Formation and evolution of flapping and ballooning waves in magnetospheric plasma sheet

By adopting Lembége & Pellat’s 2D plasma-sheet model, we investigate the flankward flapping motion and Sunward ballooning propagation driven by an external source (e.g., magnetic reconnection) produced initially at the sheet center. Within the ideal MHD framework, we adopt the WKB approximation to obtain the Taylor–Goldstein equation of magnetic perturbations. Fourier spectral method and Runge–Kutta method are employed in numerical simulations, respectively, under the flapping and ballooning conditions. Studies expose that the magnetic shears in the sheet are responsible for the flapping waves, while the magnetic curvature and the plasma gradient are responsible for the ballooning waves. In addition, the flapping motion has three phases in its temporal development: fast damping phase, slow recovery phase, and quasi-stabilized phase; it is also characterized by two patterns in space: propagating wave pattern and standing wave pattern. Moreover, the ballooning modes are gradually damped toward the Earth, with a wavelength in a scale size of magnetic curvature or plasma inhomogeneity, only 1–7% of the flapping one; the envelops of the ballooning waves are similar to that of the observed bursty bulk flows moving toward the Earth.     

Influence of plasma pedestal profiles on access to ELM-free regimes in ITER

The influence of current density and pressure gradient profiles in the pedestal on the access to the regimes free from edge localized modes (ELMs) like quiescent H-mode in ITER is investigated. Using the simulator of MHD modes localized near plasma boundary based on the KINX code, calculations of the ELM stability were performed for the ITER plasma in scenarios 2 and 4 under variations of density and temperature profiles with the self-consistent bootstrap current in the pedestal. Low pressure gradient values at the separatrix, the same position of the density and temperature pedestals and high poloidal beta values facilitate reaching high current density in the pedestal and a potential transition into the regime with saturated large scale kink modes. New version of the localized MHD mode simulator allows one to compute the growth rates of ideal peeling-ballooning modes with different toroidal mode numbers and to determine the stability region taking into account diamagnetic stabilization. The edge stability diagrams computations and sensitivity studies of the stability limits to the value of diamagnetic frequency show that diamagnetic stabilization of the modes with high toroidal mode numbers can help to access the quiescent H-mode even with high plasma density but only with low pressure gradient values at the separatrix. The limiting pressure at the top of the pedestal increases for higher plasma density. With flat density profile the access to the quiescent H-mode is closed even with diamagnetic stabilization taken into account, while toroidal mode numbers of the most unstable peeling-ballooning mode decrease from n = 10?40 to n = 3?20.     

Alfvén eigenmode evolution computed with the VENUS and KINX codes for the ITER baseline scenario

A new application of the VENUS code is described, which computes alpha particle orbits in the perturbed electromagnetic fields and its resonant interaction with the toroidal Alfvén eigenmodes (TAEs) for the ITER device. The ITER baseline scenario with Q = 10 and the plasma toroidal current of 15 МА is considered as the most important and relevant for the International Tokamak Physics Activity group on energetic particles (ITPA-EP). For this scenario, typical unstable ТАЕ-modes with the toroidal index n = 20 have been predicted that are localized in the plasma core near the surface with safety factor q = 1. The spatial structure of ballooning and antiballooning modes has been computed with the ideal MHD code KINX. The linear growth rates and the saturation levels taking into account the damping effects and the different mode frequencies have been calculated with the VENUS code for both ballooning and antiballooning TAE-modes.     

Stabilization of ballooning modes by nonparaxial cells

An analysis is made of the effect of high-curvature stabilizing nonparaxial elements (cells) on the MHD plasma stability in open confinement systems and in confinement systems with closed magnetic field lines. It is shown that the population of particles trapped in such cells has a stabilizing effect not only on convective (flute) modes but also on ballooning modes, which govern the maximum possible β value. In the kinetic approach, which distinguishes between the effects of trapped and passing particles, the maximum possible β values consistent with stability can be much higher than those predicted by the MHD model.     

Magnetic geometry, plasma profiles, and stability

The history of the stability of short wavelength modes, such as MHD instabilities and drift waves, has been a long and tortuous one as increasingly realistic representations of the equilibrium magnetic geometry have been introduced. Early work began with simple slab or cylindrical models where plasma profiles and magnetic shear were seen to play key roles. Then the effects of toroidal geometry, in particular the constraints imposed by periodicity in the presence of magnetic shear, provided a challenge for theory, which was met by the ballooning transformation. More recently the limitations on the conventional ballooning theory arising from effects such as toroidal rotation shear, low magnetic shear, and the presence of the plasma edge have been recognized. These have led in turn to modifications and extensions of this theory. These developments have produced a continuously changing view of the stability of the “universal” drift wave, for example. After a survey of this background, we describe more recent work of relevance to currently important topics, such as transport barriers characterized by the presence of strong rotation shear and low magnetic shear and the edge localized modes that occur in H-mode. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 7, pp. 588–598. Based on an invited talk given at the 11th European Fusion Theory Meeting, Aix-en-Provence, France, September 2005. The text was submitted by the author in English.     

Impacts of pellets injected from the low-field side on plasma in ITER

Impacts of pellets injected from the low-field side (LFS) on plasma in ITER are investigated using the 1.5D BALDUR integrated predictive modeling code. In these simulations, the pellet ablation is described using the neutral gas shielding (NGS) model. The pellet ablation model is coupled with the plasma core transport model, which is a combination of the MMM95 anomalous transport model and NCLASS neoclassical transport model. The boundary conditions are assumed to be at the top of the pedestal, in which the pedestal parameters are predicted using a pedestal model based on the theoretical-based pedestal width scaling (either magnetic and flow shear stabilization width scaling, or flow shear stabilization width scaling, or normalized poloidal pressure width scaling) and the infinite-n ballooning mode pressure gradient limit. These pedestal models depend sensitively on the density at the top of the pedestal, which can be strongly influenced by the injection of pellets. The combination of the MMM95 and NCLASS models, together with the pedestal and NGS models, is used to simulate the time evolution of the plasma current, ion and electron temperatures, and density profiles for ITER standard type-I ELMy H-mode discharges during the injection of LFS pellets. It is found that the injection of pellets results in a complicated plasma scenario, especially in the outer region of the plasma and the plasma conditions at the boundary in which the pellet has an impact on increasing the plasma edge density, but reducing the plasma edge temperature. The LFS pellet has a stronger impact on the edge as compared to the center. For fusion performance, the pellet can result in either enhancement or degradation, depending sensitively on the pellet parameters; such as the pellet size, pellet velocity, and pellet frequency. For example, when a series of deuterium pellets with a size of 0.5 cm, velocity of 1 km/s, and frequency of 2 Hz are injected into the ITER plasma from the LFS, the plasma performance, evaluated in terms of Q _fusion, can increase to 72% of that before the use of pellets. It is also found that the injection of pellets results in an increase in the ion and electron densities, but does not enhance the central plasma density. On the other hand, it results in the formation of another peak of the plasma density in the outer region near the plasma edge. The formation of the density peak results in the reduction of plasma transports near the edge by decreasing the contributions of ion-temperature-gradient and trapped electron modes, as well as kinetic ballooning modes.     

Formation of an internal transport barrier and magnetohydrodynamic activity in experiments with the controlled density of rational magnetic surfaces in the T-10 Tokamak

Results are presented from experiments on the formation of an internal electron transport barrier near the q = 1.5 rational surface in the T-10 tokamak. The experiments were carried out in the regime with off-axis electron cyclotron resonance (ECR) heating followed by a fast plasma current ramp-up. After suppressing sawtooth oscillations by off-axis ECR heating, an internal transport barrier began to form near the q = 1.5 rational surface. In the phase of the current ramp-up, the quality of the transport barrier improved; as a result, the plasma energy confinement time increased 2–2.5 times. The intentionally produced flattening of the profile of the safety factor q(r) insignificantly affected magnetohydrodynamic activity in the plasma column in spite of the theoretical possibility of formation of substantial m/n = 3/2 and 2/1 magnetic islands. Conditions are discussed under which the flattening of the profile of the safety factor q near low-order rational surfaces leads to the formation of either an internal transport barrier or the development of an island magnetic structure induced by tearing modes.     

Numerical simulation of drift-resistive ballooning turbulence in the presence of the GA mode in the plasma edge tokamak

Drift-resistive ballooning turbulence is simulated numerically based on a quasi-three-dimensional computer code for solving nonlinear two-fluid MHD equations in the scrape-off layer plasma in a tokamak. It is shown that, when the toroidal geometry of the magnetic field is taken into account, additional (geodesic) flux terms associated with the first poloidal harmonic (∼sinθ) arise in the averaged equations for the momentum, density, and energy. Calculations show that the most important of these terms is the geodesic momentum flux (the Stringer-Windsor effect), which lowers the poloidal rotation velocity. It is also shown that accounting for the toroidal field geometry introduces experimentally observed, special low-frequency MHD harmonics—GA modes—in the Fourier spectra. GA modes are generated by the Reynolds turbulent force and also by the gradient of the poloidally nonuniform turbulent heat flux. Turbulent particle and heat fluxes are obtained as functions of the poloidal coordinate and are found to show that, in a tokamak, there is a “ballooning effect” associated with their maximum in the weak magnetic field region. The dependence of the density, temperature, and pressure on the poloidal coordinate is presented, as well as the dependence of turbulent fluxes on the toroidal magnetic field.     

On the nature of global plasma oscillations in a tokamak. Part II: Spatial structure and propagation of perturbations observed at the T-10 tokamak

Large-scale plasma oscillations (so-called MHD oscillations) observed at the T-10 tokamak are investigated. The central electron cyclotron heating was used to enhance oscillations at the m/n = 1/1 mode with the goal of determining the internal characteristics of the process. The spatially resolved electron cyclotron emission diagnostics allowed analyzing the propagation characteristics of plasma perturbations. The experiments have revealed that excitation of oscillations in a particular mode occur simultaneously in the entire area located within the corresponding rational magnetic surface. The propagation of plasma perturbations along the torus is found to be inhomogeneous. The electron cyclotron emission diagnostics allowed finding eigen (resonance) frequencies of plasma oscillations from the parameters of their inhomogeneous propagation in the plasma core and comparing them with spectra of oscillations of the magnetic field induced by the plasma current in the edge plasma, which were recorded by magnetic probes. It is established that the frequencies of eigenmodes are independent of the electron temperature, plasma density, and auxiliary heating power. Even spatial harmonics of the principal magnetic surface are observed under strong excitation of oscillations. The rational magnetic surfaces that determine oscillation harmonics retain their position during the entire steady-state phase of the total plasma current in spite of the strong sharpening of the temperature profile due to central heating.     

MHD stability of a collisionless anisotropic plasma in a system with an internal conductor

A study is made of the MHD stability of a collisionless anisotropic-pressure plasma in a nonparaxial magnetic configuration with an internal conductor in cylindrical geometry. A stability criterion for flutelike modes is obtained, and the families of marginally stable profiles of the longitudinal and transverse plasma pressures are calculated by using the Chew-Goldberger-Low anisotropic MHD equations. Possible marginally stable plasma states are considered with allowance for the expected turbulent relaxation and self-organization processes, on the one hand, and isotropization processes, on the other. A stability criterion for Alfvén modes is also derived in the Chew-Goldberger-Low model.     

Influence of the radial profile of the electric potential on the confinement of a high-β two-component plasma in a gas-dynamic trap

One of the most important problems to be studied in the gas-dynamic trap (GDT) facility is the investigation of MHD stability and cross-field transport in a plasma with a relatively high value of β = πp/B ². Recent experiments demonstrated that the radial electric field produced in the plasma by using radial limiters and coaxial end plasma collectors improves plasma stability in axisymmetric magnetic mirror systems without applying special MHD stabilizers. The experimental data presented in this work show that stable plasma confinement can be achieved by producing a radial potential drop across a narrow region near the plasma boundary. Creating radial electric fields of strength 15–40 V/cm causes a shear plasma flow, thereby substantially increasing the plasma confinement time. When all the radial electrodes were grounded, the confinement was unstable and the plasma confinement time was much shorter than the characteristic time of plasma outflow through the magnetic mirrors. Measurements of cross-field plasma fluxes with the use of a specially designed combined probe show that, in confinement modes with differential plasma rotation, transverse particle losses are negligibly small as compared to longitudinal ones and thus can be ignored. It is also shown that, when the GDT plasma is in electric contact with the radial limiters and end collectors, the growth rate of interchange instability decreases considerably; such a contact, however, does not ensure complete MHD stability when the electrodes are at the same potential.     

Equilibrium,stability, and estimate of plasma confinement in the L-5 compact torsatron

Possible parameters of a plasma in a compact torsatron that is to be constructed at the Prokhorov Institute of General Physics, Russian Academy of Sciences (the L-5 project) are discussed. The properties of the original vacuum configuration created by the external coils are described. The equilibrium of a plasma with a free boundary and the stability of local MHD modes are investigated. The effective magnetic field ripples and the structural factor of the bootstrap current in the 1/ν regime are calculated, as well as collisionless losses of trapped α-particles. The dependence of these properties on the relative plasma pressure is examined. It is shown that the maximum possible <β> (the ratio of the gas-kinetic plasma pressure to the magnetic field pressure, averaged over the volume of the plasma column) consistent with equilibrium exceeds 2.0%. The power of the external sources for plasma heating in the anticipated operating modes is estimated using the present-day scalings. The efficiency of different methods for calculating the magnetic fields and, accordingly, the magnetic surfaces created by the external coils is analyzed in the Appendix.     

Pressure profiles of a plasma confined by the magnetic field of a ring current

Pressure profiles p(ψ) marginal with respect to convective instability in a toroidal tubular plasma confined by the magnetic field of an internal levitated ring current and external ring currents are studied as functions of the shape of the magnetic separatrix. Configurations are found in which the maximum plasma pressure in a finite-width layer near the plasma boundary decreases by two orders of magnitude at the expense of artificially raising the effective length (characterized by the integral ∮dl/B) of the magnetic field lines near the separatrix surface. It is shown that, in the case of a straight cylindrical tubular plasma, which is the limiting case of a toroidal configuration with an arbitrarily large aspect ratio, the sufficient condition for the plasma to be MHD stable against both convective and kink perturbations is satisfied for local values β≤0.4. __________ Translated from Fizika Plazmy, Vol. 26, No. 6, 2000, pp. 519–528. Original Russian Text Copyright ￠ 2000 by Popovich, Shafranov.     

Three-dimensional rotational plasma flows near solid surfaces in an axial magnetic field

A rotational flow of a conducting viscous medium near an extended dielectric disk in a uniform axial magnetic field is analyzed in the magnetohydrodynamic (MHD) approach. An analytical solution to the system of nonlinear differential MHD equations of motion in the boundary layer for the general case of different rotation velocities of the disk and medium is obtained using a modified Slezkin–Targ method. A particular case of a medium rotating near a stationary disk imitating the end surface of a laboratory device is considered. The characteristics of a hydrodynamic flow near the disk surface are calculated within the model of a finite-thickness boundary layer. The influence of the magnetic field on the intensity of the secondary flow is studied. Calculations are performed for a weakly ionized dense plasma flow without allowance for the Hall effect and plasma compressibility. An MHD flow in a rotating cylinder bounded from above by a retarding cap is considered. The results obtained can be used to estimate the influence of the end surfaces on the main azimuthal flow, as well as the intensities of circulating flows in various devices with rotating plasmas, in particular, in plasma centrifuges and laboratory devices designed to study instabilities of rotating plasmas.     

On the Helical MHD Mode in a Finite-Conductivity Tokamak Plasma

A helical MHD perturbation in a finite-conductivity tokamak plasma has been considered in the straight-cylinder model in a situation where there is no resonance surface q = m/n in plasma. The radial eigenfunction of the helical mode, in addition to the large-scale component described at σ_||→ ∞ by the ideal MHD equation, contains a small-scale component localized near the wall and near discontinuities in the radial profiles of the unperturbed quantities. At smooth profiles, the small-scale component is attached to the wall and is smaller in magnitude than the large-scale component. Therefore, beyond a thin near-wall plasma layer, the mode is close to the large-scale ideal MHD mode. The presence of the small-scale component is necessary to satisfy the boundary conditions for the perturbed field on the wall.     

Low-frequency instabilities of collisionless plasma and the 16-moment approximation

Using the 16-moment equations that take into account heat fluxes in anisotropic collisionless plasma, the properties of magnetohydrodynamic (MHD) instabilities are investigated. For all instabilities occurring in the MHD approach (the normal incompressible firehose instability, the second compressible almost longitudinal firehose instability, and the almost transverse mirror instability of slow magnetosonic modes, as well as thermal instability caused by the heat flux directed along the magnetic field), their kinetic analogs are considered. The kinetic dispersion relation in the low-frequency range in the vicinity of the ion thermal velocity is analyzed. The flow of plasma ions along the magnetic field is taken into account. The thresholds and instability growth rates obtained in the MHD and kinetic approaches are found to be in good agreement. This indicates that the 16-moment MHD equations adequately describe the dynamics of collisionless plasma.     

Stability and variations of plasma parameters in the L-2M stellarator during excitation of the induction current in the regime of ECR plasma heating

Results are presented from experimental studies of variations in the plasma parameters during the excitation of a multiaxis magnetic configuration by the induction current (up to 17 kA) in the basic magnetic configuration of the L-2M stellarator in the regime of ECR heating at a microwave power of ～200 kW (～1 MW m^?3) and an average plasma density of (1–2) × 10¹⁹ m^?3. The current direction was chosen to reduce the net rotational transform (the so-called “negative“ current). The current was high enough for the rotational transform to change its sign inside the plasma column. Computer simulations of the L-2M magnetic structure showed that the surface with a zero rotational transform is topologically unstable and gives rise to magnetic islands, i.e., to a multiaxis magnetic configuration. Magnetic measurements showed that, at negative currents above 10 kA, intense bursts of MHD oscillations with a clearly defined toroidal mode number n = 0 were observed in the frequency range of several kilohertz. Unfortunately, the experimental data are insufficient to draw the final conclusion on the transverse structure of these oscillations. The radial temperature profiles along the stellarator major radius in the equatorial plane were studied. It is found that the electron temperature decreases by a factor of 1.3 in the plasma core (r/a ≤ 0.6) and that the temperature jump is retained near the boundary. A change in turbulent fluctuations of the plasma density during the excitation of a negative current was studied using wave scattering diagnostics. It is found that the probability density function of the increments of fluctuations in the plasma core differs from a Gaussian distribution. The measured distribution is heavy-tailed and broadens in the presence of the current. It is found that the spectrum of turbulent fluctuations and their Doppler shift near the plasma boundary are nonuniform in the radial direction. This may be attributed to the shear of the poloidal velocity. The experimental results indicate that the formation of regions with a zero rotational transform in the plasma core somewhat intensifies plasma transport.     

Effect of helical magnetic fields on plasma stability in tokamaks

Physical mechanisms for destabilization of MHD perturbations by external quasistatic magnetic fields and rotating helical magnetic fields in a tokamak plasma are identified using a numerical model of tearing modes in a viscous high-temperature plasma. The critical conditions for the onset of MHD perturbations and their dynamic model are compared with the experimental results from the JET tokamak. The model is used to predict how the stray magnetic fields will influence plasma stability in a tokamak reactor (ITER). __________ Translated from Fizika Plazmy, Vol. 26, No. 8, 2000, pp. 675–682. Original Russian Text Copyright ￠ 2000 by Savrukhin.     

Ideal internal kink modes in a differentially rotating cylindrical plasma

The Velikhov effect leading to magnetorotational instability (MRI) is incorporated into the theory of ideal internal kink modes in a differentially rotating cylindrical plasma column. It is shown that this effect can play a stabilizing role for suitably organized plasma rotation profiles, leading to suppression of MHD (magnetohydrodynamic) instabilities in magnetic confinement systems. The role of this effect in the problem of the Suydam and the m = 1 internal kink modes is elucidated, where m is the poloidal mode number. Published in Russian in Fizika Plazmy, 2008, Vol. 34, No. 7, pp. 589–597. The text was submitted by the authors in English.