About the third integral of charged particle motion in strongly curved magnetic fields

Charged particle motion is studied in magnetic fields with an inversion of field direction and a strong curvature in the reversal region, that means field structures which are expected to play a crucial role in energetics and dynamics of space plasma. Investigations are performed in a typical field model. Due to its symmetry and stationarity two of the integrals of motion of the resulting Hamiltonian immediately arise. The question is analyzed whether the system is integrable (this means regular solutions exist) and of what kind the third integral is. Two different third integrals are found, which are valid in different parts of the phase space. Their validity is estimated analytically for particles, crossing the neutral plane (z = 0) -- in addition the action integral I_z previously unusual in plasma applications is verified numerically. Further numerical research establishes that there are no more third integrals -- all remaining parts of the phase space are filled with chaotic solutions. Because in strongly curved field reversals the conservation of the magnetic moment as an integral of motion is shown to be restricted to very small energies or very large pitch angles, the unusual I_z-integral will be an important tool for solution of plasma problems of cosmical current sheets and plasma boundaries.