Stochastic cooling in Penning traps

Stochastic cooling in storage rings was a great success: the present paper gives a complete theory for the application of the same general concepts to Penning traps. The structural difference between a storage ring and a Penning trap requires a complete revision of the starting points on which to base the theory. Not surprisingly, however, the final results exhibit many similarities. One of the main differences is that the noise effects are best treated, in a Penning trap, by introducing a limiting energy ${\varepsilon }_{\lim }$, proportional to the noise amplitude, that represents the minimum energy attainable with stochastic cooling. The theory shows that stochastic cooling in a Penning trap can be very useful when one wants rapidly to cool the energy of the trapped particles down to limiting energies greater than kT, T being the noise temperature associated with the detection circuits.