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Physics of Plasmas / Volume 16 / Issue 4 / ARTICLES / Magnetically Confined Plasmas, Heating, Confinement

Phys. Plasmas 16, 042510 (2009); http://dx.doi.org/10.1063/1.3099055 (7 pages)

Variational symplectic algorithm for guiding center dynamics and its application in tokamak geometry

Hong Qin, Xiaoyin Guan, and William M. Tang

Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA

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(Received 20 January 2009; accepted 24 February 2009; published online 21 April 2009)

A variational symplectic integrator for the guiding center motion of charged particles in general magnetic fields is developed to enable accurate long-time simulation studies of magnetized plasmas. 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 variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure and globally bounds the numerical error in energy by a small number for all simulation time steps. Compared with standard integrators, such as the fourth order Runge–Kutta method, the variational symplectic integrator has superior numerical properties over long integration time. For example, in a two-dimensional tokamak geometry, the variational symplectic integrator is able to guarantee the accuracy for both the trapped and transit particle orbits for arbitrarily long simulation time. This is important for modern large-scale simulation studies of fusion plasmas where it is critical to use algorithms with long-term accuracy and fidelity. The variational symplectic integrator is expected to have a wide range of applications.

© 2009 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. VARIATIONAL SYMPLECTIC INTEGRATOR FOR THE GUIDING CENTER MOTION
  3. APPLICATIONS TO BANANA AND TRANSIT ORBITS IN 2D TOKAMAK GEOMETRY
  4. CONCLUSION AND FUTURE WORK

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KEYWORDS and PACS

Keywords

differential equations, iterative methods, plasma simulation, plasma toroidal confinement, Tokamak devices, variational techniques

PACS

  • 52.20.Dq

    Particle orbits

  • 52.55.Fa

    Tokamaks, spherical tokamaks

  • 52.25.Xz

    Magnetized plasmas

  • 52.65.Cc

    Particle orbit and trajectory

  • 02.60.Lj

    Ordinary and partial differential equations; boundary value problems

  • 02.30.Xx

    Calculus of variations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3099055

PUBLICATION DATA

ISSN

1070-664X (print)  
1089-7674 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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