Dynamics of radiation belts of the Earth has both theoretical and practical importance, due to numerous spacecraft around the Earth. A special type of dynamics, called drift-shell bifurcation, occurs in the outer radiation belts. This phenomenon provides a new mechanism for the diffusion of particles in radiation belts, and for metastable trapping in the magnetosphere. This monograph begins with an overview of plasma dynamics in the magnetosphere, followed by a description of basic properties of drift-shell bifurcation using test-particle simulations in model magnetospheres. The text presents a review of separatrix-crossing theory and of asymptotic analysis of the second Painleve equation. This theoretical framework is then applied to the problem of drift-shell bifurcation to analyze the changes in the dynamical variables. This book is aimed at graduate students and researchers in the field of space science and plasma physics.