Design of a rapid‑cycling synchrotron for flash proton therapy

Ying Shi · Man‑Zhou Zhang, · Lian‑Hua Ou‑Yang, · Zhi‑Ling Chen, · Xiu‑Fang Li · De‑Ming Li,

Abstract The purpose of this study was to design a rapid-cycling synchrotron, making it capable of proton beam ultrahigh dose rate irradiation, inspired by laser accelerators.The design had to be cheap and simple.We consider our design from six aspects:the lattice, injection, extraction, space charge effects, eddy current effects and energy switching.Efficiency and particle quantity must be addressed when injected.The space charge effects at the injection could affect particles’ number.The eddy current effects in the vacuum chambers would affect the magnetic field itself and generate heat, all of which need to be taken into account.Fast extraction can obtain 1010 protons/pulse, equal to instantaneous dose rate up to 107 Gy/s in a very short time, while changing various extraction energies rapidly and easily to various deposition depths.In the further research, we expect to combine a delivery system with this accelerator to realize the FLASH irradiation.

Keywords FLASH · Rapid-cycling synchrotron · Proton therapy

1 Introduction

Radiotherapy aims to deliver a tumoricidal dose to irradiate tumors while reducing damage to the surrounding normal tissue.For decades, radiotherapy has been improved by using novel technologies, one of which is FLASH.In FLASH radiation therapy, single treatment pulses shorter than 500 ms are delivered at ultrahigh average dose rates exceeding 40 Gy/s, significantly exceeding the commonly used average dose rates of approximately 0.05 Gy/s.

The FLASH effect was originally reported in the 1960s,although further investigations were largely halted due to logistical difficulties in translating the findings into clinical practice.In 2014, a well-established lung fibrosis model using C57BL/6J mice was presented as the first proof-ofprinciple study [1].Doses of up to 30 Gy were delivered in two ways: a single dose > 40 Gy/s in FLASH mode and< 0.03 Gy/s in conventional (CONV) mode.The results demonstrated a complete lack of acute pneumonitis and late lung fibrosis after bilateral thoracic irradiation of mice with FLASH at doses known to trigger the development of pulmonary fibrosis in 100% of the animals after CONV irradiation.FLASH radiotherapy consistently widens the therapeutic window with better sparing of normal tissue.Their potential for clinical applications has attracted significant interest from the medical community.However, the radiobiology of FLASH radiation therapy remains unclear.In most studies, this has been explained based on oxygen depletion,free radical production/recombination, inter-track effects,and sparing of the immune system [2, 3].

Subsequent research was undertaken at Lausanne University Hospital and Stanford University School of Medicine to ascertain if the same effect is observed for object recognition ability in mice after brain irradiation and for long-term memory deficits in these animals.The results of these investigations proved to be encouraging [4–6].Ultrahigh dose rate irradiation showed better preservation of zebrafish embryos at all doses when compared to conventional irradiation.Additionally, the experiments demonstrated that the higher the dose rate, the better the growth of zebrafish embryos was preserved.Moreover, variations in the frequency and adjustments in the pulse width during FLASH radiation did not negatively impact the growth of the embryos [6–8].Research on cats and minipigs has also shown positive biological effects [9].In 2019, a 15 Gy FLASH-RT dose was administered for 90 ms to one of the most resistant and progressive skin lesions with a diameter of 3.5 cm.The skin reaction was minimal when compared to earlier conventional radiation [10].

FLASH is mainly effective for three types of tumors:radioresistant tumors requiring increased doses, recurrent tumors requiring re-radiotherapy with preservation of normal tissues, and normal tissues with high radiosensitivity.An assumption underlying several FLASH treatment planning studies is that there is no dose threshold for FLASHsparing effects [11–14].However, in further studies, a dose threshold between 5 and 10 Gy must be considered [15–18].Therefore, further biological research is required to determine whether a dose threshold triggers FLASH effects.

Most studies have used electron beams with low tissue penetration, limiting their application in clinical practice.A promising alternative to the FLASH delivery method is proton beam therapy, which can offer superior dose distribution within the tissue.Although many experiments using proton FLASH have been conducted, to date, they have been limited to small volumes or shooting through [19].There are many technological challenges in proton FLASH such as higher beam currents, dose monitoring, and beam modulation.

Given the limitations of the stored particle number and energy change time, traditional synchrotron-based proton therapy is not suitable for FLASH irradiation.The former requires large synchrotrons and a higher injection energy.The 3D ridge filter can remove the energy change time.Currently, laser plasma researchers have proposed another approach to achieving FLASH therapy: very high instantaneous dose rate, up to 109Gy/s for less than nanoseconds,but low average dose rate 1 Gy/s also shows FLASH effect[20–25].Compared to the laser plasma accelerator, the rapid-cycling synchrotron is a simpler, cheaper, and more realistic way to provide this type of dose rates.In this study,we present a design of the rapid-cycling medical synchrotron(RCMS) for proton cancer therapy facilities.The RCMS can provide several 1010protons/pulse with the advantages of small beam envelopes and a narrower inner diameter of the vacuum chamber.The repetition rate was as high as 25 Hz,and it was easy to change the energy of each spill.

2 Main RCS parameters

2.1 Dose rate and accelerator types

The ability to provide a dose of 2 Gy in a volume of 1 L is a common clinical criterion for proton therapy.This equates to 1.9×1011protons for a cube of 10 cm×10 cm×10 cm at a depth of 10–20 cm in water at 2 Gy.For the FLASH treatment, 4 Gy ( 3.8×1011protons) delivered within approximately 100 ms corresponds to a current of 600 nA or an average dose rate of 40 Gy/s [26].With current medical accelerator technology, only isochronous cyclotrons can generate such high continuous beam currents.

Cyclotrons are the most often used accelerators in proton therapy.A cyclotron generates a high-intensity continuous beam at a fixed energy.To obtain the required energy,it must use a degrader.The degrader adjusts the physical thickness or the inserted degrader material.If there is a need for a quick shift in accelerator energy, the degrader is required to change beam energy in several tens of millisecond.But shorter than 0.1 ms/energy step is a significant challenge.At the same time, when the beam travels through the degrader, scattering and ionization losses occur, resulting in an increase in the beam emittance and energy spread and also huge beam lost, especially at low energies [27, 28].For FLASH therapy, 3D ridge filter is used to avoid energy change [26].

The Linac accelerator exhibits the advantages of a higher peak current and smaller beam emittance.New linac designs have a sufficiently short time to modify the beam energy from pulse to pulse [29–31].When it comes to true, it may realize complete spot scanning in the clinic.The enormous size and expensive price of linac are also factors to consider[1, 5].

A slow-cycling synchrotron can preselect the extracted energy, eliminating the need for a degrader.Its whole cycle comprising of the injection, ramping up, extraction and subsequent return of the magnetic field, takes a few seconds.Considering this duration, the typical synchrotron usually operates at a low injection energy, resulting in a small space charge limit.Generally, slow-cycling synchrotrons deliver a lower average and instantaneous dose to patients [4, 32].

Several studies have been conducted on the laser plasma acceleration of proton beams [25, 33].Researchers have frequently combined ultrathin targets with beam optics to realize the transmission of several Gys in nanoseconds.In terms of clinical applications, some challenges, such as the maximum energy and intensity of the proton beams, low repetition rate, quality assurance, patient safety, control,and repeatability of the laser pulse output, remain to be addressed.Although proton laser plasma acceleration, to date, is not available for therapeutic use, it provides a new way to achieve FLASH therapy.Inspired by laser plasma researchers, we can use a very high instantaneous dose rate with a low average dose rate to realize the FLASH effect.

The rapid-cycling synchrotron shares similar beam characteristics with the laser plasma accelerator, but it exhibits much higher beam energy and intensity.We plan to design an RCMS capable of providing 1010protons/pulse at a repetition rate of 25 Hz.This equates to 2.5×1011protons/s,slightly more than 60 Gy in 1 min in one liter of volume,with the mean dose rate of approximately 1 Gy/s.But the length of a beam pulse is only a few tens nanoseconds.If we can change beam energy from pulse to pulse and for scattering method that means several Gys for a energy slice, the instantaneous dose rate is more than 107Gy/s.For scanning method, this means a spot requires a pulse, and the instantaneous dose rate is up to 109Gy/s, but the dose control is very difficult.

2.2 The lattice design

Taking into account practical considerations, such as cost and spatial limitations, the rapid-cycling medical synchrotron has a lattice with a short circumference of 27.2 m, composed by four arcs and four straight sections.One straight section is used for the injection, one for the acceleration,and others for the extraction.Eight dipoles have the same length of 1.5 m, and their maximum magnetic field strength are less than 1.3 T.The edge angles of dipoles are 11.25◦.Eight quadrupoles, focusing in the horizontal and vertical plane, have the same length.The normalized strength of defocusing quadrupoles is -2.2 and the normalized strength of focusing quadrupoles is 2.Considering sextupolar component induced by the eddy current, two sextupole families are used to fit the chromaticity whose strengths are -15.01 and-28.42.Figure 1 shows the layout of the lattice, where B(n)represents a dipole, QD(n) and QF(n) represent a defocusing quadrupole and a focusing quadrupole separately, and SX(n)represents a sextupole.The beta-functions and the dispersion are presented in Fig.2, and the primary physical parameters of the synchrotron ring are listed in Table 1.

Fig.1 Layout of the lattice design.B(n) represents a dipole.QD(n)and QF(n) represent a defocusing quadrupole and a focusing quadrupole, respectively.Furthermore, SX1 and SX2 are two sextupole families that fit the chromaticity

Fig.2 Twiss parameters of the RCS.The first solid line, dotted line,and the second solid line represent horizontal betatron function, vertical betatron function, and horizontal dispersion function, respectively

The horizontal and vertical betatron functions were designed to be about 5 m.The horizontal dispersion function was smaller than 3.85 m.Small beta function means small beam envelope, requiring small aperture, and could realize large acceptance.

2.3 The injection design

Usually, there are three injection methods for synchrotron,namely the single-turn injection, the multi-turn injection and the stripping injection.Single-turn on-axis injection is simplest if could meet the particle numbers needed for the clinical treatment.A linac which can provide 7 MeV proton beams was chosen as the injector of RCS [34].The revolution period of injection beam is 748 ns.The maximum time of single-turn on-axis injection depends on the descend time of injection element.If the injection beam current is 10 mA, this corresponds to 2.33×1010protons within 374 ns, which could satisfy the requirement of 1010protons perpulse.If higher particle number is required, higher injection beam current and shorter descend time of injection element is required.

Table 1 Main parameters of RCS

Fig.3 Single-turn injection design

Fig.4 Fast extraction design

Table 2 Parameters of the injection septum and kicker

The injection system is composed by a septum and a kicker.The septum is made up of a cutting plate that divides the field-free zone where the circulating beam is situated from the strong magnetic field where the injected beam is placed, therefore avoiding altering the circulating beam flow in the near area.The septum is thin enough that the injection beam stays as close to the reference orbit as feasible.The beam from the injection line is bent to a slight angle by the beam center after passing the septum.After some movement, the injection beam’s trace coincides with the closed orbit, and the direction of motion has an angle.The magnetic field produced by the kicker that installed here gives the particles a kick, forcing the beam to proceed in a direction same to the closed orbit, and the beams then move in the ring along the closed orbit.After the injection, the magnetic field strength of the kicker must be promptly decreased to zero to avoid interfering with the beams that return here (Figs.3, 4).

Sepuml and kicker parameters are listed in Table 2.

2.4 Extraction design

In comparison to injection, the energy of the extraction beam is higher, and the strength of the extraction components is larger.The beam extraction in the ring accelerator is much more complex.The multi-turn slow extraction is generally used in medical synchrotron for long pulse extraction beam [35].While employing the rapid-cycling synchrotron with a high repetition frequency, the beam stays at a energy for very short time.The single-turnfast extraction method is widely utilized and used in our design.

Table 3 Parameters of the extraction septum and kickers

Here we choose a septum and two same kickers which are easy to process in reality to kick out all the beams in one turn.Placing the kickers in front of the septum could make enough space and avoid beams hitting the extraction septum.The following is a basic outline of the process: in the ring, beams are deflected by a strong magnetic field of the kicker, pass the dipole and then enter the gap of the septum.The septum bents the beams in a much larger angle to get out of the way of other components in the ring and the beams are finally transmitted to the high-energy transport line to achieve ring separation.The ramping time of the kickers must be within the time gap of the single bunch between the turn and the last turn.In the singleturn rapid extraction, the extraction platform time must be sufficient to kick all the particles and the requirement for descent time is relaxed.The revolution time of the beam to be extracted depends on the required energy and varies from 0.15 μs to 0.3 μs.And the bunch length of circling beam is around 6 meters.So, the rising time of kicker should be less than 0.076 μs.

The length of the septum is 0.8 m and two kickers are 0.6 m apart.The septum is installed in another straight section.The height of the center orbit at the septum’s entrance is 0.044 m, and the separation height at the exit is 0.356 m.The parameters of the extraction kickers and septum are shown in Table 3.

3 Number of the storage particles

The beam losses are classified into two types: transverse beam losses and longitudinal beam losses.In the longitudinal direction, particles outside the RF acceptance or whose momentum deviation larger than the momentum acceptance of the accelerator would lose.In the transverse direction, particles would lose if they exceed the collimator’s acceptance.The stored particles’ number of a low energy synchrotron is limited by space charge effects.The space charge effects occur as a result of the charged particles’ electromagnetic field impacting particle movements as they pass through the accelerator.The tune shift is a parameter that represents the space charge effects.In the ring, the bucket longitudinal dimension is significantly larger than the transverse dimension.Therefore, the longitudinal tune shift caused by space charge effects is several orders of magnitude smaller than the transverse tune shift.The transverse particle movements have the greater influence during the injection process.The tune shift can be described by the Eq.1 in the situation of uniform beam distribution [36].

whereNBis the accumulated par ticles,r0=e2∕4πε0m0c2=1.584×10-18m is for the classical proton radius,εrmsis the transverse rms emittance about 41 mm・mrad,Bf=kbσσ∕√2πRis the bunching factor defined as the ratio of the mean to peak line charge density.When particles’ number is 1010, the tune shift is calculated to be approximately -0.0076 which is acceptable.The stored beam can reach 2×1010or even higher.When the tune shift caused by the space charge effects leads the beam’s tune to travel across the resonance line, there is a substantial chance that the particles will lose due to the resonance, resulting in a limit in the number of particlesNin the ring.

To gather more particles in the ring, the space charge limit of the ring is increased as much as possible.According to the Eq.1, there are four ways to raise the space charge limit.One method is to increase the energy of the injected beam.One is to enhance ring acceptance and increase the size of the beams.Another method is to paint the beams evenly over the transverse phase space during the injection progress.The last one is to choose a suitable initial tune that is away from strong resonance lines.

4 Eddy current effects

During the acceleration, the rapid varying magnetic field would induce eddy currents in vacuum chambers and other components.In turn the eddy current will generate various multipole fields which will affect beams’ motion.Magnetic field attenuation and delay produced by eddy current effects impair the uniformity and synchronization of the initial magnetic field inside the vacuum chambers.Eddy current loss’s thermal influence can cause temperature rise in vacuum pipes.The multipole components could cause beam tune shift and change the chromaticities.So it is necessary to consider the eddy current effect in the vacuum chambers [37].

4.1 Basic parameters

Eddy current effects are influenced by the vacuum chamber shape and size, material electrical conductivity, and magnetic field ramping rate.Low conductivity materials,thin wall thicknesses, and appropriate pipe cross section designs decrease eddy current effects in the vacuum chambers for the changing magnetic fields.According to the beam transverse envelope size, an elliptical cross section of the vacuum chamber was chosen, whereais the vacuum chamber half-width,bis the chamber half-height, andeis the chamber thickness.To reduce the eddy current, the vacuum chambers should be made by small conductivity materials, such as ceramics.But the thickness of ceramic vacuum chamber is too high and increase the magnet gap and power very much.A low conductivity material Inconel 625 is used [38] (Table 4).

The ramping is realized by changeing the strength of the dipoles and quadrupoles.

For a sinusoidal ramp, the time variation of the dipole magnetic field is provided by Eq.2 [39]

The minimum dipole strength is 0.2004 T when injected, and the maximum is 1.2294 T when extracted.Figure 5 illustrates the ramping curve of the dipole field.

4.2 Induced sextupolar component in the dipoles chambers

The eddy current magnetic field within the vacuum chamber of the dipoles has a significant impact on the dipole component, leading to magnetic field attenuation and delay.Concurrently, the sextupolar component of the eddy currentmagnetic field in the dipole vacuum chamber induces changes in chromaticities.Additionally, the quadrupole component of the eddy current magnetic field in the vacuum chamber of the quadrupole magnet section results in a lateral tune shift.

Table 4 Sectional size of the vacuum chamber

Fig.5 Sinusoidal ramping curve for the dipole field

Fig.6 Sextupole strength introduced by the sinusoidal ramping curve

The formula for the sextupolar component in elliptical vacuum chambers can be expressed by Eq.3 [39] as follows:

whereσ=0.8×106S∕m denotes the electrical conductivity of Inconel 625.Furthermore,μ0=4π×10-7denotes vacuum permeability,ρdenotes the dipole bending radius,̇Bdenotes the rate of change in the field, andJdenotes the geometric factor of the elliptical vacuum chamber.

whereadenotes the vacuum chamber half-width andbdenotes the half-height of the chamber.

The sextupole strength introduced during the sinusoidal ramping is shown in Fig.6.Whent=5.0 ms , the sextupolar exhibits a maximum value of 1.143 m-3.This is also verified in Opera software’s ELEKTRA module as shown in Fig.7.The geometrical factors andB′∕Bare related to the strength of the eddy current magnetic field’s sextupole component.

The sextupolar component induced by eddy currents is calculated as the sextupole component errors of dipoles and causes horizontal and vertical chromaticity modification described byεx,coandεy,co.

The maximum horizontal chromaticity isεx,co=34.74 ,and the minimum vertical chromaticity isεy,co=-31.95.Because of chromaticity changes caused by the sextupole component of the eddy current effects, the transverse working tune may change and cross the resonance line.When designing beam optics, it is necessary to consider the errors introduced by the sextupole component, chromaticity correction should be done in the ramping.Two sextupole families are used to fit the chromaticity to the value of 0.5 and 0.5 in the horizontal and vertical direction.

4.3 Induced dipole component in the dipoles chambers

The dipole component can also be induced by eddy currents in the dipole vacuum chamber.This can be described by Eq.5 [40] as follows:

wherea1,a2,b1, andb2denote the vacuum chambers inside the half-width, outside half-width, inside half-height, and outside half-height, respectively.Maybe the presence of the vacuum box could cause the effect of magnetic stranded for the RCS, with a time constant of 3.5254 μs.This is acceptable.Figure 8 shows the acceptable effects of magnetic stranded for the sinusoidal ramping within 0.04 s.

Fig.7 When t=0.01 s, the magnetic center plane is distributed along line x=-23 mm to x=23 mm

Fig.8 Dipole strength errors introduced by the sinusoidal ramping curve

4.4 Induced quadrupolar component in the quadrupole vacuum chamber

Fig.9 Quadrupole strength errors introduced by the sinusoidal ramping curve

Figure 9 shows that the magnetic hysteresis induced by the quadrupolar component in the vacuum chamber is small.As shown in Fig.10, the maximum tune shift introduced by the quadrupolar component is within 4×10-4.

Compared to the initial transverse tune, the transverse tune shift due to the quadrupole component of the eddy current magnetic field is significantly less than the error introduced by the quadrupole magnet (Fig.11).

Fig.10 Horizontal and vertical tune shifts introduced by quadrupolar component

Fig.12 Eddy current power loss per unit length

Fig.11 Resonance line diagram

4.5 Power loss introduced by eddy currents in the vacuum chamber

The existence of electrical resistance would lead to heating effects.When the vacuum chamber is heated to a high temperature for a long time, the vacuum inside the chamber would decrease.In an extremely high vacuum environment,the gas molecules adsorbed on the vacuum chamber wall absorb heat and diffuse into the vacuum chamber.Then the vacuum would decrease and the beam lifetime would shorten.From an engineering point of view, overheated tube temperatures can cause aging and cracking of the epoxy resin in the dipole magnet core.Generally speaking, the temperature of the vacuum chamber does not exceed 80◦C.The eddy current power loss per unit length is given by Eq.7 and is shown in Fig.12 [41].

Table 5 Thermal conductivities

anda,b,hare the vacuum chamber half-width, vacuum chamber half-height and magnet gap half-height.To visualize the effect of power loss on the vacuum chamber we perform a transient EMF research using the ELEKTRA TR module in Opera software and calculated eddy current loss distribution.The eddy current loss is proportional to the magnetic field rate of change squared.The rate of change of the magnetic field in a single cycle is not constant.In the eddy current loss thermal analysis, the average eddy current loss in a single cycle is used and the average eddy current loss factor is 0.6434 by averaging and integrating the values over a time period.The we create a static thermal analysis model in Opera software’s TEMPO ST module.The thermal conductivities of the magnet core and Inconel 625 is shown in Table 5.The exterior surface of the vacuum chamber is configured for heat dissipation by air convection and the heat transfer coefficient is 14 W∕(m2⋅K).The initial ambient temperature is 28 °C.

We multiplied the average eddy current loss factor of 0.6434 by the eddy current loss distribution of the vacuum chamber under changing magnetic fields derived from the ELEKTRA TR module’s eddy current effect simulation.We imported it as a steady-state heat source distribution into the vacuum chamber model in the TEMPO ST module.After simulation the temperature distribution of the chamber after the eddy current loss is depicted in Fig.13.

The power losses at vacuum chamber were 23.63 W, and we can observe from the picture that the highest temperature is 75.165 °C within acceptable limits for engineering applications.This result is very close to the theoretical result.

Fig.14 Variation of magnetic field with time

5 Energy switching

Multiple energy extraction will be required for FLASH proton transport.Because the beam can be extracted from the ring in a single turn, compared to the time of a cycle, the extraction time can be neglected and also the injection.Its energy may be easily altered from one cycle to the next.

Three magnetic field cycles of the RCS are shown in Fig.14.Beam is injected at the bottom(‘inject 1’ and‘inject 2’).The beam is extracted at the different position of the cycle to obtain different energy levels (‘extract 1’ and‘extract 2’).The magnetic field cycle remained constant to reduce the hysteresis effect and control difficulty.The only change is the delay between the injection and extraction,with the strength of extraction element [42].The frequency and voltage of the RF vary according to the energy.

6 Conclusion

Currently, it is still challenging to improve accelerator technology to implement proton FLASH therapy.We propose a novel design for proton FLASH therapy using arapid-cycling synchrotron.In our design, the lattice, injection, extraction, space charge effects, eddy current effects and rapid energy switching are considered.The RCS can provide 1010protons/pulse.The irradiation time of a 60 Gray plan is about 1 min, and the instantaneous dose rate could reach 107Gy/s.Compared to laser plasma accelerator or slow extraction synchrotron, this is a cheap and simple design.If higher dose rate is required, the beam intensity of a spill can be increased.

Fig.13 (Color online) Temperature distribution of the thick vacuum chamber after eddy current loss temperature rise

Author contributionsAll authors contributed to the study conception and design.Material preparation, data collection and analysis were performed by Ying Shi and Man-Zhou Zhang.The first draft of the manuscript was written by Ying Shi and all authors commented on previous versions of the manuscript.All authors read and approved the final manuscript.The software use was helped by Lian-Hua Ou-Yang.And the article was supervised and revised by Man-Zhou Zhang, Zhi-Ling Chen, Xiu-Fang Li and De-Ming Li.

Data availabilityThe data that support the findings of this study are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.j00186.00169 and https://cstr.cn/31253.11.sciencedb.j00186.00169.

Declarations

Conflict of interestMan-Zhou Zhang is an editorial board member for Nuclear Science and Techniques and was not involved in the editorial review, or the decision to publish this article.All authors declare that there are no competing interests.