Numerical Analyses of Particle Orbits:
Comparison of Drift Equation and Equation of Motion

Shun-ichi Oikawa, Yutaka Matsumoto, Masahito Hishiki, Masafumi Itagaki, Tsuguhiro Watanabe1)

Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
1)National Institute for Fusion Science, Toki, Gifu 509-5922, Japan

Particle orbits calculated by the standard drift equation and the exact equation of motion have been compared. The particle orbits of the high energy alpha particles produced by a nuclear fusion reaction in the Large Helical Device (LHD) with the magnetic axis Rax=3.6 mare traced for 20 msec. It was shown that the total loss fractions of alpha particles in the LHD calculated by both equations are almost the same irrespective of their pitch angles. The lost particles in this study are defined as those which reach the vacuum vessel walls.It was also shown that the deviation of the alpha particle orbit calculated by using the drift equation from that by the equation of motion is as large as several centimeters in a few micro second. In order to compare the two orbits appropriately, the instantaneous position, rG(t) of the gyration center was calculated from the instantaneous particle position, r(t), and the magnetic field, B(r) as rG(t) = r(t) + v(t)×b{r)/ω(r). Here the unit vector b(r) is along the magnetic field direction and ω is the cyclotron frequency of the alpha particle. From the viewpoint of plasma confinement, the deviation of the orbit for particles with pitch angles close to π/2 is most important, since the deviation is mainly across the magnetic field. In the case of other pitch angles, the deviation is mainly along the field line. It is pointed out that the approximation that b · ∇ b ≈ -eR / R for the curvature drift does not hold, especially in helical devices such as the LHD.