Poloidal Plasma Research Articles

Neoclassical poloidal plasma rotation in tokamaks during radio frequency heating

A neoclassical theory of poloidal rotation in tokamaks is developed for rf-heated plasmas. It is based on a moment expansion but, in contrast to the usual neoclassical theory, which takes into account the strong deformation of the local equilibrium distribution function due to rf heating. This distribution function is the solution, in the banana regime, of the drift kinetic equation, which includes both collisional diffusion and quasilinear rf diffusion operators. The set of closed, self-consistent transport and rotation equations is obtained in a form similar to its usual neoclassical counterpart. The parallel components of the generalized stress tensors are calculated. This allows us to solve the transport equations for the poloidal rotation that is obtained in explicit form. Modifications of the poloidal rotation due to the rf heating are also discussed.

On ion flow caused by the inductive electric field in a tokamak

It was recently pointed out that the inductive electric field in a tokamak can give rise to toroidal and poloidal plasma rotation comparable to that sometimes observed in experiments. Here it is shown that the flow velocity of heavy impurity ions, which is normally what is measured, is lower than that of the bulk plasma for rotation produced in this way. If the bulk ions and electrons are in the banana regime, the impurity rotation is at most about two thirds of the bulk plasma rotation and decreases with increasing effective ion charge (Zeff) and distance from the magnetic axis.

Axisymmetric equilibria of a gravitating plasma with incompressible flows

It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov et al. (1999) are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime β0 ≈ γ0 ≈ δ0 ≈ ε0 ≫ 1, where β0, γ0, δ0, and ε0 are related to the thermal, poloidal-current, flow and gravitating energies normalized to the poloidal-magnetic-field energy, respectively, and (b) in the high-energy regime β0 ≈ γ0 ≈ δ0 ≈ ε0 ≪ 1. It turns out that in the high-energy regime all four forces, pressure-gradient, toroidal-magnetic-field, inertial, and gravitating contribute equally to the formation of magnetic surfaces very extended and localized about the symmetry plane such that the resulting equilibria resemble the accretion disks in astrophysics.

Edge Structure of Reynolds Stress and Poloidal Flow on the HL-1M Tokamak

The measurement on radial profile of electrostatic Reynolds stress, plasma poloidal rotations, radial and poloidal electric field have been performed in the plasma boundary region of the HL-1M Tokamak using a multi-array of Mach/Langmuir probes. In the experiments of Lower Hybrid Current Drive (LHCD), Supersonic Molecular Beam Injection (SMBI), Multi-shot Pellet Injection (MPI) and Neutral Beam Injection (NBI), the correlation between the Reynolds stress and poloidal flow in the edge plasma is presented. The results indicate that a sheared poloidal flow can be generated in Tokamak plasma due to radially varying Reynolds stress.

Collisionless magnetic reconnection in a toroidal cusp

Fast collisionless magnetic reconnection is driven and observed in a toroidal magnetic cusp. For low values of the toroidal (guide) magnetic field, reconnection occurs without the formation of a macroscopic current channel. In the absence of a current channel, the measured plasma potential and poloidal flows are consistent with predictions based upon single particle theory. Only for large values of the toroidal magnetic field compared to cusp poloidal field is a current channel present. Also in this case single particle orbit theory provides a good description of the anomalous resistivity observed experimentally.

Plasma rotation induced by the Dynamic Ergodic Divertor

After introduction of the experimental options available with the DynamicErgodic Divertor (DED) and a discussion of the static aspects of the ergodic and laminar zones, the dynamic aspects of the rotating DED field are emphasized. The rotating perturbation field induces a shielding current which is modelled under different assumptions. Interaction of the shielding current with that of the DED coils results in a torque exerted by the coils on the plasma. The location of the maximum of this torque with respect to the frequency depends critically on the width of the shielding current, and for the TEXTOR-DED conditions it is in the frequency band of 1-30 kHz. The DED will have the option of operation with full power in this band so that the basic investigations on the field line penetration can be attempted. The force transferred to the plasma has two components, a weaker toroidal one and a dominant poloidal one. The toroidal force component has about the same value as the one from NBI; from the experience with NBI induced plasma rotation, a substantial plasma acceleration in the toroidal direction is expected. For neoclassical reasons it is not yet clear whether the dominant poloidal force component will result in a poloidal plasma rotation or a radial force. If the poloidal rotation is inhibited, a static radial electric field is estimated on the basis of a revisited neoclassical theory to be of the order of several kilovolts per metre.

Effect of plasma subsonic toroidal flows induced by Alfvén waves on transport processes in the edge of elongated tokamaks

There is a renewed interest in using Alfvén waves (AW) in tokamak plasmas. Previously, AW were actively explored mostly for current drive and plasma heating in tokamaks. Presently, the possibility of the anomalous and neoclassical transport suppression by AW in tokamak plasmas is being vividly discussed. AW can also induce poloidal and toroidal plasma rotation. Toroidal plasma rotation can reach the subsonic level. These flows can substantially affect neoclassical transport both in collisional and weakly collisional plasmas. In this paper, the effect of plasma subsonic toroidal flows induced by Alfvén waves on transport processes in the edge of elongated tokamak is investigated. The dependence of poloidal plasma rotation and ion heat conductivity on the elongation parameter and the ratio of induced toroidal velocity to the sonic speed are analytically obtained.

Radial electric field during dynamic processes in a tokamak and L-H transitions

Expressions for the radial electric field in tokamaks are derived with allowance for an additional contribution of the longitudinal electron viscosity (or the associated Ware drift). It is shown that, in transient processes during which the toroidal electric field at the plasma edge increases, the additional electric field can become rather strong. An increase in the shear of the poloidal plasma rotation can trigger the L-H transition. That the experimentally observed transitions to an improved confinement mode can be ascribed to this effect is illustrated by simulating discharges in the current ramp-up experiments in the Tuman-3M tokamak.

Calculation of 2D profiles for the plasma and electric field in the boundary layer of the TEXTOR-94 Tokamak

An improved version of the 2D multifluid code TECXY is used to study the plasma parameters and the electric field in the boundary layer of the TEXTOR-94 tokamak. An anomalous perpendicular shear viscosity η ⊥ is incorporated into the ion momentum balance which allows to fulfil the global (magnetic surface averaged) ambipolarity constraint for the radial electric current, and to determine the electric field in the transition layer by a second-order ordinary differential equation for E r( r). The code modelling results suggest the existence of a narrow global circulation layer for the poloidal plasma velocity just inside the separatrix which is connected with a negative electric field spike. A proper choice of η ⊥ gives better agreement with experimental velocity profiles.

Integration of magnetic and nonmagnetic measurements for current profile reconstruction in RFX

A crucial issue in magnetically confined plasmas characterized by relevant internal current redistribution, such as high beta and low field toroidal devices, is the determination of their internal magnetic structure. The article presents a method for the integration of magnetic and nonmagnetic measurements in a model which considers a plasma described by stationary ideal magnetohydrodynamic equilibrium equations, with toroidal and poloidal plasma currents represented by distributed discrete filaments and current sheets. The model also includes the massive conductors representing the vessel, the shell, and the machine windings. The discrete current sets are determined by using as input data the total currents flowing in the plasma, in the windings and in the vessel, as deduced by external integral magnetic measurements. The obtained filamentary current sets are then adjusted by imposing further constraints. One of the constraints is given by the set of local magnetic field measurements provided by external pickup coils. A further and more significant constraint is imposed by far infrared polarimeter, which gives an integral condition for each implemented measurement chord. The method is validated by using experimental data from the reversed field pinch Reversed Field eXperiment, and the results suggest that the current density distribution is rather different from that usually predicted by conventional data inversion algorithms.

Modelling of the Effect of the Sheared Poloidal Flow on the Electrostatic Turbulence on the CASTOR Tokamak

Electrostatic drift turbulence of the edge plasma in the CASTOR tokamak is studied numerically by using the Hasegawa-Wakatani equations. The fluctuations of plasma density and potential as well as the corresponding fluctuation-induced particle flux are calculated for regimes with various plasma poloidal flows. Results of numerical simulations are in a reasonable agreement with experimental results.

Local poloidal and toroidal plasma rotation velocities and ion temperature in a tokamak plasma obtained with a matrix inversion method considering asymmetries

An inversion technique is presented for the local poloidal and toroidal rotation velocities and for the ion temperature from line integrated measurements performed on Tokamak de Varennes (TdeV) [R. Decoste and TdeV Team, Proceedings of the 15th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville, 1994 (International Atomic Energy Agency, Vienna, 1995) IAEA-CN-60/A4-11]. The velocity is obtained using two matrix inversions; the first for the emissivity and the second with the velocity weighted emissivity. The temperature is obtained with three matrix inversions: emissivity, temperature weighted emissivity and rotation velocity squared. The effect of the rotation velocity represents up to 16% in the ion temperature for TdeV plasmas. The local values obtained using the lengths matrix with the magnetic flux lines from the equilibrium code are compared with those obtained by a standard Abel inversion with circular flux lines. Differences up to 20% are observed between the emissivities deduced with circular and real flux lines, whereas the rotation velocity and the ion temperature are very similar. The technique was applied for the poloidal and toroidal geometry to determine the poloidal and toroidal velocities and the emission asymmetries. Top poloidal and toroidal emissivities present strong asymmetries due to the divertor plates and the X point whereas bottom poloidal and toroidal emissivities show an inner–outer symmetry, making the inversion more reliable in this region. A first approach to model the strong asymmetry was made assuming that the emissivity has both a radial and a poloidal dependence. The best result was obtained using a radial dependence and a peaked function of the poloidal angle for the poloidal asymmetric part of the emissivity. Both emissivity and velocity asymmetries are present in the upper part of the plasma implying that the X point behaves as a source. Examples of emissivities, rotation velocities and ion temperatures observed in TdeV plasmas in H and L (high and low confinement) modes with different bottom plasma triangularity are shown.

Local effects of upstream divertor components on divertor plasma parameters and impurity retention forces

The toroidally-viewing spectroscopic imaging system on Tokamak de Varennes (TdeV) [F. Meo et al., Rev. Sci. Instrum. 68, (1997)] has given new insight into the physics of a closed divertor, where the particles interact with a vertically oriented inclined plate situated upstream from the target plate. The system has enabled two-dimensional (2D) measurements of the absolute emissivities of Hydrogen Balmer lines, as well as Carbon lines. Using the Balmer ratios, the poloidal profile of the electron density has been calculated using a Collisional-Radiative model [K. Sawada and T. Fujimoto, J. Appl. Phys. 78, 2913 (1994)]. Results show that the plasma parameters are locally affected by the divertor components particularly the inclined plate. This inclined plate constitutes an extra recycling surface which causes an increase in the atomic density and a decrease in the electron density in this region and affecting the plasma parameters at the target plate. Finally, the calculated poloidal plasma parameters are projected onto the field lines and are used in one-dimensional simplified (1D) particle and momentum balance equations. The simplified particle balance equation has shown that the extra neutrals from the inclined plate increase the parallel velocity locally. According to the simplified 1D fluid model, the analysis of the momentum balance equation has allowed the calculation of the poloidal profile of the ion temperature and hence the ion thermal force. The ∇Ti force on the impurity ions increases in the region of the inclined plate, which may seriously affect the impurity retention in the divertor.

Effect of triangular and elongated plasma shape on the sawtooth stability

In the TCV tokamak the sawtooth period and the sawtooth amplitude areobserved to depend strongly on the shape of the poloidal plasma cross section.Systematic scans of plasma elongation and triangularity show small sawteethwith short periods at high elongation or low and negative triangularity, andlarge sawteeth with long periods at low elongation or high triangularity.Additional central electron cyclotron heating power further amplifies theshape dependence of the sawtooth properties. The sawtooth period can increaseor decrease with additional heating power depending on the plasma shape.This shape dependence is determined by the role of ideal or resistiveMHD in triggering the sawtooth crash. For plasma shapes where additional heating and, consequently, a higher pressure shortens the sawtooth period, the low experimental limit of the pressure gradient within the q = 1 surface is consistent with ideal MHD predictions. The observed decrease of this limit with elongation is also in qualitative agreement with ideal MHD theory.

Transport of intense LH pulses into a tokamak plasma

Application of lower-hybrid (LH) power in short, intense pulses in the 5–10 GW range should overcome the limiting effects of Landau damping, and thereby permit the penetration of LH power into the interior of large-scale plasmas. We show that, under such very intense LH pulses, wave coupling may deteriorate because of nonlinear density changes due to the ponderomotive force effects in front of the grill. Ponderomotive forces are also likely to induce strong plasma bias and consequent poloidal and toroidal plasma rotation. Although backward electric currents, created in the plasma by intense LH pulses, dissipate a large portion of the radio frequency power absorbed, the current drive efficiency is acceptable. We use a numerical simulation of wave–particle interactions to analyse the applicability of standard quasilinear theory to the case of large energy flux densities. The initial results indicate the existence of important restrictions on the use of the quasilinear approximation. The results of the present paper also indicate that some of the effects considerably alter some ideas of Cohen et al.

Plasma and Mode Rotations in a Reversed-Field Pinch Device, TPE-1RM20

In a reversed-field pinch (RFP) device, TPE-1RM20, the rotation velocities of impurity ions and the magnetic modes are studied in connection to their roles on the dynamo activities. It is observed that the deceleration of the plasma poloidal rotation synchronizes with the deceleration of both poloidal and toroidal mode rotations at a discrete dynamo event. It is shown that the plasma poloidal rotation velocity in the case of high-Θ discharges becomes faster than that in the case of low-Θ discharges (Θ; pinch parameter). The radial electric field is estimated to be positive around r/a∼0.52 under some assumptions. Measurements reveal that the plasma poloidal rotation is in the electron diamagnetic direction around r/a∼0.52. This indicates that the poloidal rotation does not simply depend on Er×B flow. Through the present experimental results, some new subjects in the RFP plasma research are discussed.

Direct Observation of Ion-Bernstein-Wave-Induced Poloidal Flow in TFTR

Shearing of the plasma poloidal rotation velocity was observed during application of ion Bernstein wave power in the Tokamak Fusion Test Reactor. The first evidence of corroboration between measured poloidal velocity shearing and actively induced Reynolds stress effects is presented. A model reproduces salient experimental features: The observed sheared flow occurs near the tritium fifth harmonic cyclotron resonance layer and depends strongly on the tritium density in agreement with the model. Furthermore, the model reproduces the observed insensitivity of the induced rotation to the tritium density in the region between the third deuterium harmonic layer and the fifth tritium harmonic layer.

Imaging x-ray crystal spectrometers for the National Spherical Torus Experiment

A new type of high-resolution x-ray imaging crystal spectrometers is described for implementation on the National Spherical Torus Experiment (NSTX) to provide spatially and temporally resolved data on the ion temperature, toroidal and poloidal plasma rotation, electron temperature, impurity ion-charge state distributions, and impurity transport. These data are derived from observations of the satellite spectra of heliumlike argon, Ar XVII, which is the dominant charge state for electron temperatures in the range from 0.4 to 3.0 keV and which is accessible to NSTX. Experiments at the Torus Experiment for Technology Oriented Research (TEXTOR) demonstrate that a throughput of 2×105 photons/s (corresponding to the count-rate limit of the present detectors) can easily be obtained with small, nonperturbing argon gas puffs of less than 1×10−3 Torr l/s, so that it is possible to record spectra with a small statistical error and a good time resolution (typically 50 and 1 ms in some cases). Employing a novel design, which is based on the imaging properties of spherically bent crystals, the spectrometers will provide spectrally and spatially resolved images of the plasma for all experimental conditions, which include ohmically heated discharges as well as plasmas with rf and neutral-beam heating. The conceptual design, experimental results on the focusing properties, and relevant spectral data from TEXTOR are presented.

Magnetohydrodynamics Stability Analysis of the KT-2 Tokamak Plasma

The stability of the KT-2 tokamak plasma has been analyzed in the framework of ideal and resistive linearized magnetohydrodynamics. KT-2 is the Korean tokamak project that involves a large-aspect-ratio divertor tokamak with an up-down symmetric plasma cross section. First, equilibria with monotonic q profiles are investigated. Starting from four ballooning stable reference equilibria with ever broader pressure profiles and with an aspect ratio of 5.6, an ellipticity of 1.8, a triangularity of 0.6, and a total plasma current of 500 kA, the effects on the shape of the poloidal plasma cross section (ellipticity and triangularity), the aspect ratio, and the total plasma current on the ballooning and ideal and resistive external kink instabilities are studied. Also, advanced tokamak scenarios have been investigated. A local profile optimization study is performed for a lower total current, i.e., Ip = 300 kA, and a magnetic field of 2 T. Next, the stability of the marginal ballooning stable equilibria with respect to so-called infernal modes is analyzed.

Structure of parallel-velocity-shear-driven mode in toroidal plasmas

It is shown that the Fourier-ballooning representation is appropriate for the study of short-wavelength drift-like perturbation in toroidal plasmas with a parallel velocity shear (PVS). The radial structure of the mode driven by a PVS is investigated in a torus. The Reynolds stress created by PVS turbulence, and proposed as one of the sources for a sheared poloidal plasma rotation, is analyzed. It is demonstrated that a finite ion temperature may strongly enhance the Reynolds stress creation ability from PVS-driven turbulence. The correlation of this observation with the requirement that ion heating power be higher than a threshold value for the formation of an internal transport barrier is discussed.