# Transformative Technology for FLASH Radiation Therapy
## 4 Fixed-Field Gradient Accelerators for FLASH-RT  
### Scaling Fixed-Field Gradient Accelerator  
Fixed-field gradient accelerators (FFGA), previously called fixed-field alternating gradient (FFAG) accelerators, are synchro-cyclotron-style accelerators based on cycled radio-frequency acceleration. Similar to synchro-cyclotrons, FFAGs generally operate at high repetition rates; e.g., the superconducting synchro-cyclotron (S2C2) from IBA (Ion Beam Applications) operates at 1 kHz [44]. Compared to synchro-cyclotrons, a crucial difference of FFGAs is their strong focusing optics (no different from the optical principle of present-day pulsed synchrotrons) which results in a much smaller beam size, as well as the efficient handling of space charge defocusing effects, a concern when aiming at high-charge bunches.  
FFGA proton accelerators (aka \"scaling FFAG\") were developed at KEK (Ko Enerugi Kasokuki Kenkyu Kiko) in the late 1990s, with a proof-of-principle 500 MeV ring in 1999 [45] and a full-scale 150 MeV ring that provided the first beam in 2005 [46]. Two such rings are in operation in Japan, at Kyushu University (providing the beam for condensed matter research) and at the Kyoto University research reactor (providing the beam for KUCA, an ADS-Reactor Critical Assembly) [46]. These rings have demonstrated a 100 Hz capability based on a single RF system; however, they may even do better as their lattice lends itself to multiple RF systems (in the manner of a folded linac).  
Kyoto and Kyushu rings use so-called radial optics, an alternation of positive- and negative- bend radial sector strong focusing dipoles; compact rings, in addition, are obtained using spiral-sector optics. This has been demonstrated by the RACCAM (Recherche en Accelerateurs pour Applications Medicals) project [47], which has produced a design with a multiple-extraction ring (Figure 6), RACCAM-constructed, as a proof of principle, and a strong-focusing spiral sector FFGA dipole [48]; and validated the design with 3D magnetic field measurements which proved that the expected performance was reached [49].  
The RACCAM spiral-sector ring design allows a \(>\)5 Gy/min dose rate, based on bunch-to-voxel delivery to a volume of 1 L (I). The reference volume (1 l) is centered at a 10 cm depth and comprises 20 \(\times\) 20 \(\times\) 20, 5 \(\times\) 5 \(\times\) 5 mm\({}^{3}\) voxels [47]. This delivery mode requires a total of 10\({}^{11}\) protons and, for a uniform, spread-out Bragg peak, 10\({}^{9}\) protons per bunch (ppb) in the most distal layer. Thus, the average dose rate is 5 Gy \(\times\) 1/60 s, i.e., \(\sim\)0.1 Gy/s over 1 l, which is higher than a typical conventional dose rate but not FLASH-compatible (\(>\)40 Gy/s).  
Figure 6: RACCAM multiple-extraction proton therapy FFGA ring. Reproduced with permission from Ref. [49].  
Increasing the dose rate could be split between the repetition rate, pushing beyond 100 Hz; bunch charge, pushing beyond 10\({}^{9}\) ppb; and decreasing the irradiated volume. In particular, with the assumption of a 100 Hz repetition rate, a required <200 ms irradiation time imposes \(\sim\)30 voxels and \(\sim\)4 mL; current-wise, this is <l> =10\({}^{9}\) ppb \(\times\) e\({}_{\rm c}\)\(\times\) 100 Hz = 16 nA, where e\({}_{\rm c}\) is the elementary charge. An increase of the repetition rate by a factor of 10, to 1 kHz, would allow the irradiation of a \(\sim\)40 mL volume irradiation in 200 ms; it would also bring the necessary bunch charge for the proper average and IDRs to 4 \(\times\) 10\({}^{9}\) protons; current-wise, this is \(\sim\)1 uA.  
It can be seen from what precedes that increasing the average current (via repetition rate and/or bunch charge) and instantaneous current (via bunch charge) towards FLASH requirements is challenging but possible. An intermediate option is to consider a smaller target volume, i.e., a few 10s of ml, which would relax the repetition rate and bunch charge constraints.