Geometric Phase of the Gyromotion for Charged Particles in a Time-dependent Magnetic Field
Authors: Jian Liu and Hong Qin
Abstract:
We study the dynamics of the gyrophase of a charged particle in a magnetic fi eld which is uniform in space
but changes slowly with time. As the magnetic fi eld evolves slowly with time, the changing of the gyrophase is
composed of two parts. The rst part is the dynamical phase, which is the time integral of the instantaneous
gyrofrequency. The second part, called geometric gyrophase, is more interesting, and it is an example of
the geometric phase which has found many important applications in different branches of physics. If the
magnetic fi eld returns to the initial value after a loop in the parameter space, then the geometric gyrophase
equals the solid angle spanned by the loop in the parameter space. This classical geometric gyrophase is
compared with the geometric phase (the Berry phase) of the spin wave function of an electron placed in the
same adiabatically changing magnetic fi eld. Even though gyromotion is not the classical counterpart of the
quantum spin, the similarities between the geometric phases of the two cases nevertheless reveal the similar
geometric nature of the different physics laws governing these two physics phenomena.
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Submitted to: Physics of Plasmas (March 2011)
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Download PPPL-4637 (pdf 176KB 7pp)
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