Coordinates for mapping the distribution of magnetically trapped particles

Dipole representations of the earth's magnetic field have been found to have insufficient accuracy for the study of magnetically trapped particles. A coordinate system consisting of the magnitude of the magnetic field B and the integral invariant I has been found to organize adequately measurements made at different geographic locations. The present paper shows that a parameter L = ƒ(B,I) can be defined that retains most of the desirable properties of I and that has the additional property of organizing measurements along lines of force. Since the parameter L is the analog of a physical distance in a dipole field (the equatorial radius of a magnetic shell), it is usually found to present fewer conceptual difficulties than the integral invariant I.