The role of empirical formulae in the design of complex systems

We discuss the general concepts underlying the design strategies of complex devices like Tokamaks and Free Electron Lasers (FEL). Regarding the FEL, starting from the desired output performances, the key parameters are embedded to get a set of semi-analytical/empirical equations yielding straightforward and reliable estimates of gain and power. In a similar way, the guiding elements of a fusion reactor, to reach the prescribed fusion gain Q and power, are defined in terms of scaling relations involving pivotal quantities like radius and magnetic field. General formulae characterizing a physical system may be the consequence of an unknown symmetry. The onset of specific instabilities represent the breaking of a symmetry characterizing given equilibrium conditions. In this article, we comment on the analogy between two different physical devices, and even though wedonotspecify any underlying symmetry, we aim to stimulate further research in this direction.