and expansion. This kind of motion can cause the heating of the ions in the discharge. The simplest of these wave modes are described and an estimate is given of the power available to the waves as a result of the interaction of the electrons in the discharge with an axial electric field. This interaction can cause the attenuation or spontaneous growth of the waves, depending upon the circumstances. It is likely that in high current gas discharge experiments there are examples of growing and decaying waves of this type.

ISSN:0031-9171    

DOI:10.1063/1.1705999

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The problem of instabilities in colliding ionized hydrogen beams, which has been treated by Kahn and Parker in the special case of zero temperature, is solved for the nonzero temperature case by taking Maxwell distributions for the equilibrium density functions. At sufficiently high temperature it is found that the random thermal motion will prevent growing oscillations. The boundary between the stable and unstable regions is plotted as a function of energy and density parameters. Certain phenomena associated with solar particle streams are discussed in terms of these results.

ISSN:0031-9171    

DOI:10.1063/1.1706000

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

In their Geneva paper, Trubnikov and Kudryavtsev calculated the cyclotron radiation from a hot plasma. In doing this, the assumption was made that the individual particles radiated as though they were in a vacuum. We have investigated this approximation by calculating the absorption length directly from the Boltzmann equation, and we find that indeed this assumption is correct whenever (&ohgr;p/&ohgr;e)2≪m2, wheremis the harmonic number of the radiation in question, &ohgr;pis the plasma frequency, and &ohgr;eis the cyclotron frequency. For a contained plasma, the left hand side of this inequality is of the order of magnitude of one, and thus the inequality is well satisfied for the dominant radiation from a plasma at high temperature.The angular independence of the absorption coefficient has been calculated, and this together with a more careful examination of the mechanism of thermonuclear energy transfer to the electrons, leads to a modification of the results presented by Trubnikov and Kudryavtsev at Geneva. In addition, it is shown that by the use of reflectors the critical size can be reduced by two orders of magnitude.

ISSN:0031-9171    

DOI:10.1063/1.1706001

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The general theory of irreversible processes, developed by Prigogine and Balescu, is applied to the case of long range interactions in ionized gases. A similar diagram technique permits the systematic selection of all the contributions to the evolution of the distribution function, to an order of approximation equivalent to Debye's equilibrium theory. The infinite series which appear in this way can be summed exactly. The resulting evolution equations have a clear physical significance: they describe interactions of ``quasi particles,'' which are electrons or ions ``dressed'' by their polarization clouds. These clouds are not a permanent feature, as in equilibrium theory, but have a nonequilibrium, changing shape, distorted by the motions of the particles. From the mathematical point of view, these equations exhibit a new type of nonlinearity, which is very directly related to the collective nature of the interactions.

ISSN:0031-9171    

DOI:10.1063/1.1706002

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

We calculate the asymptotic value of the pair probability density &rgr;2(r2,r1) for finding a fluid particle at a pointr2far in the interior of a fluid, when it is known that there is a particle atr1in contact with the walls (rigid) of the container. This value is different from the well‐known expression for the asymptotic value of &rgr;2(r2,r1) when bothr2andr1are in the interior of the fluid. Our derivation is based on the virial theorem for total momentum fluctuations in an equilibrium system and makes use of the assumption that there are no long range correlations in a fluid. Application is made of our result to re‐derive simply the expression for the second virial coefficient and the exact equation of state of a hard‐sphere gas in one dimension. Quantum systems are also treated.

ISSN:0031-9171    

DOI:10.1063/1.1706003

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

Some results are given on the connection existing between the Lee‐Huang‐Yang theory for the interacting Bose systems, and the Bogoliubov theory.

ISSN:0031-9171    

DOI:10.1063/1.1706004

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The one‐dimensional equilibrium spectra in isotropic turbulence are given for the physical transfer theories of Heisenberg, Kova´sznay, and Obukhoff. These results are then compared with the experimental measurements of the spectrum of ∂3u1/∂x13fluctuations. For two of the theories (Heisenberg's and Kova´sznay's), reasonable agreement is obtained fork&eegr;< 0.04, but for larger values ofk&eegr;there is considerable divergence between the theoretical and experimental results. The relationship between the equilibrium and similarity spectra are also discussed for these two theories.

ISSN:0031-9171    

DOI:10.1063/1.1706005

出版商:AIP    

年代:1960

数据来源: AIP