An RF linear accelerator using CW or low amplitude pulsed RF excitation which can efficiently accelerate charged particles from 0.1 C to relativistic velocities in excess of 0.9 C. A charged particle source feeds charged particles having velocities of about 0.1 C into a first type RF LINAC having a plurality of side coupled resonator cavities each having a drift tube in the middle. The RF length of the cavities is set relative to the velocity of the particles and the RF excitation wavelength such that the particles experience in-phase accelerating E fields in the gaps on either side of the drift tube and are shielded from decelerating E fields while inside the drift tubes. The RF coupling cavities establish sufficient phase change between adjacent resonators such that the particles arrive in the adjacent resonator cavities in synchronization with oscillations in the standing wave therein so as to experience further acceleration. The first RF LINAC accelerates the particles to 0.5 C approximately. The charged particles are then passed through a conventional RF LINAC with a CW source which is optimized to accelerate the particles from 0.5 C to relativistic velocities. A variable phase change RF coupler couples the RF between the first RF LINAC and the second RF LINAC such that a variable degree of synchronization can be achieved such that the energy of the particle beam exiting said second RF LINAC can be modulated by varying the phase change. A conventional CW RF LINAC is also disclosed with a duty cycle controlling system for operating the RF and charged particle sources with variable duty cycles so as to achieve control of average beam power and enable higher momentary beam energies than would otherwise be the case for CW LINACs.