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Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere

 Jinxing Li, Hong Qin, Zuyin Pu, Lun Xie, and Suiyan Fu

Phys. Plasmas 18, 052902 (2011); doi:10.1063/1.3589275 (7 pages) 

Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately calculate the particles’orbits for an arbitrary long simulating time with good conservation property. When a time-independent convection and corotation electric field is considered, the VSI method can give the accurate single particle orbit, while the RK4 method gives an incorrect orbit due to its intrinsic error accumulation over a long integrating time.

A local noncircular equilibrium model and its application to residual zonal flow calculations

Deng Zhou1,2 and Weihong Yu1,2

1Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China
2Centre for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China

A local up-down symmetric tokamak equilibrium model is proposed. The model, with constant plasma shape parameters, is a special case of the more general Miller’s local model [R. L. Miller et al., Phys. Plasmas 5, 973 (1998)]. Correspondingly, the equilibrium is determined only by a given reference flux surface, the local safety factor, the local pressure profile, and the profile of local toroidal field function. Although it is not complete, the model is particularly suitable for analytically investigating the effect of plasma shape factors on the radially localized plasma modes, like reversed shear Alfvenic eigenmodes, ballooning mode, etc. As an example of the application, the residual zonal flow in a shaped plasma is evaluated, and the result is in qualitative agreement with the previous investigations

 

 

Ion orbit loss and pedestal width of H-mode tokamak plasmas in limiter geometry

Ion orbit loss and pedestal width of H-mode tokamak plasmas
in limiter geometry 

PHYSICS OF PLASMAS 18, 032504 2011

Xiaotao Xiao,, Lei Liu,  Xiaodong Zhang, and Shaojie Wang

A simple analytical model is proposed to analyze the effects of ion orbit loss on the edge radial
electric field in a tokamak with limiter configuration. The analytically predicted edge radial electric
field is consistent with the H-mode experiments, including the width, the magnitude, and the
well-like shape. This model provides an explanation to the H-mode pedestal structure. Scaling of the
pedestal width based on this model is proposed. © 2011 American Institute of Physics. 

A gyrokinetic collision operator for magnetized Lorentz plasmas

Chang Liu, Hong Qin, Chenhao Ma, and Xiongjie Yu 

Phys. Plasmas 18, 032502 (2011)

A gyrocenter collision operator for magnetized Lorentz plasmas is derived using the Fokker–Plank method. The gyrocenter collision operator consists of drift and diffusion terms in the gyrocenter coordinates, including the diffusion of the gyrocenter, which does not exist for the collision operator in the particle phase space coordinates. The gyrocenter collision operator also depends on the transverse electric field explicitly, which is crucial for the correct treatment of collisional effects and transport in the gyrocenter coordinates. The gyrocenter collision operator derived is applied to calculate the particle and heat transport fluxes in a magnetized Lorentz plasma with an electric field. The particle and heat transport fluxes calculated from our gyrocenter collision operator agree exactly with the classical Braginskii’s result [ S. I. Braginskii, Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1, p. 205 : P. Helander and D. J. Sigmar, Collisional Transport in Magnetized Plasmas (Cambridge University, Cambridge, 2002), p. 65 ], which validates the correctness of our collision operator. To calculate the transport fluxes correctly, it is necessary to apply the pullback transformation associated with gyrocenter coordinate transformation in the presence of collisions, which also serves as a practical algorithm for evaluating collisional particle and heat transport fluxes in the gyrocenter coordinates.

 

 

Relativistic collision operators for modeling noninductive current drive by waves

Y. J. Hu (胡友俊), Y. M. Hu (胡业民), and Y. R. Lin-Liu (林留玉仁)

 Phys. Plasmas 18, 022504 (2011)

A weakly relativistic Fokker–Planck operator for electron-electron collision was first used by Karney and Fisch to calculate the efficiencies of current drive by waves with fast phase velocity [ C. F. F. Karney and N. J. Fisch, Phys. Fluids 28, 116 (1985) ]. The present work extends Karney and Fisch’s work by expressing the weakly relativistic collision operator in potential form, and working out a general Legendre expansion of the potential functions. This general Legendre expansion reproduces the results in Karney and Fisch’s paper and is useful in implementing the weakly relativistic operator in Fokker–Planck codes. To justify the use of the weakly relativistic collision operator for current drive applications under ITER conditions, a comparison is made of current drive efficiencies predicted by this operator and a fully relativistic collision operator. Good agreement between efficiencies predicted by these two models is found. This suggests that the weakly relativistic collision operator is sufficiently precise for modeling the current drive schemes under ITER conditions