Long-term changes in the concentration of radiocarbon and the nature of the Hallstatt cycle

Radiocarbon (C-14) is formed in the atmosphere as a result of the interaction of thermal neutrons with nitrogen according to scheme n(N-14, C-14)p. The effectiveness of C-14 formation depends on the local spectrum of cosmic rays (CR) penetrating into the atmosphere. The local CR spectrum is determined by the level of solar activity and is characterized by the solar modulation parameter (SMP). The efficiency of formation C-14 also depends on the magnitude of the dipole moment (DM) of the geomagnetic field shielding the atmosphere from the CRs penetrating into it. C-14 concentration varies cyclically with time. The most famous long-term cycles are the similar to 2300-year (Hallstatt cycle) and the similar to 210-year (de Vries cycle). Analysis of the radiocarbon series shows that there is an amplitude modulation of the similar to 210-year cycle. The modulating signal has a main period of about 2300 years. The nature of this modulation is analysed. Is it related to changes in solar activity or to variations in the geomagnetic field? Two models of amplitude modulation of radiocarbon variations are considered. In the first model (AM-1), there is amplitude modulation of similar to 210-year variations of the SMP with a period of 2300 years. As a result of the simulation, it is shown that the amplitude of the similar to 210-year oscillations in the concentration of radiocarbon does not depend on the phase of the 2300-year modulation. This contradicts the observations. In the second case (AM-2), the modulation of similar to 210-year variations of the SMP is absent. But the existence of similar to 2300-year oscillations of the dipole moment is allowed. In the second case, unlike AM-1, the amplitude of the 210-year oscillations in the C-14 production rate depends on the phase of the 2300-year variations in the dipole moment, which agrees with the observations. Based on the comparison of AM-1 and AM-2 models of amplitude modulation, it can be concluded that changes in the dipole moment of the geomagnetic field are responsible for the observed similar to 2300-year variations in the concentration of radiocarbon.