Canonical Hamiltonian Guiding Center Dynamics and Its Intrinsic Magnetic Moment

The concept of guiding center is potent in astrophysics, space plasmas, fusion researches, and arc plasmas to solve the multi-scale dynamics of magnetized plasmas. In this letter, we rigorously prove that the guiding center dynamics can generally be described as a constrained canonical Hamiltonian system with two constraints in six dimensional phase space, and that the solution flow of the guiding center lies on a canonical symplectic sub-manifold. The guiding center can thus be modeled as a pseudo-particle with an intrinsic magnetic moment, which properly replaces the charged particle dynamics on time scales larger than the gyro-period. The complete dynamical behaviors, such as the velocity and force, of the guiding center pseudo-particle can be clearly deduced from the model. Furthermore, a series of related theories, such as symplectic numerical methods, the canonical gyro-kinetic theory, and canonical particle-in-cell algorithms can be systematically developed based on the canonical guiding center system. The canonical guiding center theory also provides an enlightenment for the origin of the intrinsic magnetic moment.