Abstract A theoretical investigation of the properties of a plasma in the vicinity of a magnetic dipole is made, and the conditions for stability of the plasma derived and applied to the Earth's radiation belt. During solar flares oscillations may be set up in the plasma, and the frequency of such oscillation is calculated. A comparison is made between the theoretical frequency and the frequency of the fluctuation observed by the space probe, Pioneer IV. The current and density observed in the newly discovered third radiation belt at 8–10 Earth radii, is shown to be consistent with the present theoretical estimate. The present method also provides an explanation of magnetic storms and shows the possibility of considering the effect of interaction between the dipole field and current in the belt, a feature which is difficult to consider in the microscopic theory.