Studies of fluctuations in the high-temperature plasma of modern stellarators by the microwave scattering technique

Microwave scattering diagnostics are described that allow direct measurements of the turbulent processes in the high-temperature plasma of magnetic confinement systems. The first physical results are presented from fluctuation measurements carried out in 2000–2001 in three stellarators: L-2M (Institute of General Physics, Moscow), LHD (National Institute of Fusion Science, Toki), and TJ-II (CIEMAT, Madrid). Plasma density fluctuations in the axial (heating) regions of the L-2M and LHD stellarators were measured from microwave scattering at the fundamental harmonic of the heating gyrotron radiation. In the TJ-II stellarator, a separate 2-mm microwave source was used to produce a probing beam; the measurements were performed at the middle of the plasma radius. Characteristic features of fluctuations, common for all three devices, are revealed by the methods of statistical and spectral analysis. These features are the wide frequency Fourier and wavelet spectra, autocorrelation functions with slowly decreasing tails, and non-Gaussian probability distributions of the magnitudes and the increments in the magnitude of fluctuations. Observations showed the high level of coherence between turbulent fluctuations in the central region and at the edge of the L-2M plasma. The drift-dissipative instability and the instability driven by trapped electrons are examined as possible sources of turbulence in a high-temperature plasma.     

New possibilities for the mathematical modeling of turbulent transport processes in plasma

A new mathematical model is proposed for the probability distributions of the characteristics of the processes observed in turbulent plasmas. The model is based on formal theoretical considerations related to probabilistic limit theorems for a nonhomogeneous random walk and has the form of a finite mixture of Gaussian distributions. The reliability of the model is confirmed by the results of a statistical analysis of the experimental data on density fluctuations in high-temperature plasmas of the L-2M, LHD, and TJ-II stellarators and the local fluctuating flux in the TAU-1 linear device and in the edge plasma of the L-2M stellarator with the use of the estimation-maximization algorithm. It is shown that low-frequency structural turbulence in a magnetized plasma is related to non-Brownian transport, which is determined by the characteristic temporal and spatial scales of the ensembles of stochastic plasma structures. Mechanisms that could be responsible for the random nature of time samples of the local turbulent flux in TAU-1 are indicated. A new physical concept of the intermittence of plasma turbulent pulsations is developed on the basis of the statistical separation of mixtures in terms of the model proposed. The intermittence of plasma pulsations is shown to be associated with the generation of plasma structures (solitons and vortices) and their nonlinear interaction, as well as with their damping and drift.     

Dependence of the energy lifetime on the type of anomalous losses in stellarators

A relatively simple model of transport process in stellarators that was proposed earlier by the author on the basis of neoclassical theory makes it possible to determine the density and temperature profiles of the plasma components, the ambipolar electric field profile, and the particle and energy lifetimes from the given device parameters and given particle and energy sources with allowance for anomalous losses. The results of numerical simulations carried out with this model for the L-2M, ATF, CHS, and LHD stellarators over broad ranges of plasma densities and absorbed powers showed that the plasma energy lifetimes in these devices coincide to within factors on the order of two with those found from empirical scalings. A specific model of anomalous losses was chosen for calculations. Results are presented from simulations with a more general form of the anomalous thermal conductivity. Namely, the thermal conductivity is chosen to be K _j ^(a) ≈ N ^α T _j ^β B ₀ ^?γ , where N(r) is the plasma density and T _j (r) is the temperature of the jth plasma component (j = e, i). The parameters α, β, and γ are set equal to α = 1, β = 2, and γ = 1; α = 0.5, β = 2.5, and γ = 1; α = 1.5, β = 2, and γ = 2; α = 1, β = 2.5, and γ = 2; and α = 1.5, β = 2.5, and γ = 2. The simulations have been done for the L-2M and LHD stellarators. It is found that, in all the five models, the calculated energy lifetimes τ _c are essentially independent of the functional form of the anomalous thermal conductivity and coincide to within a factor on the order of two with those following from the LHD scaling.     

Could reversed-field pinches and quasi-helical stellarators benefit from transport suppression in tokamaks?

The trapped particle theory of turbulent transport successfully explains key features of tokamak transport: the canonical L-mode, supershort plasma profiles, and the transport suppression by negative magnetic shear and poloidal rotation. Here, this theory is applied to reversed-field pinch (RFP) profiles, which can be justified if the magnetic fluctuations are suppressed, and to stellarators. A canonical density profile for RFPs is suggested, and it is found that no analogue of the transport suppression by negative shear in tokamaks is possible in RFPs. In quasi-helical stellarators, on the other hand, it appears possible to create an analogue of the tokamak reversed shear mode in the entire plasma volume.     

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.     

Use of internal current rings in long closed magnetic confinement systems

A closed magnetic confinement system is considered in the shape a corrugated torus into one or several mirror cells of which current rings are introduced that reverse the magnetic field on the axis. An internal current ring surrounded by plasma creates a magnetic configuration with an average magnetic well on the axis. The axial plasma region of such a configuration is stabilized by cusps, whereas the outer region can be stabilized by a divertor, provided that the plasma pressure gradually decreases toward the periphery. The use of internal current rings may be profitable in stellarators in which the confinement region can be divided into several regions by magnetic mirrors.     

Effect of the periodic ripple in an axial confining magnetic field on the Alfvén heating of a cylindrical plasma

In a uniform axial magnetic field, the structure of local Alfvén resonance and the resonant absorption of RF power are governed by collisions, finite ion Larmor radius effects, and electron inertia. It is shown that, in a cylindrical plasma in a constant, periodically rippled, axial magnetic field, the structure of Alfvén resonance and the absorption of RF power can strongly depend on the ripple amplitude. The conditions under which the effect in question is dominant are intrinsic, e.g., to the modular Wendelstein stellarators.     

Onset condition of the subcritical geodesic acoustic mode instability in the presence of energetic-particle-driven geodesic acoustic mode

An analytic model is developed for understanding the abrupt onset of geodesic acoustic mode (GAM) in the presence of chirping energetic-particle-driven GAM (EGAM). This abrupt excitation phenomenon has been observed on LHD plasma. Threshold conditions for the onset of abrupt growth of GAM are derived, and the period doubling phenomenon is explained. The phase relation between the mother mode (EGAM) and the daughter mode (GAM) is also discussed. This result contributes to the understanding of “trigger problems” of laboratory and nature plasmas.     

Neoclassical transport in stellarators without collisionless ion loss

For quasi-isodynamic stellarators with poloidally closed contours of the magnetic field strength and high plasma beta neoclassical transport coefficients are computationally obtained over a large range of mean free paths. In particular, a long-mean-free-path regime is found in which quasi-neutrality obtains without radial electric field.     

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U₀. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2v_T/R (where v_T is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ? of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.     

Self-consistent modeling of radio-frequency plasma generation in stellarators

A self-consistent model of radio-frequency (RF) plasma generation in stellarators in the ion cyclotron frequency range is described. The model includes equations for the particle and energy balance and boundary conditions for Maxwell’s equations. The equation of charged particle balance takes into account the influx of particles due to ionization and their loss via diffusion and convection. The equation of electron energy balance takes into account the RF heating power source, as well as energy losses due to the excitation and electron-impact ionization of gas atoms, energy exchange via Coulomb collisions, and plasma heat conduction. The deposited RF power is calculated by solving the boundary problem for Maxwell’s equations. When describing the dissipation of the energy of the RF field, collisional absorption and Landau damping are taken into account. At each time step, Maxwell’s equations are solved for the current profiles of the plasma density and plasma temperature. The calculations are performed for a cylindrical plasma. The plasma is assumed to be axisymmetric and homogeneous along the plasma column. The system of balance equations is solved using the Crank-Nicholson scheme. Maxwell’s equations are solved in a one-dimensional approximation by using the Fourier transformation along the azimuthal and longitudinal coordinates. Results of simulations of RF plasma generation in the Uragan-2M stellarator by using a frame antenna operating at frequencies lower than the ion cyclotron frequency are presented. The calculations show that the slow wave generated by the antenna is efficiently absorbed at the periphery of the plasma column, due to which only a small fraction of the input power reaches the confinement region. As a result, the temperature on the axis of the plasma column remains low, whereas at the periphery it is substantially higher. This leads to strong absorption of the RF field at the periphery via the Landau mechanism.     

Plasma protein characteristics of long-term hemodialysis survivors

Hemodialysis (HD) patients are under recurrent circulatory stress, and hemodialysis has a high mortality rate. The characteristics of plasma proteomes in patients surviving long-term HD remain obscure, as well as the potential biomarkers in predicting prognoses. This study reports the proteome analyses of patient plasma from non-diabetic long-term HD (LHD, dialysis vintage 14.9±4.1 years, n = 6) and the age/sex/uremic etiology-comparable short-term HD (SHD, dialysis vintage 5.3±2.9 years, n = 6) using 2-DE and mass spectrometry. In addition, a 4-year longitudinal follow-up of 60 non-diabetic HD patients was subsequently conducted to analyze the baseline plasma proteins by ELISA in predicting prognosis. Compared to the SHD, the LHD survivors had increased plasma vitamin D binding proteins (DBP) and decreased clusterin, apolipoprotein A-IV, haptoglobin, hemopexin, complement factors B and H, and altered isoforms of α1-antitrypsin and fibrinogen gamma. During the 45.7±15 months for follow-up of the 60 HD patient cases, 16 patients died. Kaplan-Meier analysis demonstrated that HD patients with the lowest tertile of the baseline plasma DBP level have a significantly higher mortality rate. Multivariate Cox regression analysis further indicated that DBP is an independent predictor of mortality. In summary, the altered plasma proteins in LHD implicated accelerated atherosclerosis, defective antioxidative activity, increased inflammation/infection, and organ dysfunction. Furthermore, lower baseline plasma DBP in HD patients is related to mortality. The results suggest that the proteomic approach could help discover the potential biomarker in HD prognoses.     

Role of the plasma interaction with magnetic field in the “missing power” problem

It is shown that, at rapid changes of the heating power, the magnetically confined equilibrium plasma almost completely absorbs the injected energy, so that its only small part goes to the magnetic field. The result is obtained within the standard MHD theory with use of exact consequences of the force-balance equations in toroidal geometry. It is assumed that, when heated, the plasma evolves from one equilibrium state to another with the magnetic field frozen-in. Another constraint is the conservation of the toroidal magnetic flux in the plasma-wall vacuum gap. It is shown that the plasma interaction with magnetic field (which is traditionally neglected in the analysis of heat transport in tokamaks and stellarators) is the natural mechanism of fast redistribution of energy in the plasma, observed in some experiments in these devices at switchon of powerful heat sources.     

Determination of the radius, volume and surface area of plasma lipoproteins using fluorescent probes

The effect of radiationless energy transfer between the fluorescent probes was used to determine the radius, volume and surface area of the blood plasma lipoprotein. Anthracene and p-terphenyl, distributed over the whole volume of lipids of a lipoprotein particle, and HSPH-14 localized on its surface served as energy donor and acceptor probes. Human blood lipoproteins of very low (LVLD), low (LLD2), and high (LHD2 and LHD3) density were studied. All the fluorescence-measured lipoprotein volumes were rather close to the data resulted from the weight analysis. The surface areas were equal to 230, 210, 400 and 330 m2 per 1 g of lipoprotein and the radii--11, 11, 7.5, 7.2 nm, respectively. All the measurements were made in solutions, without any denaturating effects on lipoprotein, its concentration being 1 mg/ml and lower.     

Ambipolarity condition and possibility of multivalued steady-state solutions to transport equations in stellarators

The possibility of steady-state multivalued solutions to transport equations in stellarators is considered. It is shown that the ambipolarity condition is necessary but not sufficient to find the ambipolar electric field, because the functions entering into it (the plasma density and temperature, as well as their spatial derivatives) depend on the ambipolar field. To do this correctly, it is necessary to solve the full set of time-independent transport equations (including diffusion and heat conduction equations). The possible existence of multivalued solutions to this set of equations is analyzed numerically. It is shown that, under certain conditions that depend on the form and magnitude of particle and heat sources, such solutions can exist. Their form is determined by the initial value of the ambipolar field, the source magnitudes, and the boundary conditions. Discontinuous solutions in which the radial profile of the ambipolar field undergoes jumps are found. In this case, however, the particle and energy fluxes remain continuous, because the discontinuities of the electric field are balanced by the discontinuities of the density and temperature gradients.     

Steady solutions to neoclassical transport equations and the absence of bifurcated states

The question of whether two-valued solutions can exist for an ambipolar electric field in stellarators and rippled tokamaks is considered. Steady solutions to transport equations in the limit of infrequent collisions are obtained in the purely neoclassical transport theory (that is, without allowance for possible anomalous losses). It is shown that, given the particle and heat sources, these equations have only one steady continuous solution, i.e., the steady states are nonbifurcating.     

Mapping QTLs for heading synchrony in a doubled haploid population of rice in two environments

Simultaneous heading of plants within the same rice variety, also refer to heading synchrony, is an important factor that affects simultaneous ripening of the variety. Understanding of the genetic basis of heading synchrony may contribute to molecular breeding of rice with simultaneous heading and ripening. In the present study, a doubled haploid （DH） population, derived from a cross between Chunjiang 06 and TN1 was used to analyze quantitative trait locus （QTL） for heading synchrony related traits, i.e., early heading date （EHD）, late heading date （LHD）, heading asynchrony （HAS）, and tiller number （PN）. A total of 19 QTLs for four traits distributed on nine chromosomes were detected in two environments. One QTL, qHAS-8 for HAS, explained 27.7% of the phenotypic variation, co-located with the QTLs for EHD and LHD, but it was only significant under long-day conditions in Hangzhou, China. The other three QTLs, qHAS-6, qHAS-9, and qHAS-10, were identified under short-day conditions in Hainan, China, each of which explained about 11% of the phenotypic variation. Two of them, qHAS-6 and qHAS-9, were co-located with the QTLs for EHD and LHD. Two QTLs, qPN-4 and qPN-5 for PN, were detected in Hangzhou, and qPN-5 was also detected in Hainan. However, none of them was co-located with QTLs for EHD, LHD, and HAS, suggesting that PN and HAS were controlled by different genetic factors. The results of this study can be useful in marker assisted breeding for improvement of heading synchrony.