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Sugama, H.; Nishimura, S.

National Inst. for Fusion Science, Toki, Gifu (Japan)

National Inst. for Fusion Science, Toki, Gifu (Japan)

AbstractAbstract

[en] A detailed comparison is made between moment-equation methods presented by Sugama and Nishimura and by Taguchi for calculating neoclassical transport coefficients in general toroidal plasmas including nonsymmetric systems. It is shown that these methods can be derived from the drift kinetic equation with the same collision model used for correctly taking account of collisional momentum conservation. In both methods, the Laguerre polynomials of the energy variable are employed to expand the guiding-center distribution function and to obtain the moment equations, by which the radial neoclassical transport fluxes and the parallel flows are related to the thermodynamic forces. The methods are given here in the forms applicable for an arbitrary truncation number of the Laguerre-polynomial expansion so that their accuracies can be improved by increasing the truncation number. Differences between results from the two methods appear when the Laguerre-polynomial expansion is truncated up to a finite order because different weight functions are used in them to derive the moment equations. At each order of the truncation, the neoclassical transport coefficients obtained from the Sugama-Nishimura method show the Onsager symmetry and satisfy the ambipolar-diffusion condition intrinsically for symmetric systems. Also, numerical examples are given to show how the transport coefficients converge with the truncation number increased for the two methods. (author)

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Jan 2008; 14 p; 33 refs., 2 figs.

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ANNULAR SPACE, APPROXIMATIONS, BOLTZMANN-VLASOV EQUATION, CALCULATION METHODS, CHARGED-PARTICLE TRANSPORT THEORY, CLOSED CONFIGURATIONS, CONFIGURATION, DIFFERENTIAL EQUATIONS, DIFFUSION, EQUATIONS, FUNCTIONS, MAGNETIC FIELD CONFIGURATIONS, MATHEMATICAL SOLUTIONS, PARTIAL DIFFERENTIAL EQUATIONS, POLYNOMIALS, SPACE, TRANSPORT THEORY, TRAPPING

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Sugama, H.; Horton, W.

National Inst. for Fusion Science, Nagoya (Japan)

National Inst. for Fusion Science, Nagoya (Japan)

AbstractAbstract

[en] Entropy production and Onsager symmetry in neoclassical transport processes of magnetically confined plasmas are studied in detail for general toroidal systems including nonaxisymmetric configurations. We find that the flux surface average of the entropy production defined from the linearized collision operator and the gyroangle-averaged distribution function coincides with the sum of the inner products of the thermodynamic forces and the conjugate fluxes consisting of the Pfirsch-Schlueter, banana-plateau, nonaxisymmetric parts of the neoclassical radial fluxes and the parallel current. We prove from the self-adjointness of the linearized collision operator that the Onsager symmetry is robustly valid for the neoclassical transport equations in the cases of general toroidal plasmas consisting of electrons and multi-species ions with arbitrary collision frequencies. It is shown that the Onsager symmetry holds whether or not the ambipolarity condition is used to reduce the number of the conjugate pairs of the transport fluxes and the thermodynamic forces. We also derive the full transport coefficients for the banana-plateau and nonaxisymmetric parts, separately, and investigate their symmetry properties. The nonaxisymmetric transport equations are obtained for arbitrary collision frequencies in the Pfirsch-Schlueter and plateau regimes, and it is directly confirmed that the total banana-plateau and nonaxisymmetric transport equations satisfy the Onsager symmetry. (author)

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Jul 1995; 44 p

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AbstractAbstract

[en] In a previously formulated full neoclassical transport matrix for general non-symmetric toroidal plasmas, full neoclassical characteristics of magnetic configurations are described by the three mono-energetic viscosity coefficients M (parallel viscosity against flows), N (driving force for bootstrap currents), and L (radial diffusion)[1]. In this paper, we discuss methods to derive analytical expressions for these mono-energetic coefficients. Although this previous formulation has been applied to some recently designed devices [2] to date, these applications were based on a direct numerical calculation of the linearized drift kinetic equation(LDKE)[3]. For the calculations requiring many iterative processes such as configuration optimization studies and the equilibrium calculations including the

^{s}elfconsistent bootstrap currents^{,}however, the analytical expressions are indispensable. We mainly discuss here about the some improvements to previous analytical theories on the driving force for the bootstrap currents (N) in collisionless regimes. The treatment of the parallel viscosity against the flows (M) in general non-symmetric toroidal plasmas in general collisionality range is basically identical to that in symmetric plasmas [4,5], and we have already showed in Ref.[1] the asymptotic expressions of M in all collisionality ranges. Therefore this coefficient is basically out of scope of this paper. However, we should note here that, even in symmetric plasmas such as tokamaks, LDKE including full parts of the linearized Vlasov and collision operators could not be solved analytically. The parallel viscosity is derived using banana-, plateau-, and Pfirsch-Schlueter- asymptotic expansions of LDKE [4,6] in which some parts of the linearized Vlasov and collision operators are treated as higher order effects. Since such results are valid for limited collision frequency ranges, appropriate interregimes connection formulas were used [4,5]. In addition to this basic difficulty [6], some complexities of N and L in non-symmetric toroidal plasmas are caused by a co-existence of various types of trapped orbits and their complex radial drifts. The large perturbation due to the bounce averaged motion of the ripple trapped particles must be treated another specific analytical method [7,8]. To approximately reproduce the direct numerical solution obtained from the LDKE including the full parts of the linearized Vlasov and the pitch-angle-scattering (PAS) operators [1], we have to decompose this radial drift into appropriate few components. The formulation in Ref. [1] enables us to derive the viscosity coefficients only from the solution of the LDKE without the field particle collision tem. This method will be useful also in deriving analytical expressions for N, L. Another essential difficulty in non-symmetric toroidal plasmas is a fact that we cannot express analytically the full parts of the perturbation in the collisionless banana (or 1/ v) regime. (Author)Primary Subject

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166 p; ISBN 84-7834-513-2; ; 2005; 6 p; Editorial CIEMAT; Madrid (Spain); International Stellerator Workshop; Madrid (Spain); 3-7 Oct 2005

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Sugama, H.; Horton, W.

National Inst. for Fusion Science, Nagoya (Japan)

National Inst. for Fusion Science, Nagoya (Japan)

AbstractAbstract

[en] Neoclassical transport processes of electrons and ions are investigated in detail for toroidally rotating axisymmetric plasmas with large flow velocities on the order of the ion thermal speed. The Onsager relations for the flow-dependent neoclassical transport coefficients are derived from the symmetry properties of the drift kinetic equation with the self-adjoint collision operator. The complete neoclassical transport matrix with the Onsager symmetry is obtained for the rotating plasma consisting of electrons and single-species ions in the Pfirsch-Schlueter and banana regimes. It is found that the inward banana fluxes of particles and toroidal momentum are driven by the parallel electric field, which are phenomena coupled through the Onsager symmetric off-diagonal coefficients to the parallel currents caused by the pressure gradient and by the flow shear, respectively. (author)

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Jan 1997; 32 p

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Sugama, H.; Horton, W.

National Inst. for Fusion Science, Nagoya (Japan)

National Inst. for Fusion Science, Nagoya (Japan)

AbstractAbstract

[en] We present a dynamical model for the L-H transition consisting of three ordinary differential equations. This model describes temporal evolutions of three characteristic variables, i.e., the free energy contained in the pressure gradient, the turbulent kinetic energy and the shear flow energy in the resistive pressure-gradient-driven turbulence. The model equations have stationary solutions corresponding to the L and H-modes and their stabilities depend on the energy input to the peripheral region. Changing the energy input parameter yields the L to H and H to L transitions. We also find the parameter region in which the H-mode stationary solution becomes unstable and bifurcate to the limit cycle which shows periodic oscillations like ELM. It depends on the viscosity for the shear flow which the type of the L-H transition is, a first-order or second-order transition. (author)

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Aug 1994; 19 p; IAEA-CN--60/D-P-I-11

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Sugama, H.; Nishimura, S.

National Inst. for Fusion Science, Toki, Gifu (Japan)

National Inst. for Fusion Science, Toki, Gifu (Japan)

AbstractAbstract

[en] A novel method to obtain the full neoclassical transport matrix for general toroidal plasmas by using the solution of the linearized drift kinetic equation with the pitch-angle-scattering collision operator is shown. In this method, the neoclassical coefficients for both poloidal and toroidal viscosities in toroidal helical systems can be obtained, and the neoclassical transport coefficients for the radial particle and heat fluxes and the bootstrap current with the non-diagonal coupling between unlike-species particles are derived from combining the viscosity-flow relations, the friction-flow relations, and the parallel momentum balance equations. Since the collisional momentum conservation is properly retained, the well-known intrinsic ambipolar condition of the neoclassical particle fluxes in symmetric systems is recovered. Thus, these resultant neoclassical diffusion and viscosity coefficients are applicable to evaluating accurately how the neoclassical transport in quasi-symmetric toroidal systems deviates from that in exactly-symmetric systems. (author)

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May 2002; 32 p; 40 refs., 5 figs.

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Sugama, H.; Horton, W.

National Inst. for Fusion Science, Nagoya (Japan)

National Inst. for Fusion Science, Nagoya (Japan)

AbstractAbstract

[en] Neoclassical and anomalous transport fluxes are determined for axisymmetric toroidal plasmas with weak electrostatic fluctuations. The neoclassical and anomalous fluxes are defined based on the ensemble-averaged kinetic equation with the statistically averaged nonlinear term. The anomalous forces derived from that quasilinear term induce the anomalous particle and heat fluxes. The neoclassical banana-plateau particle and heat fluxes and the bootstrap current are also affected by the fluctuations through the parallel anomalous forces and the modified parallel viscosities. The quasilinear term, the anomalous forces, and the anomalous particle and heat fluxes are evaluated from the fluctuating part of the drift kinetic equation. The averaged drift kinetic equation with the quasilinear term is solved for the plateau regime to derive the parallel viscosities modified by the fluctuations. The entropy production rate due to the anomalous transport processes is formulated and used to identify conjugate pairs of the anomalous fluxes and forces, which are connected by the matrix with the Onsager symmetry. (author)

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May 1995; 56 p

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Sugama, H.; Horton, W.

National Inst. for Fusion Science, Nagoya (Japan)

National Inst. for Fusion Science, Nagoya (Japan)

AbstractAbstract

[en] Transport processes and resultant entropy production in magnetically confined plasmas are studied in detail for toroidally rotating systems with electrostatic turbulence. A new gyrokinetic equation is derived for rotating plasmas with large flow velocities on the order of the ion thermal speed. Neoclassical and anomalous transport of particles, energy, and toroidal momentum are systematically formulated from the ensemble-averaged kinetic equation with the gyrokinetic equation. As a conjugate pair of the thermodynamic force and the transport flux, the shear of the toroidal flow, which is caused by the radial electric field shear, and the toroidal viscosity enter both the neoclassical and anomalous entropy production. The interaction between the fluctuations and the sheared toroidal flow is self-consistently described by the gyrokinetic equation containing the flow shear as the thermodynamic force and by the toroidal momentum balance equation including the anomalous viscosity. Effects of the toroidal flow shear on the toroidal ion temperature gradient driven modes are investigated. Linear and quasilinear analyses of the modes show that the toroidal flow shear decreases the growth rates and reduces the anomalous toroidal viscosity. (author)

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Aug 1996; 42 p

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Sugama, H.; Watanabe, T.-H.

National Inst. for Fusion Science, Toki, Gifu (Japan)

National Inst. for Fusion Science, Toki, Gifu (Japan)

AbstractAbstract

[en] Collisionless time evolution of zonal flows in helical systems are investigated. An analytical expression describing the collisionless response of the zonal-flow potential to the initial potential and a given turbulence source is derived from the gyrokinetic equations combined with the quasineutrality condition. The dispersion relation for the geodesic acoustic mode (GAM) in helical systems is derived from the short-time response kernel for the zonal-flow potential. It is found that helical ripples in the magnetic field strength as well as finite orbit widths of passing ions enhance the GAM damping. The radial drift motions of particles trapped in helical ripples cause the residual zonal-flow level in the collisionless long-time limit to be lower for longer radial wave lengths and deeper helical ripples. On the other hand, a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport. The validity of our analytical results is verified by gyrokinetic Vlasov simulation. (author)

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Sep 2005; 19 p; 22 refs., 4 figs.

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ANALYTICAL SOLUTION, CHARGED-PARTICLE TRANSPORT, CLOSED PLASMA DEVICES, DISPERSION RELATIONS, HELICAL CONFIGURATION, KINETIC EQUATIONS, LANDAU DAMPING, MAGNETIC CONFINEMENT, MAGNETOHYDRODYNAMICS, NEOCLASSICAL TRANSPORT THEORY, PLASMA, PLASMA DRIFT, TRAPPED-PARTICLE INSTABILITY, TURBULENCE, VORTEX FLOW

CHARGED-PARTICLE TRANSPORT THEORY, CONFIGURATION, CONFINEMENT, DAMPING, EQUATIONS, FLUID FLOW, FLUID MECHANICS, HYDRODYNAMICS, INSTABILITY, MATHEMATICAL SOLUTIONS, MECHANICS, PLASMA CONFINEMENT, PLASMA INSTABILITY, PLASMA MACROINSTABILITIES, RADIATION TRANSPORT, THERMONUCLEAR DEVICES, TRANSPORT THEORY

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Sugama, H.; Okamoto, M.; Wakatani, M.

National Inst. for Fusion Science, Nagoya (Japan)

National Inst. for Fusion Science, Nagoya (Japan)

AbstractAbstract

[en] A K

_{ε}anomalous transport model for resistive interchange turbulence is presented and applied to the transport analysis of ECH plasmas in Heliotron E. In this model, the turbulent kinetic energy K ≅ 1/2<υ tilde^{2}> and its viscous dissipation rate ε characterize the local turbulence and the anomalous transport coefficient is given by D ∼ K^{2}/ε, which has some nonlocal properties not included in the conventional expressions since their temporal and spatial variations are determined by taking into account the transport of the turbulent energy itself. In the case of the homogeneous turbulence where the anomalous transport may be described in terms of the local plasma parameters, the dimensional analysis applied to our model yields the two types of local parameter expressions of the anomalous diffusivity in the high and low collisional cases. We find a familiar diffusivity for the resistive interchange turbulence derived in the high collisional case and we have another one similar to the gyro-reduced Bohm (GRB) diffusivity in the low collisional case. However, it is shown from the transport simulation using our model that, in the region where the turbulence inhomogeneity is significant, the anomalous diffusivity deviates from the local parameter expression due to the transport terms in the K_{ε}equations. Our model explains the experimental results consistently in that it gives the GRB or LHD scaling for the energy confinement time and reproduces the experimentally obtained profile of the anomalous diffusivity which has large values in the peripheral region in contrast with the GRB model. (author)Primary Subject

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Sep 1992; 17 p; 14. international conference on plasma physics and controlled nuclear fusion research; Wuerzburg (Germany); 30 Sep - 7 Oct 1992; IAEA-CN--56/D-4-20

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