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.
