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  • 1
    Online Resource
    Online Resource
    Theory of Tokamak Plasmas. (1989)
    San Diego :Elsevier Science & Technology,
    Details
    Keywords: Electronic books.
    Type of Medium: Online Resource
    Pages: 1 online resource (374 pages)
    Edition: 1st ed.
    ISBN: 9781483293264
    URL: https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=4042643
    DDC: 538/.6
    Language: English
    Note: Front Cover -- Theory of Tokamak Plasmas -- Copyright Page -- Table of Contents -- PREFACE -- ACKNOWLEDGMENT -- CHAPTER 1. TOROIDAL CONFIGURATION -- 1.1 Introduction -- 1.2 General Coordinates -- 1.3 Basis Vectors and Metric Tensor -- 1.4. Gradient, Divergence and Curl -- 1.5 Christoffel Symbols -- 1.6 Representation of a Magnetic Field -- 1.7 Magnetic Surfaces -- 1.8 Magnetic Surface Destruction -- 1.9 The Standard Map -- Problems -- References -- CHAPTER 2. EQUILIBRIUM -- 2.1 Introduction -- 2.2 The Virial Theorem -- 2.3 Field Line Curvature -- 2.4 General Form of Equilibrium Magnetic Field -- 2.5 Covariant and Contravariant Representations of B -- 2.6 Physical Cylindrical Coordinates -- 2.7 The Grad-Shafranov Equation -- 2.8 Tokamak Ordering -- 2.9 Cylindrical Tokamak Equilibrium -- 2.10 Shafranov Shift in a Second Order Equilibrium -- 2.11 The Second Order Equilibrium Field -- 2.12 High Beta Equilibrium -- 2.13 Flux Conserving Equilibria -- 2.14 Equilibrium Scaling -- 2.15 Pfirsch Schlüter Currents -- 2.16 Plasma Rotation -- Problems -- References -- CHAPTER 3. GUIDING CENTER MOTION -- 3.1 Introduction -- 3.2 Hamiltonian Formulation of Guiding Center Motion -- 3.3 Particle Orbits -- 3.4 Integral Invariants -- 3.5 Toroidal Precession -- 3.6 Particle Orbits in a Tokamak -- 3.7 Diamagnetic Current -- 3.8 Confinement of Fusion Alpha Particles -- Problems -- References -- CHAPTER 4. LINEAR IDEAL MODES -- 4.1 Introduction -- 4.2 Plasma Kinetic and Potential Energy -- 4.3 Self Adjointness of the Potential Energy -- 4.4 The Energy Principle -- 4.5 A Convenient Form for δW -- 4.6 The Energy Principle in Cylindrical Geometry -- 4.7 MHD Instabilities in Low β Tokamaks -- 4.8 Kink Mode -- 4.9 The m = 1 External Kink -- 4.10 The Internal Kink Mode -- 4.11 Ballooning Instabilities -- 4.12 Magnetic Well. , 4.13 Ballooning Mode in a Shifted Circular Equilibrium -- 4.14 The Mercier and Suydam Criteria -- 4.15 Modification of the Ballooning Equation -- 4.16 Axisymmetric Modes -- 4.17 Numerical Determination of MHD Spectrum -- 4.18 Shape and Aspect Ratio Dependence -- Problems -- References -- CHAPTER 5. LINEAR RESISTIVE MODES -- 5.1 Introduction -- 5.2 The Tearing Mode -- 5.3 The m = 1 Tearing Mode -- 5.4 The Skin Current Profile -- 5.5 Toroidal and Shaping Effects -- 5.6 The Resistive Surface Kink Mode -- 5.7 Optimized Profiles -- 5.8 The Rippling Mode -- 5.9 The Resistive Interchange Mode -- 5.10 Resistive Ballooning -- 5.11 Diamagnetic Rotation -- Problems -- References -- CHAPTER 6. NONLINEAR BEHAVIOR -- 6.1 Introduction -- 6.2 The Reduced Equations -- 6.3 Nonlinear External Kink -- 6.4 Vacuum Bubbles -- 6.5 Nonlinear Internal Kink -- 6.6 Nonlinear Ballooning Modes -- 6.7 Complete Resistive Reconnection -- 6.8 Nonlinear Tearing Mode Analysis -- 6.9 Sawtooth Oscillations -- 6.10 Major Disruptions -- 6.11 Troyon Limit -- 6.12 Murakami Limit -- 6.13 Stabilization of Tearing Modes -- Problems -- References -- CHAPTER 7. HYBRID KINETIC - MHD MODES -- 7.1 Introduction -- 7.2 Resonant Particle Loss -- 7.3 Trapped Particle Destabilization of the Internal Kink -- 7.4 Trapped Particle Distribution Function -- 7.5 Mode Dispersion Relation -- 7.6 The Fishbone Cycle -- 7.7 Resistive Modifications -- 7.8 Destabilization of Ballooning Modes -- 7.9 Stabilization of the Sawtooth -- 7.10 Alpha Particle Effects -- Problems -- References -- CHAPTER 8. TRANSPORT -- 8.1 Introduction -- 8.2 The Drift Kinetic Equation -- 8.3 Cross Field Diffusion -- 8.4 Bootstrap Current -- 8.5 Ware Pinch -- 8.6 Magnetic Field Ripple Transport -- 8.7 Diffusion Due to Magnetic Perturbations -- 8.8 Diffusion in a Stochastic Field -- 8.9 Magnetic Island Induced Diffusion. , 8.10 Anomalous Transport -- 8.11 Confinement Scaling -- Problems -- References -- CHAPTER 9. PHASE INTEGRAL METHODS -- 9.1 Introduction -- 9.2 Connection Formulae -- 9.3 Attractive Potential Well -- 9.4 Potential Barrier -- 9.5 Boundary Conditions -- 9.6 Eigenvalue Problems -- Problems -- References -- INDEX.
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  • 2
    Electronic Resource
    Electronic Resource
    Alpha particle effects on the internal kink and fishbone modes (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 3369-3377 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870485
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  • 3
    Electronic Resource
    Electronic Resource
    Near threshold anomalous transport in the standard map (1998)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 8 (1998), S. 757-767 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Anomalous transport is investigated near threshold in the standard map. Very long time flights, and a large anomaly in the transport, are shown to be associated with a new form of multi-island structures causing orbit sticking. The phase space structure of these traps, and the exponents of the characteristic long time tails associated with them are determined. In general these structures are very complex, but some cases, consisting of layers of islands, allow simple modeling. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166361
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  • 4
    Electronic Resource
    Electronic Resource
    Gyrokinetic simulations in general geometry and applications to collisional damping of zonal flows : The 41st annual meeting of the division of plasma physics of the american physical society (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 1857-1862 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A fully three-dimensional gyrokinetic particle code using magnetic coordinates for general geometry has been developed and applied to the investigation of zonal flows dynamics in toroidal ion-temperature-gradient turbulence. Full torus simulation results support the important conclusion that turbulence-driven zonal flows significantly reduce the turbulent transport. Linear collisionless simulations for damping of an initial poloidal flow perturbation exhibit an asymptotic residual flow. The collisional damping of this residual causes the dependence of ion thermal transport on the ion–ion collision frequency, even in regimes where the instabilities are collisionless. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.874008
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  • 5
    Electronic Resource
    Electronic Resource
    Fusion performance analysis of plasmas with reversed magnetic shear in the Tokamak Fusion Test Reactor (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 3247-3262 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A case for substantial loss of fast ions degrading the performance of tokamak fusion test reactor plasmas [Phys. Plasmas 2, 2176 (1995)] with reversed magnetic shear (RS) is presented. The principal evidence is obtained from an experiment with short (40–70 ms) tritium beam pulses injected into deuterium beam heated RS plasmas [Phys. Rev. Lett. 82, 924 (1999)]. Modeling of this experiment indicates that up to 40% beam power is lost on a time scale much shorter than the beam–ion slowing down time. Critical parameters which connect modeling and experiment are: The total 14 MeV neutron emission, its radial profile, and the transverse stored energy. The fusion performance of some plasmas with internal transport barriers is further deteriorated by impurity accumulation in the plasma core. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873565
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  • 6
    Electronic Resource
    Electronic Resource
    Neoclassical simulations of fusion alpha particles in pellet charge exchange experiments on the Tokamak Fusion Test Reactor (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 2826-2833 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Neoclassical simulations of alpha particle density profiles in high fusion power plasmas on the Tokamak Fusion Test Reactor [Phys. Plasmas 5, 1577 (1998)] are found to be in good agreement with measurements of the alpha distribution function made with a sensitive active neutral particle diagnostic. The calculations are carried out in Hamiltonian magnetic coordinates with a fast, particle-following Monte Carlo code which includes the neoclassical transport processes, a recent first-principles model for stochastic ripple loss and collisional effects. New calculations show that monotonic shear alpha particles are virtually unaffected by toroidal field ripple. The calculations show that in reversed shear the confinement domain is not empty for trapped alphas at birth and allow an estimate of the actual alpha particle densities measured with the pellet charge exchange diagnostic. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873717
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  • 7
    Electronic Resource
    Electronic Resource
    Toroidal Alfvén eigenmodes in TFTR deuterium–tritium plasmas : The 39th annual meeting of division of plasma physics of APS (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 1703-1711 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872818
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  • 8
    Electronic Resource
    Electronic Resource
    Ripple-induced energetic particle loss in tokamaks (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 3043-3054 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The threshold for stochastic transport of high energy trapped particles in a tokamak due to toroidal field ripple is calculated by explicit construction of primary resonances, and a numerical examination of the route to chaos. Critical field ripple amplitude is determined for loss. The expression is given in magnetic coordinates and makes no assumptions regarding shape or up-down symmetry. An algorithm is developed including the effects of prompt axisymmetic orbit loss, ripple trapping, convective banana flow, and stochastic ripple loss, which gives accurate ripple loss predictions for representative Tokamak Fusion Test Reactor [R. Hawryluk, Plasma Phys. Controlled Fusion 33, 1509 (1991)] and International Thermonuclear Experimental Reactor [K. Tomabechi, Proceedings of the 12th International Conference on Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1989), Vol. 3, p. 214] equilibria. The algorithm is extended to include the effects of collisions and drag, allowing rapid estimation of alpha particle loss in tokamaks. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871641
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  • 9
    Electronic Resource
    Electronic Resource
    Energetic particle transport in compact quasi-axisymmetric stellarators (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 3509-3520 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Hamiltonian coordinate, guiding center code calculations of the confinement of suprathermal ions in quasi-axisymmetric stellarator (QAS) designs have been carried out to evaluate the attractiveness of compact configurations which are optimized for ballooning stability. A new stellarator particle following code is used to predict the confinement of thermal and neutral beam ions in a small experiment with R=145 cm, B=1–2 T and for alpha particles in a reactor size device. As for tokamaks, collisional pitch angle scattering drives ions into ripple wells and stochastic field regions, where they are quickly lost. In contrast, however, such losses are enhanced in QAS so that high edge poloidal flux has limited value in improving ion confinement. The necessity for reduced stellarator ripple fields is emphasized. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873611
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  • 10
    Electronic Resource
    Electronic Resource
    Effective temperatures, sawtooth mixing, and stochastic diffusion ripple loss of fast H+ minority ions driven by ion cyclotron heating in the Tokamak Fusion Test Reactor (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 2430-2436 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This paper presents studies of the H+ minority ions driven by Ion Cyclotron Radio Frequency (ICRF) heating in the Tokamak Fusion Test Reactor (TFTR) [R. J. Hawryluk et al., Phys. Plasmas 5, 1577 (1998)] deuterium plasmas using primarily passive H° flux detection in the energy range of 0.2–1.0 MeV. The measured passive H+ energy spectra are compared with active (Li pellet charge exchange) results. It is shown that in the passive mode the main donors for the neutralization of H+ ions in this energy range are C5+ ions. The measured effective H+ tail temperatures range from 0.15 MeV at an ICRF power of 2 MW to 0.35 MeV at 6 MW. Radial redistribution of ICRF-driven H+ ions was detected when giant sawtooth crashes occurred during the ICRF heating. The redistribution affected ions with energy below 0.7–0.8 MeV. The sawtooth crashes displaces H+ ions outward along the plasma major radius into the stochastic ripple diffusion domain where those ions are lost in ∼10 msec. These observations are consistent with the model of the redistribution of energetic particles developed previously to explain the results of deuterium-tritium (DT) alpha-particle redistribution due to sawtooth oscillations observed in TFTR. The experimental data are also consistent with numerical simulations of H+ stochastic ripple diffusion losses.© 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873539
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