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A Study Of The Guiding Center Approximation, Qun Yao

Dissertations, Theses, and Masters Projects

A Hamiltonian treatment for the motion of a charged particle in a toroidal magnetic field is given. Assuming the plasma equilibrium, Boozer coordinates are used. The Hamiltonian of the exact trajectory is given in the guiding center coordinates. The higher order corrections to the standard drift Hamiltonian are derived. It is shown that the exact Hamiltonian depends on both the field strength and the shape of the magnetic surfaces (the metric of Boozer coordinates) while the standard drift Hamiltonian depends only on the field strength. The first order correction to the standard drift Hamiltonian, in gyroradius to system size, depends …