Instabilities In Tokamaks Research Articles

Control of the vertical instability in tokamaks

The problem of control of the vertical instability is studied for a massless filamentary plasma with finite resistivity included for the shell and active control coil. Stability boundaries are determined. The system can be stabilized up to a critical decay index, which is predominantly a function of the geometry of the passive stabilizing shell. A second, smaller, critical index, which is a function of the geometry of the control coils, determines the limit of stability in the absence of derivative gain in the control circuit. The system is also studied numerically in order to incorporate the non-linear effects of power supply dynamics. The power supply bandwidth requirement is determined by the open-loop growth rate of the instability. The system is studied for a number of control coil options which are available on the DIII-D tokamak. It is found that many of the coils will not provide adequate stabilization and that the use of inboard coils is advantageous in stabilizing the system up to the critical index. A hybrid control system which utilizes such inboard coils on a time-scale which is faster than the vessel L/R time is proposed. Experiments carried out on DIII-D confirm the appropriateness of the model. Using the results of the model study, DIII-D plasmas with decay indices exceeding 90% of the critical index have been stabilized. Measurement of the plasma vertical position is also discussed.

Modelling the effects of the sawtooth instability in tokamaks using a current viscosity term

A new method for modelling the sawtooth instability and other MHD activity in axisymmetric tokamak transport simulations is proposed. A hyper-resistivity (or current viscosity) term is included in the mean field Ohm's law to describe the effects of the three-dimensional fluctuating fields on the evolution of the inverse transform q characterizing the mean fields. This term has the effect of flattening the current profile while dissipating energy and conserving helicity. A fully implicit MHD transport and two-dimensional toroidal equilibrium code has been developed to calculate the evolution in time of the q-profile and the current profile using this new term. The results of this code are compared with the Kadomtsev reconnection model in the circular cylindrical limit.

Plasma modelling for the control of vertical instabilities in tokamaks

A linearized non-rigid MHD consistent displacement model is shown to be adequate to the study of the vertical stability of a plasma in an air core or iron core tokamak. This simple but accurate approach, which can be extended to the study of shape and radial position control, can be used in determining the limits of validity of the linear approximation and simulating the behaviour of a detection system based on a set of flux measurements. The method provides a basis for the optimization of position measurements and feedback parameters. The features of the model are illustrated, with reference to the study of the vertical stability of a NET configuration, showing the significance of the choice of the input signal.

Alpha-particle effects on high-n instabilities in tokamaks

Hot alpha particles and thermalized helium ash particles in tokamaks can have significant effects on high toroidal mode number instabilities such as the trapped-electron drift mode and the kinetically calculated magnetohydrodynamic ballooning mode. In particular, the effects can be stabilizing, destabilizing, or negligible, depending on the parameters involved. In high-temperature tokamaks capable of producing significant numbers of hot alpha particles, the predominant interaction of the mode with the alpha particles is through resonances of various sorts. In turn, the modes can cause significant anomalous transport of the alpha particles and the helium ash. Here, results of comprehensive linear eigenfrequency–eigenfunction calculations are presented for relevant realistic cases to show these effects.

Ballooning instabilities in tokamaks with sheared toroidal flows

The ballooning-mode eikonal representation is applied to the linearized incompressible magnetohydrodynamic (MHD) equations in axisymmetric systems with toroidal mass flows to obtain a set of initial value partial differential equations in which the time t and the poloidal angle theta are the independent variables. To derive these equations, the eikonal function S is assumed to satisfy the usual condition B.gradS=0 to guarantee that the modes vary slowly along the magnetic field. In addition, to resolve the V.grad operator acting on perturbed quantities, the eikonal must also satisfy the condition dS/dt=0. this induces a Doppler shift in S. This description of the instability, however, is incompatible with normal mode solutions of the MHD equations because the wave vector gradS becomes time dependent when the velocity shear is finite. Nevertheless, the author is able to investigate the effects of the sheared toroidal flows on localized ballooning instabilities because the initial value formulation of the problem developed does not constrain the solutions to evolve as exp (i omega t). Fixed boundary MHD equilibria with isothermal toroidal flows that model the JET device are generated numerically with a variational inverse moments code. As the initial value evaluations are evolved in time, periodic burst of ballooning activity are observed which are correlated with the formation of a ballooning structure at the outside edge of the torus that becomes displaced by 2 pi in the extended poloidal angle domain from one burst to the next. The velocity shear has a stabilizing influence on plasma ballooning.

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Nonlinear state of m=1 instability in tokamaks with nonmonotonic q profiles.

The nonlinear saturated state of the m = 1, n = 1 ideal MHD instability is calculated for a large--aspect-ratio tokamak. When the q(r) profile is nonmonotonic with ..delta..q = (q/sub min/-1)>0, the amplitude xi of the nonlinear state is given by xi/sup 2/q''/..delta..q = 7.9((..delta..q/sub c//..delta..q)/sup 3//sup ///sup 2/-1), where ..delta../sup q//sub c/ is the critical value of ..delta..q at which the system is marginally stable. This nonlinear state is similar to that seen during the sawtooth crash in large tokamaks and may be related to the steady-state oscillations seen when sawteeth are suppressed by lower-hybrid current drive.

Some Aspects of Alpha Particle Transport and Kinetic Instabilities in Tokamaks and Mirrors

Several aspects of energetic alpha behavior in a burning fusion plasma are considered. Alpha losses during slowing down and alpha-induced plasma rotation are discussed as the basis for important measurements. Potential kinetic instabilities (alpha-driven Alfvén waves in both toroidal and mirror systems) are considered from the point of view of threshold requirements. The possibility that other synergistic effects (e.g., orbit drift and shear Alfvén wave driven transport) might trigger these instabilities is also noted.

Suppression of MHD instabilities using RF waves in tokamaks.

Recent progresses in theories and experiments on the suppression of resistive MHD instabilities in tokamaks using RF waves are reviewed. Topics are focussed on (i) the m=2 tearing mode stabilization with lower hybrid current drive as well as electron cyclotron resonance heating for the prevension of major disruptions and (ii) the sawtooth mode stabilization using lower hybrid waves. New quasilinear theories on the magnetic island behavior under the presence of RF waves are also discussed.

Effects of finite ion Larmor radius on high-n ballooning instability in tokamaks.

Effects of the recently proposed electrostatic ballooning formulation on high-n ballooning instability in a tokamak are investigated. It is found that coupling to drift waves (through finite ion Larmor radius) further destabilizes ballooning instability. The critical poloidal beta is reduced by a factor of 2.

On the mode equations for the electrostatic ballooning instability in tokamaks

Some discrepancies are pointed out for kinetic and fluid dispersion relations of low-frequency electrostatic modes in tokamaks. It is shown that both electrons and ions contribute to the ballooning term, which is subject to finite ion Larmor radius correction.

High-beta approach and related MHD instabilities in tokamak.

The experimental and theoretical researches on high-beta tokamaks are surveyed. The basic properties of ballooning modes and the recent progress in high-beta studies are discussed with emphasis on the beta scaling laws, the accessibility to the “second stability” high-beta region, the excitation of new instabilities, the degradation of the plasma confinement and the future plans for high-beta tokamaks.

Stability conditions of feedback control system of vertical plasma position in tokamaks with a resistive shell

Stability conditions of axisymmetric instabilities in tokamaks with a resistive shell and an active feedback control system are examined analytically, assuming a ring-shaped plasma. Using equations of plasma motion and equivalent circuits, the basic properties of the feedback control system are discussed. Above a critical n-index, the fast-growing mode is stabilized; the slow-growing mode is stabilized when the feedback loop gain is larger than the critical value, which is proportional to the n-index. The dependence of the stability condition on the positions and time constants of the shell and the control windings is discussed.

Saturation of trapped-ion instability by two-dimensional electrostatic trapping

The non-linear evolution of trapped-ion instability in Tokamaks is investigated. The authors first derive a kinetic model of mode coupling, but show that it cannot be readily applied to resonant curvature-driven modes. They then show that non-linear saturation can result from trapping of resonant particles in the electrostatic potential of the wave. This mechanism is strongly enhanced by the radial structure of the mode, resulting in very low amplitudes at saturation.

Mode coupling and anomalous dissipation in magnetohydrodynamic turbulence

An energy-conserving model of magnetohydrodynamic turbulence is described that predicts both mode coupling and turbulent dissipation. The dissipation takes the form of anomalous resistivity and viscosity due to turbulent magnetic fields. The model predicts a dual cascade of energy to large wavenumbers and magnetic flux to small wavenumbers. Turbulent rearrangement of equilibrium magnetic shear generates resonant fluctuations via a mixing length process. The effect of the turbulence on the disruptive instability in tokamaks is discussed.

Reply to the Comments by R. Marchand and P.N. Guzdar on the paper “Absolute dissipative drift-wave instabilities in tokamaks” by L. Chen, M.S. Chance, C.Z. Cheng

Reply to the Comments by R. Marchand and P.N. Guzdar on the paper “Absolute dissipative drift-wave instabilities in tokamaks” by L. Chen, M.S. Chance, C.Z. Cheng

Comments on “Absolute dissipative drift-wave instabilities in tokamaks”, by L. Chen, M.S. Chance, C.Z. Cheng

In a recent paper, Chen et al. considered the destabilization of the universal mode in a tokamak by electron-ion collisions. In their analysis, a large-aspect-ratio tokamak with circular concentric flux surfaces was assumed and collisions were modelled by a parallel friction term in the electron equation of motion. Attention was focused on perturbations with large toroidal mode numbers, and use was made of the simplifying ballooning-mode representation. The particular form of the ballooning-mode formalism used, however, necessitated a truncated Taylor series in ωde/ω (to be defined later) and, thereby, resulted in an approximate eigenmode equation.

Characteristics of a modulated neutral beam as a remote suppressor for plasma instabilities

Modulated neutral beams are investigated as localized suppressor probes for trapped particle instabilities in Tokamaks. Criteria of spatial localization is discussed. An approximate method to solve the joint velocity and configuration space diffusion of modulated beam ions is devised. The resulting control source number density profile along magnetic field lines has been found. This profile is reasonably localized and its amplitude is roughly independent of frequency of modulation.

Passive Feedback Control of Plasma Position in a Tokamak

The effect of many passive coils on the positional instabilities in tokamaks is numerically investigated in the case of t ≪τ e (effective skin time of the coils), assuming the rigid shift of the plasma column. In order to make the positional stability region of the decay index broader, the passive coils must be located as close as to the plasma surface with the optimum position. The skin time of the coils is determined mainly by the number, cross section area and the conductivity of the coils. Application of the analysis to two small tokamaks shows the fairly good agreements with the experimental results.

Effect of impurities on nonpotential instabilities in Tokamaks

The role of impurities is considered in nonpotential drift oscillations and in perturbations of g-mode and Suydam-Mercier types, occurring in axisymmetric circular cross-section Tokamaks. The following three regimes are discussed: (1) the hydrodynamic regime (both main and impurity ions are hydrodynamic), (2) the mixed regime (main ions are of kinetic, impurity ions are of hydrodynamic type), (3) the kinetic regime (both types of ions are kinetic). It has been established that in a number of limiting cases the impurities play the role of a stabilizing factor.