New techniques for radiotherapy and radiosurgery are provided. In some aspects of the invention, multiple sources of radiation with characteristics that are projected to constructively interfere at a treatment target are provided. In other aspects, hardware directs multiple radiation sources from the same side of a treatment target, and focuses the initiation of substantial interference on a leading structure in the target. In other aspects, refractive models updated by live feedback are used to improve dosage distribution by, among other things, optimizing the number, length, superposition, overlap, angle and nature of radiation beams. In additional aspects, interstitial beacons and radiation path diversion structures are inserted to improve dosage distribution to a target and avoid critical neighboring structures. In particle therapy, regionally actuable external magnetic fields are also provided, to improve dosage accuracy and avoid collateral damage.