[Table of Contents]

Plasma and Fusion Research

Volume 5, S1048 (2010)

Regular Articles

Algebraic Analysis Approach for Multibody Problems II
Shun-ichi OIKAWA, Koichiro HIGASHI and Hideo FUNASAKA
Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
(Received 6 January 2009 / Accepted 8 June 2009 / Published 26 March 2010)


The algebraic model (ALG) proposed by the authors has sufficiently high accuracy in calculating the motion of a test particle with all the field particles at rest. When all the field particles are moving, however, the ALG has relatively poor prediction ability on the motion of the test particle initially at rest. None the less, the ALG approximation gives a good results for the statistical quantities, such as variance of velocity changes or the scattering cross section, for a sufficiently large number of Monte Carlo trials. For a 108-body problem, which corresponds to full three-dimensional Coulomb interactions within the Debye sphere in a fusion plasma, the ALG approximation is 263 times as fast as the 6-stage 5-th order Runge-Kutta-Fehlberg method with an absolute error tolerance of 10−16.


multibody problem, algebraic approximation, binary interaction approximation, direct integration method

DOI: 10.1585/pfr.5.S1048


  • [1] A. W. Appel, SIAM J. Sci. Stat. Comput. 6, 85 (1985).
  • [2] J. E. Barnes and P. Hutt, Nature 324, 446 (1986).
  • [3] P. P. Brieu, F. J. Summers and J. P. Ostriker, APJ 453, 566 (1995).
  • [4] J. Makino and M. Taiji, APJ 480, 432 (1997).
  • [5] S. Oikawa and H. Funasaka, Plasma Fusion Res. 3, S1073 (2008).
  • [6] S. Oikawa, H. Funasaka, K. Higashi and Y. Kitagawa, Binary Interaction Approximation to N-Body Problems, to be appeared in Plasma Fusion Res. 4 (2009).
  • [7] E. Fehlberg, NASA Technical Report 315 (1969).
  • [8] E. Fehlberg, Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Warmeleitungsprobleme, Computing (Arch. Elektron. Rechnen), vol. 6, (1970) pp. 61-71.
  • [9] R. S. Cohen, L. Spitzer, Jr., and P. McR. Routly, Phys. Rev. 80, 230 (1950).
  • [10] W. M. Stacey, Jr., FUSION PLASMA ANALYSIS, (Krieger, Malabar, 1992).

This paper may be cited as follows:

Shun-ichi OIKAWA, Koichiro HIGASHI and Hideo FUNASAKA, Plasma Fusion Res. 5, S1048 (2010).