  We propose a tunable phonon laser prototype with a large trapped ion array,
where some of the ions are effectively pinned by optical tweezers, thus
isolating a subset of ions that mimics an acoustic cavity used as a phonon
lasing resonator. The cavity loss can then be controlled by the tweezer
strength and the "wall thickness", the number of pinned ions for isolation. We
pump the resonator by applying blue-sideband lasers, and investigate the lasing
dynamics of the cavity modes such as threshold behavior, population
distribution, the second-order coherence, and line-narrowed spectrum. This
scheme can be generalized to resonators consisting of multiple cavity modes
formed by a few ions, where we demonstrate mode competition and synchronization
as lasing modes have developed.
