Cross-field renormalized statistical approach: short-wave low-frequency stationary spectra in a magnetized current-carrying plasma

Abstract

The low-frequency (frequencies not exceeding the ion gyrofrequency) shortwave (wavelengths smaller than the ion gyroradius) potential, cross-field and magnetic stationary fluctuation spectra in a magnetized currentcarrying plasma, are studied by using the canonical distribution method, the new general renormalized statistical approach with cross-field correlations, and the self-similar transformation technique. The cross correlations are found to influence substantially the spectra formation, distorting the stationary plasma state.

Cross-Field Correlations in Plasma Fluctuation Spectra

“…1. As follows from (11), the role of magnetic nonlinearities is not dominant in this region. We see that the form of ( 21) and ( 22) is in consonance with its physical content.…”

“…v and v m are the kinematic and magnetic viscosities, respectively, that arise due to electron-electron ``collisions'' [1,11],…”

“…The simplest procedure [1,2,4,6,9] to obtain solutions in the nonlinear case, is to split the right-hand-sides of ( 14) and ( 15) into parts that are identically zero due to the symmetry properties of the matrix elements M(1, 2) and M m (1,2). Considering the terms containing straight and cross correlations independently, we see that the relevant symmetry conditions are satis¢ed by linear solutions ( 19) and (20) where T i T e for the LW excitations, while the ``mixed'' part is zero if the cross spectra intensities acquire the equilibrium-like appearance [2,8,11]:…”

Cross-Field Correlations in Plasma Fluctuation Spectra

“…1. As follows from (11), the role of magnetic nonlinearities is not dominant in this region. We see that the form of ( 21) and ( 22) is in consonance with its physical content.…”

“…v and v m are the kinematic and magnetic viscosities, respectively, that arise due to electron-electron ``collisions'' [1,11],…”

“…The simplest procedure [1,2,4,6,9] to obtain solutions in the nonlinear case, is to split the right-hand-sides of ( 14) and ( 15) into parts that are identically zero due to the symmetry properties of the matrix elements M(1, 2) and M m (1,2). Considering the terms containing straight and cross correlations independently, we see that the relevant symmetry conditions are satis¢ed by linear solutions ( 19) and (20) where T i T e for the LW excitations, while the ``mixed'' part is zero if the cross spectra intensities acquire the equilibrium-like appearance [2,8,11]:…”

Stationary Fluctuation Spectra and Anomalous Transport in a Dynamically Recharging Colloidal Plasma: Renormalized Approach

“…27 we obtain from ( 14) and ( 15) in a manner similar to [16] (see also [14]), the equations governing the £uctuation spectra intensities and renormalized damping coe¤cients (renormalized widths):…”

Nonlinear Interaction of the Long-Wave Low-Frequency Electromagnetic Plasma Excitations and Anomalous Diffusion

“…Essential nonlinear features of the system are nicely revealed by means of the cross-Ðeld renormalized statistical approach [3] based on the general renormalized statistical approach by Sytenko and Sosenko [1]. Also, it develops the IchimaruÏs idea [11] that the presence of Ñuctuations in the turbulent plasma makes it necessary to introduce the modi-Ðed binary operator.…”

Cross-Field Correlations in Plasma Fluctuation Spectra

“…1. As follows from (11), the role of magnetic nonlinearities is not dominant in this region. We see that the form of ( 21) and ( 22) is in consonance with its physical content.…”

“…v and v m are the kinematic and magnetic viscosities, respectively, that arise due to electron-electron ``collisions'' [1,11],…”

“…The simplest procedure [1,2,4,6,9] to obtain solutions in the nonlinear case, is to split the right-hand-sides of ( 14) and ( 15) into parts that are identically zero due to the symmetry properties of the matrix elements M(1, 2) and M m (1,2). Considering the terms containing straight and cross correlations independently, we see that the relevant symmetry conditions are satis¢ed by linear solutions ( 19) and (20) where T i T e for the LW excitations, while the ``mixed'' part is zero if the cross spectra intensities acquire the equilibrium-like appearance [2,8,11]:…”

Stationary Fluctuation Spectra and Anomalous Transport in a Dynamically Recharging Colloidal Plasma: Renormalized Approach

“…27 we obtain from ( 14) and ( 15) in a manner similar to [16] (see also [14]), the equations governing the £uctuation spectra intensities and renormalized damping coe¤cients (renormalized widths):…”

Nonlinear Interaction of the Long-Wave Low-Frequency Electromagnetic Plasma Excitations and Anomalous Diffusion

“…Essential nonlinear features of the system are nicely revealed by means of the cross-Ðeld renormalized statistical approach [3] based on the general renormalized statistical approach by Sytenko and Sosenko [1]. Also, it develops the IchimaruÏs idea [11] that the presence of Ñuctuations in the turbulent plasma makes it necessary to introduce the modi-Ðed binary operator.…”

Cross-Field Correlations in Plasma Fluctuation Spectra

“…1. As follows from (11), the role of magnetic nonlinearities is not dominant in this region. We see that the form of ( 21) and ( 22) is in consonance with its physical content.…”

“…v and v m are the kinematic and magnetic viscosities, respectively, that arise due to electron-electron ``collisions'' [1,11],…”

“…The simplest procedure [1,2,4,6,9] to obtain solutions in the nonlinear case, is to split the right-hand-sides of ( 14) and ( 15) into parts that are identically zero due to the symmetry properties of the matrix elements M(1, 2) and M m (1,2). Considering the terms containing straight and cross correlations independently, we see that the relevant symmetry conditions are satis¢ed by linear solutions ( 19) and (20) where T i T e for the LW excitations, while the ``mixed'' part is zero if the cross spectra intensities acquire the equilibrium-like appearance [2,8,11]:…”

Stationary Fluctuation Spectra and Anomalous Transport in a Dynamically Recharging Colloidal Plasma: Renormalized Approach

“…27 we obtain from ( 14) and ( 15) in a manner similar to [16] (see also [14]), the equations governing the £uctuation spectra intensities and renormalized damping coe¤cients (renormalized widths):…”

Nonlinear Interaction of the Long-Wave Low-Frequency Electromagnetic Plasma Excitations and Anomalous Diffusion

“…Essential nonlinear features of the system are nicely revealed by means of the cross-Ðeld renormalized statistical approach [3] based on the general renormalized statistical approach by Sytenko and Sosenko [1]. Also, it develops the IchimaruÏs idea [11] that the presence of Ñuctuations in the turbulent plasma makes it necessary to introduce the modi-Ðed binary operator.…”