The New Algorithm Describing the Drift of Charge in a Weakly Inhomogeneous Magnetic Field

In this work, we consider the motion of a charge on a plane in a weakly inhomogeneous magnetic field. The path can be found with a combination of rapid circular movements and a slow drift of the center of this circle. Drift is occurred due to heterogeneity and a Hamilton system in the plane. The Hamilton system matches with the magnetic field. There are also approximations to the main Hamilton function, which form a series in powers of a small parameter characterizing the inhomogeneity of the magnetic field. The First approximation is the sum of the famous "Berry connectivity" and an unknown term. With the new universal algorithm high-ordered approximations and unknown term can be found. The general algorithm which solves this type of problem with the adiabatic approximation allows to explore a wide range of issues from the field of both classical and quantum mechanics with a greater precision than before.