Home » Publications

Category Archives: Publications

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



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


Hong Qin1,2 and Ronald C. Davidson2

1Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA  
2Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

The Courant–Snyder (CS) theory and the Kapchinskij–Vladimirskij (KV) distribution for high-intensity beams in an uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are noncommutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation and reduces beam pulsation.

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.



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

Xiaotao Xiao and Shaojie Wang

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

Lei Qi and Shaojie Wang

Phys. Plasmas 16, 062504 (2009)

A previous gauge-invariant gyrokinetic equation based on an approximate canonical Hamiltonian coordinate system is extended to an exact canonical Hamiltonian coordinate system with the time scale well separated. By using this formalism a new orbit-averaged gyrokinetic equation, which is valid for both trapped and passing particles, is established.

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

Jinhong Yang, Qingquan Yu, Sizheng Zhu, and G. Zhuang

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

The electron temperature difference between the o-point and the x-point of a magnetic island is studied numerically by solving the two-dimensional energy transport equation. It is found that, even without a localized radio-frequency heating at the island’s o-point, there is usually a temperature difference between these two points. This difference depends on the radial profile of the heating power deposition, the ratio between the parallel and the perpendicular heat conductivity and the island width, and it takes a minimum when the island width is about twice the local heat diffusion layer width. The effect of the temperature difference on the island growth is further studied, and the peaked heating power density profile at magnetic axis is found be destabilizing.