Inhibition and Utilization of Integer Resonance in GeV/mA Class High Power Circular Accelerator

GeV-class proton beam with an average power of several megawatts has many important applications in particle physics towards the intensity frontier, as well as in the advanced energy and material science. There are three different types of constructed accelerators for high power proton beam production: The cyclotron, linear accelerator and rapid-cycling synchrotron. The highest beam power of these accelerators currently is 1.4 MW. Studies have shown that the energy efficiency of the PSI cyclotron is about two times of the other types. Thus, the isochronous accelerator is a good technical route to develop proton machines with high beam power and high power efficiency. The isochronous fixed-field alternating gradient accelerators (FFAGs) scheme is a promising candidate for next-generation GeV-class high power proton driver. There are two bottle-neck problems in the development of GeV/mA class FFAG: As an isochronous accelerator, radial tune of isochronous FFAG is approximately increasing with beam energy in a linear way, and thus the integer resonance crossing problem becomes an inevitable problem. Single turn extraction with very low beam losses is also a verry important issue of high power isochronous FFAG. To the author’s knowledge, high beam extraction efficiency for beam energy of GeV-class is still unresolved. To solve those problems, an idea of integer resonance suppressor (IRS) which intentionally introduces the third harmonic magnetic field was proposed. One IRS is made up of two pair of coils, and each pair has independent power supply to generate the required harmonic magnetic bump. IRS can not only inhibit the radial oscillation and beam size blowup caused by integer resonance crossing but also contribute to a controllable coherent oscillation which is helpful to beam extraction with high efficiency. In the CYCIAE-FFAG design, νr=3 resonance is the lowest order resonance. Third harmonic field of only 1 Gs (1 Gs=10-4 T) can drive large coherent oscillation and then the following intrinsic resonance 3νr=10 will lead to serious beam size blowup effect. However, IRS can compensate the driving error and minimize the coherent oscillation before reaching the detrimental resonance. IRS provides a possibility of relaxing the requirement of magnet manufacture and installation. Our simulations show that third harmonic field of 10 Gs is acceptable with proper IRS settings. In the PSI 590 MeV ring cyclotron, beam is eccentrically injected to give rise to coherent oscillation. However, in CIAE-FFAG design, the beam was injected centrally and controllable amplitude of coherent oscillation was introduced in the integer resonance crossing process. The IRS scheme makes it possible to have knobs to adjust the amplitude and phase of coherent oscillation, which will be much easier to enlarge the turn separation. Taking the CYCIAE-FFAG project for example, simulations in this paper show that IRS can not only reduce the beam size growth rate to less than 5%, but also enlarge the turn separation to 3 cm. That is to say, IRS not only acts as resonance suppressor, but also plays the role of separation optimizer between the last and second last turn. The result shows that IRS is a potential solution for resonance crossing and extraction problems of GeV/mA class circular accelerator.