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## Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere

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

**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

^{1}Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China

^{2}Centre 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

## Electron shielding current in neutral beam current drive in general tokamak equilibria and arbitrary collisionality regime

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

Phys. Plasmas 19, 034505 (2012)

Abstract: A formula based on the solutions to the drift kinetic equation is proposed for modeling the trapped electron correction to the electron shielding current in neutral beam current drive in general tokamak equilibria and arbitrary collisionality regime

## Generalized Courant–Snyder theory and Kapchinskij–Vladimirskij distribution for high-intensity beams in a coupled transverse foc

Generalized Courant–Snyder theory and Kapchinskij–Vladimirskij distribution for high-intensity beams in a coupled transverse focusing lattice

## 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

, , , and

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.

## Gyrocenter-gauge kinetic algorithm for high frequency waves in magnetized plasmas

Zhi Yu and Hong Qin

Phys. Plasmas **16**, 032507 (2009)

A kinetic simulation algorithm for high-frequency electromagnetic waves has been developed based on the gyrocenter-gauge kinetic theory. The magnetized plasma system is simulated in the gyrocenter coordinate system. The gyrocenter distribution function F is sampled on the gyrocenter, parallel velocity, and magnetic moment coordinates. The gyrocenter-gauge function S is sampled on the Kruskal rings and shares the first five coordinates with F. The moment integral of pullback transformation is directly calculated using the Monte Carlo method and an explicit difference scheme for Maxwell’s equations in terms of potentials is adopted. The new algorithm has been successfully applied to the simulation studies of high frequency extraordinary wave, electron Bernstein wave, and the mode conversion process between the extraordinary wave and the electron Bernstein wave in inhomogeneous plasmas

## Explicit Runge–Kutta integrator with Hamiltonian correction for long-time simulations of guiding-center orbit in tokamak configu

Phys. Plasmas **15**, 122511 (2008) | Cited 2 times

Hamiltonian correction method is proposed to improve the variable time-step fourth-order Runge–Kutta methods in computing guiding-center orbits in a tokamak. It is found that the new method can significantly improve the computation efficiency of the conventional Runge–Kutta method in simulation of the long-time behavior of the guiding-center orbits

## Gyrokinetic equation in an exact canonical Hamiltonian coordinate system and its orbit-averaged form

Phys. Plasmas **16**, 062504 (2009)

## Electron temperature difference between the o-point and x-point of a magnetic island

Phys. Plasmas **16**, 092308 (2009) | Cited 1 times