A study of the effectiveness of the McIlwain coordinates in estimating cosmic-ray vertical cutoff rigidities

Abstract

The classical vertical cutoff rigidity equation can be used with the McIlwain R, λm coordinates to include the effects of the eccentricity of the geomagnetic field. Using the equation R = L cos² λm cosmic-ray cutoffs can be expressed by Pc = KLγ where K and γ are evaluated by a least-squares fit of the vertical cutoff rigidities as determined by (a) Quenby and Wenk, (b) Makino, and (c) Shea, Smart, and McCracken. None of these data sets result in the intuitively expected equation Pc = 14.9L−2. The coefficients obtained range in value from 15.02 to 16.69 depending upon the data set considered, but in all cases the exponent is very near the expected value of −2. It is concluded that the McIlwain coordinates are highly correlated with vertical cutoff rigidities with the best correlation, Pc = 15.96L−2.005, being obtained using the Shea et al. trajectory-derived cutoff values. This equation can be used for estimates of vertical cosmic-ray cutoff rigidities on or above the earth's surface with the exception of points near the cosmic-ray equator.