"The physical significance and application ofL,B₀, andR₀to geomagnetically trapped particles""

In a dipole field, many different invariant shells (I, Bm) share exactly the same lines of force. These invariant shells are therefore members of a degenerate system. In the geomagnetic field, which is assumed static and without electric field, these degenerate systems are split by azimuthal asymmetry. A distinction is made, therefore, between the use of parameters as invariants of charged particle motion (invariant representation) and their use as constants for all particles on a line of force (degenerate representation). We find that McIlwain's L value associates nondegenerate geomagnetic shells with dipole degenerate systems if L at a point in space is redefined to apply only to particles mirroring at that point. Emphasis is placed on the redefined L as an invariant parameter of particle motion and on the near equality of the L value of a particle and the equatorial radius R0 of the line of force on which the particle is mirroring. Although the original definition of L resulted in a very useful parameter, the present definition allows a physical interpretation of L as originally applied and extends its usefulness beyond that allowed by the original definition. With the present definition, the different values of L along a line of force can be identified with the radial separation of particles mirroring on that line as they drift in longitude. This separation is ≈2 per cent of the shell radius and represents the accuracy with which a single magnetic field parameter, such as the minimum field intensity B0 of a line, describes all particles on the line (a degenerate representation). Beyond 3 earth radii, it is found that R0 gives a representation of comparable accuracy. However, an invariant representation (L, Bm) or (I, Bm) is limited only by the accuracy of the determination of the mirror field Bm and the longitudinal invariant I, both of which depend on the accuracy of the magnetic field representation.