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Journal ArticleDOI

More on core‐localized toroidal Alfvén eigenmodes

01 Sep 1995-Physics of Plasmas (American Institute of Physics)-Vol. 2, Iss: 9, pp 3401-3406
TL;DR: In this article, a novel ideal toroidal Alfven eigenmode, localized in the low-shear core region of a tokamak plasma, is shown to exist, whose frequency is near the upper continuum of the toroidal gap.
Abstract: A novel type of ideal toroidal Alfven eigenmode, localized in the low‐shear core region of a tokamak plasma, is shown to exist, whose frequency is near the upper continuum of the toroidal Alfven gap. This mode converts to a kinetic‐type toroidal Alfven eigenmode above a critical threshold that depends on aspect ratio, pressure gradient, and shear. Opposite to the usual ideal toroidal Alfven eigenmode, this new mode is peaked in amplitude on the small‐major‐radius side of the plasma.
Citations
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Journal ArticleDOI
TL;DR: In this article, the interactions of these energetic particles with linear and nonlinear Alfve'n waves generated in the magnetized plasma are reviewed, and the interaction of the alpha particles produced in the nuclear reactions is discussed.
Abstract: In magnetic fusion reactors relying on the burning of deuterium and tritium, sufficient confinement of the alpha particles produced in the nuclear reactions is crucial to sustaining the burning plasma. In this article the interactions of these energetic particles with linear and nonlinear Alfve'n waves generated in the magnetized plasma are reviewed.

379 citations

Journal ArticleDOI
TL;DR: A broad review of the progress that has been made in EP physics in tokamaks and spherical tori since the first DT experiments on TFTR and JET (Joint European Torus), including stellarator/helical devices is given in this article.
Abstract: The area of energetic particle (EP) physics in fusion research has been actively and extensively researched in recent decades. The progress achieved in advancing and understanding EP physics has been substantial since the last comprehensive review on this topic by Heidbrink and Sadler (1994 Nucl. Fusion 34 535). That review coincided with the start of deuterium?tritium (DT) experiments on the Tokamak Fusion Test Reactor (TFTR) and full scale fusion alphas physics studies.Fusion research in recent years has been influenced by EP physics in many ways including the limitations imposed by the ?sea? of Alfv?n eigenmodes (AEs), in particular by the toroidicity-induced AE (TAE) modes and reversed shear AEs (RSAEs). In the present paper we attempt a broad review of the progress that has been made in EP physics in tokamaks and spherical tori since the first DT experiments on TFTR and JET (Joint European Torus), including stellarator/helical devices. Introductory discussions on the basic ingredients of EP physics, i.e., particle orbits in STs, fundamental diagnostic techniques of EPs and instabilities, wave particle resonances and others, are given to help understanding of the advanced topics of EP physics. At the end we cover important and interesting physics issues related to the burning plasma experiments such as ITER (International Thermonuclear Experimental Reactor).

222 citations

Journal ArticleDOI
K. L. Wong1
TL;DR: In toroidal magnetically confined plasmas, eigenmodes of Alfven waves can be destablized by energetic ions with velocities comparable to the Alfven velocity as discussed by the authors.
Abstract: In toroidal magnetically confined plasmas, eigenmodes of Alfven waves can be destablized by energetic ions with velocities comparable to the Alfven velocity. With the advent of tokamak experiments in which populations of energetic ions can be introduced by neutral beam injection, radio frequency wave heating or by fusion reactions, major advances have been made in Alfven eigenmode research in the past 10 years. After introducing the basic concepts on the Alfven eigenmode instability, data on this subject from various toroidal devices are described, emphasizing the interplay between experiment and theory. Experimental results on mode identification, instability drive, mode damping and saturation, and energetic ion redistribution are compared with theory.

214 citations

Journal ArticleDOI
TL;DR: In this paper, a review of the physics knowledge relevant to design of a reactor scale tokamak is presented, and projections for ITER are provided in this Chapter of the ITER Physics Basis.
Abstract: Physics knowledge (theory and experiment) in energetic particles relevant to design of a reactor scale tokamak is reviewed, and projections for ITER are provided in this Chapter of the ITER Physics Basis. The review includes single particle effects such as classical alpha particle heating and toroidal field ripple loss, as well as collective instabilities that might be generated in ITER plasmas by energetic alpha particles. The overall conclusion is that fusion alpha particles are expected to provide an efficient plasma heating for ignition and sustained burn in the next step device. The major concern is localized heat loads on the plasma facing components produced by alpha particle loss, which might affect their lifetime in a tokamak reactor.

174 citations

Journal ArticleDOI
TL;DR: In this article, the stability of the Alfven Eigenmodes in the ITER 15 MA baseline scenario was investigated and it was found that only in the outer half of the plasma (r/a>0.5) can the fast ions overcome the thermal ion Landau damping.
Abstract: This paper discusses the behaviour and consequences of the expected populations of energetic ions in ITER plasmas. It begins with a careful analytic and numerical consideration of the stability of Alfven Eigenmodes in the ITER 15 MA baseline scenario. The stability threshold is determined by balancing the energetic ion drive against the dominant damping mechanisms and it is found that only in the outer half of the plasma (r/a>0.5) can the fast ions overcome the thermal ion Landau damping. This is in spite of the reduced numbers of alpha-particles and beam ions in this region but means that any Alfven Eigenmode-induced redistribution is not expected to influence the fusion burn process. The influence of energetic ions upon the main global MHD phenomena expected in ITER's primary operating scenarios, including sawteeth, neoclassical tearing modes and Resistive Wall Modes, is also reviewed. Fast ion losses due to the non-axisymmetric fields arising from the finite number of toroidal field coils, the inclusio...

112 citations

References
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Journal ArticleDOI
TL;DR: In this article, an analytic kinetic description of the toroidicity-induced Alfven eigenmode (TAE) is presented, which includes electron parallel dynamics nonperturbatively, an effect that is found to strongly influence the character and damping of the TAE−contrary to previous theoretical predictions.
Abstract: An analytic kinetic description of the toroidicity‐induced Alfven eigenmode (TAE) is presented. The theory includes electron parallel dynamics nonperturbatively, an effect that is found to strongly influence the character, and damping of the TAE−contrary to previous theoretical predictions. A parallel conductivity model that includes collisionless (Landau) damping on the passing electrons and collisional damping on both trapped and passing electrons is used. Together, these mechanisms damp the TAE more strongly than previously expected. This is because the TAE couples (or merges) with the kinetic Alfven wave (KAW) within the gap region under conditions that depend on the gap size, the shear, the magnitude of the conductivity, and the mode numbers. The high damping could be relevant to recent experimental measurements of the TAE damping coefficient. In addition, the theory predicts a ‘‘kinetic’’ TAE, whose eigenfreqeuency lies just above the gap, whose existence depends on finite conductivity, and that is formed by the coupling of two KAW’s

197 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of resonant continuum damping is investigated for the lowmode-number, toroidicity-induced, global shear Alfven eigenmodes, which can be self-excited by energetic circulating alpha particles in an ignited tokamak plasma.
Abstract: The effect of resonant continuum damping is investigated for the low‐mode‐number, toroidicity‐induced, global shear Alfven eigenmodes, which can be self‐excited by energetic circulating alpha particles in an ignited tokamak plasma. Resonant interaction with the shear Alfven continuum is possible for these eigenmodes, especially near the plasma periphery, leading to significant dissipation, which is typically larger than direct bulk plasma dissipation rates. Two perturbation methods are developed for obtaining the Alfven resonance damping rate from the ideal fluid zeroth‐order shear Alfven eigenvalue and eigenfunction. In both methods the real part of the frequency is estimated to zeroth order, and the imaginary part, which includes the damping rate, is then obtained by perturbation theory. One method, which is applicable when the eigenfunction is nearly real, can readily be incorporated into general magnetohydrodynamic (MHD) codes. In the second method, the zeroth‐order eigenfunctions may be complex; however, the application of this method to general MHD codes needs more detailed development. Also, an analytical estimate is found for the next‐order real frequency shift of the fluid global Alfven mode. Analytical and numerical studies of this continuum damping effect indicate that it can substantially reduce the alpha particle‐induced growth rate. Thus, either it is possible to prevent instability or, if unstable, to use the Alfven resonance damping to estimate the saturation amplitude level predicted from quasilinear theory.

152 citations

Journal ArticleDOI
TL;DR: In this paper, a general theoretical approach has been formulated for analyzing two-dimensional structures of high-n toroidal Alfven eigenmodes (TAE) in large aspect-ratio, finite-β tokamaks.
Abstract: A general theoretical approach has been formulated for analyzing two‐dimensional structures of high‐n toroidal Alfven eigenmodes (TAE) in large aspect‐ratio, finite‐β tokamaks. Here, n is the toroidal wave number and β is the ratio between plasma and magnetic pressures. The present approach generalizes the standard ballooning‐mode formalism and is capable of treating eigenmodes with extended global radial structures, as well as finite coupling between discrete and continuous spectra. Employing the well‐known (s,α) model equilibrium and assuming a linear equilibrium profile, the present approach has been applied to the calculation of the resonant continuum damping rate of TAE modes. Here, s and α denote, respectively, the strengths of magnetic shear and pressure gradients. In particular, it is found that there exists a critical α value, αc(s), such that, as α→αc, the continuum damping rate is significantly enhanced and, thus, could suppress the potential TAE instability.

99 citations

Journal ArticleDOI
TL;DR: In this article, the structure of toroidicity-induced Alfven eigenmodes and kinetic TAE (KTAE) with large mode numbers is analyzed and the linear power transfer from energetic particles to these modes is calculated in the low-shear limit when each mode is localized near a single gap within an interval whose total width Delta out is much smaller than the radius of the mode location.
Abstract: The structure of toroidicity-induced Alfven eigenmodes (TAE) and kinetic TAE (KTAE) with large mode numbers is analysed and the linear power transfer from energetic particles to these modes is calculated in the low-shear limit when each mode is localized near a single gap within an interval whose total width Delta out is much smaller than the radius rm of the mode location. Near its peak where most of the mode energy is concentrated, the mode has an inner scale length Delta in, which is much smaller than Delta out. The scale Delta in is determined by toroidicity and kinetic effects, which eliminate the singularity of the potential at the resonant surface. This work examines the case when the drift orbit width of energetic particles Delta b is much larger than the inner scale length Delta in, but arbitrary compared to the total width of the mode. It is shown that the particle-to-wave linear power transfer is comparable for the TAE and KTAE modes in this case. The ratio of the energetic particle contributions to the energetic particle drive for the TAE and KTAE modes is then roughly equal to the inverse ratio of the mode energies. It is found that in the low-shear limit the energetic particle drive for the KTAE modes can be larger than that for the TAE modes.

96 citations

Journal ArticleDOI
TL;DR: In this article, the core-localized toroidicity-induced Alfven eigenmode (TAE) was shown to exist at finite plasma pressure due to finite aspect ratio effects in tokamak plasma.
Abstract: The core‐localized toroidicity‐induced Alfven eigenmode (TAE) is shown to exist at finite plasma pressure due to finite aspect ratio effects in tokamak plasma. The new critical beta for the existence of the TAE mode is given by α≊3e+2s2, where e=r/R is the inverse aspect ratio, s is the magnetic shear and α=−Rq2dβ/dr is the normalized pressure gradient. In contrast, previous critical α is given by α≊s2. In the limit of s≪√r/R, the new critical α is greatly enhanced by the finite aspect ratio effects.

85 citations