摘要:

Recent Monte Carlo calculations of the radial distribution function of a one‐component, classical, plasma are shown to be well approximated by solutions of the Born‐Green‐Yvon integral equation, almost up to densities where there is definite short range order. The Born‐Green‐Yvon solutions appear to be somewhat better than the corresponding solutions of the Percus‐Yevick and convolution‐hypernetted‐chain equations. The Born‐Green‐Yvon equation is further shown to be related to the original Debye‐Hu¨ckel equation for an ionic solution. It differs from the latter equation by accounting for more short range correlations, a feature that makes it more accurate at higher densities. The special methods used to obtain numerical solutions of the Born‐Green‐Yvon equation at high density are briefly discussed.

ISSN:0031-9171    

DOI:10.1063/1.1762149

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Nonlinear plasma oscillations in a classical, nonrelativistic, collisionless, Maxwellian electron gas are considered. There is assumed a small, sinusoidal variation in the spatial part of the initial distribution function, corresponding to excitation of wavenumber modes ±k0. The nonlinear Vlasov equation is solved to third order in the long time limit via the Montgomery‐Gorman perturbation expansion, where the expansion parameter is &egr;, the amplitude of the initial perturbation. The linear, first‐orderk0mode of the electric field is dominated by the Landau solution with (negative) damping decrement &ggr;L. The third‐orderk0mode is modified, however, by singling out the spatially uniform part of the distribution function for special treatment, much in the manner of the quasi‐linear theory. A nonlinear damping decrement results such that, for many values ofk0and &egr;, &ggr;L< &ggr;N. Thus at sufficiently long times, the modified third‐order mode dominates the solution. For certain &egr; andk0this behavior resembles the results of Knorr and Armstrong, obtained by numerical integration of the nonlinear Vlasov equation.

ISSN:0031-9171    

DOI:10.1063/1.1762150

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

An integral equation governing an instability due to ion temperature gradients is derived. In the presence of magnetic shear, localized non‐convective normal modes of instability are shown to exist if the relative temperature gradient is larger than that of density, unless the shear is exceedingly strong, i.e., the field shears through a large angle in the distance in which the temperature drops. Quasi‐modes which are less localized in the direction of the gradient can be constructed from these normal modes and a large thermal diffusion may be expected. Conversely the mass diffusion is shown to be rather slow so that it is reasonable to assume that an effective ``divertor'' should keep the actual heat loss quite small.

ISSN:0031-9171    

DOI:10.1063/1.1762151

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A self‐gravitating, infinite cylinder of conducting, homogeneous, incompressible fluid in an axial magnetic field is considered with Hall effect included. In the case of axisymmetric modes, an asymptotic analysis for small, nonzero Hall current indicates a destabilizing effect ofO(&egr;), where &egr; is the perturbation parameter. It appears that the increased instability is due to the electron‐ion diffusion current, which contributes a radial Lorentz force that is absent in the single‐fluid theory. This radial Lorentz force increases the tendency for the cylinder to break up into lengths defined by the perturbation wavenumber.

ISSN:0031-9171    

DOI:10.1063/1.1762152

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Transverse electromagnetic waves that propagate along a uniform magnetic field in an unbounded, thermally anisotropic plasma are investigated. The linearized Vlasov equation is solved to obtain the dispersion relation for the electron‐ and ion‐cyclotron waves. This dispersion relation is used to determine the critical frequencies and wavenumbers below which the wave is unstable. The electron‐cylotron wave is unstable forT⊥e>Tze. Numerical solutions for the growth and damping rates of the waves obtained from the dispersion relation show that the maximum growth rate occurs at a frequency slightly below the marginally stable frequency. For the ion‐cyclotron wave, both ion and electron thermal anisotropy are included, and cold electrons are shown to have a stabilizing influence on an unstable ion‐cyclotron wave; however, when the electrons are thermally anisotropic, they have a destabilizing effect forT⊥e>Tze.

ISSN:0031-9171    

DOI:10.1063/1.1762153

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A new wave phenomenon was observed in the course of an experimental investigation of ion cyclotron resonance heating of hydrogen and deuterium plasmas in strong magnetic fields. It was found that the waves can propagate for frequencies larger than the ion cyclotron frequencyfc, and attenuate at harmonics offcwith resulting increase in the transverse temperature‐density productn&bgr;T⊥. The harmonic number at which the waves attenuate increases with increasing gas pressure. Attenuation at harmonics up to the 8th was observed. The plasma density is typically 6 × 1017m−3, the transverse plasma temperature (Te⊥+Ti⊥) ⪕ 50‐eV equivalent, and the magnetic field 1–9 kG. A magnetic beach geometry is employed and the waves are excited by a Faraday shielded Stix coil from a 30 kW, 5.8 MHz driver. Harmonic cyclotron heating is related to large transverse wave numbers which are shown to exist in the experiment.

ISSN:0031-9171    

DOI:10.1063/1.1762154

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Numerical solutions of coupled Fokker‐Planck equations for electron and deuteron velocity distribution functions are used to investigate the non‐Maxwellian conditions existing in fast magnetic compression theta‐pinch experiments. Initial distribution functions are chosen to stimulate the post shock‐heating phase of operation and the subsequent relaxation is followed. Because of rapid changes in the deuteron distribution function, the neutron yield is found to increase significantly with time although the mean energy changes little. Distortions at high and low velocities occur in the electron distribution resulting from interaction with the ions. These distortions produce two effects: (1) At short wavelength the x‐ray flux is lower than that from a Maxwellian with the same mean energy; and (2) the edge of recombination continua of impurities are flattened relative to the spectrum produced by a Maxwellian distribution. The influence of the distorted x‐ray spectrum upon standard absorber foil techniques for temperature measurement is considered.

ISSN:0031-9171    

DOI:10.1063/1.1762155

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The nonuniform absorption of gyro‐resonant microwave energy by an electron gas is used to produce the helical configuration in gaseous magnetoplasmas. This configuration is examined both theoretically and experimentally. Stability criteria for the existence of the helix and the dependence of the properties of the helix on the plasma parameters are derived from the two‐fluid mangetohydrodynamic equations for electrons and ions. The experimental examination of the instability is accomplished by the use of a suitable diagnostic procedure using low power (≈ 50 &mgr;W), nonresonant microwave sensing signals. The detailed examination of the properties of the helical configuration verifies the theoretical predictions. Where it has been possible to measure the properties of the plasma discharge exactly, such as helix rotational frequency and discharge tube radius, excellent quantitative agreement between theory and experiment is found. Where it has only been possible to estimate the plasma parameters, such as electron temperature and longitudinal gradients, good qualitative agreement between theory and experiment is found.

ISSN:0031-9171    

DOI:10.1063/1.1762156

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

If a solenoidal fieldBcan be separated into a fundamental componentB0with closed field lines and a perturbationB1of the order &egr;, it is possible to integrate the differential equations for the field lines up to the second order in &egr;. It turns out that the rotational transform is of the order &egr; if the flux of the fieldB1through a surface limited by any closed field line ofB0does not vanish. When the transform is of the order &egr;2one can derive an explicit expression for the magnetic surfaces.

ISSN:0031-9171    

DOI:10.1063/1.1762157

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A radio frequency electromagnetic wave, polarized in the plane of incidence is incident obliquely upon a plasma half‐space, where the equilibrium plasma is taken to be homogeneous and isotropic. Employing the specular boundary condition, an exact solution of the coupled Maxwell‐Vlasov equations is derived, yielding both transverse and longitudinal waves in the plasma region. The reflection coefficient is derived, and approximately evaluated.

ISSN:0031-9171    

DOI:10.1063/1.1762158

出版商:AIP    

年代:1967

数据来源: AIP