A multi-energy extraction method of a synchrotron

Abstract

The present application relates to a multi-energy extraction method of a synchrotron, comprising the following steps: setting the dispersion and chromaticity of a synchrotron ring to meet the Hardt condition; under the action of a radio frequency electric field voltage, the energy of charged particles passes through a plurality of beam extraction stages suitable for extracting charged particle beams and a plurality of deceleration and energy reduction stages connected between the beam extraction stages in sequence with the change of the magnetic field of the synchrotron ring, and the charged particle beams are extracted at corresponding energies (E1, E2, E3) in each beam extraction stage by adjusting the beam transverse phase stability triangle area and the transverse radio frequency excitation beam emittance growth, wherein the reference particle transverse phase stability triangle area remains unchanged in each beam extraction stage, and the extraction boundary line of the beam transverse phase stability triangle in each beam extraction stage and the extraction boundary line of the reference particle transverse phase stability triangle always coincide due to the satisfaction of the Hardt condition.

Description

Technical Field

[0001] This invention relates to a method for extracting multiple energies from a synchrotron, used to extract multiple energy beams in the same cycle of the synchrotron. Background Technology

[0002] A synchrotron is a device that uses a magnetic field to control charged particles in a high vacuum, guiding them along a fixed circular orbit, and then continuously accelerating them (energy-boosting) them to high energies under the influence of an electric field. To maintain the stability of the particle orbit during the energy-boosting process, the synchrotron needs to ensure that the magnetic field amplitude and the frequency of the high-frequency accelerating electric field change synchronously with the particle energy, ultimately producing a particle beam that provides various particle beams and radiation rays for basic scientific research, clinical medicine, and industrial production. Many applications of synchrotrons require particle beams of different energies. For example, in clinical medicine, synchrotrons control the position of the Bragg peak within the human body by repeatedly changing the energy of the particle beam, thus precisely covering the lesion site without damaging surrounding healthy tissue. Figure 1 This illustrates the process of switching energy extraction in a synchrotron. The particle beam is... Figure 1 The energy platforms E1, E2, and E3, shown exemplary in the diagram and sandwiched between the dashed lines, extend from the synchrotron.

[0003] Traditional methods of extracting beams from synchrotrons are known as single-energy extraction. In single-energy extraction, the synchrotron can only extract a single energy beam within one cycle; switching the extracted energy can only be done between cycles. For example... Figure 1 As shown, after the beam is accelerated to a certain energy E1, the frequency of the magnet and the high-frequency cavity remains unchanged to ensure that the energy of the particles remains unchanged. The beam is then extracted at this energy plateau. If it is necessary to change the extraction energy, the beam is accelerated to a new energy E2 in the next cycle and extracted at the new energy plateau, and so on. Figure 1 The energies E1, E2, and E3 in the beam are within three synchrotron cycles, respectively. Therefore, it takes three synchrotron cycles to transform the beam energy from E1 to E2 and then to E3. If a beam with N energies is required, at least N synchrotron cycles are needed.

[0004] Because a single-energy beam is extracted from a single energy platform within each cycle of the synchrotron, extraction at a new energy level must be performed within a new cycle. Therefore, after extraction in each cycle, the magnetic field of the magnets needs to be reset to its initial value before the beam is re-injected and accelerated to the new energy platform. This results in a long energy switching time, requiring magnetic field reset and re-acceleration for each energy change. Furthermore, once the required number of particles for a particular energy level is reached within each cycle of the synchrotron, the remaining beam within the synchrotron is lost due to energy switching and cannot be utilized, leading to low beam utilization.

[0005] To address this, the concept of multi-energy extraction has been proposed in existing technologies. In multi-energy extraction, multiple energy platforms are provided for extraction within one cycle of synchrotron operation. The number of energy platforms is determined by demand, enabling the extraction of multiple energies in a single cycle, significantly reducing the time required to change the extracted beam energy and improving beam utilization. Currently, there are experiments and reports on multi-energy extraction internationally. HIMAC (Heavy Ion Medical Accelerator in Chiba) in Japan and HIT (Heidelberg Ion-Beam Therapy Center) in Germany have both conducted multi-energy extraction experiments. HIMAC uses a method of accelerating to high energy and then reducing the energy for extraction, while HIT uses a method of performing multi-energy extraction during acceleration.

[0006] The National Institute of Radiological Sciences, an independent administrative agency, applied for a related invention patent in Japan on March 5, 2007, with authorization announcement number JP4873563B2.

[0007] The Huizhou Ion Science Research Center and the Institute of Modern Physics, Chinese Academy of Sciences, applied for a Chinese invention patent entitled "Single-cycle Multi-step Active Energy Slow Extraction Method for Synchrotrons" on May 22, 2018. The authorization announcement date was August 21, 2020, and the authorization announcement number was CN108939317B.

[0008] In addition, Tsinghua University, the applicant of this application, also filed an invention patent application on November 19, 2021, with application number 202110867950.4 and invention title "A Control Method for a Synchrotron". This application has been published, with publication number CN113677084A.

[0009] The motion of a beam in a synchrotron can be described using a position-slope phase space. In the horizontal phase space, the x and x' coordinates of the phase diagram represent the beam's position and divergence in the x-direction. When the particle's horizontal operating point is close to the one-third integer resonance line and a hexapolar magnetic field exists, a triangular phase-stabilized region forms in the horizontal phase space, referred to below as the transverse phase-stabilized triangle. When the particle's emittance is less than the area of ​​the transverse phase-stabilized triangle (e.g., ...), the phase stability region is significantly reduced. Figure 1A (As shown) The motion of this particle is stable when the particle's emission degree is greater than the area of ​​the transverse phase-stable triangle (e.g.) Figure 1B (As shown) The motion of this particle is unstable; the particle will move outward along the boundary line of the transverse phase-stability triangle. Figure 1A The particle, indicated by reference numeral 100, is constrained within the area of ​​a transversely phase-stabilizing triangle, while Figure 1B The figure shows a particle escaping the area of ​​the transverse phase-stable triangle, indicated by reference numeral 100'. Slow extraction utilizes this property, by increasing the emittance of the excitation beam or by reducing the area of ​​the transverse phase-stable triangle, to allow particles to move from the stable region defined by the transverse phase-stable triangle into the unstable region outside the transverse phase-stable triangle, thus achieving controlled extraction of particles.

[0010] The operating point mentioned above refers to the frequency of free oscillation of particles in the lateral motion of a synchrotron. Using the horizontal and vertical operating points as the x and y axes, a resonance curve diagram can be obtained, as shown below. Figure 1D As shown. Figure 1D The black dot represents the operating point of the synchrotron, and the lines in the diagram represent resonance lines of different orders. In the slow extraction of third-order resonance, since third-order resonance only occurs in the horizontal direction, and the motion in the horizontal and vertical directions is not coupled, the third-order resonance line at this time is the vertical third-order resonance line in the diagram. Figure 1D In the middle, the one-third resonance line closest to the horizontal operating point is Q. x =5 / 3 of the vertical line, the distance from the horizontal operating point to this one-third resonance line is the distance from the black dot in the diagram to this vertical line. The operating point is determined by the magnet focusing parameters and layout. Once the magnet layout is determined, the magnet focusing parameters determine the horizontal operating point. The greater the strength of the focused quadrupole, the larger the horizontal operating point; the greater the strength of the defocused quadrupole, the smaller the horizontal operating point, and vice versa. Therefore, by adjusting the magnetic field strength of the focused quadrupole and / or the defocused quadrupole, the distance from the operating point to the one-third resonance line can be adjusted.

[0011] The area of ​​the transverse phase-stabilizing triangle is inversely proportional to the square of the hexapole magnetic field strength and directly proportional to the square of the distance from the horizontal operating point to the one-third integer resonance line. That is, the stronger the hexapole magnetic field, the smaller the stable region area; the greater the distance from the horizontal operating point to the one-third integer resonance line, the larger the stable region area. Therefore, the area of ​​the transverse phase-stabilizing triangle can be changed by adjusting the magnetic field strength of the focusing quadpole and / or defocusing quadpole to bring the operating point closer to or further away from the one-third resonance line, and / or directly by adjusting the magnitude of the hexapole magnetic field strength.

[0012] In its application filed on March 3, 2022, with application number 202210203893.4 and entitled "Multi-Energy Extraction Method for Synchrotrons," the applicant proposed a multi-energy extraction method for synchrotrons. In this method, during each beam extraction stage, the magnetic field strength of the quadrupole and / or hexapole is adjusted such that the difference between the average values ​​of the transverse phase-stabilizing triangle areas corresponding to each energy in each beam extraction stage is within the allowable variation range of the synchrotron's extraction efficiency. Thus, by adjusting the average value of the transverse phase-stabilizing triangle areas in each beam extraction stage to be as consistent as possible (i.e., within the allowable variation range), the synchrotron maintains a relatively consistent extraction efficiency during application. In this multi-energy extraction method, the transverse phase-stabilizing triangle area during extraction is no longer constant (e.g., the hexapole or quadrupole strength can be changed to cause the transverse phase-stabilizing triangle area to shrink during extraction), but the average value of the transverse phase-stabilizing triangle area during extraction of different energies is approximately consistent. In each beam extraction stage, the area of ​​the stable triangle at the end of the beam extraction is smaller than the area of ​​the transverse stable triangle at the beginning of the beam extraction stage. However, the area of ​​the transverse stable triangle at the beginning of the next beam extraction stage is larger than the area of ​​the transverse stable triangle at the end of the previous energy extraction. In other words, the area of ​​the transverse stable triangle increases before and after each energy reduction, which can suppress beam extraction overshoot caused by the increase in transverse emissivity due to energy reduction.

[0013] The shortcomings of the aforementioned multi-energy extraction method for synchrotrons are twofold. Firstly, by altering the strength of the quadrupole and / or hexapole to change the area of ​​the transverse phase-stabilizing triangle during extraction, the divergence angle of the extracted beam entering the extraction channel continuously changes during extraction. This results in a time-varying beam position at the application end, a problem that must be considered when dose uniformity is required. Secondly, although the change in extraction efficiency caused by the change in the triangle area is relatively small, it is still desirable to maintain a completely constant extraction efficiency.

[0014] Therefore, it is desirable to provide a multi-energy extraction method for synchrotrons that can effectively suppress beam overshoot while ensuring stable beam position and constant extraction efficiency at the beam application end during extraction. Summary of the Invention

[0015] The area of ​​the transverse phase-stabilizing triangle of the beam is altered by controlling the difference between the average momentum dispersion of the actual beam and the momentum of the reference particle. Here, the reference particle is defined as a particle with a certain momentum capable of moving along a designed trajectory within the synchrotron loop. The operating point of the reference particle and the area of ​​the transverse phase-stabilizing triangle are determined by machine parameters such as the magnetic field strength of the dipole, quadrupole, and hexapole magnets of the synchrotron and the momentum of the reference particle itself. Generally, the average momentum of the actual beam particles corresponds to the momentum of the reference particle.

[0016] Once the magnetic field strength of the synchronizing magnet is determined, the momentum of the reference particle corresponding to parameters such as the designed operating point and closed orbit is also uniquely determined. When the magnetic field strength of the synchronizing magnet is changed proportionally, the momentum of the reference particle corresponding to parameters such as the designed operating point and closed orbit will also change proportionally. If the strengths of the dipole, tetrapole, and hexapole magnets are changed proportionally, the corresponding momentum of the reference particle will also change proportionally, but the operating point and the area of ​​the transverse phase stability triangle remain unchanged.

[0017] When the actual beam momentum deviates from the momentum of the reference particle, the beam operating point and closed trajectory can be calculated using two parameters: dispersion and chromaticity. The dispersion effect refers to the deviation of the trajectory of a particle in the synchronization loop whose momentum deviates from that of the reference particle. The magnitude of the trajectory deviation at a point on the loop is equal to the product of the value of the dispersion function on the synchronization loop at that point and the momentum deviation between the particle and the reference particle. The chromaticity effect refers to the deviation of the operating point of a particle in the synchronization loop whose momentum deviates from that of the reference particle. The magnitude of the operating point deviation is equal to the product of the chromaticity on the synchronization loop and the momentum deviation between the particle and the reference particle.

[0018] On the one hand, due to the dispersion on the synchrotron ring, the centers of the transverse phase stability triangles of beam particles with different momentum dispersions will be dispersed. On the other hand, due to the presence of chromaticity, the operating points of beam particles with different momentum dispersions will be dispersed, resulting in an increase or decrease in the area of ​​the transverse phase stability triangle. Therefore, when designing the extraction system, special design considering the dispersion, dispersion derivative, and chromaticity on the synchrotron ring is necessary to ensure that the transverse phase stability boundary lines of particles with different momentum dispersions coincide (referred to as the Hardt condition). This can reduce beam loss at the extraction channel, improve extraction efficiency, and ensure the stability of the beam position at the application end during extraction.

[0019] Therefore, this invention provides a multi-energy extraction method for a synchrotron, comprising the following steps: setting the dispersion and chromaticity of the synchrotron's synchrotron loop to satisfy the Hardt condition; under the action of a radio frequency electric field voltage, accompanied by changes in the synchrotron loop magnetic field, causing the energy of charged particles to successively pass through several beam extraction stages suitable for extracting charged particle beams and several deceleration and energy reduction stages connecting these beam extraction stages; by adjusting the area of ​​the transverse phase-stabilizing triangle of the beam and increasing the transverse radio frequency excitation beam emittance in the beam extraction stages, the charged particle beam is extracted with corresponding energy; wherein, in each In each of the aforementioned beam extraction stages, the area of ​​the transverse phase stabilization triangle of the reference particle remains unchanged. Due to the satisfaction of the Hardt condition, the extraction boundary line of the transverse phase stabilization triangle of the beam in each beam extraction stage always coincides with the extraction boundary line of the transverse phase stabilization triangle of the reference particle. As mentioned above, the reference particle is a particle with a certain momentum that can move in the synchrotron ring according to the designed trajectory. The operating point of the reference particle and the area of ​​the transverse phase stabilization triangle are directly determined by the magnetic field strength of the dipole, quadrupole, and hexapole of the synchrotron and the momentum of the reference particle itself.

[0020] Since the extraction boundary line of the transverse phase-stabilized triangle of the beam always coincides with the extraction boundary line of the transverse phase-stabilized triangle of the reference particle during the beam extraction stage, and the area of ​​the transverse phase-stabilized triangle of the reference particle remains unchanged, the beam with momentum dispersion and the reference particle with the area of ​​the transverse phase-stabilized triangle remains unchanged are still extracted from the same extraction boundary line. This achieves an extraction efficiency that remains constant when the area of ​​the transverse phase-stabilized triangle of the beam changes.

[0021] Based on this, beam overshoot can be avoided by varying the area of ​​the beam transverse phase stabilization triangle. Preferably, the radio frequency electric field voltage and the magnetic field strengths of the dipole, tetrapole, and hexapole are adjusted before each beam extraction stage so that the area of ​​the beam transverse phase stabilization triangle at the start of each beam extraction stage is larger than the area of ​​the reference particle transverse phase stabilization triangle. Furthermore, during each beam extraction stage, the area of ​​the beam transverse phase stabilization triangle is changed by altering the deviation between the beam's average momentum and the reference particle's momentum, ensuring that the area of ​​the beam transverse phase stabilization triangle at the end of beam extraction is smaller than the area at the start of beam extraction. Therefore, the area of ​​the beam transverse phase stabilization triangle can increase during each deceleration and energy reduction stage, suppressing extraction overshoot caused by the increase in transverse emissivity due to energy reduction.

[0022] The Hardt condition in any given synchronization loop is determined by dispersion, dispersion derivative, chromaticity, operating point, hexapol magnet strength, and the positions of the hexapol magnet and electrostatic cutter. Here, the Hardt condition is satisfied only by adjusting dispersion and chromaticity. Satisfying the Hardt condition means that, considering the momentum dispersion of the beam relative to the reference particle, the beam's transverse phase stabilization triangle maintains its exit boundary line coinciding with the exit boundary line of the reference particle's transverse phase stabilization triangle during contraction. Since the area of ​​the reference particle's transverse phase stabilization triangle remains constant during each beam exit phase, the coincidence of the exit boundaries means that particles are still exited from the same exit boundary line, which is equivalent to the effect of the beam's transverse phase stabilization triangle area remaining unchanged when momentum dispersion is not considered.

[0023] Extraction efficiency is the ratio of the total number of charged particles extracted to the total number of charged particles lost within the synchrotron. The average area of ​​the transverse phase-stabilizing triangle in each beam extraction stage determines the ratio of the total number of charged particles extracted to the total number of charged particles lost within the synchrotron at that energy, and thus determines the extraction efficiency of the synchrotron at that energy. Therefore, the method of this invention maintains the extraction efficiency of the synchrotron as consistently as possible in application by adjusting the average area of ​​the transverse phase-stabilizing triangle in each beam extraction stage to be as uniform as possible (i.e., within an allowable range of variation).

[0024] Since the area of ​​the stability triangle varies only slightly across different energies, the extraction efficiency remains essentially the same at different energies. There is no situation where the area of ​​the stability triangle increases as the extraction energy decreases, leading to a drop in extraction efficiency. This facilitates the extraction of multiple energies within the same cycle while maintaining extraction efficiency.

[0025] although Figures 3A-5 The diagram shows energy platforms corresponding to three energies, E1, E2, and E3. However, it should be understood that, obviously, two or more charged particle beams with energies can be extracted within one cycle of the synchrotron, depending on the needs of the practical application.

[0026] In a preferred embodiment of the multi-energy extraction method for a synchrotron according to the present invention, in the step of keeping the area of ​​the transverse phase-stabilizing triangle of the reference particle constant and changing the deviation between the beam average momentum and the momentum of the reference particle, the momentum of the reference particle is changed by proportionally adjusting the magnetic field strength of all dipoles, quadrupoles and hexapoles.

[0027] Normally, the chromaticity on the synchronizing ring is negative. When the magnetic field strength of all magnets decreases proportionally, the momentum of the reference particle decreases, while the average momentum of the beam remains unchanged. Therefore, the average momentum of the beam is greater than the momentum of the reference particle, meaning the momentum deviation between the particle and the reference particle increases. According to the chromaticity effect, the operating point deviation is equal to the product of the chromaticity on the ring and the momentum deviation between the particle and the reference particle. Since the chromaticity is negative, the operating point deviation is negative and its absolute value increases, meaning the beam operating point decreases. If the reference particle is above the resonance line, meaning the operating point is greater than the resonance point (e.g., 5 / 3), the decrease in the beam operating point brings it closer to the resonance point, correspondingly causing a contraction in the area of ​​the transverse phase stability triangle. If the reference particle is below the resonance line, meaning the operating point is less than the resonance point (e.g., 5 / 3), the decrease in the beam operating point means it is further from the resonance point, correspondingly causing an increase in the area of ​​the transverse phase stability triangle. Therefore, the magnetic field strength of each magnet can be proportionally increased or decreased based on the position of the reference particle's operating point relative to the resonant line to achieve scaling of the beam's transverse phase stabilization triangle area relative to the reference particle's transverse phase stabilization triangle area, which remains unchanged under proportional scaling. Clearly, when proportionally amplifying the magnetic field strength of all magnets, the positional relationship between chromaticity, the reference particle's operating point, and the resonant line can be considered, and the scaling of the beam's transverse phase stabilization triangle area relative to the reference particle's transverse phase stabilization triangle area can be similarly adjusted. As mentioned above, the reference particle's momentum and operating point are uniquely determined by the design of the synchrotron ring; therefore, for any synchrotron, an appropriate degree and method of scaling the magnetic field strength of each magnet can always be found to achieve the desired relationship between the beam's transverse phase stabilization triangle area and the reference particle's transverse phase stabilization triangle area.

[0028] In a preferred embodiment of the multi-energy extraction method for a synchrotron according to the present invention, in the step of keeping the area of ​​the transverse phase-stabilized triangle of the reference particle unchanged and changing the deviation between the beam average momentum and the momentum of the reference particle, the beam average momentum is changed by a high-frequency system or an additional acceleration device.

[0029] From another perspective, understanding the chromaticity effect reveals that since the operating point deviation is equal to the product of the chromaticity on the ring and the momentum deviation between the beam particle and the reference particle, changing the momentum of the beam particle, without changing the momentum of the reference particle, can also alter the momentum deviation between the beam particle and the reference particle. Specifically, corresponding to the method of proportionally scaling the magnetic field strength of all magnets while keeping the reference particle momentum constant, if the magnetic field strength of the magnets is not changed, the reference particle momentum will naturally remain unchanged. In this case, increasing the average momentum of the beam by accelerating the beam using a high-frequency system or an additional acceleration device can similarly increase the momentum deviation between the beam particle and the reference particle. Based on the same derivation above, this also leads to a smaller beam operating point. If the reference particle is above the resonance line, i.e., the operating point is greater than the resonance point (e.g., 5 / 3), the smaller beam operating point brings it closer to the resonance point, correspondingly causing a contraction in the area of ​​the transverse phase stability triangle. If the reference particle is below the resonance line, that is, the operating point is smaller than the resonance point (e.g., 5 / 3), then the smaller beam operating point means that it is farther away from the resonance point, which correspondingly leads to a larger area of ​​the beam's transverse phase stability triangle.

[0030] Therefore, based on the discussion above, whether the momentum of the reference particle is changed by proportionally scaling the magnetic field strength of all magnets, or by directly changing the momentum of the beam through a high-frequency system or additional acceleration device, a momentum deviation between the beam and the reference particle may occur. This, in turn, changes the operating point deviation through the chromaticity effect, thereby altering the area of ​​the beam's transverse phase stability triangle (the operating point of the reference particle and the transverse phase stability triangle remain unchanged during this process). Therefore, regarding the method of changing the momentum deviation, the momentum of the beam can be changed simultaneously, either individually or in combination, or (although not preferably) by proportionally scaling the magnetic field strength of all magnets and by accelerating or decelerating the beam. For example, the momentum deviation between the beam and the reference particle can be increased by proportionally reducing the magnetic field strength of all magnets to decrease the momentum of the reference particle, while simultaneously increasing this momentum deviation by accelerating the beam. Alternatively, the momentum deviation can be increased by proportionally reducing the magnetic field strength of all magnets to decrease the momentum of the reference particle, but this momentum deviation can be reduced by decelerating the beam. Ultimately, whether the momentum deviation increases or decreases depends on the relative magnitudes of the two effects.

[0031] Other features and advantages of this application will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the application. Other advantages of this application can be realized and obtained by means of the solutions described in the description and the accompanying drawings. Attached Figure Description

[0032] The embodiments of the present invention will now be explained in detail with reference to the accompanying drawings. In the drawings:

[0033] Figure 1 The diagram illustrates the process of a synchrotron switching to extract multiple energies.

[0034] Figure 1A and Figure 1B The diagrams schematically illustrate the cases where charged particles are confined within the area of ​​the transverse phase-stabilized triangle and the cases where they escape from the area of ​​the transverse phase-stabilized triangle, without considering beam flux dispersion.

[0035] Figure 1C The diagram illustrates the situation in the multi-energy extraction method of the synchrotron according to the present invention, where the area of ​​the transverse phase-stabilized triangle of the beam shrinks towards the area of ​​the transverse phase-stabilized triangle of the reference particle, which remains unchanged. The extraction boundary between the two remains consistent due to the Hardt condition being satisfied.

[0036] Figure 1D The diagram schematically illustrates the operating point of the synchrotron and the resonance lines of different orders;

[0037] Figure 2 This is a schematic diagram of the synchrotron in an embodiment of the present invention;

[0038] Figure 3A The present invention provides a time-series diagram of the radio frequency electric field voltage, the strength of the dipolar magnetomagnetic field, the strength of the focused quadrupole magnetomagnetic field, the strength of the hexapolar magnetomagnetic field, the area of ​​the transverse phase stabilization triangle of the reference particle, the area of ​​the transverse phase stabilization triangle of the beam, and the difference between the average momentum of the beam and the momentum of the reference particle in the multi-energy extraction method of the synchrotron according to the present invention. The strengths of the dipolar, focused quadrupole, and hexapolar magnetomagnetic fields change proportionally during the beam extraction stage, while the area of ​​the transverse phase stabilization triangle of the reference particle remains unchanged.

[0039] Figure 3B To and Figure 3A The timing diagrams shown correspond to the following: radio frequency electric field voltage, dipolar ferromagnetic field strength, defocused quadrupole ferromagnetic field strength, hexapolar ferromagnetic field strength, area of ​​the transverse phase stabilization triangle of the reference particle, area of ​​the transverse phase stabilization triangle of the beam, and the difference between the average momentum of the beam and the momentum of the reference particle.

[0040] Figure 4A The present invention provides a time-series diagram of the radio frequency electric field voltage, the strength of the dipolar magnetomagnetic field, the strength of the focused quadrupole magnetomagnetic field, the strength of the hexapole magnetomagnetic field, the area of ​​the transverse phase stabilization triangle of the reference particle, the area of ​​the transverse phase stabilization triangle of the beam, the difference between the beam average momentum and the momentum of the reference particle, and the beam average momentum in the multi-energy extraction method of the synchrotron according to the present invention. In the beam extraction stage, the beam average momentum increases, while the strengths of the dipolar, quadrupole, and hexapole magnetomagnetic fields remain unchanged.

[0041] Figure 4B To and Figure 4AThe timing diagrams shown correspond to the following: radio frequency electric field voltage, dipolar ferromagnetic field strength, defocused quadrupole ferromagnetic field strength, hexapolar ferromagnetic field strength, area of ​​the transverse phase stability triangle of the reference particle, area of ​​the transverse phase stability triangle of the beam, the difference between the beam average momentum and the momentum of the reference particle, and the beam average momentum. Among them, the hexapolar ferromagnetic field strength remains unchanged during the beam extraction stage.

[0042] Figure 5 A timing diagram of the RF-KO excitation of the multi-energy extraction method for synchrotrons according to the present invention;

[0043] Figure 6 This is a flowchart of a multi-energy extraction method for a synchrotron according to the present invention.

[0044] The accompanying drawings are used to explain the technical solutions of this application and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of this application, and do not constitute a limitation on the technical solutions of this application. Detailed Implementation

[0045] A synchrotron is an acceleration device that uses a radio frequency electric field to accelerate charged particles along a circular path. The charged particles undergo cyclotronic motion within the synchrotron.

[0046] In this embodiment, as Figure 2 As shown, the synchrotron includes a ring path 6, a high-frequency cavity 4, a radio frequency excitation device, and multiple sets of confinement magnets. The high-frequency cavity 4 (RF Cavity) is located on the ring path 6. The multiple sets of confinement magnets are distributed circumferentially around the ring path 6. Each set of confinement magnets includes a dipolar magnet 1, a focusing quadrupole magnet 2, a defocusing quadrupole magnet 5, and a hexapolar magnet 3.

[0047] The magnetic field of the dipole 1 is used to deflect particles, causing charged particles to undergo cyclotronic motion. The magnetic fields of the focusing quadrupole 2 and the defocusing quadrupole 5 are used to focus the beam laterally to maintain its stability. Since particles may deviate from their central trajectory for various reasons, the quadrupoles act as a focusing force to bring them back to their central trajectory and prevent them from being lost. The magnetic field strength of the focusing quadrupole 2 and the defocusing quadrupole 5 determines the operating point of the synchrotron. The magnetic field of the hexapod 3 is used to form a triangular phase space stability region (i.e., the lateral phase stability triangle) that constrains the beam motion in the lateral phase space. The greater the magnetic field strength of the hexapod 3, the smaller the area of ​​the lateral phase stability triangle. When the magnetic field strength of the hexapod 3 reaches a certain level, the beam emission increases rapidly from the three vertices of the lateral phase stability triangle along the extended side lines (the boundary lines). When the emission increases to a certain level, charged particles can be drawn out of the annular path 6. The size of the transverse phase-stabilizing triangle is proportional to the square of the distance from the horizontal operating point of the beam to the 1 / 3 resonant line, and inversely proportional to the square of the magnetic field strength of the resonant hexapolar iron 3. The high-frequency cavity 4 is used to accelerate or decelerate particles, or simply maintain longitudinal focusing without changing the particle energy. When the synchronization phase of the radio frequency electric field is not zero, charged particles are accelerated or decelerated once each time they pass through the high-frequency cavity 4 due to the radio frequency electric field. When the synchronization phase of the radio frequency electric field is zero, it is used to maintain longitudinal focusing without changing the particle energy. The parameters of the magnetic fields of all magnets in the synchrotron and the radio frequency electric field of the high-frequency cavity 4 are kept synchronized with the energy of the charged particles, thereby constraining the particles to move along a fixed annular path 6.

[0048] Radio frequency excitation devices are used to apply RF-KO excitation to extract the beam, such as... Figure 5 As shown, RF-KO (transverse radio frequency knock-out) excitation refers to the phenomenon where a transverse radio frequency electric field is generated to kick the beam, thereby gradually increasing the beam emittance and leading to its extraction. Before the extraction of charged particles, the beam emittance is less than the area of ​​the transverse phase-stabilizing triangle. The function of RF-KO is to increase the beam emittance by applying a transverse electric field to the beam while keeping all synchrotron parameters constant. When the beam emittance increases to a level greater than or equal to the area of ​​the transverse phase-stabilizing triangle, the beam rapidly increases along the extended sides of the triangle (the extraction boundary) and is thus extracted. This transverse electric field is the RF-KO excitation. Using RF-KO for extraction allows other parameters to remain constant during extraction, significantly reducing the operational complexity of the synchrotron.

[0049] This embodiment proposes a multi-energy extraction method for synchrotrons, which extracts charged particles at progressively decreasing energies within one cycle of the synchrotron. One cycle refers to the accelerator's operating cycle, typically on the order of a few seconds, during which the charged particle can travel along the circular path 6 millions to tens of millions of times.

[0050] The multi-energy extraction method of the synchrotron in this application is illustrated below and in the accompanying drawings using the example of extracting energy only three times within a synchrotron cycle. However, the number of times energy is extracted within a synchrotron cycle is clearly exemplary and not limiting. Figure 6 The flowchart shown illustrates that the multi-energy extraction method for a synchrotron according to the present invention includes the following steps:

[0051] Step S1: Accelerate charged particles to the first energy using a radio frequency electric field to form a beam.

[0052] A radio frequency electric field is applied in the high-frequency cavity 4, exerting a force on the charged particles in approximately the same direction as their motion. When the charged particles are positively charged, the direction of the radio frequency electric field is the same as the direction of their motion. When the charged particles are negatively charged, the direction of the radio frequency electric field is opposite to the direction of their motion. Each time a charged particle passes through the high-frequency cavity 4, it is accelerated by the radio frequency electric field, thereby increasing its energy. During the acceleration of the charged particles, the strengths of the magnetic fields of the diode 1, the focusing tetrapole 2, the defocusing tetrapole 5, and the hexapole 3 change accordingly, causing the charged particles to maintain their motion along the circular path 6. Accelerating the charged particles to a preset energy is existing technology and will not be described in detail here.

[0053] Step S2: Maintain the charged particles in the beam at the first energy during the first beam extraction phase, and extract a portion of the beam during the first beam extraction phase.

[0054] Based on the magnitude of the first energy, the radius of the annular path 6, and the respective positions of the dipole 1, focusing quadrupole 2, defocusing quadrupole 5, and hexapod 3, the magnetic field strength of the dipole 1, focusing quadrupole 2, defocusing quadrupole 5, and hexapod 3, as well as the voltage, frequency, and phase of the radio frequency electric field in the high-frequency cavity 4, required to maintain the charged particles at the first energy and allow them to move along the annular path 6, can be calculated. After accelerating the charged particles to the first energy, RF-KO excitation is applied through the radio frequency excitation device to extract a portion of the beam. The duration of the first beam extraction phase is determined by the time required for the radio frequency excitation device to extract the beam. The first energy is determined by the requirements of the target to be bombarded by the extracted charged particles.

[0055] Since a portion of the beam needs to be extracted during this process, the voltage of the radio frequency electric field in the high-frequency cavity 4 needs to be kept at a low value during the first beam extraction stage. This can reduce the momentum dispersion of the extracted beam. In this embodiment, when the voltage of the radio frequency electric field is 100V, the maximum momentum dispersion of the beam for a proton with an energy of 60MeV decreases to 0.1%.

[0056] In the first beam extraction stage, the magnetic field strengths of the dipole, tetrapole, and hexapole magnets are proportionally reduced, thus decreasing the momentum of the reference particle while maintaining its operating point. Since the average momentum of the beam remains constant, the momentum difference between the beam and the reference particle increases during this first stage. When the chromaticity is negative and the operating point of the reference particle is above the third-order resonance line, this increased momentum difference means the deviation between the beam and the reference particle's operating point is negative and its absolute value increases. This implies that the beam's operating point is moving away from the reference particle's operating point and downwards towards the third-order resonance line, resulting in a decrease in the area of ​​the beam's transverse phase stability triangle. Figure 3A and Figure 3B As shown, the area curve of the transverse phase-stabilized triangle of the beam gradually decreases from the start of beam extraction to the end of beam extraction in the first beam extraction stage.

[0057] Step S3: Increase the voltage value of the radio frequency electric field to the deceleration voltage value. During this process, the magnetic field strength of the diode 1 remains unchanged, the magnetic field strength of the focusing quadrupole 2 increases or the magnetic field strength of the defocusing quadrupole 5 decreases, and the magnetic field strength of the hexapod 3 decreases.

[0058] The deceleration voltage can be 500V. In this step, the magnetic field strength of the hexapolar iron 3 decreases by 50% to 100%, that is, the magnetic field strength of the hexapolar iron 3 decreases to 0% to 50% of the magnetic field strength before the decrease.

[0059] Step S4: Change the synchronization phase of the radio frequency electric field so that the radio frequency electric field applies a force to the charged particle in the opposite direction of its motion, maintain the deceleration voltage value so that the energy of the charged particle decreases until the energy of the charged particle decreases from the first energy to the second energy, the magnetic field strength of the dipole 1 gradually decreases, the magnetic field strength of the focusing quadrupole 2 or the defocusing quadrupole 5 gradually decreases, and the magnetic field strength of the hexapod 3 remains unchanged.

[0060] In this step, since the direction of the force exerted by the radio frequency electric field in the high-frequency cavity 4 on the charged particles is opposite to the direction of motion of the charged particles, the particles are decelerated each time they pass through the high-frequency cavity 4, resulting in a decrease in energy.

[0061] The duration of the first deceleration period required for the charged particle to decrease from the first energy to the second energy can be calculated based on the voltage value of the radio frequency electric field in the high-frequency cavity 4, the mass of the charged particle, the charge of the charged particle, the radius of the ring path 6, the first energy, and the second energy. Thus, by maintaining the radio frequency electric field at the deceleration voltage value for the first deceleration period while decelerating the charged particle, the first energy can be reduced to the second energy.

[0062] Thus, in step S3, energy reduction preparation is carried out by first increasing the voltage value of the radio frequency electric field to increase the area of ​​the longitudinal phase stabilization region. In step S4, the voltage value of the radio frequency electric field is maintained at this higher voltage value to decelerate the charged particles, which can reduce the longitudinal loss caused by the beam during the process of reducing the energy to the second extraction energy. At the same time, in step S3, increasing the normalized magnetic field strength of the focusing quadrupole 2 or decreasing the normalized magnetic field strength of the defocusing quadrupole 5 can move the horizontal operating point away from the resonance line before energy reduction, and decreasing the normalized magnetic field strength of the hexapod 3 can increase the area of ​​the transverse triangular phase stabilization region, which can reduce the transverse beam loss caused by the beam during the process of reducing the energy to the second extraction energy.

[0063] Step S5: Reduce the voltage value of the radio frequency electric field and change the synchronization phase of the radio frequency electric field so that the radio frequency electric field no longer decelerates the charged particles, so as to maintain the charged particles at the second energy.

[0064] After the energy of the charged particles decreases to the second energy, the magnetic field strength of the dipole 1 stops decreasing, the magnetic field strength of the focusing quadrupole 2 decreases or the magnetic field strength of the defocusing quadrupole 5 increases, and at the same time, the magnetic field strength of the hexapod 3 is increased until it is lower than the magnetic field strength of the hexapod at the end of the first beam extraction stage, so that the area of ​​the transverse phase stabilization triangle at the end of the first beam extraction stage is smaller than the area of ​​the transverse phase stabilization triangle at the beginning of the second beam extraction stage.

[0065] Step S6: Maintain the charged particles in the beam at the second energy level to reach the second beam extraction stage, and extract a portion of the beam during this second beam extraction stage.

[0066] In the second beam extraction stage, the magnetic field strengths of the dipole, tetrapole, and hexapole magnets are proportionally reduced, thus decreasing the momentum of the reference particle while maintaining its operating point. Since the average momentum of the beam remains constant, the momentum difference between the beam and the reference particle increases during this stage. When the chromaticity is negative and the operating point of the reference particle is above the third-order resonance line, this increased momentum difference means the deviation between the beam and the reference particle's operating point is negative and its absolute value increases. This implies that the beam's operating point is moving away from the reference particle's operating point and downwards towards the third-order resonance line, resulting in a decrease in the area of ​​the beam's transverse phase stability triangle. Figure 3A and Figure 3B As shown, the area curve of the transverse phase-stabilized triangle of the beam gradually decreases from the beginning to the end of the second beam extraction stage.

[0067] Compared with the first beam extraction stage, it can be noted that the area of ​​the beam transverse phase stabilization triangle at the end of each subsequent beam extraction stage is larger than the area at the beginning of each preceding beam extraction stage. Therefore, the area of ​​the beam transverse phase stabilization triangle increases during each deceleration and energy reduction stage, which can suppress extraction overshoot caused by the increase in transverse emittance due to energy reduction.

[0068] After slowing the charged particles to the second energy, the magnetic field strength of the focusing quadrupole 2 is reduced or the magnetic field strength of the defocusing quadrupole 5 is increased, and the magnetic field strength of the hexapod 3 is increased, the charged particles need to be maintained for the duration of the second beam extraction phase. During this second beam extraction phase, a portion of the beam can be extracted using a radio frequency (RF) excitation device. The length of the second beam extraction phase is determined by the time required for the RF excitation device to extract the beam. The second energy is determined by the requirements of the target to be bombarded by the extracted charged particles. The second energy is less than the first energy.

[0069] Step S7: Increase the voltage value of the radio frequency electric field to the deceleration voltage value. During this process, the magnetic field strength of the diode 1 remains unchanged, the magnetic field strength of the focusing tetrapole 2 increases or the magnetic field strength of the defocusing tetrapole 5 decreases, and the magnetic field strength of the hexapole 3 decreases.

[0070] The deceleration voltage can be 500V. In this step, the magnetic field strength of the hexapolar iron 3 decreases by 50% to 100%, that is, the magnetic field strength of the hexapolar iron 3 decreases to 0% to 50% of the magnetic field strength before the decrease.

[0071] Step S8: Change the synchronization phase of the radio frequency electric field so that the radio frequency electric field applies a force opposite to the direction of motion of the charged particle, maintain the deceleration voltage value so that the energy of the charged particle decreases until the energy of the charged particle decreases from the second energy to the third energy, the magnetic field strength of the dipole 1 gradually decreases, the magnetic field strength of the focusing quadrupole 2 or the defocusing quadrupole 5 gradually decreases, and the magnetic field strength of the hexapod 3 remains unchanged.

[0072] In this step, since the direction of the force exerted by the radio frequency electric field in the high-frequency cavity 4 on the charged particles is opposite to the direction of motion of the charged particles, the particles are decelerated each time they pass through the high-frequency cavity 4, resulting in a decrease in energy.

[0073] The duration of the second deceleration period required for the charged particle to decrease from the second energy to the third energy can be calculated based on the voltage value of the radio frequency electric field in the high-frequency cavity 4, the mass and charge of the charged particle, the radius of the ring path 6, the second energy, and the third energy. Thus, by maintaining the radio frequency electric field at the deceleration voltage value for the entire second deceleration period while decelerating the charged particle, the second energy can be reduced to the third energy.

[0074] Thus, in step S7, energy reduction preparation is carried out by first increasing the voltage value of the radio frequency electric field to increase the area of ​​the longitudinal phase stabilization region. In step S8, the voltage value of the radio frequency electric field is maintained at this higher voltage value to decelerate charged particles, which can reduce the longitudinal loss caused by the beam during the process of reducing to the third energy. At the same time, in step S7, increasing the normalized magnetic field strength of the focusing quadrupole 2 or decreasing the normalized magnetic field strength of the defocusing quadrupole 5 can move the horizontal operating point away from the resonance line before energy reduction, and decreasing the normalized magnetic field strength of the hexapod 3 increases the area of ​​the transverse phase stabilization triangle, which can reduce the transverse beam loss caused by the beam during the process of reducing to the third energy.

[0075] Step S9: Reduce the voltage value of the radio frequency electric field and change the synchronization phase of the radio frequency electric field so that the radio frequency electric field no longer decelerates the charged particles, so as to maintain the charged particles at the third energy.

[0076] After the energy of the charged particles decreases to the third energy, the magnetic field strength of the dipole 1 stops decreasing, the magnetic field strength of the focusing quadrupole 2 decreases or the magnetic field strength of the defocusing quadrupole 5 increases, and at the same time, the magnetic field strength of the hexapod 3 is increased until it is lower than the magnetic field strength of the hexapod at the end of the second beam extraction stage, so that the area of ​​the transverse phase stabilization triangle at the end of the second beam extraction stage is smaller than the area of ​​the transverse phase stabilization triangle at the beginning of the third beam extraction stage.

[0077] Step S10: Maintain the charged particles in the beam at the third energy to reach the third beam extraction stage, and extract part of the beam during the third beam extraction stage.

[0078] In the third beam extraction stage, the magnetic field strengths of the dipole, tetrapole, and hexapole magnets are proportionally reduced, thus decreasing the momentum of the reference particle while maintaining its operating point. Since the average momentum of the beam remains constant, the momentum difference between the beam and the reference particle increases during this stage. When the chromaticity is negative and the operating point of the reference particle is above the third-order resonance line, this increased momentum difference means the deviation between the beam and the reference particle's operating point is negative and its absolute value increases. This implies that the beam's operating point is moving away from the reference particle's operating point and downwards towards the third-order resonance line, resulting in a decrease in the area of ​​the beam's transverse phase stability triangle. Figure 3A and Figure 3B As shown, the area curve of the transverse phase-stabilized triangle of the beam gradually decreases from the beginning to the end of the third beam extraction stage.

[0079] After slowing the charged particles to the third energy, the magnetic field strength of the focusing quadrupole 2 is reduced or the magnetic field strength of the defocusing quadrupole 5 is increased, and the magnetic field strength of the hexapod 3 is increased, the charged particles need to be maintained for the duration of the third beam extraction phase. During this third beam extraction phase, a portion of the beam can be extracted using a radio frequency (RF) excitation device. The length of the third beam extraction phase is determined by the time required for the RF excitation device to extract the beam. The third energy is determined by the requirements of the target to be bombarded by the extracted charged particles. The third energy is less than the second energy.

[0080] It should be understood that the embodiments described above specifically address the preconditions where the chromaticity is negative and the operating point of the reference particle is above the third-order resonance line. These preconditions are determined by the design of the synchronization ring. For other combinations where the chromaticity is positive and / or the operating point of the reference particle is below the third-order resonance line, the magnetic field strength of the dipole, tetrapole, and hexapole can be proportionally reduced or increased in each beam extraction stage to achieve the effect of keeping the area of ​​the transverse phase stability triangle of the reference particle unchanged while the area of ​​the transverse phase stability triangle of the beam particle shrinks towards the area of ​​the transverse phase stability triangle of the reference particle.

[0081] Figure 1C The diagram schematically illustrates the situation where the area of ​​the transverse phase-stabilized triangle of the beam shrinks towards the area of ​​the transverse phase-stabilized triangle of the reference particle, which remains unchanged, in the multi-energy extraction method of the synchrotron according to the present invention. During the shrinkage of the transverse phase-stabilized triangle area of ​​the beam particle in the beam extraction stage, due to the satisfaction of the Hardt condition, the extraction boundary line of the transverse phase-stabilized triangle of the beam (solid line in the figure) always coincides with the extraction boundary line of the transverse phase-stabilized triangle of the reference particle (dashed line in the figure). Figure 1C As shown. This means that the beam with momentum dispersion and the reference particle with the transverse phase-stabilized triangle area remaining unchanged are still drawn from the same extraction boundary, thus achieving an extraction efficiency that remains constant regardless of changes in the transverse phase-stabilized triangle area of ​​the beam.

[0082] Figure 4A and Figure 4BA timing diagram of another embodiment of the multi-energy extraction method for a synchrotron according to the present invention is shown, the difference being that, in each beam extraction stage, instead of changing the reference particle momentum, altering the beam's operating point, and consequently changing the size of the beam's transverse phase-stabilizing triangle area by proportionally scaling the magnet strengths of the dipole, tetrapole, and hexapole magnets, the average momentum of the beam itself is directly changed through a high-frequency system or an additional acceleration device (not shown), thereby changing the difference in momentum between the beam particles and the reference particles, and thus altering the size of the beam's transverse phase-stabilizing triangle area due to the chromaticity effect. Figure 4A and Figure 4B As shown, the magnet strength of the dipolar, tetrapolar, and hexapolar iron remains constant in each beam extraction stage. At this time, the reference particle's operating point, momentum, and the area of ​​the transverse phase stability triangle remain constant. By directly changing the beam's average momentum, the difference between the beam's average momentum and the reference particle's momentum is changed, thereby changing the size of the beam's transverse phase stability triangle area.

[0083] In an illustrative embodiment, the magnetic field strengths of the dipole 1, tetrapole, and hexapole 3 change with time according to the following formula:

[0084]

[0085] Among them, B i B represents the strength of the magnetic field before the change. f T represents the intensity of the changed magnetic field. r B(t) represents the total duration of the change (in seconds), and B(t) represents the strength of the magnetic field at time t (in tons for dipolar iron, tons / m for tetrapolar iron, and tons / m for hexapolar iron). 2 ), where t is time (in seconds). This formula provides a specific curve of the magnetic field changing over time, but is not limited to this curve; any curve with a smooth transition over time is acceptable.

[0086] In one illustrative embodiment, the radio frequency electric field in the high-frequency cavity 4 can be a high-frequency electric field. The frequency of this radio frequency electric field varies synchronously with the magnetic field of the diode 1. The frequency of the radio frequency electric field can be calculated using the following formula:

[0087]

[0088] Where B(t) is the magnetic field of the dipolar iron (in T), ρ is the deflection radius of the dipolar iron (in m), c is the speed of light in vacuum (in m / s), e is the charge of the charged particle, E0 is the rest energy of the charged particle (in eV), and R is the equivalent radius of the synchrotron (in m).

[0089] In one illustrative embodiment, the phase of the radio frequency electric field in the high-frequency cavity 4 is calculated using the following formula:

[0090]

[0091] Where V(t) is the radio frequency voltage (in V), ρ is the rate of change of the magnetic field of the dipolar iron with time (in T / s), φ is the phase change with time t (in rad), ρ is the deflection radius of the dipolar iron (in m), and R is the equivalent radius of the synchrotron (in m).

[0092] It will be understood by those skilled in the art that all or some of the steps, systems, or apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all components may be implemented as software executed by a processor, such as a digital signal processor or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software may be distributed on a computer-readable medium, which may include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

Claims

1. A method for extracting multiple energies from a synchrotron, characterized in that, Includes the following steps: The dispersion and chromaticity of the synchronization loop of the synchrotron are set to satisfy the Hardt condition; Under the influence of the radio frequency electric field voltage, and accompanied by changes in the synchrotron magnetic field, the energy of charged particles successively passes through several beam extraction stages suitable for extracting the charged particle beam, as well as several deceleration and energy reduction stages connecting these beam extraction stages. In each of the beam extraction stages, the area of ​​the transverse phase stabilization triangle of the reference particle remains unchanged. By adjusting the area of ​​the transverse phase stabilization triangle of the beam and increasing the transverse radio frequency excitation beam emittance, the charged particle beam is extracted with corresponding energies E1, E2, and E3 in each of the beam extraction stages. Since the Hardt condition is satisfied, the extraction boundary line of the transverse phase stabilization triangle of the beam in each of the beam extraction stages always coincides with the extraction boundary line of the transverse phase stabilization triangle of the reference particle. The reference particle is a particle with a certain momentum that can move in the synchrotron ring according to the designed trajectory. The working point and the area of ​​the transverse phase stability triangle of the reference particle are directly determined by the magnetic field strength of the dipole, quadrupole and hexapole of the synchrotron and the momentum of the reference particle itself. Specifically, before each beam extraction stage, the radio frequency electric field voltage and the magnetic field strength of the dipole, tetrapole, and hexapole are adjusted so that the area of ​​the beam's transverse phase stabilization triangle at the beginning of each beam extraction stage is larger than the area of ​​the reference particle's transverse phase stabilization triangle. Furthermore, during each beam extraction stage, the area of ​​the beam's transverse phase stabilization triangle is altered by changing the deviation between the beam's average momentum and the reference particle's momentum, ensuring that the area of ​​the beam's transverse phase stabilization triangle at the end of beam extraction is smaller than the area at the beginning of beam extraction. In each of the aforementioned beam extraction stages, the magnetic field strength of all dipole, tetrapole, and hexapole magnets is proportionally reduced or increased to change the momentum of the reference particle while simultaneously maintaining the Hardt condition.

2. The multi-energy extraction method for a synchrotron according to claim 1, characterized in that, In the step of changing the deviation between the beam mean momentum and the momentum of the reference particle, in at least one beam extraction stage, the beam itself is accelerated by a high-frequency system or an additional acceleration device to change the beam mean momentum.

3. The multi-energy extraction method for a synchrotron according to claim 1, characterized in that, In the step of changing the deviation between the beam's average momentum and the momentum of the reference particle, in at least one beam extraction stage, the beam itself is decelerated by a high-frequency system or an additional acceleration device to change the beam's average momentum.

4. The multi-energy extraction method for a synchrotron according to any one of claims 1 to 3, characterized in that, The difference between the average areas of the transverse phase stabilization triangles of the beam in each beam extraction stage is within the range of variation allowed by the extraction efficiency of the synchrotron.

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