The most fruitful means now known for accelerating particles to very high energies are: (1) to give repeated small pushes by an alternating electric field, as in the cyclotron or linear accelerator, and (2) to give a steady push produced by a varying magnetic flux, as in the betatron. The first of these, which may be called "resonance acceleration'' gives promise of reaching higher ultimate energies, and will be the subject of this paper. The problem of keeping the particles
in step with the accelerating electric field for a very large number of cycles seems at first sight to be a formidable one, not only because of intrinsic difficulties such as the well-known relativistic limit of the cyclotron, but also because of practical limits on the accuracy of construction of machines. However, an appreciation of the property of "phase stability'' shows the way to a simple solution of this problem. If the particle is moving in a circular orbit, the angular velocity must just
match the applied electric frequency for resonance to be maintained; if the motion is in a straight line, there is a corresponding relation between the linear velocity, and the product of the electrode repeat length by the frequency. It can now be shown that, in general, if the angular or linear velocity varies with the energy, it is not necessary to make the exact match mentioned above, since particles started sufficiently near the right velocity will fall into a stable motion in which the velocity,
energy, and phase oscillate about equilibrium values. (The phase describes the time relation between the arrival of the particle at an acceleration gap and the field across the gap.) The equilibrium energy is that value which achieves the exact match between velocity and frequency. If this energy is now made to vary slowly by changing the frequency or magnetic field in the circular case, the stability will remain and the actual energy will oscillate about the varying equilibrium value. In the linear
case, the variation is produced by the changing repeat length as the particle travels down the tube. Thus acceleration is accomplished with complete stability of the motion at all times, provided that the rate of variation is not too great, and that adequate focusing of the beam is provided. The focusing problem in the linear case has been discussed by Dr. Alvarez; in the circular case it is the same as in the cyclotron and betatron. This stability takes care of relativistic difficulties as well
as tolerances in the machine. The circular orbit machines can be divided into three types: (1) magnetic field variation (synchrotron), which is most suitable for accelerating electrons; (2) frequency variation (synchro-cyclotron), most suitable for ions; and (3) variation of both quantities. The third type has the advantage that the size of the orbit can be held constant by maintaining a certain relation between the field and frequency, but it involves all the practical difficulties
inherent in both of the other types. Methods of obtaining the variations and details of design will be illustrated by descriptions of the 300 MeV synchrotron and the 184'' synchro-cyclotron now under construction at Berkeley. There will also be a discussion of future possibilities, leading to the eventual attainment of the billion-volt range.
Further development of the synchrotron idea.