Muon Spectra, Expected Characteristics of Inclined Muon Monitors by Means of Generating Functions and an Analysis of the Diurnal Variation at Kiruna

Abstract

Successive generations in the nucleon-meson cascade are calculated by means of generating functions. Expected muon spectra at different zenith angles and levels are in excellent agreement with measurements in the 0.2-50 GeV/c momentum range. A functional relation between the absolute value and slope of the primary spectrum and the inelasticity is established. On the average 1.6 intranuclear collisions in an air nucleus are taken into account. The calculated electron and positron content in an unshielded inclined muon telescope is 30%, with 100% detector efficiency. Coupling functions taking into account up to seven generations in the cascade, allowing for the primary composition are calculated. Expected time variations from anisotropies of different angular distributions in inclined meson telescopes at a high latitude station are given. Time characteristics such as expected times of maxima, phase differences and amplitude ratios for the north and south directed telescopes at Kiruna are computed for a variational spectrum of the form Pβ cos Λ, where Λ is the angle between the asymptotic direction and the axis of the anisotropy. The reduction in amplitude due to three dimensional cascading is only 0.4-0.4+2.0%. A peculiar and persistent phase shift in the Kiruna north directed telescope is interpreted as being due to Forbush decreases and temperature effects. The yearly difference vector of the two telescopes over nearly one solar cycle has been analysed. Based on a variational spectrum with β = 0.0 and selected values of the free space amplitude, the phase and upper cut-off Pu of the anisotropy are derived. The variation of Pu with time shows a pronounced solar cycle dependence.