In what sense are telescopic heliostats telescopic?

A pair of binoculars focussed at infinity and aimed at the sun emit intense beams from the eyepieces.

Definition: A telescopic heliostat is a heliostat in which the emergent rays are increased in concentration and divergence.

A telescopic heliostat is not telescopic in the sense that it can throw a beam of sunlight farther. If that were the only consideration, a plane-mirror heliostat would be the best choice. A telescopic heliostat concentrates sunlight while keeping the emergent rays as parallel as possible—which is precisely the action of a telescope focussed at infinity. An inevitable consequence of the concentration, is that the emerging light rays are more divergent than a natural sunbeam, so beam spread from a telescopic heliostat is greater than from a conventional heliostat.

An optical cross-section of a telescopic heliostat shows it to be an afocal, off-axis, Cassegrain telescope. Both mirrors are parabolic.

The object of a heliostat is to hit a target of low angular elevation. (Note how much sunlight falls to the ground in the process.) Image quoted from NRG Energy.

If hitting a distant target were the object of a heliostat we would stick with plane mirrors; but the object of a heliostat is to hit a low target. There are practical limits to the height that a boiler or beam-down optics can be elevated above the ground, so the goal of a heliostat is to redirect sunlight to a target of low angular elevation.

When 100% of the sunlight incident on a horizontal surface at angle of incidence θ_i emerges redirected at an angle of reflection of θ_r, the sunlight has been concentrated by a factor of cosθ_i / cosθ_r . The Second Law of Thermodynamics forbids this concentration without a compensating increase in divergence. Since plane mirrors cannot accomplish the required increase in divergence, they cannot accomplish the desired efficient redirection of light.

Consider, for example, the Ivanpah Solar Project in California. According to the 2010 environmental impact statement for this project, each power tower is 140 m tall measured to the top of the boiler. Ivanpah units 1 and 2 each have 55,000 heliostats, with each heliostat carrying 14 m² of mirror. Let's say 1 m² of mirror typically shades 1.5 m² of ground. Each unit occupies about 915 acres (3.7 million m²) of land, but only 55,000 x 14 x 1.5 = 1.2 million m2 are typically shaded, a land utilization of only a third. To achieve full utilization we would need to squeeze three times as many heliostats into the view above—but they would only block each others' view!

Mutual blocking is worst at the farthest edge of a heliostat field, so land utilization there is really poor. Ultimately it makes more sense to build another tower than to extend a low-utilization field to greater radius. Approximating an Ivanpah unit as a circle, it has a radius of 1085 m. From the farthest edge of the field the top of the boiler has an angular elevation of arctan(140/1085) = 7.4°.