  It is pointed out that the three established adiabatic invariants are
separating invariants in the sense of Liouville. It is widely claimed that no
more than three adiabatic invariants can exist for the motion of a point
charge. However, additional independent (not separating) adiabatic invariants
do exist. For a force free motion, the components of angular momentum provide
two additional constants of motion. This result can be generalized to the
Hamilton Jacobi equation. The number of independent constants of motion is
reduced if there is a global symmetry. For a gyrating particle, neglecting a
gyro helix type of invariant, four 'useful' invariants could exist. A radial
drift invariant, corresponding to the average of the radial coordinate of the
particle, is a constant of motion for a confined gyrating particle. For the
special case of a screw pinch where each gyro center moves on a magnetic flux
surface without mirror trapping, the radial drift invariant is the radial
coordinate of the gyro center. For a screw pinch, the set of constants of
motion consising of the energy, parallel velocity and radial drift invariant is
convenient to model the equilibrium. Local Maxwellian distribution functions
expressed in this set of invariants are demonstrated to provide MHD-type of
equilibria, for which it is straightforward to model the radial profiles of the
particle and field components.
