This will be hard to explain. You might want to try to draw it.
Think of a cylinder with a piston inside, oriented vertically for discussion purposes, closed at both ends so that movement of the piston can pressurize both sides. The piston is attached to a motor to move it up and down.
On the left
side for discussion: A tube coming out the bottom goes to a regenerator at the bottom. At the top of the regenerator is a manifold. One outlet from the regenerator goes into the upper part of the cylinder. Another outlet goes through a small heat exchanger set up as a target for a solar tracking fennel lens. The exit of this solar collector goes into the top part of the cylinder. On the upstroke of the piston, the manifold directs gas from the cylinder straight to the regenerator. On the down stroke, the manifold directs the gas through the solar target.
So far this is essentially a sterling engine, however instead of a power cylinder there is a tube coming out of the hot side that goes into a heat exchange condenser trough a valve. The condenser is submerged in fluid in the bottom half of a box (call it the evaporator). The gas flowing through the condenser then goes through a pressure reduction device, extracting energy in the process, and the exhaust gas is blown into the evaporator. A tube connects the evaporator to the bottom of the cylinder through a valve. On the upstroke the condenser valve is closed and the evaporator valve is opened. The opposite occurs on the down stroke.
The whole device can be insulated to reduce heat loss.
Theory of operation: 1: On the down stroke, gas is pushed through the regenerator to extract heat from it, and then is heated in the solar collector. This causes it to try to expand and increases the pressure in the system. Some of the gas is pushed into the condenser where the increased pressure causes pressure induced condensation. The heat of condensation is transferred to the evaporator fluid. Condensate flows to a drain, essentially a vertical tube with a fishing float that can pull up a needle valve when the fluid is high enough.
2: On the upstroke, gas is pushed through the regenerator to give heat to it, this causes the gas to contract, lowering the pressure and pulling gas from the evaporator into the cylinder. This gas is replaced by gas from the pressure reduction device and evaporation of the fluid. The energy extracted from the pressure reduction device can be injected into the evaporator fluid by stirring it.
Note the energy collected from the solar collector is pumped into the evaporator several times in the recycling of heat of condensation. The “at cost” energy input is the energy needed to move the piston back and forth. This consists of friction on the piston and air resistance going through the regenerator.