The spectral line shapes for hydrogen-like heavy ion emitters embedded in strongly correlated two-component electron-ion plasmas are investigated with numerical simulations. For that purpose the microfield fluctuations are calculated by molecular dynamics simulations where short range quantum effects are taken into account by using a regularized Coulomb potential for the electron-ion interaction. The microfield fluctuations are used as input in a numerical solution of the time-dependent Schroedinger equation for the radiating electron. In distinction to the standard impact and quasistatic approximations the method presented here allows to account for the correlations between plasma ions and electrons. The shapes of the Ly-alpha line in Al are investigated in the intermediate regime. The calculations are in good agreement with experiments on the Ly-alpha line in laser generated plasmas.
The distribution of the electric microfield at a charged particle moving in a two-component plasma is calculated. The theoretical approximations are obtained via the parameter integration technique and using the screened pair approximation for the generalized radial distribution function. It is shown that the two-component plasma microfield distribution shows a larger probability of high microfield values than the corresponding distribution of the commonly used OCP model. The theory is checked by quasiclassical molecular-dynamics simulations. For the simulations a corrected Kelbg pseudopotenti…
The electric microfield distribution at charged particles is studied for two-component electron-ion plasmas using molecular dynamics simulation and theoretical models. The particles are treated within classical statistical mechanics using an electron-ion Coulomb potential regularized at distances less than the de Broglie length to take into account the quantum-diffraction effects. The potential-of-mean-force (PMF) approximation is deduced from a canonical ensemble formulation. The resulting probability density of the electric microfield satisfies exactly the second-moment sum rule without the …
In the present paper we introduce a full and closed system of atomic kinetic equations on fractions of atomic energy levels taking into account the effect of the plasma ions electric microfield mixing dynamics. The system of equations that we present is deduced from a full quantum multi-atomic states density matrix master equation. The analytical derivation of this atomic kinetic system of equations is based on the introduction of a new hierarchy chain of equations involving a new set of statistical atomic variables. The final system of atomic kinetic equations is obtained by introducing relat…
The low-frequency electric microfield distribution in a Coulomb plasma is calculated for various plasma parameters, from weak to strong Coulomb coupling and from zero to strong electron screening. Two methods of numerical calculations are employed: the adjustable-parameter exponential approximation and the Monte Carlo simulation. The results are represented by analytic fitting formulas suitable for applications.
In the present paper we give numerical estimations of the plasma ion electric microfield mixing dynamics rate. This rate was deduced from a quantum atomic density matrix formalism and corresponds to the mixing dynamics effect of energy levels by the plasma ion electric microfield. The rate in question is to be added to the usual collisional-radiative model for the modeling of dielectronic satellites originating from multi-excited atomic configurations to diagnose high density plasma regimes generated by the interaction of X-ray free electron lasers (XFEL's) with solid density matter. The obtai…
The electric microfield distribution (MFD) at an impurity ion is studied for two-component (TCP) electron-ion plasmas using molecular dynamics simulation and theoretical models. The particles are treated within classical statistical mechanics using an electron-ion Coulomb potential regularized at distances less than the de Broglie length to take into account quantum-diffraction effects. Corrections to the potential-of-mean-force exponential (PMFEX) approximation recently proposed for MFD in a strongly coupled TCP [Phys. Rev. E 72, 036403 (2005)] are obtained and discussed. This has been done b…
In the present paper we propose the use of desnity matrix formalism for the calculation of the atomic spectroscopic properties of autoionizing states in dense plasmas, i.e. warm dense matter and strongly coupled plasmas. This is motivated by the importance of taking into account the effect of the electric microfield generated by the plasma charge constituents in the calculation of the atomic populations of autoionizing states. For autoionizing states, electron densities justifying the statistical approach exceed solid density bringing serious doubts to the statistical approach even in dense pl…
In the present paper we propose to update the standard calculation of Stark line profiles for autoionizing atomic states in dense plasmas, i.e. warm dense matter and strongly coupled plasmas. This is motivated by the importance of taking into account the effect of the electric microfield generated by the plasma charge constituents in the calculation of the atomic populations of autoionizing states which leads to the modification of the calculation of Stark line profiles in the frame of the standard theory. This is due to the properties of the autoionizing atomic states that are far from Boltzm…
A general formulation is developed to demonstrate that atomic autoionizing (AI) resonances are broadened and shifted significantly due to plasma effects across bound-free continua. The theoretical and computational method presented accounts for broadening mechanisms: electron collisional, ion microfields (Stark), thermal Doppler, core excitations, and free-free transitions. {\it Extrinsic} plasma broadening redistributes and shifts AI resonance strengths while broadly preserving naturally {\it intrinsic} asymmetries of resonance profiles. Integrated oscillator strengths are conserved as resona…
We present the first measurements of a plasma velocity-space cross-correlation matrix. A singular value decomposition is applied to this inherently Hermitian matrix, and the relation between the eigenmodes and the plasma kinetic fluctuation modes is explored. A generalized wave admittance is introduced for these eigenmodes.
A master equation was formulated to study intrinsic charge fluctuations of a grain in a plasma as ions and primary electrons are attached to the grain through collisional collection, and secondary electrons are emitted from the grain. Two different plasmas with Maxwellian and non-Maxwellian distributions were considered. The fluctuations could be bistable in either plasma when the secondary electron emission is present, as two stable macrostates, associated with two stable roots of the charge net current, may exist. Metastablity of fluctuations, manifested by the passage of the grain charge be…
Single-point measurements of fluctuations in the scrape-off layer of magnetized plasmas are generally found to be dominated by large-amplitude bursts which are associated with radial motion of blob-like structures. A stochastic model for these fluctuations is presented, with the plasma density given by a random sequence of bursts with a fixed wave form. Under very general conditions, this model predicts a parabolic relation between the skewness and kurtosis moments of the plasma fluctuations. In the case of exponentially distributed burst amplitudes and waiting times, the probability density f…
The reliability of Langmuir probe measurements for plasma-turbulence investigations is studied on GEMR gyro-fluid simulations and compared with results from conditionally sampled I-V characteristics as well as self-emitting probe measurements in the near scrape-off layer of the tokamak ASDEX Upgrade. In this region, simulation and experiment consistently show coherent in-phase fluctuations in density, plasma potential and also in electron temperature. Ion-saturation current measurements turn out to reproduce density fluctuations quite well. Fluctuations in the floating potential, however, are …
The charge states of ions in dense plasmas fluctuate due to collisional ionization and recombination. Here we show how, by modifying the ion interaction potential, these fluctuations can mediate energy exchange between the plasma electrons and ions. Moreover, we develop a theory for this novel electron-ion energy transfer mechanism. Calculations using a random walk approach for the fluctuations suggest that the energy exchange rate from charge state fluctuations could be comparable to direct electron-ion collisions. This mechanism is, however, predicted to exhibit a complex dependence on the t…
A stochastic differential equation for the plasma density dynamics is derived, consistent with the experimentally measured distribution and the theoretical quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. The sensitivity of intermittency to the nonlinear dynamics is investigated by analyzing the Langevin representation of two intermittent distributions, showing the agreement between the quadratic nonlinearity and the gamma distri…
The current-driven electrostatic ion-cyclotron (EIC) instability is studied in presence of a transverse dc electric fields in a collisional magnetized dusty plasma. We derive the appropriate charging equation self consistently by using the Vlasov equation.
Plasma fluctuations in the scrape-off layer of the Alcator C-Mod tokamak in ohmic and high confinement modes have been analyzed using gas puff imaging data. In all cases investigated, the time series of emission from a single spatially-resolved view into the gas puff are dominated by large-amplitude bursts, attributed to blob-like filament structures moving radially outwards and poloidally. There is a remarkable similarity of the fluctuation statistics in ohmic plasmas and in edge localized mode-free and enhanced D-alpha high confinement mode plasmas. Conditionally averaged wave forms have a t…
Fluctuation signatures of rotation reversals and non-local transport events in KSTAR L-mode plasmas
Seoul National University（首尔大学）；National Fusion Research Institute（韩国核融合研究院）；University of California, San Diego（加州大学圣地亚哥分校）；Pohang University of Science and Technology（浦项科技大学）；National Institute of Fusion Science（日本核融合科学研究所）
Probability Distributions Functions (PDFs) of fluctuations of plasma edge parameters are skewed curves fairly different from normal distributions, whose shape appears almost independent of the plasma conditions and devices. We start from a minimal fluid model of edge turbulence and reformulate it in terms of uncoupled Langevin equations, admiting analytical solution for the PDFs of all the fields involved. We show that the supposed peculiarities of PDFs, and their universal character, are related to the generic properties of Langevin equations involving quadratic nonlinearities.
Three kinds of electrostatic modes are experimentally observed to propagate along magnetic-field lines for the first time in the pair-ion plasma consisting of only positive and negative fullerene ions with an equal mass. It is found that phase lags between the density fluctuations of positive and negative ions vary from 0 to $π$ depending on the frequency and is fixed at $π$ in the cases of ion acoustic and ion plasma waves, respectively. In addition, a new mode with the phase lag about $π$ appears in an intermediate-frequency band between the acoustic and plasma waves.
Using the Langevin approach and the multiscale technique, a kinetic theory of the time and space nonlocal fluctuations in the collisional plasma is constructed. In local equilibrium a generalized version of the Callen-Welton theorem is derived. It is shown that not only the dissipation but also the time and space derivatives of the dispersion determine the amplitude and the width of the spectrum lines of the electrostatic field fluctuations, as well as the form factor. There appear significant differences with respect to the non-uniform plasma. In the kinetic regime the form factor is more sen…
We have derived tractable cubic (p=3) and quartic (p=4) fluctuation-dissipation theorems (FDTs) for the classical one-component plasma in a form that links a single (p+1)-point dynamical structure function to a linear combination of pth-order density response functions amenable to calculation from model plasma kinetic equations. For p greater than or equal to 3, we note the emergence of "remainder" contributions comprised of clusters of lower-order dynamical structure functions which can be ultimately traded for response functions vis-a-vis the linear and quadratic FDTs. Our analysis paves the…
The propagation of microwaves across a turbulent plasma density layer is investigated with full-wave simulations. To properly represent a fusion edge-plasma, drift-wave turbulence is considered based on the Hasegawa-Wakatani model. Scattering and broadening of a microwave beam whose amplitude distribution is of Gaussian shape is studied in detail as a function of certain turbulence properties. Parameters leading to the strongest deterioration of the microwave beam are identified and implications for existing experiments are given.
High speed camera imaging is a powerful tool to probe the spatiotemporal features of unsteady processes in plasmas, usually assuming light fluctuations to be a proxy for the plasma density fluctuations. In this article, we systematically compare high speed camera imaging with simultaneous measurements of the plasma parameters -- plasma density, electron temperature, floating potential -- in a modestly magnetized Argon plasma column at low pressure (1 mTorr, magnetic fields ranging from 160 to 640~G). The light emission was filtered around $488\pm5$~nm, $750\pm5$~nm, $810\pm5$~nm. We show that …
A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation theorem is derived. This kinetic fluctuation-dissipation theorem reduces to the standard "fluid" one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equati…
In this work, we use a passive advection model for ion temperature fluctuations, in order to investigate their effects on Doppler Spectral line shapes. The relevance of the model is discussed in the framework of the Braginskii equations, and the subsequent Probability Density Function evaluation relies on results obtained in neutral fluids. The resulting Doppler line profiles are shown to exhibit characteristic exponential tails.
The control of fluctuations generated in an electron cyclotron resonance (ECR) plasma is attempted by changing microwave powers. It is found that when a cage is introduced in the vacuum chamber, the fluctuations change from turbulent state to chaotic state in the high microwave power region while it changes from chaotic state to periodic state in the low microwave power region. This result suggests that the geometry of the cage affects the state of the instability. Moreover it is found that the superposition of multicusped fields created by small permanent magnets reduces the chaotic dimension…
The energy budget of a collisionless plasma subject to electrostatic fluctuations is considered, and the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion is calculated. This excess measures how much thermal energy is "available" for conversion into plasma instabilities, and therefore constitutes a nonlinear measure of plasma stability. A distribution function with zero available energy defines a "ground state" in the sense that its energy cannot decrease by any linear or nonlinear plasma motion. In a Vlasov plas…
A self-consistent kinetic theory of Thomson scattering of an electromagnetic field by a non-uniform plasma is derived. We draw the readers' attention to the inconsistency in recent results on the Thomson scattering in inhomogeneous plasma, which leads to violation of the Fluctuation-Dissipation Theorem. We show that not only the imaginary part, but also the derivatives of the real part of the dielectric susceptibility determine the amplitude and the width of the Thomson scattering spectral lines. As a result of inhomogeneity, these properties become asymmetric with respect to inversion of the …
Large-amplitude, intermittent fluctuations are ubiquitous in the boundary region of magnetically confined plasmas and lead to detrimental plasma-wall interactions in the next-generation, high duty cycle fusion power experiments. Using gas puff imaging data time series from the scrape-off layer in the Alcator C-Mod device, it is here demonstrated that the large-amplitude fluctuations can be described as a super-position of pulses with fixed shape and constant duration. By applying a new deconvolution algorithm on the data time series with a two-sided exponential pulse function, the arrival time…
Using numerical simulations, we investigate the equilibrium dynamics of a single component fluid with Yukawa interaction potential. We show that, for a wide range of densities and temperatures, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. Since the Yukawa potential can describe the ion-ion interactions in a plasma, the model has significant applicability for both analyzing and interpreting the results of x-ray scattering data from high power lasers and fourth generation light sources.
The Bandt-Pompe permutation entropy and the Jensen-Shannon statistical complexity are used to analyze fluctuating time series of three different plasmas: the magnetohydrodynamic (MHD) turbulence in the plasma wind tunnel of the Swarthmore Spheromak Experiment (SSX), drift-wave turbulence of ion saturation current fluctuations in the edge of the Large Plasma Device (LAPD) and fully-developed turbulent magnetic fluctuations of the solar wind taken from the WIND spacecraft. The entropy and complexity values are presented as coordinates on the CH plane for comparison among the different plasma env…
We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations. This novel model (termed as GK-E&B) employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields. It, thus, not only includes kinetic effects, such as wave-particle interaction and microscopic (ion Larmor radius scale) physics; but also is computationally more efficient than the conventional formulation described in terms of pot…
Turbulent plasma edge density fluctuations can broaden a traversing microwave beam degrading its quality. This can be a problem for scenarios relying on a high spatial localization of the deposition of injected microwave power, like controlling MHD instabilities. Here we present numerical estimations of the scattering of a microwave beam by density fluctuations over a large parameter range, including extrapolations to ITER. Two codes are used, the full-wave code IPF-FDMC and the wave kinetic equation solver WKBeam. A successful comparison between beam broadening obtained from DIII-D experiment…
The role of turbulence in setting boundary plasma conditions is presently a key uncertainty in projecting to fusion energy reactors. To robustly diagnose edge turbulence, we develop and demonstrate a technique to translate brightness measurements of HeI line radiation into local plasma fluctuations via a novel integrated deep learning framework that combines neutral transport physics and collisional radiative theory for the $3^3 D - 2^3 P$ transition in atomic helium. The tenets for experimental validity are reviewed, illustrating that this turbulence analysis for ionized gases is transferable…
Intermittent fluctuations in the boundary of magnetically confined plasmas are investigated by numerical turbulence simulations of a reduced fluid model describing the evolution of the plasma density and electric drift vorticity in the two-dimensional plane perpendicular to the magnetic field. Two different cases are considered, one describing resistive drift waves in the edge region and another including only the interchange instability due to unfavorable magnetic field curvature in the scrape-off layer. Analysis of long data time series obtained by single-point recordings are compared to pre…
A master equation is formulated to model the states of the grain charge in a general multi-component plasma, where there are electrons and various kinds of positive or negative ions that are singly or multiply charged. A Fokker-Planck equation is developed from the master equation through the system-size expansion method. The Fokker-Planck equation has a Gaussian solution with a mean and variance governed by two initial-value differential equations involving the rates of the attachment of ions and electrons to the dust grain. Grain charging in a plasma containing electrons, protons and alpha p…
A general formalism for the treatment of density fluctuations in Coulomb plasmas is presented and applied to the treatment of temperature relaxation in multi-component quantum plasmas when the separate components (electrons and ions) relax to LTE much faster than the mutual equilibration rate. The underlying theory is based upon the Random Phase Approximation with static local field corrections (LFCs) to account for short-range correlations between the particles. A general formula for the electron-ion equilibration rate, similar to the one given by Daligault and Dimonte, is derived. However a …
Following the analysis on linear spectra of shear Alfvén fluctuations excited by energetic particles (EPs) in the Divertor Tokamak Test (DTT) facility plasmas [T. Wang et al., Phys. Plasmas 25, 062509 (2018)], in this work, nonlinear dynamics of the corresponding mode saturation and the fluctuation induced EP transport is studied by hybrid magnetohydrodynamic-gyrokinetic simulations. For the reversed shear Alfvén eigenmode driven by magnetically trapped EP precession resonance in the central core region of DTT plasmas, the saturation is mainly due to radial decoupling of resonant trapped EPs. …
It is pointed out that the unmagnetized inhomogeneous plasmas can support a low frequency electromagnetic ion wave as a normal mode like Alfven wave of magnetized plasmas. But this is a coupled mode produced by the mixing of longitudinal and transverse components of perturbed electric field due to density inhomogeneity. The ion acoustic wave does not remain electrostatic in non-uniform plasmas. On the other hand, a low frequency electrostatic wave can also exist in the pure electron plasmas. But the magnetic field fluctuations in both electron as well as in electron-ion plasmas are coupled wit…
We present that a statistical method known as the Complexity-Entropy analysis is useful to characterize a state of plasma turbulence and flux in the resonant magnetic perturbation (RMP) edge localized mode (ELM) control experiment. The RMP ELM suppression phase with the stochastic pedestal top temperature fluctuation can be distinguished from the natural ELM free phase with the chaotic fluctuation. It is discussed that the stochastic temperature fluctuation localized near the pedestal top can be originated from the narrow layer of the field penetration near the pedestal top. The forced magneti…
This paper presents a complete theoretical framework for plasma turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by-order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the fluctuations. The equilibrium d…
Understanding the statistics of fluctuation driven flows in the boundary layer of magnetically confined plasmas is desired to accurately model the lifetime of the vacuum vessel components. Mirror Langmuir probes (MLPs) are a novel diagnostic that uniquely allow to sample the plasma parameters on a time scale shorter than the characteristic time scale of their fluctuations. Sudden large-amplitude fluctuations in the plasma degrade the precision and accuracy of the plasma parameters reported by MLPs for cases in which the probe bias range is of insufficient amplitude. While some data samples can…
The results of a theoretical investigation of the energy loss of charged particles in a magnetized classical plasma due to the electric field fluctuations are reported. The energy loss for a test particle is calculated through the linear-response theory. At vanishing magnetic field the electric field fluctuations lead to an energy gain of the charged particle for all velocities. It has been shown that in the presence of strong magnetic field this effect occurs only at low-velocities. In the opposite case of high-velocities the test particle systematically loses its energy due to the interactio…
We report the observation of a quasi-coherent density fluctuation (QCF) by the Doppler backscattering system in the scrape-off layer (SOL) region of the DIII-D tokamak. This QCF is observed in high-power, high-performance hybrid plasmas with near double-null divertor (DND) shape during the electron cyclotron heating period. This mode is correlated with a steepened SOL density profile and leads to significantly elevated particle and heat fluxes between ELMs. The SOL QCF is a long-wavelength ion-scale fluctuation and propagates in the ion diamagnetic direction in the plasma frame. Its radial exp…
Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness $S$ and kurtosis $K$. Similar statistical characteristics of variabilities have…
A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribu…
Traditionally devoted to electron density profile measurement we show that fast frequency sweeping reflectometry technique can bring valuable and innovative measurements onto plasma turbulence. While fast frequency sweeping technique is traditionally devoted to electron density radial profile measurements we show in this paper how we can handle the fluctuations of the reflected signal to recover plasma density fluctuation measurements with a high spatial and temporal resolution. Large size turbulence related to magneto-hydrodynamic (MHD) activity and the associated magnetic islands can be dete…
We report on a recently developed laser-probing diagnostic which allows direct measurements of ray-deflection angles in one axis, whilst retaining imaging capabilities in the other axis. This allows us to measure the spectrum of angular deflections from a laser beam which passes though a turbulent high-energy-density plasma. This spectrum contains information about the density fluctuations within the plasma, which deflect the probing laser over a range of angles. %The principle of this diagnostic is described, along with our specific experimental realisation. We create synthetic diagnostics us…
The Large Volume Plasma device(LVPD), a cylindrically shaped, linear plasma device of dimension( $ϕ=2m $, $ L =3m $) have successfully demonstrated the excitation of Electron Temperature Gradient(ETG) turbulence[ Mattoo et al.,[1]]. The observed ETG turbulence shows significant power between $ω\sim (25-90 krad/s )> Ω_{ci}(= 8 krad/s )$, corresponding to the wavenumber, $ k_y ρ_e ~ (0.1- 0.2)$ where, $ Ω_{ci}$ and $ρ_e(=5 mm ) $, ion cyclotron frequency and electron Larmor radius, respectively. The observed frequency and wave number matches well with theoretical estimates corresponding to Whist…
Plasma turbulence, and edge density fluctuations in particular, can under certain conditions broaden the cross-section of injected microwave beams significantly. This can be a severe problem for applications relying on well-localized deposition of the microwave power, like the control of MHD instabilities. Here we investigate this broadening mechanism as a function of fluctuation level, background density and propagation length in a fusion-relevant scenario using two numerical codes, the full-wave code IPF-FDMC and the novel wave kinetic equation solver WKBeam. The latter treats the effects of…
Radial profiles of the ion saturation current and its fluctuation statistics are presented from probe measurements in L-mode, neutral beam heated plasmas at the outboard mid-plane region of KSTAR. The familiar two-layer structure, seen elsewhere in tokamak L-mode discharges, with a steep near-SOL profile and a broad far-SOL profile, is observed. The profile scale length in the far-SOL increases drastically with line-averaged density, thereby enhancing plasma interactions with the main chamber walls. Time series from the far-SOL region are characterised by large-amplitude bursts attributed to t…
The effect of changes in plasma parameters, that are characteristic near or at an L-H transition in fusion edge plasmas, on fluctuation correlation lengths are analysed by means of drift-Alfven turbulence computations. Scalings by density gradient length, collisionality, plasma beta, and by an imposed shear flow are considered. It is found that strongly sheared flows lead to the appearence of long-range correlations in electrostatic potential fluctuations parallel and perpendicular to the magnetic field.
Predicting the dynamics of a thermonuclear plasma during a magnetic confinement experiment is fundamental in order to make nuclear fusion a reliable source of energy. The development of a set of equations describing the plasma evolution on a given time scale is the main requirement to reach this goal. A limited amount of works have studied in a self-consistent way collisional transport and fluctuation induced transport. The motivation of this work stems from the fundamental importance of the self-consistency of the adopted description in order to understand transport processes on the energy co…
Subcritical transition of an inhomogeneous plasma where turbulences with different characteristic space-time scales coexist is analyzed with methods of statistical physics of turbulences. We derived the development equations of the probability density function (PDF) of the spectrum amplitudes of the fluctuating electro-static potential. By numerically solving the equations, the steady state PDFs were obtained. Although the subcritical transition is observed when the turbulent fluctuations are ignored, the PDF shows that the transition is smeared out by the turbulent fluctuations. It means that…
