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  • 11
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Results obtained from experiments utilizing high-power ion cyclotron range of frequencies (ICRF) heating to stabilize sawtooth oscillations on Tokamak Fusion Test Reactor (TFTR) [Hawryluk et al., Plasma Phys. Controlled Fusion 33, 1509 (1991)] are reviewed. The key observations include existence of a minimum ICRF power required to achieve stabilization, a dependence of the stabilization threshold on the relative size of the ICRF power deposition profile to the q=1 volume, and a peaking of the equilibrium pressure and current profiles during sawtooth-free phases of the discharges. In addition, preliminary measurements of the poloidal magnetic field profile indicate that q on axis decreases to a value of 0.55±0.15 after a sawtooth-stabilized period of ∼0.5 sec has transpired. The results are discussed in the context of theory, which suggests that the fast ions produced by the ICRF heating suppress sawteeth by stabilizing the m=1 magnetohydrodynamic (MHD) instabilities believed to be the trigger for the sawtooth oscillations. Though qualitative agreement is found between the observations and the theory, further refinement of the theory coupled with more accurate measurements of experimental profiles will be required in order to complete quantitative comparisons.
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  • 12
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Toroidal Alfvén eigenmodes (TAE) were excited by the energetic neutral beam ions tangentially injected into plasmas at low magnetic field in the Tokamak Fusion Test Reactor (TFTR) [Proceedings of the 11th International Conference on Plasma Physics and Controlled Fusion Research (IAEA, Vienna, 1987), Vol. 1, p. 51]. The injection velocities were comparable to the Alfvén speed. The modes were identified by measurements from Mirnov coils and beam emission spectroscopy (BES). TAE modes appear in bursts whose repetition rate increases with beam power. The neutron emission rate exhibits sawtoothlike behavior and the crashes always coincide with TAE bursts. This indicates ejection of fast ions from the plasma until these modes are stabilized. The dynamics of growth and stabilization were investigated at various plasma currents and magnetic fields. The results indicate that the instability can effectively clamp the number of energetic ions in the plasmas. The observed instability threshold is discussed in light of recent theories. In addition to these TAE modes, intermittent oscillations at three times the fundamental TAE frequency were observed by Mirnov coils, but no corresponding signal was found in BES. It appears that these high-frequency oscillations do not have a direct effect on the plasma neutron source strength.
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 985-993 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A high-n WKB-ballooning mode equation is employed to study toroidicity-induced shear Alfvén eigenmodes (TAE) in s-α space, where s=(r/q)(dq/dr) is the magnetic shear and α=−(2Rq2/B2)(dp/dr) is the normalized pressure gradient for tokamak plasmas. In the ballooning mode first stability region, TAE modes are found to exist only for α less than some critical value αc. It is found that these TAE modes reappear in the ballooning mode second stability region for bands of α values. The global envelope structures of these TAE modes are studied by the Wentzel–Kramers–Brillouin (WKB) method and are found to be bounded radially if the local mode frequency has a maximum in radius.
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  • 14
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 2802-2807 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effects of finite drift orbit width (FOW) and Larmor radius (FLR) of fast particles on the stability of low-n toroidicity-induced Alfvén eigenmodes (TAE) are studied. The formulation is based on the solution of the low frequency gyrokinetic equation (ω(very-much-less-than)ωc, where ωc is particle cyclotron frequency). A quadratic form has been derived in terms of invariant variables; energy E, magnetic moment μ, and toroidal angular momentum Pcursive-phi. The growth rate of the TAE is computed perturbatively using numerical averaging over the fast particle drift orbit. This new computational capability improves the NOVA-K code [G. Y. Fu, C. Z. Cheng, and K. L. Wong, Phys. Fluids B 5, 4040 (1994)] which included FOW effects in the growth rate calculation based on small radial orbit width approximation. The new NOVA-K version has been benchmarked for different regimes of particle TAE excitation. It is shown that both FOW and FLR effects are typically stabilizing; the TAE growth rate can be reduced by as much as a factor of 2 for tokamak fusion test reactor supershots [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)]. However, FOW may be destabilizing for the global modes, which are localized at the plasma edge. © 1999 American Institute of Physics.
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  • 15
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 3389-3397 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A high-n stability code, HINST, has been developed to study the stability of TAE (toroidicity induced Alfvén eigenmodes) in large tokamaks such as the International Thermonuclear Experimental Reactor (ITER) [D. E. Post, Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 239] where the spectrum of unstable TAE modes is shifted toward medium to high-n modes. The code solves the two-dimensional (2-D) eigenmode problem by expanding the eigenfunction in terms of basis functions. Based on the Fourier-ballooning formalism the eigenmode problem is reduced to a system of coupled one-dimensional equations, which is solved numerically by using the finite element method. The numerical method allows one to include nonperturbatively nonideal effects such as: finite ion Larmor radius, trapped electron collisional damping, etc. The 2-D numerical results of TAE and resonance TAE (RTAE) modes are compared with those from local ballooning calculations and the global magnetohydrodynamic nonvariational code NOVA [C. Z. Cheng and M. S. Chance, J. Comput. Phys. 71, 124 (1987)]. The results show that for ITER-like plasma parameters, TAE and RTAE modes can be driven unstable by alpha particles for n=10–20. The growth rate for the most unstable mode is within the range γ/ωA(similar, equals)0.3%–1.5%. The most unstable modes are localized near r/a(similar, equals)0.5 and have a broad radial mode envelope width. © 1998 American Institute of Physics.
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  • 16
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Purely alpha-particle-driven toroidal Alfvén eigenmodes (TAEs) with toroidal mode numbers n=1–6 have been observed in deuterium–tritium (D–T) plasmas on the tokamak fusion test reactor [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)]. The appearance of mode activity following termination of neutral beam injection in plasmas with q(0)〉1 is generally consistent with theoretical predictions of TAE stability [G. Y. Fu et al. Phys. Plasmas 3, 4036 (1996)]. Internal reflectometer measurements of TAE activity is compared with theoretical calculations of the radial mode structure. Core localization of the modes to the region of reduced central magnetic shear is confirmed, however the mode structure can deviate significantly from theoretical estimates. The peak measured TAE amplitude of δn/n∼10−4 at r/a∼0.3−0.4 corresponds to δB/B∼10−5, while δB/B∼10−8 is measured at the plasma edge. Enhanced alpha particle loss associated with TAE activity has not been observed. © 1998 American Institute of Physics.
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  • 17
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A band of high-frequency modes in the range 50–150 kHz with intermediate toroidal mode numbers 4〈n〈10 are commonly observed in the core of supershot plasmas on TFTR [R. Hawryluk, Plasma Phys. Controlled Fusion 33, 1509 (1991)]. Two distinct varieties of magnetohydrodynamic (MHD) modes are identified, corresponding to a flute-like mode predominantly appearing around the q=1 surface and an outward ballooning mode for q(approximately-greater-than)1. The flute-like modes have nearly equal amplitude on the high-field and low-field side of the magnetic axis, and are mostly observed in moderate performance supershot plasmas with τE〈2τL, while the ballooning-like modes have enhanced amplitude on the low-field side of the magnetic axis and tend to appear in higher performance supershot plasmas with τE(approximately-greater-than)2τL, where τL is the equivalent L-mode confinement time. Both modes appear to propagate in the ion diamagnetic drift direction and are highly localized with radial widths Δr∼5–10 cm, fluctuation levels ñ/n, T˜e/Te〈0.01, and radial displacements ξr∼0.1 cm. Unlike the toroidally localized high-n activity observed just prior to major and minor disruptions on TFTR [E. D. Fredrickson et al., Proceedings of the 15th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville, Spain (International Atomic Energy Agency, Vienna, 1995), No. IAEA-CN-60/A-2-II-5], these modes are typically more benign and may be indicative of MHD activity excited by resonant circulating beam ions. © 1996 American Institute of Physics.
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  • 18
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
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  • 19
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 3369-3377 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effects of alpha particles on the internal kink and fishbone modes are studied analytically. The nonadiabatic contribution from untrapped alpha particles is negligible. Finite inverse aspect ratio, plasma β, and plasma shaping effects can significantly enhance the trapped particle drift reversal domain in the pitch angle space and reduce the bounce-averaged magnetic drift frequency. The decrease of the drift magnitude and drift reversal effects on the ideal kink mode is small, but the βα threshold for the fishbone mode can be much lower than previously predicted [B. Coppi, S. Migliuolo, F. Pegoraro, and F. Porcelli, Phys. Fluids B 2, 927 (1990)]. Moreover, the fishbone mode could be excited by alpha particles, even when the plasma is stable in the ideal magnetohydrodynamic (MHD) limit. In addition, the ion diamagnetic drift frequency (finite ion Larmor radius effect) has a strong destabilizing effect on the fishbone mode when it is comparable with the trapped alpha-averaged precessional drift frequency, even though it stabilizes the plasma in the ideal MHD limit.
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  • 20
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A three-dimensional (3-D) hybrid gyrokinetic-MHD (magnetohydrodynamic) simulation scheme is presented. To the 3-D toroidal MHD code, MH3D-K the energetic particle component is added as gyrokinetic particles. The resulting code, mh3d-k, is used to study the nonlinear behavior of energetic particle effects in tokamaks, such as the energetic particle stabilization of sawteeth, fishbone oscillations, and alpha-particle-driven toroidal Alfvén eigenmode (TAE) modes.
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