# Investigation into the Uniformization of Proton Beams for FLASH Therapy
###### Abstract  
FLASH proton therapy is widely considered in many labs. However, achieving a dose rate sufficient for FLASH is challenging, especially when using the scanning method. A beam uniformization process using a nonlinear magnet is employed to reduce the scanning time, supplemented by multi-energy extraction to enhance the dose rate. The impact of octupole fields, multipole field components, and step field on the transport line are tested. The nonlinear effect of the magnetic fields on the transverse motion of the particle beam is used to establish a uniform dose distribution at the target. Different schemes are investigated and the octupole approach was finally selected.  
FLASH; proton therapy; step-like magnet; multipole field; uniformization +
Footnote †: journal: Medical  
Several methods, such as shoot-through, 3D modulators, layer stacking, and scanning by deflecting cavities, are under development [11].  
Proton therapy based on the use of an synchrotron accelerator adopts a third-order resonance, slow extraction method [12], making it challenging to meet the FLASH dose rate requirements [1]. In this paper, beam expansion with uniformization is considered an effective approach. To achieve beam expansion through uniformization, the utilization of higher-order or specially shaped magnetic fields is needed to modulate beam shape and density [13; 14]. Leveraging the domestically produced proton therapy system, the research focuses on beam uniformization in the transport line, experimenting with different types of magnets to expand and homogenize the initially Gaussian-distributed beam. This progress forms a uniform distribution in a single energy slice and reaches the required dose within a short time according to the different beam currents. No scanning time is required. By incorporating multi-energy extraction to enhance the dose rate, the goal of FLASH therapy can be achieved. Additionally, the integration of a rapid-cycling synchrotron accelerator [15] can offer more advanced modulation methods and a higher particle number in the same time scale, reducing the impact of radiation on the environment, lowering the accelerator performance requirements, and enabling the clinical translation of FLASH therapy.  
Unlike the other beam modulation devices, which are mainly located in the nozzle, the higher-order or specially shaped magnet often sits in the transport line and should be designed together with the transport line. This scheme of homogenizing nonlinear magnet elements to ensure uniformization in the transport line is called beam-broadening homogenization, for which the use of a multipole magnet for beam spot homogenization was first proposed by [PERSON] [16]. [PERSON] and [PERSON] verified the homogenization effect of the octupole magnet via numerical calculation for a specific optical path [17]. Later, they demonstrated that the homogenization of Gaussian beam spots requires odd-order multipolar fields, such as octupole magnets and dodecapole magnets [18]. [PERSON] proposed a step-like field magnet (SFM) and studied its uniformization effect [19]. Both domestically and internationally, schemes for beam transport uniformization include nonlinear magnets with two pairs of octupole magnets and twelve-pole magnets in the ESS long-pulse target transport line [20], and two pairs of octupole nonlinear magnets in the CLAPA-II laser accelerator at Peking University [21]. A step-like magnet was designed for the IFIF-HEBT transport lines [20]. A comparison is made among different non-linear magnets and combinations to determine the optimal uniformization method.