Identifying optimum design parameters and operating conditions of thermoacoustic engines or refrigerators is crucial for the further development of such devices. This publication proposes an optimization criterion for the stack of a thermoacoustic device with the objective of maximizing the amplification of acoustic energy by the stack. For this purpose, the stack is described as an acoustic multi-port, represented mathematically by its scattering matrix. It is shown how the scattering matrix may be deduced from the standard thermo-acoustic governing equations. Then an acoustic power balance is deduced from the scattering matrix. The spectral norm and the eigenvectors of the scattering matrix identify optimal acoustic states. Stack design operating parameters and frequencies with maximum amplification of acoustic power are identified for various stack configurations. The corresponding acoustic states are interpreted physically.