Professor Valentina Zharkova gave a presentation of her Climate and the Solar Magnetic Field hypothesis at the Global Warming Policy Foundation in October, 2018. Principal component analysis (PCA) of the solar background magnetic field observed from the Earth, revealed four pairs of dynamo waves, the pair with the highest eigen values are called principal components (PCs). PCs are shown to be produced by magnetic dipoles in inner and outer layers of the Sun, while the second pair of waves is assumed produced by quadruple magnetic sources and so on. The PC waves produced by a magnetic dipole and their summary curve were described analytically and shown to be closely related to the average sunspot number index used for description of solar activity. Based on this correlation, the summary curve was used for the prediction of long-term solar activity on a millennial timescale. This prediction revealed the presence of a grand cycle of 350-400 years, with a remarkable resemblance to the sunspot and terrestrial activity features reported in the past millennia: Maunder (grand) Minimum (1645-1715), Wolf (grand) minimum (1200), Oort (grand) minimum (1010-1050), Homer (grand) minimum (800-900 BC); the medieval (900-1200) warm period, Roman (400-10BC) and other warm periods. This approach also predicts the modern grand minimum upcoming in 2020-2055. By utilising the two principal components of solar magnetic field oscillations and their summary curve, we extrapolate the solar activity backwards one hundred millennia and derive weaker oscillations with a period of 2000-2100years (a super-grand cycle) reflecting variations of magnetic field magnitude. The last super-grand minimum occurred during Maunder Minimum with magnetic field growing for 500 years (until ~2150) and decreasing for another 500 years. The most likely nature of this interaction will be discussed and used to explain long-term variations of solar magnetic field and irradiance observed from the Earth.