On the derivation of Dessler-Parker-Sckopke relation

We propose a simple derivation of the known Dessler-Parker-Sckopke (DPS) relation which connects the magnetic field produced by the ring current with the kinetic energy of its particles. We start from the distribution function of particles which depends on the integrals of motion in an axially-symmetric magnetic field and calculate the corresponding moments (current and kinetic energy). Unlike the derivation of the DPS relation given in the pioneer works, the approach proposed here is more straightforward and is based on the first principles.