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Energetic Particle-induced Geodesic Acoustic Mode

Description: A new energetic particle-induced Geodesic Acoustic Mode (EGAM) is shown to exist. The mode frequency, mode structure, and mode destabilization are determined non-perturbatively by energetic particle kinetic effects. In particular the EGAM frequency is found to be substantially lower than the standard GAM frequency. The radial mode width is determined by the energetic particle drift orbit width and can be fairly large for high energetic particle pressure and large safety factor. These results are consistent with the recent experimental observation of the beam- driven n=0 mode in DIII-D. The new mode is important since it can degrade energetic particle confinement as shown in the DIII-D experiments. The new mode may also affect the thermal plasma confinement via its interaction with plasma micro-turbulence.
Date: September 12, 2008
Creator: Fu, G. Y.
Partner: UNT Libraries Government Documents Department

Vertical Stability in a Current-carrying Stellarator

Description: An analytic stability criterion is derived for the vertical mode in a large aspect ratio stellarator. The effects of vacuum magnetic field generated by helical coils are shown to be stabilizing due to enhancement of field line bending energy. For wall at infinite distance from the plasma, the amount of external poloidal flux needed for stabilization is given by f = [k(subscript 2)-K]/[K(subscript 2) + 1] where k is the axisymmetric elongation and f is the ratio of vacuum rotational transform to the total transform.
Date: October 1, 1999
Creator: FU, G.Y.
Partner: UNT Libraries Government Documents Department

Excitation of high-n toroidicity-induced shear Alfven eigenmodes by energetic particles and fusion alpha particles in tokamaks

Description: The stability of high-n toroidicity-induced shear Alfven eigenmodes (TAE) in the presence of fusion alpha particles or energetic ions in tokamaks is investigated. The TAE modes are discrete in nature and thus can easily tap the free energy associated with energetic particle pressure gradient through wave particle resonant interaction. A quadratic form is derived for the high-n TAE modes using gyro-kinetic equation. The kinetic effects of energetic particles are calculated perturbatively using the ideal MHD solution as the lowest order eigenfunction. The finite Larmor radius (FLR) effects and the finite drift orbit width (FDW) effects are included for both circulating and trapped energetic particles. It is shown that, for circulating particles, FLR and FDW effects have two opposite influences on the stability of the high-n TAE modes. First, they have the usual stabilizing effects by reducing the wave particle interaction strength. Second, they also have destabilizing effects by allowing more particles to resonate with the TAE modes. It is found that the growth rate induced by the circulating alpha particles increase linearly with toroidal mode number n for small {kappa}{sub {theta}}{rho}{sub {alpha}}, and decreases as 1/n for {kappa}{sub {theta}}{rho}{sub {alpha}} {much gt} 1. The maximum growth rate is obtained at {kappa}{sub {theta}}{rho}{sub {alpha}} on the order of unity and is nearly constant for the range of 0.7 < {upsilon}{sub {alpha}}/{upsilon}{sub A} < 2.5. On the other hand, the trapped particle response is dominated by the precessional drift resonance. The bounce resonant contribution is negligible. The growth rate peaks sharply at the value of {kappa}{sub {theta}}{rho}{sub {alpha}} such that the precessional drift resonance occurs for the most energetic trapped particles. The maximum growth rate due to the energetic trapped particles is comparable to that of circulating particles.
Date: July 1, 1992
Creator: Fu, G.Y. & Cheng, C.Z.
Partner: UNT Libraries Government Documents Department

Existence of core localized toroidicity-induced Alfven eigenmode

Description: 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 {alpha}{approx} 3{epsilon} + 2s{sup 2}, where {epsilon} = r/R is the inverse aspect ratio, s is the magnetic shear and {alpha} = -Rq{sup 2}d{beta}/dr is the normalized pressure gradient. In contrast, previous critical {alpha} is given by {alpha} {approx} s{sup 2}. In the limit of s << {radical}r/R, the new critical {alpha} is greatly enhanced by the finite aspect ratio effects.
Date: February 1, 1995
Creator: Fu, G. Y.
Partner: UNT Libraries Government Documents Department

On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven by Energetic Particles

Description: It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low uctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
Date: June 4, 2010
Creator: Fu, G. Y.
Partner: UNT Libraries Government Documents Department

On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles

Description: It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
Date: October 1, 2010
Creator: Fu, G.Y.
Partner: UNT Libraries Government Documents Department

Alpha-driven magnetohydrodynamics (MHD) and MHD-induced alpha loss in the Tokamak Fusion Test Reactor

Description: Alpha-driven toroidal Alfven eigenmodes (TAEs) are observed as predicted by theory in the post neutral beam phase in high central q (safety factor) deuterium-tritium (D-T) plasmas in the Tokamak Fusion Test Reactor (TFTR). The mode location, poloidal structure and the importance of q profile for TAE instability are discussed. So far no alpha particle loss due to these modes was detected due to the small mode amplitude. However, alpha loss induced by kinetic ballooning modes (KBMs) was observed in high confinement D-T discharges. Particle orbit simulation demonstrates that the wave-particle resonant interaction can explain the observed correlation between the increase in alpha loss and appearance of multiple high-n (n {ge} 6, n is the toroidal mode number) modes.
Date: February 1, 1997
Creator: Chang, Z.; Nazikian, R. & Fu, G.Y.
Partner: UNT Libraries Government Documents Department

Recent progress in linear and nonlinear studies of toroidal Alfven eigenmode

Description: TAE modes are studied in linear and nonlinear regimes using several kinetic/MHD hybrid models. It is shown that the stability of TAE mode is largely determined by its radial mode structure. The calculated stability thresholds are correlated well with observations, including the recently observed alpha-driven TAE modes in the TFTR DT experiments. In the nonlinear regime, quasilinear simulations with multiple modes show that the saturation level is enhanced by nonlinear wave-particle resonance overlapping when the linear growth rate exceeds a critical value. A fully self-consistent {delta}f noise reduction method for the 3D particle/MHD hybrid model is developed.
Date: May 1, 1997
Creator: Fu, G.Y.; Chen, Y. & Budny, R.
Partner: UNT Libraries Government Documents Department

Energetic particle physics issues for ITER

Description: This paper summarizes our present understanding of the following energetic/alpha particle physics issues for the 21 MA, 20 TF coil ITER Interim Design configuration and operational scenarios: (a) toroidal field ripple effects on alpha particle confinement, (b) energetic particle interaction with low frequency MHD modes, (c) energetic particle excitation of toroidal Alfven eigenmodes, and (d) energetic particle transport due to MHD modes. TF ripple effects on alpha loss in ITER under a number of different operating conditions are found to be small with a maximum loss of 1%. With careful plasma control in ITER reversed-shear operation, TF ripple induced alpha loss can be reduced to below the nominal ITER design limit of 5%. Fishbone modes are expected to be unstable for {beta}{sub {alpha}} > 1%, and sawtooth stabilization is lost if the ideal kink growth rate exceeds 10% of the deeply trapped alpha precessional drift frequency evaluated at the q = 1 surface. However, it is expected that the fishbone modes will lead only to a local flattening of the alpha profile due to small banana size. MHD modes observed during slow decrease of stored energy after fast partial electron temperature collapse in JT-60U reversed-shear experiments may be resonant type instabilities; they may have implications on the energetic particle confinement in ITER reversed-shear operation. From the results of various TAE stability code calculations, ITER equilibria appear to lie close to TAE linear stability thresholds. However, the prognosis depends strongly on q profile and profiles of alpha and other high energy particles species. If TAE modes are unstable in ITER, the stochastic diffusion is the main loss mechanism, which scales with ({delta}B{sub r}/B){sup 2}, because of the relatively small alpha particle banana orbit size. For isolated TAE modes the particle loss is very small, and TAE modes saturate via the resonant ...
Date: December 31, 1996
Creator: Cheng, C. Z.; Budny, R. & Fu, G. Y.
Partner: UNT Libraries Government Documents Department

3D simulation studies of tokamak plasmas using MHD and extended-MHD models

Description: The M3D (Multi-level 3D) tokamak simulation project aims at the simulation of tokamak plasmas using a multi-level tokamak code package. Several current applications using MHD and Extended-MHD models are presented; high-{beta} disruption studies in reversed shear plasmas using the MHD level MH3D code, {omega}{sub *i} stabilization and nonlinear island saturation of TAE mode using the hybrid particle/MHD level MH3D-K code, and unstructured mesh MH3D{sup ++} code studies. In particular, three internal mode disruption mechanisms are identified from simulation results which agree which agree well with experimental data.
Date: December 31, 1996
Creator: Park, W.; Chang, Z.; Fredrickson, E. & Fu, G.Y.
Partner: UNT Libraries Government Documents Department

Plasma simulation studies using multilevel physics models

Description: The question of how to proceed toward ever more realistic plasma simulation studies using ever increasing computing power is addressed. The answer presented here is the M3D (Multilevel 3D) project, which has developed a code package with a hierarchy of physics levels that resolve increasingly complete subsets of phase-spaces and are thus increasingly more realistic. The rationale for the multilevel physics models is given. Each physics level is described and examples of its application are given. The existing physics levels are fluid models (3D configuration space), namely magnetohydrodynamic (MHD) and two-fluids; and hybrid models, namely gyrokinetic-energetic-particle/MHD (5D energetic particle phase-space), gyrokinetic-particle-ion/fluid-electron (5D ion phase-space), and full-kinetic-particle-ion/fluid-electron level (6D ion phase-space). Resolving electron phase-space (5D or 6D) remains a future project. Phase-space-fluid models are not used in favor of delta f particle models. A practical and accurate nonlinear fluid closure for noncollisional plasmas seems not likely in the near future.
Date: January 19, 2000
Creator: Park, W.; Belova, E.V. & Fu, G.Y.
Partner: UNT Libraries Government Documents Department

Stability of the toroidicity-induced Alfven eigenmodes in JT-60U ICRF experiments

Description: It is shown that the stability of toroidicity-induced Alfven eigenmodes (TIE) in JT-60U ICRF experiments is strongly dependent on mode location. This dependence results in sequential excitation of high-n TIE modes as the central safety factor, q, drops in time.
Date: April 1, 1996
Creator: Fu, G.Y.; Cheng, C.Z.; Kimura, H.; Ozeki, T. & Saigusa, M.
Partner: UNT Libraries Government Documents Department

Alpha Particle-Driven Toroidal Alfven Eigenmodes in Tokamak Fusion Test Reactor Deuterium-Tritium Plasmas: Theory and Experiments

Description: The toroidal Alfvén eigenmodes (TAE) in the Tokamak Fusion Test Reactor [K. Young, et al., Plasma Phys. Controlled Fusion 26, 11 (1984)]deuterium-tritium plasmas are analyzed using the NOVA-K code [C.Z. Cheng, Phys. Reports 211, 1 (1992)]. The theoretical results are compared with the experimental measurements in detail. In most cases, the theory agrees with the observations in terms of mode frequency, mode structure, and mode stability. However, one mode with toroidal mode number n = 2 is observed to be poloidally localized on the high field side of the magnetic axis with a mode frequency substantially below the TAE frequency.
Date: July 9, 1998
Creator: Budny, R.; Chang, Z.; Fu, G.Y. & Nazikian, R.
Partner: UNT Libraries Government Documents Department

Kinetic Damping of Toroidal Alfven Eigenmodes

Description: The damping of Toroidal Alfven Eigenmodes in JET plasmas is investigated by using a reduced kinetic model. Typically no significant damping is found to occur near the center of the plasma due to mode conversion to kinetic Alfven waves. In contrast, continuum damping from resonance near the plasma edge may be significant, and when it is, it gives rise to damping rates that are compatible with the experimental observations.
Date: May 3, 2005
Creator: Fu, G.Y.; Berk, H.L. & Pletzer, A.
Partner: UNT Libraries Government Documents Department

Toroidal Alfven wave stability in ignited tokamaks

Description: The effects of fusion-product alpha particles on the stability of global-type shear Alfven waves in an ignited tokamak plasma are investigated in toroidal geometry. Finite toroidicity can lead to stabilization of the global Alfven eigenmodes, but it induces a new global shear Alfven eigenmodes, which is strongly destabilized via transit resonance with alpha particles. 8 refs., 2 figs.
Date: January 1, 1989
Creator: Cheng, C.Z.; Fu, G.Y. & Van Dam, J.W.
Partner: UNT Libraries Government Documents Department

Magnetohydodynamics stability of compact stellarators

Description: Recent stability results of external kink modes and vertical modes in compact stellarators are presented. The vertical mode is found to be stabilized by externally generated poloidal flux. A simple stability criterion is derived in the limit of large aspect ratio and constant current density. For a wall at infinite distance from the plasma, the amount of external flux needed for stabilization is given by Fi = (k2 {minus} k)=(k2 + 1), where k is the axisymmetric elongation and Fi is the fraction of the external rotational transform. A systematic parameter study shows that the external kink mode in QAS can be stabilized at high beta ({approximately} 5%) without a conducting wall by magnetic shear via 3D shaping. It is found that external kinks are driven by both parallel current and pressure gradient. The pressure contributes significantly to the overall drive through the curvature term and the Pfirsch-Schluter current.
Date: January 3, 2000
Creator: Fu, G.Y.; Ku, L.P.; Cooper, W.A. & Hirshman, S.H.
Partner: UNT Libraries Government Documents Department

Robustness and flexibility in compact quasiaxial stellarators: Global ideal MHD stability and energetic particle transport

Description: Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal magnetohydrodynamic stability is evaluated as well as energetic particle transport. It is found that tokamak intuition is relevant to understanding the magnetohydrodynamic stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the non-periodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD stability are not anticorrelated in these equilibria, stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties.
Date: January 27, 2000
Creator: Redi, M.H.; Diallo, A.; Cooper, W.A. & Fu, G.Y.
Partner: UNT Libraries Government Documents Department

Properties of High Beta, Quasi-Axisymmetric NCSX Stellarator Configurations

Description: Quasi-axisymmetry, external kinks and ballooning stability are studied with respect to the plasma shaping and variation in the pressure and current profiles for NCSX. We show that while the kink stability may require a delicate boundary shaping, most quasi-axisymmetry may be achieved using a few low order modes that eliminate the large mirror fields arising partly from boundary shaping for the kink stability. In addition, we demonstrate that the kink and ballooning instability may be improved in the NCSX configurations by a more peaked pressure profile or a broader current profile. Finally, we show numerically that it is possible to construct a quasi-axisymmetric configuration that is stable to the external kink at all current levels for which the edge rotational transform is less than 0.5.
Date: September 28, 1999
Creator: Boozer, A.; Fu, G.Y.; Ku, L.P.; Monticello, D. & Reiman, A.
Partner: UNT Libraries Government Documents Department

Properties of High Beta, Quasi-Axisymmetric NCSX Stellarator Configurations

Description: Quasi-axisymmetry, external kinks and ballooning stability are studied with respect to the plasma shaping and the variation in the pressure and current profiles for NCSX. We show that while the kink stability may require a delicate boundary shaping, most quasi-axisymmetry may be achieved using a few low order modes that eliminate the large mirror fields arising partly from boundary shaping for the kink stability. In addition, we demonstrate that the kink and ballooning instability may be improved in the NCSX configurations by a more peaked pressure profile or a broader current profile. Finally, we show numerically that it is possible to construct a quasi-axisymmetric configuration that is stable to the external kink at all current levels for which the edge rotational transform is less than 0.5.
Date: November 1, 1999
Creator: Boozer, A.; Reiman, A.; Monticello, D.; Fu, G.Y. & Ku, L.P.
Partner: UNT Libraries Government Documents Department

Global Hybrid Simulations of Energetic Particle-driven Modes in Toroidal Plasmas

Description: Global hybrid simulations of energetic particle-driven MHD modes have been carried out for tokamaks and spherical tokamaks using the hybrid code M3D. The numerical results for the National Spherical Tokamak Experiments (NSTX) show that Toroidal Alfven Eigenmodes are excited by beam ions with their frequencies consistent with the experimental observations. Nonlinear simulations indicate that the n=2 mode frequency chirps down as the mode moves out radially. For ITER, it is shown that the alpha-particle effects are strongly stabilizing for internal kink mode when central safety factor q(0) is sufficiently close to unity. However, the elongation of ITER plasma shape reduces the stabilization significantly.
Date: December 14, 2004
Creator: Fu, G. Y.; Breslau, J.; Fredrickson, E.; Park, W. & Strauss, H. R.
Partner: UNT Libraries Government Documents Department

Physics Design of the National High-power Advanced Torus Experiment

Description: Moving beyond ITER toward a demonstration power reactor (Demo) will require the integration of stable high fusion gain in steady-state, advanced methods for dissipating very high divertor heat-fluxes, and adherence to strict limits on in-vessel tritium retention. While ITER will clearly address the issue of high fusion gain, and new and planned long-pulse experiments (EAST, JT60-SA, KSTAR, SST-1) will collectively address stable steady-state highperformance operation, none of these devices will adequately address the integrated heat-flux, tritium retention, and plasma performance requirements needed for extrapolation to Demo. Expressing power exhaust requirements in terms of Pheat/R, future ARIES reactors are projected to operate with 60-200MW/m, a Component Test Facility (CTF) or Fusion Development Facility (FDF) for nuclear component testing (NCT) with 40-50MW/m, and ITER 20-25MW/m. However, new and planned long-pulse experiments are currently projected to operate at values of Pheat/R no more than 16MW/m. Furthermore, none of the existing or planned experiments are capable of operating with very high temperature first-wall (Twall = 600-1000C) which may be critical for understanding and ultimately minimizing tritium retention with a reactor-relevant metallic first-wall. The considerable gap between present and near-term experiments and the performance needed for NCT and Demo motivates the development of the concept for a new experiment — the National High-power advanced-Torus eXperiment (NHTX) — whose mission is to study the integration of a fusion-relevant plasma-material interface with stable steady-state high-performance plasma operation.
Date: July 18, 2007
Creator: Menard, J E; Fu, G -Y; Gorelenkov, N; Kaye, S M; Kramer, G; Maingi, R et al.
Partner: UNT Libraries Government Documents Department

3D simulation studies of tokamak plasmas using MHD and extended-MHD models

Description: The M3D (Multi-level 3D) tokamak simulation project aims at the simulation of tokamak plasmas using a multi-level tokamak code package. Several current applications using MHD and Extended-MHD models are presented; high-{beta} disruption studies in reversed shear plasmas using the MHD level MH3D code, {omega}{sub *i} stabilization and nonlinear island rotation studies using the two-fluid level MH3D-T code, studies of nonlinear saturation of TAE modes using the hybrid particle/MHD level MH3D-K code, and unstructured mesh MH3D{sup ++} code studies. In particular, three internal mode disruption mechanisms are identified from simulation results which agree well with experimental data.
Date: January 1997
Creator: Park, W.; Chang, Z.; Fredrickson, E.; Fu, G. Y.; Pomphrey, N.; Strauss, H. R. et al.
Partner: UNT Libraries Government Documents Department

Toroidal Alfvén Eigenmodes in TFTR Deuterium-Tritium Plasmas

Description: 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 delta n/n~10(superscript -4) at r/a~0.3-0.4 corresponds to delta B/B~10-5, while dB/B~10(superscript -8) is measured at the plasma edge. Enhanced alpha particle loss associated with TAE activity has not been observed.
Date: January 1, 1998
Creator: Fu, G.Y.; Berk, H.; Nazikian, R.; Batha, S.H.; Chang, Z. & al, et
Partner: UNT Libraries Government Documents Department

Effect of plasma rotation on sawtooth stabilization by beam ions

Description: The sawtooth period in JET ELM-free H-Mode plasmas is increasing with Neutral Beam Injection (NBI) power. For injected power PNBI 12MW no large sawtooth crash is observed during the ELM-free period. However, as the edge stability is improved and external kink modes and ELMs are delayed, a possible sawtooth crash at a high plasma beta becomes a concern. In JET DT experiments, delaying sawteeth was found to be crucial in the quest for high fusion power. Fast particles are known to provide stabilizing effect on sawteeth, however, sawtooth stabilization by NBI ions is not clearly understood, since NBI ions are usually not ''fast'' enough to stabilize the m/n = 1/1 internal kink mode which is believed to cause the crash. In order to understand the observed sawteeth stabilization in tokamak experiments with NBI heating, the internal kink m/n = 1/1 mode stability of JET plasmas was modeled using the NOVA-K code, which is also benchmarked with the nonperturbative version of NOVA and the M3D code. Comparison of m/n = 1/1 mode stabilization by NBI ions in JET and TFTR and application of the nonlinear stabilization criteria is given.
Date: June 23, 2000
Creator: Gorelenkov, N. N.; Nave, M. F. F.; Budny, R.; Cheng, C. Z.; Fu, G. Y.; Hastie, J. et al.
Partner: UNT Libraries Government Documents Department