I've come upon Dr. J. Marvin Herndon's theory that the earth's magnetic field is generated by a hot nuclear reactor operating in the center of the earth. This is backed by various papers, some of them peer reviewed:
His theory purports to explain various anomalies such as the high level of He3 in basalt in Hawaii and their dependency with time. A recent Herndon arXiv paper is:
Uniqueness of Herndon's Georeactor: Energy Source and Production Mechanism for Earth's Magnetic Field http://arxiv.com/abs/0901.4509
His papers suggest that the natural reactors sometimes seen in uranium deposits must also occur at the center of the earth. He says that the conventional explanation for the earth's magnetic field fails because the Rayleigh number for the core is inappropriate as far as determining whether convection exists.
Since this is not accepted geology, what are the problems with the theory?