Pitch angle scattering and effective collision frequency caused by stochastic magnetic fields

2008 ◽  
Vol 15 (2) ◽  
pp. 022304 ◽  
Author(s):  
Marcus Neuer ◽  
Karl H. Spatschek
Keyword(s):  
Magnetic Fields ◽  
Pitch Angle ◽  
Collision Frequency ◽  
Effective Collision Frequency ◽  
Angle Scattering ◽  
Stochastic Magnetic Fields ◽  
Effective Collision

Theory of energy flux and polarization changes of a radio wave with two magnetoionic components undergoing self demodulation in the ionosphere

1974 ◽  
Vol 341 (1626) ◽  
pp. 361-381 ◽  
Keyword(s):  
Electron Temperature ◽  
Radio Wave ◽  
Phase Difference ◽  
Incident Wave ◽  
Unit Volume ◽  
Collision Frequency ◽  
Lower Ionosphere ◽  
Effective Collision Frequency ◽  
Composite Wave ◽  
Effective Collision

The absorption of a powerful plane radio wave vertically incident on the lower ionosphere is studied. If it contains the two magnetoionic components with roughly equal amplitudes, the power absorbed per unit volume can be either greater or less than the sum of the powers for the separate components, depending on their phase difference. This is determined by the polarization of the incident wave, and the heights where the absorption is a maximum can be changed by changing this polarization. The power absorbed causes an increase in the electron temperature and thence in the effective collision frequency. This is studied first for an unmodulated wave. If the wave is amplitude modulated, the increase of collision frequency varies periodically in the modulation cycle. This results in self demodulation which is different for the two magnetoionic components because of their different rates of absorption. The result is that the polarization of the composite wave varies periodically over the modulation cycle.

THE NONLINEAR INTERACTION OF A RADIO-FREQUENCY WAVE WITH AN INHOMOGENEOUS PLASMA SLAB: I. KINETICS OF HIGH-TEMPERATURE AIR IN THE PRESENCE OF AN ELECTROMAGNETIC FIELD

1965 ◽  
Vol 43 (11) ◽  
pp. 2021-2035 ◽  
Author(s):  
Robert J. Papa ◽  
Carl T. Case
Keyword(s):  
High Temperature ◽  
Radio Frequency ◽  
Electron Temperature ◽  
Collision Frequency ◽  
Inhomogeneous Plasma ◽  
Frequency Wave ◽  
Effective Collision Frequency ◽  
Plasma Slab ◽  
Radio Frequency Wave ◽  
Effective Collision

A radio-frequency wave is normally incident upon an inhomogeneous plasma slab. The plasma slab is composed of partially ionized high-temperature air corresponding to the characteristics of the plasma sheath surrounding hypersonic reentry vehicles. The isotropic part of the electron velocity distribution function is Maxwellian because of electron–electron collisions. The electromagnetic wave is intense enough to heat selectively the electron gas, altering the various electron production and loss processes. The high-frequency limit is considered, and expressions are obtained for the electron number density and effective collision frequency as a function of electron temperature. The effective collision frequency takes into account the effects of electron–neutral and electron–ion collisions for momentum transfer. From an energy balance equation, the electron temperature is found to be a function of both the frequency and field strength of the wave. The electron temperature is found also to exhibit an instability that gives rise to a hysteresis effect.

Reimagining full wave rf quasilinear theory in a tokamak

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Peter J. Catto ◽  
Elizabeth A. Tolman
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Collision Frequency ◽  
Velocity Space ◽  
Wave Number ◽  
Temporal Behaviour ◽  
Full Wave ◽  
Effective Collision Frequency ◽  
Space Boundary ◽  
Effective Collision

The velocity dependent resonant interaction of particles with applied radiofrequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto (J. Plasma Phys., vol. 86, 2020, 815860302). The behaviour is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719–2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836–1844). For a wave of parallel wave number ${k_{||}}$ interacting with weakly collisional plasma species of collision frequency $\nu$ and thermal speed ${v_{\textrm{th}}}$ , the effective collision frequency becomes of order $\nu {({k_{||}}{v_{th}}/\nu )^{2/3}} \gg \nu $ . The narrow boundary layers that arise because of the diffusive nature of the collisions allow a physically meaningful wave–particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behaviour of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave–particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

THE NONLINEAR INTERACTION OF A RADIO-FREQUENCY WAVE WITH AN INHOMOGENEOUS PLASMA SLAB: II. NONLINEAR REFLECTION AND TRANSMISSION COEFFICIENTS OF AN INHOMOGENEOUS PLASMA SLAB

1965 ◽  
Vol 43 (11) ◽  
pp. 2036-2044 ◽  
Author(s):  
Robert J. Papa ◽  
Carl T. Case
Keyword(s):  
Collision Frequency ◽  
Inhomogeneous Plasma ◽  
Critical Value ◽  
Effective Dielectric Constant ◽  
Reflection And Transmission ◽  
Electric Field Amplitude ◽  
Transmission Coefficients ◽  
Effective Collision Frequency ◽  
Plasma Slab ◽  
Effective Collision

When a radio-frequency plane wave is incident upon an inhomogeneous, lossy plasma slab, part of the electromagnetic energy is reflected, part is absorbed by the plasma medium, and part is transmitted. At sufficiently high power levels (about 1 watt cm2 at X-band frequencies), the equation of state of the plasma is altered, which produces a change in the effective dielectric constant of the medium. In the high-frequency limit, the effective dielectric constant of the medium is expressed as a function of the electron density and an effective collision frequency. The electron density and effective collision frequency at each point in the medium are functions of the electron temperature. In Part I, the electron temperature (Te) at each point (z) in the slab has been expressed in terms of the local value of E2/ω2, where E = electric field amplitude and ω = signal frequency, i.e., Te = Te(z, E2/ω2). Using the predetermined functional dependence of Te on z and E2/ω2, the electromagnetic field distribution and the net reflection and transmission coefficients of the plasma slab are computed by employing the Runge–Kutta technique to integrate Maxwell's equations numerically step by step. For each value of ω, relatively small changes in the reflection and transmission coefficient are produced as [Formula: see text] is increased up to a critical value of [Formula: see text], where Einc = incident electric field amplitude. For values of [Formula: see text] greater than this critical value, there is a sharp increase in the reflection coefficient and a sharp drop in the transmission coefficient.

Effective collision frequency of electrons in noble gases

1981 ◽  
Vol 14 (9) ◽  
pp. 1485-1495 ◽  
Author(s):  
P Baille ◽  
J -S Chang ◽  
A Claude ◽  
R M Hobson ◽  
G L Ogram ◽  
...  
Keyword(s):  
Noble Gases ◽  
Collision Frequency ◽  
Effective Collision Frequency ◽  
Effective Collision
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