# Plasma and Fusion Research

## Volume 3, 057 (2008)

# Regular Articles

- Japan Atomic Energy Agency, Naka, Ibaraki, 311-0193 Japan

### Abstract

The conjugate variable method, an essential ingredient in the path-integral formalism of classical statistical dynamics, is used to apply the Hamilton-Lie perturbation theory to a system of ordinary differential equations that does not have the Hamiltonian dynamic structure. The method endows the system with this structure by doubling the unknown variables; hence, the canonical Hamilton-Lie perturbation theory becomes applicable to the system. The method is applied to two classical problems of plasma physics to demonstrate its effectiveness and study its properties: a non-linear oscillator that can explode and the guiding center motion of a charged particle in a magnetic field.

### Keywords

one-form, Hamilton-Lie perturbation method, conjugate variable, non-linear oscillator, guiding center motion, plasma physics

### Full Text

### References

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This paper may be cited as follows:

Shinji TOKUDA, Plasma Fusion Res. 3, 057 (2008).