Contribution to the expression of particle movement in magnetic mirror systems in cyclic variables

The aim of this paper is to express the Hamiltonian function of a particle in a static, axially symmetric magnetic field in convenient variables. Assuming adiabaticity (the relative change of the magnetic field during one cyclotron revolution can be neglected), the Hamiltonian function is determined with cyclicity in two degrees of freedom.For the determination of the Hamiltonian function either the Carthesian, or the orthogonal curvilinear system was used as a starting coordinate system. The latter consists of a natural system of lines of force and equipotentials of the field. In both cases a Hamiltonian function of the formH=H(P₁ P ₂,P ₃,Q ₃) is obtained, where P_i are generalized impulses and Q₃ longitudinal coordinates.The form of the Hamiltonian function is very simple; it facilitates appreciably the integration of the equations of motion and provides simple expressions for the integrals of motion.The author wishes to express his thanks to Ing. J. Váa, the Director of the Institute, for his interest in the work and to Dr. M. Scidl for encouragement.