Telescopic heliostats: designing heliostats as if thermodynamics mattered

Sunlight falls to the ground in an array of conventional heliostats—and the central tower is unnecessarily tall—because thermodynamics is ignored in the optical design. Since any optical system could be handling thermal radiation, all optical design is constrained by the Second Law of Thermodynamics.

It's not nice to fool Mother Nature. Redirecting sunlight toward a lower angular elevation is a sneaky way to increase its flux—therefore the Second Law of Thermodynamics demands that the light's divergence increase as well. In plain terms, thermodynamics permits us to make the sun look closer, but not hotter.  A high-performance heliostat must be an optical device that increases the flux and divergence of sunlight while keeping parallel rays parallel, in other words, a telescope.

The twin beams of light emerging from these 7x binoculars focussed at infinity and pointed at the sun are quite collimated, even though the solar flux has been increased about 49 times. Calculations indicate that 6x magnification would be optimal for a telescopic heliostat.

The Cassegrain configuration as it is usually described—a parabolic primary with a hyperbolic secondary—is not actually a telescope until an eyepiece is added. A secondary mirror having instead a parabolic profile would move the focal point to infinity, and thus serve as the eyepiece.

The necessity of telescopic heliostats

A telescopic heliostat converts sunlight into an intense—but slightly divergent—beam of light.

A drawback of solar power plants that use mirrors (heliostats) to beam sunlight onto an elevated target is that one heliostat might block a neighboring heliostat's view of the target. Trying to reduce this blocking causes the land utilization of an optimized plant of this type to be low. Since the blocking problem is the worst at the far edges of the heliostat field, for a given target height, the blocking effect also limits the useful radius of the heliostat field—and thus limits the power rating of the entire plant.

The heliostat blocking problem is actually a consequence of the Second Law of Thermodynamics: thermal radiation cannot be concentrated without increasing its divergence. When we try to redirect sunlight from a high-elevation sun toward a low-elevation target using an array of parallel mirrors, we are attempting exactly such an evasion of the Second Law.

Redirecting sunlight toward a low elevation target without a compensating increase in beam divergence is an attempt to evade the Second Law of Thermodynamics—the heliostat blocking effect rises up to trump our attempt.

A telescopic heliostat, by dealing realistically with the need for increased beam divergence can largely eliminate the heliostat blocking problem, and thereby increase by an order of magnitude the power rating of a solar plant having a given target height. About half of this prospective improvement comes from increased utilization of land within the heliostat field, and half from increasing the useable radius of the field. 

Concentrating a sunbeam causes its divergence to increase: that fact is inescapable. Nonetheless, there is room to increase the divergence of natural sunlight. For example, a very narrow-beam flashlight may have a beam divergence (the full angular spread between its half-intensity shoulders) of 5 degrees. That is about ten times the divergence of natural sunlight. So a sunbeam can be concentrated about 100 times without increasing its divergence beyond that of a very narrow-beam flashlight beam.

This narrow-beam flashlight has about ten times the divergence of natural sunlight.  Concentrating a sunbeam to this level of divergence allows a hundred-fold increase in intensity.