Low Collision Frequency Research Articles

Lower-hybrid-resonance heating of a plasma in a parallel-plate waveguide

Wave propagation in a parallel-plate metallic waveguide partially filled with an inhomogeneous, anisotropic plasma column is studied as an eigenvalue problem using the complete cold-plasma dielectric tensor. Although the accessibility condition may not be met, the collisional energy absorption at the lower-hybrid resonance greatly exceeds the resistive loss at the waveguide walls resulting in a very high plasma heating efficiency. The heating continues to be effective even for very low collision frequencies encountered in thermonuclear plasmas. Detailed numerical results for the heating efficiency, energy flux into the plasma, energy density and dissipation density in the plasma column as well as group velocity are presented. Also the effects of density profile, collision frequency, and waveguide eigenmodes are discussed.

The enhancement factor of collisional diffusion near the rational surface

The diffusion coefficients for a plasma column with a helical magnetic perturbation are calculated. For both classical and neoclassical regimes, the diffusion rate is enhanced near the flux surface where (rotational transform angle)/2π is rational. It is due to the fact that the geodesic curvature stays constant along a flux line on the rational surface. The guiding center drift perpendicular to the flux surface is thus unidirectional. For a low collision frequency case, the banana size becomes large. For the collisional regime, it results in a large parallel current. The diffusion rate for both regimes are given by simply replacing the coloidal component of the magnetic field for the axially symmetric case by the component perpendicular to the helix, i.e. B σ + ( kr/ m) B z .

Effect of Longitudinal Electric Field on Toroidal Diffusion

The driving toroidal electric field in Tokamaks is shown to lead to a significant pinching effect at low collision frequency. For ${\ensuremath{\beta}}_{\ensuremath{\theta}}=\frac{8\ensuremath{\pi}p}{B_{\ensuremath{\theta}}^{}{}_{}{}^{2}}<1$, where ${B}_{\ensuremath{\theta}}$ is the poloidal field, this pinching is more rapid than outward diffusion in the banana and plateau regimes of toroidal transport theory.

Microwave Transmission Through a Magnetoplasma Slab Near the Plasma Cutoffs

The extraordinary wave transmission through the afterglow of an rf-excited, electrodeless, helium discharge has been investigated experimentally. The discharge approximates a low collision frequency plasma slab of relatively uniform electron density in a uniform magnetic field. Measurements were performed at 18.0 and 9.15 GHz. A transmission minimum occurs very close to the higher frequency cutoff and a large decrease in transmission occurs close to the lower frequency cutoff. The plasma cutoff positions are approximately independent of energy in the electron energy range from thermal energy to a few electron volts and of pressure in the pressure range from 0.08 to 2.5 Torr. The position of the transmission minimum coincides with the position of the emission peak previously observed.

Asymptotic solution of the Fokker-Planck equation at low collision frequency

An asymptotic solution has been obtained for the case of low collision frequency using a Fokker-Planck collision operator suitable for the study of the effect of electron-ion collisions on the 'Universal' instability in an inhomogeneous plasma. The solution, obtained under certain approximations, contains fractional powers of the collision-rate coefficient and this eliminates the divergence occurring in the expression for physical quantities like perturbed density when obtained by using a direct iterative method. Also, an approximate study of the solutions over various ranges of the velocity variable is given.

Bragg Cut-Off Effects on Neutron Wave Propagation in Graphite

Theoretical and experimental studies concerning the effects of Bragg cut-off on the neutron wave propagation in graphite are presented, as analyzed from the two following factors related to the Bragg cut-off. First, the inordinately long mean free path of cold neutrons of energies below the Bragg cut-off causes in some cases serious problems due to the deep penetration and the strong leakage of the cold neutrons. Secondly, the extremely low collision frequency of about 2,500 rad/sec for the cold neutrons produces a “singular frequency” at a point of even lower frequency, wherein the waves do not decay exponentially in the propagating direction. The peculiar behavior of these cold neutrons severely restricts the conditions of experiment under which one can derive an exact value for the propagation parameter in graphite. In certain cases, however, one can obtain meaningful approximate information about wave propagation from experiments conducted beyond these limiting conditions, provided that certain precau...

Bragg Cut-Off Effects on Neutron Wave Propagation in Graphite

Theoretical and experimental studies concerning the effects of Bragg cut-off on the neutron wave propagation in graphite are presented, as analyzed from the two following factors related to the Bragg cut-off. First, the inordinately long mean free path of cold neutrons of energies below the Bragg cut-off causes in some cases serious problems due to the deep penetration and the strong leakage of the cold neutrons. Secondly, the extremely low collision frequency of about 2,500 rad/sec for the cold neutrons produces a “singular frequency” at a point of even lower frequency, wherein the waves do not decay exponentially in the propagating direction. The peculiar behavior of these cold neutrons severely restricts the conditions of experiment under which one can derive an exact value for the propagation parameter in graphite. In certain cases, however, one can obtain meaningful approximate information about wave propagation from experiments conducted beyond these limiting conditions, provided that certain precautions are taken in carrying out the experiment and in interpreting the results. Analysis to explain these phenomena and experiments to reveal the effects in graphite are described.

Effect of Ion Collisions and Other Terms on the Resistive-g Instability in Plasmas

The treatment is based on guiding center equations, which include collisional diffusion across the magnetic field lines. The eigenvalues of the resulting differential equation are found using phase integral methods. The localized resistive-g mode becomes stable at sufficiently low collision frequencies, the dominant stabilizing mechanism depending on the shear. For strong magnetic shear [shear length < radius of curvature of field lines × ¼(M/m)¼] ion collisional effects are found to first produce stability, whereas for weak magnetic shear the dominant effect comes from the electron acoustic term in Ohm's law. Analytic stability criteria are derived which show satisfactory agreement with a recent numerical solution of the same problem, but underline the danger of extrapolation based on the numerical solution.

Harmonic Generation in a Plasma due to a Velocity-Dependent Collision Frequency

Harmonic components associated with the plasma electron velocity distribution function often result from a strong radio-frequency field. In this analysis, an expression is obtained for the third harmonic current which is a result of a velocity-dependent collision frequency. By introducing a low-collision frequency approximation and a collision frequency of the form ν = kvμ, the successive integrations necessary to obtain the third harmonic current are readily performed. As a result of this approximation which is valid for typical harmonic generation experiments, the third harmonic current is then shown to depend only upon various moments of the static isotropic part of the electron velocity distribution function. An estimate of this current is obtained by assuming a Maxwellian distribution. It is then shown that for a typical discharge configuration the third harmonic obtained due to this mechanism is small although not negligible compared to that observed experimentally.