New Index Characterizing Magnetic Field Turbulence in Relation to the Galactic Cosmic Ray Intensity Variation in the Period 1968 – 2023

Data on the \(B_{y}\) and \(B_{z}\) components of the heliospheric magnetic field (HMF) were used to study the relationships between the Power Spectral Density (PSD) (\(PSD\propto f^{-\nu } \), \(f\) is the frequency) of HMF turbulence and the rigidity spectrum variation (RSV) of the galactic cosmic ray (GCR) intensity (\(\delta D(R)/D(R) \propto R^{- \gamma } \)). A new common exponent \(\nu _{yz}\) was constructed to account for the contributions of both the \(B_{y}\) and \(B_{z}\) components of the HMF. The period from 1969 to 2022 was considered, divided into five subperiods based on the global solar magnetic field (GSMF) polarities: i) 1969 – 1979 (\(A>0\)) (positive polarity—magnetic field lines directed away from the Sun’s northern hemisphere), ii) 1980 – 1990 (\(A<0\)) (negative polarity—magnetic field lines directed towards the Sun’s northern hemisphere), iii) 1991 – 2002 (\(A>0\)), iv) 2003 – 2013 (\(A<0\)), and v) 2014 – 2022 (\(A>0\)). The analysis of these five subperiods confirmed a close relationship between the PSD and the RSV, determined by the exponents \(\nu _{yz}\) and \(\gamma \), respectively. These exponents, calculated from independent sources, may be important parameters in the study of long-term GCR variations in the heliosphere.