The perpendicular permittivity of magnetized toroidal plasmas with elliptic magnetic surfaces

The Vlasov equation for charged particles is analyzed in an axially symmetric toroidal plasma configuration with an elliptic cross section of magnetic surfaces. The asymptotic solution of the Vlasov equation is found. The analytical expressions for the perpendicular component of the dielectric permittivity tensor are obtained. These expressions are used for theoretical analyses of the trapped and untrapped ion influence on the collisionless cyclotron wave dissipation. The evaluated dielectric tensor components can be used for computer calculations of the radio frequency field structure and the collisionless dissipated power related to trapped and untrapped ions in tokamak plasmas. It is shown that ion cyclotron resonance dissipation in tokamaks depends on toroidicity and ellipticity parameters and does not depend on plasma temperature. This work was supported by the State University of Rio de Janeiro (UERJ), Rio de Janeiro Research Foundation (FAPERJ) and Brazilian National Council of Research (CNPq).     

Toroidicity and shape dependence of peeling mode growth rates in axisymmetric toroidal plasmas

The growth rate of the peeling mode instability with large toroidal mode number is calculated for general axisymmetric toroidal plasmas, including tokamaks and the spherical torus(ST) equilibia by using formalism presented by Connor et al.Analytic equilibia with non-zero edge current density and quasi-uniform current profiles are assumed. It is found that in sharp D-shape tokamak plasma, the derivative of the safety factor with respect to the poloidal flux becomes very large,making the perturbed poloidal motion very large, in turn making a significant reduction of the growth rate of the peeling mode, similar to the X-point effect in diverted plasma. The large aspect ratio effect is also studied, which reduces the growth rate further.     

The parallel permittivity of magnetized toroidal plasmas with elliptic magnetic surfaces

The asymptotic solution of the Vlasov equation under the drift approximation, for an axially symmetric toroidal plasma configuration with an elliptic cross section of magnetic surfaces, is presented. The analytical expressions for the parallel component of the dielectric permittivity tensor are obtained. These expressions are used for theoretical analyses of the trapped and untrapped electron influence on the collisionless wave dissipation. The evaluated dielectric tensor components can be used for computer calculations of the radio frequency field structure and the collisionless dissipated power related to trapped and untrapped electrons in tokamak plasmas.This work was supported by the State University of Rio de Janeiro (UERJ), Rio de Janeiro Research Foundation (FAPERJ) and Brazilian National Council of Research (CNPq).     

Rotational stabilization of resistive wall modes by the shear alfvén resonance

It is found that resistive wall modes with a toroidal number n = 1 in tokamaks can be stabilized by plasma rotation at a low Mach number, with the rotation frequency being lower than the ion bounce frequency but larger than the ion and electron precession drift frequencies. The stabilization is the result of the shear-Alfvén resonance, since the thermal resonance effect is negligible in this rotation frequency range. This indicates that tokamaks can operate at normalized pressure values beyond the no-wall stability limit even for low values of plasma rotation, such as those expected in fusion reactor scale devices.     

Stability of the collisional plasma flow in a magnetic field

A collisional plasma flow moving along a magnetic field at a velocity lower than the speed of sound is considered. It has been found that stationary small perturbations increase downstream in the flow. The mechanism of the increase is related to the fact that subsonic ideal-plasma flows respond to external perturbations primarily by a change in the pressure of the plasma. As a result, the pressure under perturbation of the velocity changes so that the stationary flow is decelerated and accelerated if the force is directed along and against the velocity, respectively. This phenomenon can be explained under the assumption that the effective mass of the plasma is negative. If the velocity of the flow is inhomogeneous in the transverse direction, the viscosity force plays a role of the external perturbing force. In this case, the effective transverse viscosity coefficient, which should be treated as negative, can be renormalized instead of the effective mass. The sign of the effective specific heat or the effective transverse thermal conductivity coefficient changes similarly if the velocity of the flow is lower than the speed of sound but is higher than the thermal velocity of ions calculated from the sum of the ion and electron temperatures. A downstream increase in the stationary perturbations is called in this work spatial instability. The downstream growth rate has been determined. The numerical analysis of the evolution of perturbations illustrates the development of the spatial instability of subsonic collisional plasma flows moving along the magnetic field.     

Dynamic transport simulation code including plasma rotation and radial electric field

A new one-dimensional transport code named TASK/TX, which is able to describe dynamic behavior of tokamak plasmas, has been developed. It solves simultaneously a set of flux-surface averaged equations composed of Maxwell’s equations, continuity equations, equations of motion, heat transport equations, fast-particle slowing-down equations and two-group neutral diffusion equations. The set of equations describes plasma rotations in both toroidal and poloidal directions through momentum transfer and evaluates the radial electric field self-consistently. The finite element method with a piecewise linear interpolation function is employed with a fine radial mesh near the plasma surface. The Streamline Upwind Petrov–Galerkin method is also used for robust calculation. We have confirmed that the neoclassical properties are well described by the poloidal neoclassical viscous force. The modification of density profile during neutral beam injection is presented. In the presence of ion orbit loss, the generation of the inward radial electric field and torque due to radial current is self-consistently calculated.     

Most electron heat transport is not anomalous; it is a paleoclassical process in toroidal plasmas

It is hypothesized that radial electron heat transport in magnetically confined toroidal plasmas results from paleoclassical Coulomb collision processes (parallel electron heat conduction and magnetic field diffusion). In such plasmas the electron temperature is equilibrated along magnetic field lines a long length L (> poloidal periodicity length piR0q), which is the minimum of the electron collision length and an effective field line length. Thus, diffusing field lines induce a radial electron heat diffusivity M identical with L/(piR0q) approximately 10>1 times the magnetic field diffusivity eta/mu0 approximately nue(c/omegap)2.     

Effect of neutral pressure on the He plasma flow measurement in a linear device

Axial and azimuthal flow velocities have been measured in a linear plasma device called NAGDIS-II (NAGoya DIvertor Simulator-II), along with plasma density and electron temperature, using a vector Mach probe composed of two Mach probes, one of which is for the axial flow, and the other is for the azimuthal flow. To study the effect of neutral pressure on the deduction of the Mach numbers, the ratio of upstream to downstream currents are measured by changing the neutral pressure for the deduction of flow velocities. Helium plasma was generated with pressure of 2–35 mTorr. Since the ion gyro-radius at the magnetic flux of 300 G is larger than the probe size, an unmagnetized collisionless Mach probe theory was used for the deduction of Mach numbers and their variations. In order to check the range of collisionality, plasma density (n_e = 10¹⁰–10¹¹ cm^?3) and electron temperature (T_e = 2–9 eV) are measured by a single electric probe using a conventional collisionless probe theory. Variations of Mach number, electron temperature and plasma density with collisionless models are to be compared with those using collisional models for different pressures where ionization and ion-neutral collision are included. Mach numbers by the collisionless model are found to be overestimated by 120% for the maximum difference even in weakly collisional plasmas. A clear flow reversal exists in the axial direction with higher pressure plasma, even in the linear machine. Azimuthal flows are also measured simultaneously along with axial flows, yet they seem to be very small in the present cold ion plasma (T_i/T_e << 1).     

Dimits shift in realistic gyrokinetic plasma-turbulence simulations

In simulations of turbulent plasma transport due to long wavelength (k perpendicular rhoi < or = 1) electrostatic drift-type instabilities, we find a persistent nonlinear up-shift of the effective threshold. Next-generation tokamaks will likely benefit from the higher effective threshold for turbulent transport, and transport models should incorporate suitable corrections to linear thresholds. The gyrokinetic simulations reported here are more realistic than previous reports of a Dimits shift because they include nonadiabatic electron dynamics, strong collisional damping of zonal flows, and finite electron and ion collisionality together with realistic shaped magnetic geometry. Reversing previously reported results based on idealized adiabatic electrons, we find that increasing collisionality reduces the heat flux because collisionality reduces the nonadiabatic electron microinstability drive.     

参量调制驱动环形等离子体稳态电流的简化分析

本文用简化模型分析托卡马克装置,建议用等离子体往径向速度振荡和角向磁场振荡的相互作用产生一个定常环向电动势以驱动稳态电流。这可由按一定相位差调制两个外加参量来达到。按反应堆参数估计,这种调制频率可以是工业频率。     

Gyrokinetic microtearing turbulence

The nonlinear dynamics of microtearing modes in standard tokamak plasmas are investigated by means of ab initio gyrokinetic simulations. The saturation levels of the magnetic field fluctuations can be understood in the framework of a balance between (small poloidal wave number) linear drive and small-scale dissipation. The resulting heat transport is dominated by the electron magnetic component, and the transport levels are found to be experimentally relevant. Microtearing modes thus constitute another candidate for explaining turbulent transport in such toroidal systems.     

Poloidal spin up and electric-field generation related to displacement current and neoclassical transport

Summary In accordance with the conventional orderings of neoclassical theory, poloidal and toroidal accelerations with constant parallel flow can be driven by heat transport in the absence of external momentum input and with vanishing parallel viscous stress. In a transient phase in which the heat transport is the primary source of the time dependence, the torque generating the rotation is provided at third order in the adiabatic expansion by the surface-averaged (non-ambipolar) displacement current, which is also responsible for charge build-up and for the radial electric field. The heat transport equation has been solved in a narrow layer interfaced with the intensely heated plasma core through heat flux continuity, assuming neoclassical multicollisional coefficients with self-consistent suppression mechanism of anomalous transport. Starting from low temperature in the edge layer, a strong temperature gradient, a mass poloidal rotation in the ion direction and a strongly negative sheared radial electric field can be generated, in agreement with the observations, and reach a stationary state after a displacement current-dominated triggering phase (intrinsically non-ambipolar) lasting few milliseconds. Momentum input becomes important on longer time scale and is responsible for the toroidal rotation, decoupled from temperature gradient and for a further development of the radial electric field. The results show the ability of edge transport processes to adapt flexibly to a high temperature imposed on the inner side of the edge layer and support the view that the edge processes are an integral part of a more fundamental global process involving possibly an internal bifurcation of state.     

HT-7超导托卡马克边界等离子体参量及其涨落的实验研究

利用径向可移动朗缪尔三探针和马赫探针对HT-7超导托卡马克边界等离子体参量及其涨落进行了空时空分辨测量.给出了欧姆放电及其与低杂波电流驱动共同作用下边界等离子体电位φ_p、电子温度T_e和电子密度n_e及其涨落的径向分布.实验表明,在限制器附近,存在一由E_r×B确定的极向旋转速度剪切层.在剪切层内,T_e和n_e分布较陡,且φ_p,T_e和n_e的相对涨落水平下降明显.这说明剪切层对边界区的等离子体涨落具有抑制作用.低杂波驱动使径向电场梯度变陡,从而使剪切程度加深但对剪切层宽度无影响.此外,测量表明等离子体环向速度马赫数M_φ存在径向梯度.环向流的这种径向梯度可能是形成径向电场所需的平均极向流的一种重要驱动源 关键词： 托卡马克 边界涨落 低杂波驱动     

Reduced heat transport between edge-localized-mode bursts at low collisionality and small poloidal Larmor radius

Nondimensional parameter dependence of heat transport between edge localized modes (ELMs) is examined for H mode plasmas. The electron heat diffusivity between ELMs is reduced to the level of ion neoclassical transport in the plasma edge region which is affected by ELM burst. At lower edge collisionality, the heat flux assigned to the heat transport between ELMs is reduced and the ELM loss power is enhanced. During the inter-ELM phase, the energy confinement time becomes larger with decreasing the edge collisionality and poloidal Larmor radius.     

Role of poloidal E × B drift in divertor heat transport in DIII-D

Simulations for DIII-D high confinement mode plasmas with the multifluid code UEDGE show a strong role of poloidal E × B drifts on divertor heat transport, challenging the paradigm of conduction-limited scrape-off layer (SOL) transport. While simulations with reduced drift magnitude are well aligned with the assumption that electron heat conduction dominates the SOL heat transport, simulations with drifts predict that the poloidal convective E × B heat transport dominates over electron heat conduction in both attached and detached conditions. As poloidal E × B flow propagates across magnetic field lines, poloidal transport with shallow magnetic pitch angles can reach values that are of the same order as would be provided by sonic flows parallel to the field lines. These flows can lead to strong convection-dominated divertor heat transport, increasing the poloidal volume of radiative power front, consistent with previous measurements at DIII-D. Due to these convective flows, the Lengyel integral approach, assuming zero convective fraction, is expected to provide a pessimistic estimate for the radiative capability of impurities in the divertor. For the DIII-D simulations shown here, the Lengyel integral approach underestimates the radiated power by a factor of 6, indicating that, for reliable DIII-D divertor power exhaust predictions, full two-dimensional (2D) calculations, including drifts, would be necessary.     

HL-1M装置边缘参数测量

在HL－1M装置上利用马赫／郎缪尔探针分别在欧姆放电,低杂波注入,中性束注入,离子回旋加热和电子回旋加热等情况下测量下刮离层和等离子体边缘的极向流速度和电场,得到了它们的径向分布,研究了LHW,NBI,ICRH和ECRH对改善等离子体约束性能,边缘粒子的径向传输的影响。     

Transport in boundary layer of divertor tokamaks

Study of transport in the boundary layer of tokamak plasma in presence of magnetic divertors is extended to the second order in ion collision frequency. Numerical results for ion and energy losses to the collector plates are presented for toroidal and poloidal divertors. For the toroidal case, the Wiener-Hopf solution for the second order distribution function is obtained. An error occurring in an earlier first order calculation is pointed out and corrected first order fluxes are also given. For the poloidal divertor, asymmetry observed in ion and energy transport is found to persist in the second order result.     

H-mode in tokamaks attributed to absence of trapped ions in poloidally rotating plasma

It is proposed that the suppression of transport in the H-mode in tokamaks is caused by the absence of trapped ions in the transport barrier. If the poloidal Mach number M=v _θ B/(v _TiB_θ) is large there are exponentially few trapped ions. This criterion agrees with experimental observations of H-mode plasmas. The recently observed transport suppression by reversed shear also points to the dominant role of trapped particles in turbulent transport. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 427–430 (25 March 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Effects of plasma parameters on viscosity

A numerical code is developed to study the effect of ion density and temperature (as well as ion pressure and temperature gradients) on the amplitude of the local maxima of the poloidal viscosity with respect to the poloidal Mach number using the model developed by Shaing (1993). The sum of the poloidal viscosity and ion-neutral collisions is determined from the dependence of the plasma radial current on the radial electric field in a biased electrode experiment. The experimental results in the interchangeable module stellarator agree qualitatively with the predictions of the numerical calculation regarding the effects of variation of ion density and temperature on viscosity     

Properties of geodesic acoustic modes and the relation to density fluctuations

The geodesic acoustic mode (GAM) is a high frequency branch of zonal flows, which is observed in toroidal plasmas. Because of toroidal curvature effects, density fluctuations are excited, which are investigated with the O-mode correlation reflectometer at TEXTOR. This Letter reports on the poloidal distribution of GAM induced density fluctuation and compares them with theoretical predictions. The influence of the GAM flows on the ambient turbulence is studied, too.