Self-Similarity of Continuous-Spectrum Radiative Transfer in Plasmas with Highly Reflecting Walls

Abstract

Radiative Transfer (RT) in a continuous spectrum in plasmas is caused by the emission and absorption of electromagnetic waves (EM) by free electrons. For a wide class of problems, the deviation of the velocity distribution function (VDF) of free electrons from the thermodynamic equilibrium, the Maxwellian VDF, can be neglected. In this case, RT in the geometric optics approximation is reduced to a single transport equation for the intensity of EM waves with source and sink functions dependent on the macroscopic parameters of the plasma (temperature and density of electrons). Integration of this equation for RT of radio-frequency EM waves in laboratory plasmas with highly reflecting metallic walls is substantially complicated by the multiple reflections which make the waves with the long free path the dominant contributors to the power balance profile. This in turn makes the RT substantially nonlocal with the spatial–spectral profile of the power balance determined by the spatial integrals of the plasma parameters. The geometric symmetry of the bounding walls, especially when enhanced by the diffuse reflectivity, provides a semi-analytic description of the RT problem. Analysis of the accuracy of such an approach reveals an approximate self-similarity of the power balance profile and the radiation intensity spectrum in both approximate and ab initio modeling. This phenomenon is shown here for a wide range of plasma parameters and wall reflectivity, including data from various numeric codes. The relationship between the revealed self-similarity and the accuracy of numeric codes is discussed.

Lévy Walks as a Universal Mechanism of Turbulence Nonlocality

“…Significantly greater success was achieved in the application of the above-mentioned escape probability method for the calculation of a separate component of the energy balance in tokamaks, namely, energy losses caused by the electron cyclotron radiation [46,47]. This approach extended and modified the approach [48][49][50] to heat transfer by electron cyclotron waves in thermonuclear plasmas (the current state of this issue can be found in [51]).…”

“…where T(r, v) is the Holstein function that specifies the distribution function over the free path (3) of plasma density fluctuations moving with velocity v r along the direction under study, K r = |K| is the radial component of the scattering vector, F(v r ) is the distribution function of velocity fluctuations along the minor radius of the toroidal plasma column, specified by (51) in [12] and corresponding to the motion of density fluctuations with velocities near a characteristic velocity along and against the direction of observation in experiments [54]. It is this distribution over the radial velocity that can give the spectrum of the scattered EM field in these experiments (see Figures 1 and 5 in [12]).…”