Canonical Hamiltonian Guiding Center Dynamics and Its Intrinsic Magnetic Moment
arxiv(2024)
摘要
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.
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