Instabilities In Tokamaks Research Articles

A Landau fluid model for electromagnetic plasma microturbulence

A fluid model is developed for the description of microturbulence and transport in magnetized, long mean-free-path plasmas. The model incorporates both electrostatic and magnetic fluctuations, as well as finite Larmor radius and kinetic effects. Multispecies Landau fluid equations are derived from moments of the electromagnetic gyrokinetic equation, using fluid closures which model kinetic effects. A reduced description of electron dynamics, appropriate for the study of microturbulence on characteristic ion drift and Alfvén scales, is derived via an expansion in the electron to ion mass ratio. The reduced electron equations incorporate curvature, ∇B, and linear and nonlinear E×B drift effects, needed to model the electron contribution to the drive and damping of ion gyroradius scale instabilities in tokamaks. The Landau fluid model is linearly benchmarked against gyrokinetic codes, and found to reproduce the toroidal finite beta ion temperature gradient and kinetic ballooning instabilities.

Effect of edge turbulence on threshold of multifaceted asymmetric radiation from the edge instability in tokamaks

The radiative condensation instability believed to be responsible for the occurrence of multifaceted asymmetric radiation from the edge (MARFE) in tokamaks has been investigated in the presence of a background turbulence of saturated drift resistive ballooning modes (DRBM). These modes are a natural source for edge fluctuations in tokamaks. For the m=1 MARFE, it has been shown that a modest level of DRBM turbulence can significantly lower the threshold radiation rate required for excitation of MARFEs, enhance its growth rate, and introduce a real part to the mode frequency. Some of these results are consistent with observations of onset of MARFEs in recent experiments on Joint European Torus (JET) [Proceedings of the 17th European Conference on Controlled Fusion and Plasma Heating, Amsterdam (European Physical Society, Petit-Lancy, 1990), Vol. 14b-1, p. 339] and Tokamak Experiment for Technology Oriented Research (TEXTOR) [Phys. Rev. Lett. 71, 1549 (1993)].

Nature of monster sawteeth and their relationship to Alfven instabilities in tokamaks

A correlation is explored between the presence of energetic particle modes (EPM) and long-period sawtooth oscillations in tokamak plasmas heated by rf waves. The eventual crash of these sawteeth is explained in terms of the loss of the stabilizing fast particles due to the EPM. The absence of long-period sawteeth in high q(a) discharges is explained in terms of ion loss due to toroidal Alfven eigenmodes.

Pellet driven disruptions in tokamaks

Pellet injection can trigger ballooning like instability in tokamaks, driven by the large pressure perturbation of the pellet cloud. The instability is easier to excite when pellets are injected on the low magnetic field side of the tokamak, which is the usual case. This is because the pellet pressure perturbation tends to add to the background pressure drive. When pellets are injected on the high field side, the instability is harder to excite, because the pellet pressure perturbation opposes the background pressure drive. Nonlinearly, the instability causes fragmentation of the pellet cloud, and can give anomalous pellet penetration. This effect might explain recent experimental observations.

Neutrals’ effects on stability

The physics of the neutral atoms is incorporated into a generalized description of edge instabilities in tokamaks and plasmas with a small neutral fraction. The description includes ideal and resistive ballooning modes; modes driven by a radial electron temperature gradient when the plasma is in contact with conducting material surfaces such as limitors or divertor target plates, the destabilizing effect of the parallel variation in the E×B drift frequency, and effects due to the flow of the neutral gas. The analysis considers the neutral dynamics in both the short and long neutral mean-free path limits (relative to the wavelength of the instability), since the perturbed ion–neutral coupling depends on collisionality. Moreover, parallel and cross-field variations in the equilibrium temperatures, densities, and potential are retained as well as the corresponding diamagnetic effects. In the short neutral mean-free path limit, the ion and neutral viscosities and heat fluxes must be retained, while in the long neutral mean-free path limit the neutrals are not perturbed, but the ion viscosity and heat flux must still be considered. The possible destabilizing impact of the new heat flux and viscous terms on stability is demonstrated.

Numerical simulation of feedback stabilization of axisymmetric modes in tokamaks using driven halo currents

The Tokamak Simulation Code (TSC) has been used to model a new method of feedback stabilization of the axisymmetric instability in tokamaks using driven halo (or scrape-off layer) currents. The method appears to be feasible for a wide range of plasma edge parameters. It may offer advantages over the more conventional method of controlling this instability when applied in a reactor environment.

Ion cyclotron emission due to fast Alfvén-wave radiative instabilities in tokamaks induced by newly born fusion products

The velocity distribution functions of newly born (t=0) charged fusion products (protons in DD and alpha particles in DT plasmas) of tokamak discharges can be approximated by a monoenergetic ring distribution with a finite v∥ such that v⊥≈v∥ ≈Vj, where ½MjV2j =Ej, the directed birth energy of the charged fusion-product species j of mass Mj. As the time t progresses, these distribution functions will evolve into a Gaussian in velocity (i.e. a drifting Maxwellian type), with thermal spreads given by the perpendicular and parallel temperatures T⊥j(t) =T∥j(t), with Tj(t) increasing as t increases and finally reaching an isotropic saturation value offormula hereHere Td is the temperature of the background deuterium plasma ions, M is the mass of a triton or a neutron for j=protons and alpha particles respectively, and τj≈¼τsj is the thermalization time of the fusion product species j in the background deuterium plasma, with τsj the slowing-down time. For times t of the order of τj, the distributions can be approximated by a Gaussian in the total energy (i.e. a Brysk type). Then, for times t[ges ]τsj, the velocity distributions of the fusion products will relax towards their appropriate slowing-down distributions. Here we shall examine the radiative stability of all these (i.e. a monoenergetic ring, a Gaussian in velocity, a Gaussian in energy, and the slowing-down) distributions.

Effects of negative magnetic shear on toroidicity induced eigenmode instability in tokamaks

The effects of negative magnetic shear on the toroidicity induced (TI) eigenmode instability are studied with a numerical WKB shooting scheme. The ion temperature gradient (ITG or ηi) and the parallel velocity shear (PVS) of the ions are included. It is found that for a given set of plasma parameters, the damping mechanism from a negative magnetic shear is much stronger than it is from a positive shear of equal magnitude. The effects of PVS on TI modes are demonstrated to be destabilizing.

Multifaceted asymmetric radiation from the edge impurity density limits in tokamaks with poloidal asymmetry and rotation

A linear stability analysis of two-dimensional, edge-localized thermal instabilities in tokamaks has been performed using a fluid model which incorporates the effects of large radial gradients and near-sonic rotation speeds. Sufficient stability requirements for fundamental (m=0) and harmonic (m≳0) poloidal modes are established and used to investigate the effects of rotation, poloidal asymmetry in the equilibrium solution, parallel current, and parallel momentum injection on impurity density limits. The higher density limits due to parallel heat conduction and parallel viscosity that are associated with the m≳0 modes, but that are absent for the m=0 mode, account for the onset and stability of MARFEs (multifaceted asymmetric radiation from the edge). Rotation and asymmetry in the equilibrium solution are significant in the determination of impurity density limits. The MARFE threshold density limit can be increased by driving current in the plasma edge counter to the magnetic field.

Remote feedback stabilization of tokamak instabilities*

A novel remote suppressor consisting of an injected ion beam has been used for the stabilization of plasma instabilities. A collisionless curvature-driven trapped-particle instability, an E×B flute mode and an ion temperature gradient (ITG) instability have been successfully suppressed down to noise levels using this scheme. Furthermore, the first experimental demonstration of a multimode feedback stabilization with a single sensor–suppressor pair has been achieved. Two modes (an E×B flute and an ITG mode) were simultaneously stabilized with a simple state-feedback-type method where more ‘‘state’’ information was generated from a single-sensor Langmuir probe by appropriate signal processing. The above experiments may be considered as paradigms for controlling several important tokamak instabilities. First, feedback suppression of edge fluctuations in a tokamak with a suitable form of insulated segmented poloidal limiter sections used as Langmuir-probe-like suppressors is proposed. Other feedback control schemes are proposed for the suppression of electrostatic core fluctuations via appropriately phased ion density input from a modulated neutral beam. Most importantly, a scheme to control major disruptions in tokamaks via feedback suppression of kink (and possibly) tearing modes is discussed. This may be accomplished by using a modulated neutral beam suppressor in a feedback loop, which will supply a momentum input of appropriate phase and amplitude. Simple theoretical models predict modest levels of beam energy, current, and power.

Effects of a poloidal divertor separatrix on resistive magnetohydrodynamic instabilities in a tokamak

A computer code package has been developed to simulate the linear and nonlinear evolution of long-wavelength resistive magnetohydrodynamic (MHD) instabilities in a four-node poloidal divertor tokamak (e.g., Wisconsin Tokapole II [Nucl. Fusion 19, 1509 (1979)]). Distinguishing features of this package include the use of a full set of three-dimensional (3-D) nonlinear resistive MHD equations and the inclusion of the divertor separatrix and the plasma outside the divertor separatrix in the computational domain. The present numerical results suggest that the plasma current outside the divertor separatrix tends to linearly stabilize the resistive MHD instability dominated by the m=2, n=1 mode, and, to a lesser extent, that dominated by the m=1, n=1 mode. (Here, m and n are poloidal and toroidal mode numbers, respectively.) However, the nonlinear evolution of the m=1, n=1 dominant instability is not significantly affected by the divertor configuration; the m=1, n=1 island is shown to reconnect totally by developing a large region of magnetic stochasticity. Hence, the cause of the partial reconnection observed in Tokapole II seems to lie beyond the scope of the classical resistive MHD model.

Nonlinear growth of strongly unstable tearing modes

Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long-wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded.

Trapped particle dynamics in toroidally rotating plasmas

A detailed single particle orbit analysis in toroidally rotating plasma yields new analytical formulas for the second adiabatic invariant, the bounce frequency, and the precession frequency up to the first-order correction in ρpi (poloidal ion gyroradius)/Lv (scale length of rotation velocity), for toroidal flow values of the order of ion thermal velocity. Toroidal plasma rotation effects on the trapped ion instabilities in tokamaks are investigated in the context of local theory. Toroidal plasma rotation increases both the fraction of trapped particles and their precession drift velocity. Consequently, the growth rate of trapped ion instability increases in both dissipative and collisionless regimes.

Critical error fields for locked mode instability in tokamaks

Otherwise stable discharges can become nonlinearly unstable to disruptive locked modes when subjected to a resonant m=2, n=1 error field from irregular poloidal field coils, as in DIII-D [Nucl. Fusion 31, 875 (1991)], or from resonant magnetic perturbation coils as in COMPASS-C [Proceedings of the 18th European Conference on Controlled Fusion and Plasma Physics, Berlin (EPS, Petit-Lancy, Switzerland, 1991), Vol. 15C, Part II, p. 61]. Experiments in Ohmically heated deuterium discharges with q≊3.5, n̄ ≊ 2 × 1019 m−3 and BT ≊ 1.2 T show that a much larger relative error field (Br21/BT ≊ 1 × 10−3) is required to produce a locked mode in the small, rapidly rotating plasma of COMPASS-C (R0 = 0.56 m, f≊13 kHz) than in the medium-sized plasmas of DIII-D (R0 = 1.67 m, f≊1.6 kHz), where the critical relative error field is Br21/BT ≊ 2 × 10−4. This dependence of the threshold for instability is explained by a nonlinear tearing theory of the interaction of resonant magnetic perturbations with rotating plasmas that predicts the critical error field scales as (fR0/BT)4/3n̄2/3. Extrapolating from existing devices, the predicted critical field for locked modes in Ohmic discharges on the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 30, 1183 (1990)] (f=0.17 kHz, R0 = 6.0 m, BT = 4.9 T, n̄ = 2 × 1019 m−3) is Br21/BT ≊ 2 × 10−5. Such error fields could be produced by shifts and/or tilts of only one of the larger poloidal field coils of as little as 0.6 cm with respect to the toroidal field. A means to increase the rotation frequency would obviate the sensitivity to error fields and increase allowable tolerances on coil construction.

Variational formalism for kinetic-MHD instabilities in tokamaks

A variational formalism that includes, in a consistent way, the tokamak plasma fluid response to an electromagnetic field as well as the particle-field resonant interaction effects is presented. The integrability of the unperturbed motion of the particles is used to establish a general functional similar to the classical Lagrangian for the electromagnetic field, which is extremum with respect to the field potentials. This functional is the sum of fluid terms that are closely related to the classical MHD energy and of resonant terms describing the kinetic effects. The formalism is used to study a critical issue in tokamak confinement, namely the sawteeth stabilization by energetic particles.

Weak turbulence theory of collisionless trapped electron driven drift instability in tokamaks

The toroidal collisionless trapped electron modes are analyzed in the weak turbulence regime treating both ions and trapped electrons nonlinearly in the presence of ion and electron temperature gradients. The spectral intensity of the density fluctuations in the nonlinearly saturated state is analytically obtained from the steady-state solution of the wave-kinetic equation. Distant nonlinear interactions between low-kθ and high-kθ modes of similar frequencies via trapped electron scattering (the resonance between the beat wave and the trapped electron precession drift frequencies) suppress the low-kθ [kθρs ≪(Ln/R)1/2] modes while close interactions via ion Compton scattering (nonlinear ion Landau damping) produce a monotonically decreasing spectrum from kθρs ≂(Ln/R)1/2 to kθρs≂1 according to an approximate power law k−3θ. Various fluctuation amplitudes at saturation and the fluctuation-induced anomalous particle and heat fluxes are found to be smaller than the mixing length estimates. The plasma confinement is predicted to improve with higher Ti/ Te, more peaked density profile, larger aspect ratio, and higher plasma current. Also, a significant dependence of transport on the electron temperature gradient is found which could contribute to the rigidity of the electron temperature profile often experimentally observed.

Excitation of thermonuclear cone instabilities by toroidal equilibrium distributions of high-energy alpha particles in tokamaks

The possibility of a new set of thermonuclear cone instabilities in tokamaks is demonstrated. These instabilities are caused by an inherent anisotropy existing in the alpha-particle velocity distribution function owing to the finite width of the particle orbits in combination with a spatially varying particle source. The conditions for the excitation of shear Alfvén waves by well-trapped alpha particles are studied.

Ballooning instabilities in tokamaks with sheared toroidal flows

The stability of ballooning modes in the presence of sheared toroidal flows is investigated. The eigenmodes are shown to be related by a Fourier transformation to the nonexponentially growing Floquet solutions found by Cooper [Plasma Phys. Controlled Fusion 30, 1805 (1988)]. It is further shown that the problem cannot be reduced further than to a two-dimensional partial differential equation. Next, the generalized ballooning equation is solved analytically for a circular tokamak equilibrium with sonic flows, but with a small rotation shear compared to the sound speed. With this ordering, the centrifugal forces are comparable to the pressure gradient forces driving the instability, but coupling of the mode with the sound wave is avoided. A new stability criterion is derived that explicitly demonstrates that flow shear is stabilizing at constant centrifugal force gradient.

Destabilization of Tokamak Pressure-Gradient Driven Instabilities by Energetic Alpha-Particle Populations

This paper reports on alpha-particle populations that can significantly alter existing magnetohydrodynamic (MHD) instabilities in tokamaks through kinetic effects and coupling to otherwise stable shear Alfven waves. Resonances of the trapped alpha-particle precessional drift, with the usual ballooning mode diamagnetic frequency ({omega}{sub *i}/2) and the toroidicity-induced Alfven eigenmode (TAE), are considered. These are examined for noncircular tokamaks in the high-n ballooning limit using an isotopic alpha-particle slowing down distribution and retaining the full-energy and pitch-angle dispersion in the alpha-particle drift frequency. Applying this to the Compact Ignition Tokamak (CIT) and the International Thermonuclear Experimental Reactor (ITER) indicates that ballooning instabilities can persist at betas below the ideal MHD threshold. These are especially dominated by the destabilization of the TAE mode. In addition, a hybrid fluid-particle approach for simulating alpha-particle effects on pressure-gradient driven instabilities is described.

Variational calculation of electromagnetic instabilities in tokamaks

A variational method is presented in order to determine and study linear microinstabilities in tokamaks. Exploiting the existence of a system of action and angular variables for trapped and circulating particles, a functional, extremum in the turbulent electromagnetic field, is analytically established and implemented in the code TORRID. The coupling of poloidal harmonics due to toroidal effects is investigated within the frame of a WKB formalism whose zeroth order is equivalent to the ballooning analysis. The essential features of the code TORRID are described. Curvature effects on ionic modes profiles and stability thresholds are presented as an example of application.