Tian Ma & Shouhong Wang, Topological Phase Transition III: Solar Surface Eruptions and Sunspots, hal-01672381, 2017

Based on the recently developed theory of heat [T. Ma & S. Wang, Statistical Theory of Heat, 2017, hal-01578634], we derived in the above paper the *anti-diffusive effect of heat*, stated as follows; see also the previous blog post:

Due to the higher rate of photon absorption and emission of the particles with higher energy levels, the photon flux will move toward the higher temperature regions from the lower temperature regions.

By the Stefan-Boltzmann law, the reversed heat flux measuring the anti-diffusive effect is expressed as

where is the heat effect coefficient. Then by the Fourier law, we derive the following law for heat transfer for the solar atmosphere:

Here on the right-hand side, the first term represents the usual diffusion of heat, the last term is the heat source due to the solar electromagnetic fields. Importantly the second term represents the anti-diffusive effect of heat, and it is this anti-diffusive effect that leads to the formation of sunspots, the solar flares and the prominences.

The anti-diffusive effect of heat may provide a new source of fuel. Basically, in a high temperature plasma system where free electrons are abundant, photons in the low temperature area experience the anti-diffusive effect and can move to the high temperature region, further raising the temperature in the high temperature region. The conversion of the thermal energy in the high-temperature region offers an alternative fuel source, which we call plasma fuel. The Sun is a natural source of photons for the low-temperature regions required for such a process to continue. This direct way of converting solar energy into a new form of fuel will be much more efficient than the photovoltaic devices.

In view of the non blow-up condition derived in the paper, the following condition is required for the anti-diffusive effect of heat to dominate the normal heat conduction:

where is the initial temperature, is the heat conduction coefficient, and is the anti-diffusive effect coefficient. Both and depend on the plasma material. Therefore, for a given plasma system, the larger the domain and the higher the initial temperature, the stronger the anti-diffusive effect. Consequently an effective plasma device for converting solar energy into a fuel source can be achieved by increasing the domain size and/or the initial temperature.

In conclusion, the anti-diffusive effect of heat we discovered in this paper may lead to a new efficient way of converting solar energy directly to a form of fuel, much more efficient than the photovoltaic devices.

*Tian Ma, Shouhong Wang*

September 24, 2018