Asymptotic cones of acceptance and their use in the study of the daily Variation of cosmic radiation

The dependence of the counting rate of a cosmic ray detector on the asymptotic directions of approach of the primary cosmic radiation is discussed. By means of a simulation of the geomagnetic field that uses spherical harmonics up to the sixth degree, and an arbitrary anisotropy in the primary cosmic radiation, a method for calculating the time variations in the counting rate of a cosmic ray detector is developed. Resolving the arbitrary anisotropy as a Fourier series in longitude, the amplitude and phases of the diurnal (24-hourly) and semidiurnal (12-hourly) components of the daily variation are calculated for a number of stations. No simple relationship is observed between the phases and the latitudes and longitudes, geographic or geomagnetic. Moreover, the theoretical calculations point out that a difference of more than five hours between the diurnal phases at two different places could arise purely from the known geomagnetic configuration. A study of the time-averaged diurnal component of the daily variation experimentally observed by 22 neutron monitors during the International Geophysical Year (1957-1958) reveals good agreement with the theoretical calculations and leads to the following conclusions: (1) The results are consistent with an anisotropy that is independent of rigidity in the range 1-200 bv, the exponent of the power law which fits the data being 0.0 ± 0,05. (2) The anisotropy varies as the cosine of the asymptotic latitude and has a maximum in the direction 85° to the east of the earth-sun line. (3) The maximum amplitude of the average anisotropy is 4 × 10<SUP>−3</SUP> times the average cosmic ray flux