the highest allowed by the second law of thermodynamics. The most well-known ideal cycle is the Carnot cycle, although a useful Carnot engine is not known to have been invented. The theoretical efficiencies for both, Ericsson and Stirling cycles acting in the same limits are equal to the Carnot Efficiency for same limits. Comparison with the Brayton cycle The first cycle Ericsson developed is now called the "Brayton cycle", commonly applied to gas turbine engines. The second Ericsson cycle is the cycle most commonly referred to as simply the "Ericsson cycle". The (second) Ericsson cycle is also the limit of an ideal gas-turbine Brayton cycle, operating with multistage intercooled compression, and multistage expansion with reheat and regeneration. Compared to the Brayton cycle which uses adiabatic compression and expansion, the second Ericsson cycle uses isothermal compression and expansion, thus producing more net work per stroke. Also the use of regeneration in the Ericsson cycle increases efficiency by reducing the required heat input. For further comparisons of thermodynamic cycles, see heat engine. Ericsson engine The Ericsson engine is based on the Ericsson cycle, and is known as an "external combustion engine", because it is externally heated. To improve efficiency, the engine has a regenerator or recuperator between the compressor and the expander. The engine can be run open- or closed-cycle. Expansion occurs simultaneously with compression, on opposite sides of the piston. Regenerator Ericsson coined the term "regenerator" for his independent invention of the mixed-flow counter-current heat exchanger. However, Rev. Robert Stirling had invented the same device, prior to Ericsson, so the invention is credited to Stirling. Stirling called it an "economiser" or "economizer", because it increased the fuel economy of various types of heat processes. The invention was found to be useful, in many other devices and systems, where it became more widely used, since other types of engines became favored over the Stirling engine. The term "regenerator" is now the name given to the component in the Stirling engine. The term "recuperator" refers to a separated-flow, counter-current heat exchanger. As if this weren't confusing enough, a mixed-flow regenerator is sometimes used as a quasi-separated-flow recuperator. This can be done through the use of moving valves, or by a rotating regenerates with fixed baffles, or by the use of other moving parts. When heat is recovered from exhaust gases and used to preheat combustion air, typically the term recuperator is used, because