A method for maximizing the brightness of the bunches in a particle injector by converting a highly space-charged beam to a relativistic and emittance-dominated beam. The method includes 1) determining the bunch charge and the initial kinetic energy of the highly space-charge dominated input beam; 2) applying the bunch charge and initial kinetic energy properties of the highly space-charge dominated input beam to determine the number of accelerator cavities required to accelerate the bunches to relativistic speed; 3) providing the required number of accelerator cavities; and 4) setting the gradient of the radio frequency (RF) cavities; and 5) operating the phase of the accelerator cavities between −90 and zero degrees of the sinusoid of phase to simultaneously accelerate and bunch the charged particles to maximize brightness, and until the beam is relativistic and emittance-dominated.