Double dynamo effect on solar activity and the modern grand solar minimum

In this paper we present prediction of solar activity for the next three solar cycles and millennium using as a proxy the solar background magnetic field based on principal component analysis. Using symbolic regression analysis we present mathematical formulae for the dipole magnetic waves and calculate their summary curve, which is shown linked to solar activity index. Extrapolation of the PCs backward for 3000 years reveals the 350-400 year grand cycles superimposed on 22 year-cycles whose the occurrence has a remarkable resemblance to sunspot activity reported in the past including Maunder, Wolf, Oort, Homeric and other grand solar minima and warming periods. The summary curve calculated for the next millennium predicts further three grand cycles with the closest grand minimum, which started in 2020 and expected to last to 2053. These grand cycle variations are probed by α − Ω dynamo model with meridional circulation. Dynamo waves are found generated with close frequencies whose interaction leads to beating effects responsible for the grand cycles (350-400 years) superimposed on a standard 22 year cycle. We present also butterfly diagrams for the modern grand solar minimum and compare with that occurred during Maunder Minimum. The dynamo approach is also extended by considering magnetic waves produced by quadruple magnetic sources and their interference with the dipole waves. The revised summary curve for the last 400 years is shown to account for the additional minima of solar activity occurred at the beginning of 19th (Dalton minimum) and 20th centuries.