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Author(s):
S. Satake, H. Sugama, M. Okamoto and M. Wakatani
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Title:
Classification of Particle Orbits near the Magnetic Axis in a Tokamak by Using Constants of Motion
Date of publication:
Jan. 2001
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Key words:
particle orbit, neoclassical transport theory
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Abstract:
A classification of particle orbits near the magnetic axis in a tokamak is presented in a space of constants of motion (COM), which is important to apply Lagrangian formulation of neoclassical transport theory to the region near the axis. Orbit types are distinguished by the number of the turning points of sigma_parallel=upsilon_parallel/|upsilon_parallel| and sigma_theta=dot{theta}/|dot{theta}| on each orbit, where upsilon__parallel is the velocity parallel to the magnetic field, and dot {theta} is the poloidal angular velocity. As a set of COM, (varepsilon, mu, <gamma> ) is taken, where varepsilon is the energy of a particle, mu is the magnetic moment, and < gamma> is the bounce-averaged minor radius position of a particle orbit. Compared with a familiar set of COM (upsilon, mu_s, gamma_s) where upsilon is the particle velocity, gamma_s is the minor radius at which an orbit crosses the mid- plane, and xi_s=upsilon_ parallel/upsilon evaluated at the crossing point, the set of COM (varepsilon, mu, <gamma>) is more suitable in practice for Lagrangian formulation of neoclassical transport theory, in which the particle diffusion is described by the change of average posirion of particles <gamma> by collisions. Near the magnetic axis, it is found that there are overlaps in ragions of orbit types in the (varepsilon, mu, <gamma>) space and that <gamma>has a minimum value for given varepsilon.
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