摘要:

Nearly all kinetic treatments of fast wave minority heating of inhomogeneous plasma in the cyclotron range of frequencies assume the magnetic field varies in the direction perpendicular to the magnetic field. However, the toroidal magnetic field of a tokamak varies along a field line due to the rotational transform and causes a small number of trapped particles to turn in the region of cyclotron resonance. In order to include the effects of rotational transform and, hence, trapped particles in the kinetic plasma response, a simplified, concentric circle flux surface model of a tokamak is employed. The most important result of this work is the derivation of response functions for Maxwellian and bi‐Maxwellian minority ions which generalize and extend previous replacementZfunction forms obtained from a slab approximation of a tokamak (which also retains the variation of the strength of the magnetic field along a field line). The plasma response functions obtained include both passing and trapped ions, off‐axis heating, and are valid for arbitrary minority ion concentrations. The response function for a bi‐Maxwellian in the case of strong anisotropy substantially modifies the Maxwellian result. Anisotropy and the effects of toroidal geometry are illustrated graphically and tend to enter at higher toroidal mode numbers. For minority concentrations of the order or less than a critical value, the plasma response functions are used to obtain the standard transmission coefficient previously obtained for straight magnetic‐field models. The expression for the transmission coefficient is shown to be valid for more general unperturbed distribution functions of pitch angle and speed on each flux surface providedk∥&rgr;≪1, wherek∥is the parallel wave number and &rgr; the minority gyroradius.

ISSN:0899-8221    

DOI:10.1063/1.860679

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Lower‐hybrid (LH) wave propagation is studied for a general magnetic‐field configuration. The ray‐tracing equations in the geometric optics approximation are analytically and numerically solved in flux surface coordinates by using asymptotic techniques. In particular, the effects of elongation, triangularity, and the Shafranov shift on wave penetration are pointed out. Numerical applications devoted to the study of current drive generation for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion31, 1135 (1991)] plasma parameters will also be presented.

ISSN:0899-8221    

DOI:10.1063/1.860680

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The effect of rigid toroidal rotation on the stability of a tokamak to external kink modes is examined. For simplicity a surface current model is assumed. For a high‐&bgr; tokamak it is shown that to leading order the equations governing stability in the presence of rotation are identical to those for a static plasma with &bgr; replaced by &bgr;+S, where &bgr; is the plasma beta andSis a parameter which provides a measure of the rotation rate. For a circular cross‐section tokamak the critical beta for stability to external kink modes in the presence of rigid toroidal rotation is given, to leading order in the inverse aspect ratio &egr;, by &bgr;=0.21&egr;−S. For an elliptical cross‐section tokamak the largest critical beta is obtained for a vertical elongation of 2.2 and is given, to leading order in &egr;, by &bgr;=0.37&egr;−S. The lower limit on the kink safety factorq* or the Mercierqincreases with increase inS. Quantitative estimates of this increase can be obtained from the stability boundaries for the static problem.

ISSN:0899-8221    

DOI:10.1063/1.860966

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Research on forming, compressing, and accelerating milligram‐range compact toroids using a meter diameter, two‐stage, puffed gas, magnetic field embedded coaxial plasma gun is described. The compact toroids that are studied are similar to spheromaks, but they are threaded by an inner conductor. This research effort, namedmarauder(Magnetically Accelerated Ring to Achieve Ultra‐high Directed Energy and Radiation), is not a magnetic confinement fusion program like most spheromak efforts. Rather, the ultimate goal of the present program is to compress toroids to high mass density and magnetic field intensity, and to accelerate the toroids to high speed. There are a variety of applications for compressed, accelerated toroids including fast opening switches, x‐radiation production, radio frequency (rf) compression, as well as charge‐neutral ion beam and inertial confinement fusion studies. Experiments performed to date to form and accelerate toroids have been diagnosed with magnetic probe arrays, laser interferometry, time and space resolved optical spectroscopy, and fast photography. Parts of the experiment have been designed by, and experimental results are interpreted with, the help of two‐dimensional (2‐D), time‐dependent magnetohydrodynamic (MHD) numerical simulations. When not driven by a second discharge, the toroids relax to a Woltjer–Taylor equilibrium state that compares favorably to the results of 2‐D equilibrium calculations and to 2‐D time‐dependent MHD simulations. Current, voltage, and magnetic probe data from toroids that are driven by an acceleration discharge are compared to 2‐D MHD and to circuit solver/slug model predictions. Results suggest that compact toroids are formed in 7–15 &mgr;sec, and can be accelerated intact with material species the same as injected gas species and entrained mass ≥1/2 the injected mass.

ISSN:0899-8221    

DOI:10.1063/1.860681

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

In the weak radiation drive regime, the coupling between the thermal instability driven by impurity radiation and the self‐consistent flow profile modification leads to a simple dynamical system that can be approximated by the Volterra–Lotka equations. In this system the shear flow acts as a predator and the temperature fluctuations act as prey. The solutions are oscillatory, and their behavior resembles that of edge‐localized modes (ELM’s). The solutions of the simplified model are compared with the three‐dimensional and two‐dimensional nonlinear numerical results for this instability.

ISSN:0899-8221    

DOI:10.1063/1.860682

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Data from several current tokamak experiments indicate that the equilibrium perpendicular velocity field can become strongly sheared accompanying the transition from the L mode to the H mode, i.e. improved, confinement, and that fluctuation levels are reduced. Linear theory suggests that velocity shear can stabilize ion‐temperature‐gradient (ITG) modes when the frequency shift experienced by the mode due to the radial dependence of the Doppler shift is comparable to the growth rate. To confirm the predictions of linear theory and to explore nonlinear issues, e.g., self‐generated shear flows, saturation amplitudes, and the concomitant energy transport levels, two‐ and three‐dimensional gyrokinetic simulations of ITG modes have been performed. The simulations were done with and without magnetic shear in a slab configuration using the partially linearized (&dgr;f) algorithm to reduce statistical noise. The simulations confirm theoretical analyses of the stabilizing and destabilizing effects of imposed perpendicular velocity fields. The ion energy transport levels at saturation follow the trends of the linear growth rates and the mixing‐length estimates. The gyrokinetic simulations are in qualitative agreement with the results of gyrofluid simulations, and exhibit saturation amplitudes and energy transport similar to those in gyrofluid simulations. These transport levels are generally lower than those typically reported in the laboratory experiments; including toroidal driving terms significantly increases the transport levels in the simulations.

ISSN:0899-8221    

DOI:10.1063/1.860683

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Convective momentum transport associated withV⋅@/B∇Vin the momentum equation is calculated for arbitrary values of the poloidalE×BMach numberMp. Here,Vis the plasma flow velocity. The physics origin of the convective momentum transport is associated with the coupling of the poloidal variation of the viscosity‐driven flux to that of the flow velocity in the magnetic surface. When the radial gradient scale length of the plasma velocity is of the order of the ion poloidal gyroradius, &rgr;pi, the convective momentum transport becomes comparable to the ion viscosity. AtMp&bartil;1, the ion viscosity associated with shock—the shock viscosity—approximately balances the convective momentum transport to maintain the lowest‐order ambipolarity. The implications of the effects of shock and convective momentum transport for the previous L–H transition bifurcation theory [K. C. Shaing and E. C. Crume, Jr., Phys. Rev. Lett.63, 2369 (1989)] are discussed, and an extended bifurcation theory including these effects is presented. It is shown that the experimentally relevant plasma viscosity,effectiveplasmaviscosity, is very similar to that obtained without including compressibility effects, even if shock exists.

ISSN:0899-8221    

DOI:10.1063/1.860684

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

To study diamagnetic and compressibility effects for stellarators, toroidally averaged equations describing resistive pressure‐driven modes are developed. Linear stability results are given for cylindrical geometry and toroidal geometry. When toroidal coupling is included, both the analytical theory and numerical calculations show that diamagnetic effects can be destabilizing when they are small. However, for parameters appropriate to the Advanced Toroidal Facility (ATF) experimental device [J. F. Lyonetal., Fusion Technol.10, 179 (1986)] the diamagnetic effects are large and stabilizing. The linear results also show that for the specific cases reported here compressibility effects tend to cancel toroidal effects. Cylindrical calculations which include diamagnetic effects may then be adequate for the study of the experimental data.  

ISSN:0899-8221    

DOI:10.1063/1.860685

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A two‐dimensional analysis of the toroidal Alfve´n eigenmodes (TAE) is presented, based on an integrodifferential equation describing the shear Alfve´n perturbation of a toroidal plasma equilibrium in terms of coupling among the toroidal Alfve´n continua with the usual gap structure. Using a method similar to the Van Kampen–Case analysis for the Vlasov equation, exact analytic expressions are derived for the dispersion function and the two‐dimensional eigenmode structure. The dispersion function is expressed in terms of Cauchy‐type integrals, which explicitly expresses the global character of TAE modes and facilitates the calculation of their damping. The continuum‐damped TAE modes are shown to be, in general, not true eigenmodes of the toroidal plasma equilibrium, but rather resonances corresponding to zeros of the analytic continuation of the dispersion function onto unphysical sheets of its Riemann surface. Approximate but explicit expressions for the dispersion relation and the eigenfunction are also obtained in the limit of vanishing inverse aspect ratio.

ISSN:0899-8221    

DOI:10.1063/1.860686

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The poloidal mass flow and ion energy transport driven by friction between thermal ions and fast ions resulting from neutral beam injection are investigated. Transport coefficients are derived which relate the poloidal mass flow and the radial ion heat flux to the fast ion friction and the radial temperature gradient. An Onsager symmetry condition shows that the coefficient of the fast ion friction in the radial heat flux is the negative of the coefficient of the temperature gradient in the poloidal mass flow. Numerical results are given for the banana regime. The driven poloidal mass flow can be significantly larger than the standard neoclassical poloidal rotation driven by the ion temperature gradient. The resulting viscous heating of the ions can be larger than the standard neoclassical ion heat conduction term in the ion energy equation. The driven ion energy flux contains a convective contribution, due to the diffusional mixing of the fast ions and thermal ions. This energy flux is inward (a heat pinch) in the case of coinjection, and can be significantly larger than the standard neoclassical energy flux.

ISSN:0899-8221    

DOI:10.1063/1.860687

出版商:AIP    

年代:1993

数据来源: AIP