Design of synchrotron for proton FLASH radiotherapy

Proton FLASH, which combines the advantages of a better spatial dose distribution of protons with the unique temporal effect of FLASH radiotherapy, is currently a hot topic of international research. In this study, a series of innovative methods are proposed to manipulate the beam with the longitudinal dynamics and to extract particles from the synchrotron, thus meeting the dose rate requirements for proton FLASH point scanning radiotherapy in a 1L volume in the target area.


Introduction
FLASH radiotherapy is a non-invasive treatment that is administered with extremely high dose rates (usually> 40Gy/s) in a very short time (<500ms) to release the beam on the cancer site of the human body.While ensuring the effect of tumor treatment, it greatly reduces the damage to normal tissue cells [1].
Proton therapy is a precise tumor therapy.Its energy radiation is concentrated in the tumor target area, causing little damage to nearby tissues and organs and low side effects.Proton FLASH radiotherapy is technically demanding and currently lacks equipment support.There are only a few devices that have been modified to achieve small target section, fixed-energy penetrating irradiation by proton radiotherapy equipment, which cannot give full play to the advantages of proton spatial dose distribution.
In combination with the splitting of small beam bunches, a synchrotron scheme for point scanning of proton FLASH radiotherapy is proposed for the first time.The synchrotron is used to control the number of particles required for a single scan point and to rapidly change energy, which solves the problems of long intervals between different energies and scan points of conventional point scanning and increases the dose rate in the target area.It provides a possible technical route to support the development of proton FLASH radiotherapy and enriches the application of synchrotron.

Demand and challenge
Generally, the proton energy range of medical accelerators is 70 to 250 MeV, the corresponding range is 35 to 375 mm, and the subcutaneous depth is smaller than that.In the volume of 1 L, to meet the minimum dose rate requirement of 40 Gy/s for proton FLASH therapy, the number of particles required for 100 ms was 3.8e11 [2].Based on the fact that 3.8e11 particles are required to complete 1 L volume proton flash-therapy irradiation within 100 ms, the number of particles required to meet the dose rate of 40 Gy/s at different volumes and irradiation times is calculated, as shown in figure1.To achieve proton flash therapy of tumor within 1 L volume, it is necessary to ensure that the target area receives 3.8e11 particles within 100 ms or 1.9e12 particles within 500 ms, with a corresponding flow intensity of 608 nA.Considering that the transmission efficiency of the transport line is 80%, the current intensity at the outlet of the accelerator is required to reach 760 nA, which is close to the upper limit of 800 nA of the current accelerator current intensity used in radiotherapy.Considering the time required for energy conversion and the possible particle loss in the process of energy conversion, it is difficult for the existing radiotherapy machines to meet the requirements of tumor proton radiotherapy within 1L volume.Since the beam size at the exit of the accelerator is on the order of mm, and the target area size is generally on the order of cm, the beam size at the exit of the accelerator should be amplified and expanded.According to the transverse beam expansion mode, it can be classified into passive scattering method and pen beam scanning (PBS) method.
In order to ensure that the target dose rate meets the demand of proton FLASH therapy, a reasonable scattering structure should be designed to reduce particle loss by using scattering method to expand the beam.In order to reduce the scanning time, it is necessary to reduce the beam scanning interval by using the pen beam scanning method.At the same time, the beam energy switching time should be shortened to reduce the total irradiation time.
For discrete point scanning, in order to realize the discrete scanning process after beam splitting, for the 1L volume commonly used in medicine, within the range of 10×10×10 cm, and considering the point interval of 5 mm, 9,261 bunches (21×21×21) need to be divided within the irradiation time [3].Even without considering the time of acceleration and other processes, When the irradiation time is 100 ms, the time interval of different clusters is 10.8 us, and when the irradiation time is 420 ms, the time interval of different clusters is 45.4 us.It can be seen that extending the total irradiation time can reduce the difficulty of generating short bunches.

Design of synchrotron
In order to reduce the requirements for single-cycle storage of particles, the fast cycle synchrotron is designed with a working repetition frequency of 25Hz and a period of 40ms.Since the strength of the main magnet of the fast cycle synchrotron generally changes in a sinusoidal way, the extraction mode of fixed energy platform cannot be adopted like that of the slow cycle accelerator, so the particle extraction process is adjusted to a continuous variable energy extraction.In discrete beam bunch extraction, the continuous variable energy extraction process needs to achieve variable energy splitting extraction, while in continuous beam extraction process, it needs to rely on RF system to achieve continuous variable energy extraction.
The intensity waveform curve of the single-cycle main magnet is shown in the figure2.The whole cycle is divided into the acceleration section (injection to acceleration to 70MeV, tacc), the continuous variable energy extraction section (variable energy extraction stage, text), and the magnetic field fall stage (the magnetic field restores to the magnetic field value corresponding to the injected energy, tfall).For a synchrotron with a circumference of 40m, the field strength of the variable energy extraction phase ranges from 0.81T for a magnet of 70MeV to 1.59T for a magnet of 250MeV and 0.25T for an injected energy of 7MeV.The magnetic field intensity corresponding to 70MeV energy is 0.81T.From 0.25T corresponding to the injected energy, the field intensity reaches 0.81T corresponding to 70MeV after 8.9ms acceleration process, and then increases the energy to 250MeV after 11.1ms, which corresponds to the continuous energy extraction process.In the falling process on the other side of the sinusoidal waveform, The magnetic field intensity dropped from the corresponding 250 MeV to 70 MeV, and the whole continuous energy extraction process took 22.11ms.Such a cycle can achieve 2 complete scanning layers of irradiation.
We apply the rectangular pulses on the bunch, and adjust the barrier voltage distribution to divide the bunch into different density regions as figure3 shows.Kicker kicks out particles in a specific phase range through Kicker action, waiting for new particles to fill the kick out phase range, and then continue to kick out particles with kicker action.Repeat the above steps to produce enough small bunchs.The effect of rectangular pulses on the bunch is specified in other articles.The total irradiation time was set at 420 ms, and the duration of a single cycle was 40 ms, corresponding to two vertical scanning layers.The initial single cycle bunch was divided into 21×21×2=882 pieces by using the "bunch dilution method", and the number of particles per piece was about 1/882 (1.13‰) of the initial bunch.The velocity of phase motion of particles in longitudinal phase space is proportional to the momentum dispersion:  = 2,  is the slippery phase factor and  is the momentum dispersion of the particles.
After separating the bunch, new particles fill the Kicker phase range before they can be extracted, so the time required for new particles to fill the specific phase range is the time interval for the bunch to be extracted.The formula for calculating the time t required for this phase shift is as follows: where,  is the phase range kicked by kicker,  is the momentum dispersion of the particle to be calculated in the small density region,  is the cyclotron period,  0 is the pulse duration kicked by kicker, corresponding to the sum of the kicker rising edge and flat top segment.The above equation shows that the time interval of each kick is only related to the pulse duration of the kicker, momentum dispersion, and slip phase factor.Considering that the particles in the phase range of kicker rising edge cannot be successfully extracted, in order to reduce the beam loss ratio caused by kicker rising edge, the total pulse duration of Kicker kicking can be extended appropriately.
When =-0.63，=2‰, the kicker rising edge is 9 ns, the flat top section is 22.5 ns,  0 is 31.5 ns, and the time interval of kicking out the bunches is 25 us.In this way, the requirements of the bunches interval ≤25 us can be satisfied, that is, the fast splitting of bunches can be realized.
The extraction process takes "kicker + electrostatic deflector + Lambertson magnet" to complete as figure 4 shows.kicker first acts on particles of a specific phase to realize the pre-separation of the particles to be extracted and the circulating beam.Kicked particles enter the diaphragm of the electrostatic deflector and are deflected by the electrostatic deflector into the Lambertson magnet, thus entering the transport line for transmission to the target station.
Before the kicker action, the momentum dispersion of Bucket2 particles was elevated by "bunch dilution method" to accelerate the phase motion speed and realize the effect of fast beam splitting.At the same time, due to the transverse and longitudinal coupling effect, the horizontal coordinates of the particles to be extracted were also close to the electrostatic deflector diaphragm, thus reducing the parameter requirements of kicker.The key parameters of synchrotron scheme design are shown in table 1.

Conclusion
By manipulating the beam longitudinal phase space to generate regions with different densities, we kick out some particles through kicker action in specific phase space, and the remaining particles will be supplied to kicker action region due to phase motion.By increasing momentum dispersion and phase motion speed, 9,261 beam bunches can be extracted in 420ms.The energy of these bunches covers 70~250 MeV, which can give full play to the advantages of spatial dose distribution of protons and meet the requirements of proton FLASH.The proposed synchrotron solution to achieve proton FLASH radiotherapy needs to be optimized to reduce the strength requirements of some components, and the transfer and deflection techniques after the extracted beam need to be carefully studied to adapt to the high-frequency scanning.

Figure 1 .
Figure 1.The number of particles required to meet the dose rate of 40 Gy/s at different volumes and irradiation times.

Figure 2 .
Figure 2. The intensity waveform curve of the main magnet.

Figure 3 .
Figure 3.The longitudinal phase space of the bunch to be extracted.

14thFigure 4 .
Figure 4.The schematic diagram of the extraction process.

Table 1 .
The key parameters of the synchrotron.