EP4319493A1

EP4319493A1 - Cyclotron capable of accelerating alpha particles and h2+ particles, and high-gain method and high-precision method

Info

Publication number: EP4319493A1
Application number: EP22936716.4A
Authority: EP
Inventors: Tianjue ZHANG; Wei Fu; Fei Wang; Zhichao CHU; Zhiguo YIN; Chuan Wang; Suping Zhang; Bohan ZHAO; Sumin WEI; Jingyuan Liu; Zhaojun JIN
Original assignee: China Institute of Atomic of Energy
Current assignee: China Institute of Atomic of Energy
Priority date: 2022-05-23
Filing date: 2022-09-15
Publication date: 2024-02-07
Also published as: WO2023226245A1; CN114916118A

Abstract

The present application provides a cyclotron and a high-gain, high-precision method for accelerating α particles and H₂ ⁺ particles. The cyclotron comprises a dual ECR ion source system, a dual-beam injection and transmission system based on magnetic analyzer, a main magnet system, a high-frequency system based on 8th harmonics, and a dual-beam extraction system for precise control of α beam energy using deflector. The high-gain method includes doubling the frequency of the RF cavity, reducing the cavity height and the angle of the dees by half compared to the 4th harmonic high-frequency cavity, and adapting the internal rod diameter, cavity outer radius, angle width, and dees thickness accordingly. The high-precision method includes setting the beam extraction point position, observing the radial distribution of the beam on the target, and adjusting the deflector position in real-time during beam commissioning. In the present application, a cyclotron capable of accelerating alpha and H₂ ⁺ particles is developed for the first time in the world; a double-beam high-brightness merging injection of the particles and the H₂ ⁺ particles is realized for the first time, and a compact cyclotron uses an eighth-harmonic high-frequency cavity for acceleration for the first time.

Description

BACKGROUND

Technical field

This application belongs to the field of cyclotron, specifically relating to a cyclotron for accelerating α particles and H₂ ⁺ particles and a high energy gain, high-precision method.

Description of Related Art

Multi-purpose, high-yield, high-energy gain, and precise energy extraction cyclotrons have important applications in fields such as nuclear physics, public health, advanced energy, and national defense. At present, there are bottleneck problems that restrict the development of multi-purpose, high-yield, high-energy gain, and precise energy extraction cyclotrons as following.
First, the cyclotrons are single-purpose, α particle cyclotrons are specialized cyclotrons used to produce α emitters for diagnosis and treatment. The typical nuclide is ²¹¹At, and the physical characteristics of ²¹¹At determine that it can be used as a good carrier for diagnosis and treatment. By combining radio immunoimaging with α-ray targeted therapy, the dosage can be determined based on the uptake of the imaging agent in the tumor and other organs in the body, thus achieving effective tumor treatment while ensuring that important organs are not damaged. However, due to the single purpose of the α particle cyclotron, it can only produce α particles and cannot meet the diverse isotope production needs. The reason for the single-purpose cyclotron is that different particle cyclotrons have different requirements for the high-frequency cavity parameters for accelerating particles. If the cyclotron is switched to produce another type of particle, it is necessary to readjust the high-frequency cavity parameters and magnetic field parameters that are the main technical parameters of the cyclotron. The workload of adjusting these two types of parameters is no less than that of rebuilding a cyclotron. Due to the difficulty and workload of implementation, most cyclotrons have been single-purpose cyclotrons for a long time.
Second, the design of high-frequency cavity with fourth harmonic is difficult to achieve peak acceleration. This is because the high-frequency cavity is a fourth harmonic high-frequency cavity, and in order to achieve peak acceleration, the angle width of the high-frequency cavity must be 45 degrees, so that the high-frequency voltage that particles are accelerated with when entering or leaving the high-frequency gap is the peak voltage. However, the 45-degree high-frequency cavity is only an ideal value. In the actual physical space of the cyclotron magnetic field valley reserved for the angle width of the high-frequency cavity, it is always less than 45 degrees. The cyclotron has eight magnetic poles arranged in two layers, with four magnetic poles uniformly distributed on up and down. The magnetic field valley is located between the magnetic poles, and the two high-frequency cavities are symmetrically installed in the magnetic field valley of the upper and lower parts. The reason why the space reserved for the angle width of the high-frequency cavity is less than 45 degrees is that the magnetic pole angle width is greater than 45 degrees. To satisfy the isochronism, magnetic pole shims are installed on both sides of each magnetic pole, which occupy the space originally reserved for the high-frequency cavity, resulting in the actual deflection angle of the high-frequency cavity in the magnetic field valley being less than 45 degrees.
Third, not all the particles injected from the ion source to the cyclotron are the expected α particles and H₂ ⁺ particles, and there are relatively more impurities. For conventional H^- ions, impurities are generally not considered because they are rare. When α particles and H₂ ⁺ particles share a transmission system, the difficulty lies in balancing the need to separate impurities from both ion sources and the engineering cost.
Fourth, the energy of the particles near the extraction point may not be the desired energy. This is because the energy of the particles depends on their radial position near the extraction point: the closer they are to the large radius, the higher their energy, and the closer they are to the small radius, the lower their energy. The differences in initial phase among the particles cause variations in the energy extracted at the extraction point.
In summary, the existing technology for cyclotrons has bottleneck issues, including a single application, difficulty in achieving peak acceleration with the high-frequency cavity design, impurities in injected particles, and variability in particle energy near the extraction point.

SUMMARY

The present application provides a cyclotron and a high-gain, high-precision method for accelerating α particles and H₂ ⁺ particles, which aims to solve the problems of the single-purpose of existing cyclotrons, difficulty in achieving peak acceleration in high-frequency cavities, impurities in injected particles, and unpredictable particle energies near the extraction point.
To solve these technical problems, the present application provides the following technical solution:
A cyclotron for accelerating α particles and H₂ ⁺ particles, comprising a dual Electron Cyclotron Resonance (ECR) ion source system 1, a dual-beam injection and transmission system 2 based on a magnetic analyzer, a main magnet system 3, a high-frequency system 4 based on octupole harmonics, and a dual-beam extraction system 5 based on electrostatic deflectors for precise control of the energy of the extracted α beam.
The dual-beam injection and transmission system 2 is arranged between the dual-particle extraction ports of the dual Electron Cyclotron Resonance ion source system 1 and the lower surface of the main magnet system 3 of the cyclotron. The main magnet system 3 is arranged in two layers on both sides of the center plane of the cyclotron, with four uniformly distributed magnetic poles and main magnet cover plates on the outer side of each magnetic pole. The magnetic field valley region is located between each magnetic pole in each layer. The high-frequency system 4 based on the 8th harmonic is arranged in two layers on both sides of the center plane of the cyclotron, and is symmetrically arranged at 180 degrees in the magnetic field valley region of each layer. The dual-beam extraction system 5 includes α particle extraction channel and H₂ ⁺ particle extraction channel, which are respectively arranged on the outermost circle of the cyclotron beam trajectory.
The cyclotron that accelerates α particles and H₂ ⁺ particles shares the magnet parameters and high-frequency parameters of the dual-beam injection and transmission system 2, achieving isochronous acceleration of α particles and H₂ ⁺ particles.
The dual Electron Cyclotron Resonance (ECR) ion source system 1 includes a α particle ion source injection system 1-1 and an H₂ ⁺ particle source injection system 1-2. The dual-beam extraction system 5 includes a α particle extraction channel 5-1 and an H₂ ⁺ particle extraction channel 5-2. The dual-beam extraction system 5 extracts α particles by electrostatic deflection and strips H₂ ⁺ particles to extract a high intensity proton beam.
The dual-beam injection and transmission system 2 based on a magnetic analyzer is a system that uses the same set of transfer lines for α particles and H₂ ⁺ particles. The beam passes through the ± 30 degrees dipole magnet of the 30-degree analysis magnet 2-2 of the dual-beam injection and transmission system 2, separating α particles and H₂ ⁺ particles with normalized emittance of 0.2πmm mrad. The normalized α particles and H₂ ⁺ particles are injected into the central region of cyclotron through the front solenoid 2-1, 30-degree analysis magnet 2-2, rear solenoid coil 2-3, x-y guiding magnet 2-4, and beam focusing device 2-5. The 30-degree analysis magnet 2-2 is used for impurity ion analysis.
The dual-beam extraction system 5, which precisely controls the energy of the extracted α beam based on deflector, strictly limits the particle phase width in the injection center region during the cyclotron design phase to control the energy dispersion of the extracted α particles and reduce beam loss in the extraction region. During the cyclotron commissioning phase, the upper computer control system adjusts the position of deflector and voltage in real time to precisely control the beam extraction point by adjusting the deflector position and voltage.
The high-frequency system 4 based on octupole harmonic employs the same type of λ/2 coaxial resonators with double gaps. The cavity height is reduced by half, as well as the dees deflection angle, and the inner rod diameter, cavity outer radius, angle width, and dees thickness are adjusted accordingly.
Furthermore, to achieve isochronous acceleration of both α particles and H₂ ⁺ particles, the particle's cyclotron frequency is calculated based on the principle of isochronous acceleration: $f = \frac{qeB}{2 πm} \approx 15.2 \frac{q}{A} \cdot B [MHz]$
where B is the magnetic field strength in Tesla, q is the charges of the particle, and A is the mass of the particle.
Furthermore, the separation of normalized emittance of 0.2 dnmm mrad for α particles and H₂ ⁺ particles is achieved by using a 30-degree analysis magnet 2-2. The deflection radius and angle for impurity particles and non-impurity particles in the dipole magnet are different, which is used to calculate the deflection angle and radius for α particles and H₂ ⁺ particles, thus filtering out impurities that are not α particles or H₂ ⁺ particles.
To filter out non-a particles and H₂ ⁺ impurities, the mass resolution m/Δm is calculated for the particles in the dipole deflection magnet. The mass resolution m/Δm can be expressed as: $\frac{m}{Δm} = \frac{M_{x} (1,3)}{2 [|Y_{x}| s_{1} + \frac{δW}{W} M_{x} (1,3) + s_{2}]}$
where m is the desired particle mass, Δm is the mass deviation, M_x is the transmission matrix of the dipole magnet, Y_x is the known radial amplification rate, δW/W is the known beam energy spread, s ₁ and s ₂ are the known slit width and image slit width, respectively. The transmission matrix M_x is calculated based on the known conditions, and the motion of α particles and H₂ ⁺ particles through the dipole deflection magnet, including the deflection radius ρ ₀ and deflection angle θ, can be calculated using the transmission matrix M_x. Particles that do not belong to the deflection radius ρ ₀ and deflection angle θ are filtered out as impurities. The mass resolution m/Δm in formula (2) is shared by both α particles and H₂ ⁺ particles, and the higher value of the mass resolution m/Δm for the two types of particles is taken as the common mass resolution m/Δm.
Furthermore, after passing through the 30-degree analysis magnet 2-2, the α particles and H₂ ⁺ particles enter the dual-beam injection and transmission system 2, with an energy ratio of 2:1 to ensure consistent magnetic rigidity, since they use the same dual beam injection line transfer system.
Furthermore, the reducing a height of a cavity by less than half and reducing the angle of dees by half comprises: reducing the height of the cavity from 2.4 m to 0.9 m and reducing the angle of dees from 45 degrees to 22.5 degrees; the adjusting an inner rod diameter, a cavity outer radius angle width, and a dees thickness adaptively comprises: setting a minimum inner rod diameter to 40 mm, setting a cavity angular width to 40 degrees, and setting a dees thickness to 12 mm to 14 mm; the cavity angular width of 40 degrees means that an angular width of the cavity in a range of an outer 85% radius from a center of the cyclotron is increased.
Furthermore, the phase width of the small bunch injection is 5 to 10 degrees.
Furthermore, the high-current proton beam is extracted by stripping H₂ ⁺ particles. After passing through the stripper, the particles become H⁺ particles, and the orbit radius is reduced, leading to one or more revolutions in the cyclotron before extraction. The number of revolutions is determined by the extraction energy and the size of the beam envelope.
A method for performing peak acceleration in a high-frequency system 4 based on the 8th harmonic 4, comprising the following steps:

Step 1: setting the height of the 8th harmonic high-frequency cavity to 0.9 m and the angle of dees to 22.5 degrees.
Step 2: setting the minimum inner rod diameter to 40 mm.
Step 3: increasing the cavity angular width to 40 degrees to increase a vacuum area inside the cavity, leaving only enough space for water-cooled wiring between a cavity side and the main magnet system of the cyclotron, increasing the cavity angular width to 40 degrees means that an angular width of the cavity in a range of an outer 85% radius from a center of the cyclotron is increased;
Step 4: setting the thickness of dees to 12 mm to 14 mm to increase the distributed capacitance.
Step 5: adopting a conical accelerating electrode design to reduce the distribution of useless electric fields and reduce losses.

A method for precise control of the beam extraction point, comprising the following steps:

Step 1: designing the amplitude and phase of the first harmonic, using resonance-induced precession to increase the turn separation of beam trajectory, and determining the preset position of the deflector. The preset position of the deflector is to place the deflector between the outermost and second outermost beam trajectories.
Step 2: obtaining the designed first harmonic distribution through magnetic field compensation.
Step 3: beam commissioning and observing the radial distribution particles.
Step 4: checking if the beam has reached the extraction point. If not, proceed to step 5. If the beam has reached the extraction point, proceed to step 6. The extraction point is the preset position of the deflector.
Step 5: adjusting, in real-time, a deflector position and a high voltage, and returning to step 3; and
Step 6: extracting the beam.

BENEFICIAL EFFECT

1. For the first time internationally, a cyclotron based on external high intensity ion source has been developed, for accelerating α particles and H₂ ⁺ particles without adjusting any of the magnet and high-frequency cavity such cyclotron's key technical parameters, achieving isochronous acceleration of α particles and H₂ ⁺ particles.
2. The present application implements double beam high-brightness merge injection of α particles and H2+ particles for the first time. Using dual ECR ion sources, the beam is separated into normalized emittance 0.2πmm mrad α particles and H₂ ⁺ particles through ±30 degree dipole magnets, and the beam is injected into the center of the cyclotron through a transport system consisting of a solenoid coil, dipole magnet, quadrupole magnet, beam collimator, and solenoid coil. The dual-beam can use the same transport system, reducing construction costs further.
3. α particles and H₂ ⁺ particles can be extracted through a dual-beam extraction system. The dual-beam extraction system extracts α particles by electrostatic deflection and extracts high-intensity proton beams by stripping H₂ ⁺. The core technology lies in the precise control of the energy and energy dispersion of the extracted α beam by electrostatic deflection, strictly controlling the production of toxic nuclide ²¹⁰At during the production of ²¹¹At. The stripping H₂ ⁺ method extracts proton beams with an intensity twice that of the H₂ ⁺ particle beam, achieving high-yield production of medical isotopes based on solid targets.
4. For the first time, a compact cyclotron uses an eighth-harmonic high-frequency cavity for acceleration, successfully solving the problem of the resonant frequency of the traditional fourth-harmonic high-frequency cavity's difficulty in adapting to the lower particle cyclotron frequency and the compact spatial structure of the main magnet valley, achieving efficient isochronous acceleration of maximum energy gain.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 shows the overall layout of the cyclotron for accelerating α particles and H₂ ⁺ particles according to the present application.
Fig. 2 is a schematic diagram of the dual-beam injection system according to the present application.
Fig. 3 shows the integral phase slip in the isochronous acceleration process of α particles and H₂ ⁺ particles.
Fig. 4 shows the process flow diagram of the adjustable deflector position according to the present application.
Fig. 5-1 shows a schematic diagram of the fourth harmonic cavity with a 45-degree angle.
Fig. 5-2 shows a schematic diagram of the eighth harmonic cavity with a 22.5-degree angle.

DESCRIPTION OF THE EMBODIMENTS

Design principle of this present application

1. The design principle of high energy gain of the eight harmonic cavity: first, due to the limitation of the cyclotron magnetic field design, the physical space of the existing magnetic field valley is insufficient to support the 45-degree angle of the fourth harmonic cavity. Since the angle cannot reach 45 degrees, particles cannot achieve peak voltage acceleration when entering and leaving the acceleration gap, resulting in insufficient energy gain. To solve the problem of insufficient physical space for the 45-degree angle of the magnetic field valley, under the condition of selecting the same type of λ/2 (where λ is the wavelength) coaxial cavity with double gaps, the frequency is doubled, the cavity height is reduced by half or less, and the angle of the dees is reduced by half compared to the fourth harmonic acceleration: the cavity height is reduced from 2.4 m to 0.9 m, and the angle of the dees is reduced from 45 degrees to 22.5 degrees. Second, the design basis of the eight harmonic cavity is a height of 0.9 m and an angle of 22.5 degrees, under which the voltage for the particle passing through the acceleration slit can reach the peak voltage. However, simulation results show that when the cavity height is 0.9 m, the frequency is still too high. Although the frequency cannot be reduced by raising the cavity height because there needs to be space for cable routing between the upper and lower cover plates of the high-frequency cavity. Thirdly, the method of reducing frequency can be determined by the resonant frequency f formula $f = \frac{1}{\sqrt{LC}}$
From the above frequency relation, it can be seen that the frequency can be lowered by increasing the capacitance and inductance. If the relationship between the outer shell and the inner rod of the cavity is approximated to a coaxial line, according to the formula for the inductance per unit length of a coaxial line: $L_{0} = \frac{μ_{0}}{2 π} \ln \frac{b}{a}$
It can be seen that:

1) reducing the diameter of the inner rod is equivalent to reducing a, so the inductance increases and the frequency decreases, which is the first method to reduce the frequency of the cavity. However, reducing the diameter of the inner rod will result in a decrease in mechanical strength of the cavity and an increase in surface current, which will increase the power loss. The solution is to first determine a lower limit of the inner rod diameter that ensures mechanical strength. In this embodiment, the lower limit of the inner rod diameter is 40 mm;
2) increasing the outer radius angle width of the cavity by 40 degrees is the second method to lower the frequency of the cavity. By increasing the outer radius angle width of the cavity by 40 degrees, the cavity can be made as close as possible to the magnet lining and the side of the cavity to increase the vacuum layer of the cavity. The term "as close as possible" means that only the space for water-cooled cables is left between the magnet lining and the side of the cavity. The term "increasing the outer radius angle width of the cavity by 40 degrees" means that the angle width of the cavity from the center of the synchrotron outward to the back 85% radius range is increased. Under certain assumptions, the formula for the side capacitance of a coaxial cavity is: $C_{s} = 4 ε_{0} a \ln (\frac{b - a}{d})$

Increasing the outer radius angle width is equivalent to increasing b and can also increase the capacitance. Slightly increasing the thickness of the dees to 12 mm to 14 mm increases the distributed capacitance (analogous to the formula for parallel plate capacitance), which is the third method for reducing the cavity frequency. Ultimately, the goal is to achieve a lower cavity frequency while ensuring a sufficient inner rod diameter. Finally, a nose cone-shaped acceleration electrode design was adopted, with a smooth electrode surface effectively reducing excessive concentration of gap electric fields, avoiding discharge risks, reducing unnecessary electric field distributions, and reducing losses. Combining these points results in a cavity with a power loss of less than 7 kW at a relatively small acceleration gap angle width, while also ensuring a time transit factor of approximately 0.987, achieving a two-fold benefit. Assuming a uniform distribution of gap electric fields, the energy gain of particles passing through the gap once is as follows. $ΔW = {qeV}_{D} |\frac{\sin (\frac{hθ}{2})}{\frac{hθ}{2}}| \cos φ_{c}$
Here, $τ = |\frac{\sin (hθ / 2)}{hθ / 2}|$
is the transit factor, q is the particle charge, V_D is the peak acceleration voltage, h is the harmonic number, θ is the acceleration gap angle, and ϕ_c is the phase when the particle reaches the centerline of the gap. Therefore, the higher the transit factor, the higher the energy gain.
In summary, changing from the fourth harmonic to the eighth harmonic, although the angle of 22.5 degrees of the eighth harmonic is guaranteed, the cavity frequency is still too high at a height of 0.9 m. To lower the frequency, a balance point was found by reducing the inner stem diameter, increasing the outer radius angle width of the cavity, and slightly increasing the thickness of dees: excessively reducing the inner stem diameter can lower the frequency but also decrease mechanical strength; increasing the outer radius angle width of the cavity can increase the capacitance but is limited by the physical space of the magnetic field valley region; increasing the dees thickness can also increase the capacitance and lower the frequency, but it can also increase the total height of the cavity. Therefore, a balance point was found with a cavity height reduced from 2.4 m to 0.9 m, angle of dees reduced from 45 degrees to 22.5 degrees, a minimum inner stem diameter of 40 mm, a cavity angular width of 40 degrees, and dees thickness of 12 mm to 14 mm.
2. Design principle for precise control of particle energy at the extraction point: The difficulty lies in the fact that the energy of particles near the extraction point may not be the desired energy, and there is always a gap between the actual energy and the desired energy. This application adopts the method of combining small phase width injection with adjustment of the deflector position. Since the magnitude of the difference in the radial position of particles at the extraction point is related to the phase width of the particle injection, the role of small phase width is to reduce the phase difference within the phase width range of a cluster of particles at the injection point, thereby reducing the radial position difference of particles at the extraction point (energy spread reduction). The difficulty of small phase width extraction lies in how to select the required phase for extraction, as not every phase can be extracted, only a few phases can be extracted. At the same time, the range of small phase width should also consider that the extracted beam current will not decrease, and if the width is too narrow, the extracted beam current will decrease. Therefore, the phase width of small phase width injection is set to 5 to 10 degrees. The effectiveness of small phase width extraction is also directly related to the position adjustment of the deflector: in the design, there is a matching relationship between which phase of particles and which extraction point, but in practical commissioning, although simulation calculations can be as accurate as possible, the actual position of particles is not the theoretical calculated position, and various error factors result in a gap between theory and reality. Therefore, relying solely on small phase width still cannot achieve the desired particle position at the extraction point. The conventional method is to adjust the phase width from the injection port, as the deflector (beam extraction position) position is not adjustable. When adjusting the phase width still cannot make the particles reach the expected extraction point, the tuning process continues, which is very time-consuming and difficult. This application adopts target-oriented reverse thinking, turning the fixed deflector into adjustable, and using the adjustable deflector position for error compensation of theoretical and practical errors. In summary, only the combination of small phase width injection and adjustable deflector position can solve the problem of precise control of particle energy at the extraction point.
3. The design principle of sharing a transmission system between α particles and H₂ ⁺ particles: The first key point in sharing a transmission system between dual ion sources is how to select the number of ions while considering the need to separate impurities from both ion sources. In Formula (2), the relatively high mass resolution of m/Δm for the two particles is chosen as the common mass resolution of m/Δm. For example, the mass of a α particle is 4 with a Δm of 1, while the mass of an H₂ ⁺ particle is 2 with a Δm of 1. Therefore, the high mass resolution is 4/1=4 instead of 2/1=2. However, the mass resolution should not be too high, which would increase the engineering cost. Another key point in sharing a transmission system between dual ion sources is to ensure the consistency of magnetic rigidity. This application ensures the consistency of magnetic rigidity by injecting energy in a 2:1 ratio. Magnetic rigidity is related to the magnetic field, the deflection radius of the deflection magnet, and the deflection radius of the non-impurity particles calculated by Formula (2). If the magnetic rigidity of the two particles is inconsistent, the bending radius of α particles and H₂ ⁺ particles will be different even if Formula (2) calculates the bending radius of non-impurity particles, and when one of the bending radii cannot reach the predetermined standard, it will also affect the filtering of impurities. Therefore, the 2:1 energy injection ratio ensures the consistency of magnetic rigidity, and Formula (2) is complementary and interdependent.
Based on the above principles, this application designs a cyclotron that can accelerate both α particles and H₂ ⁺ particles.
The cyclotron for accelerating α particles and H₂ ⁺ particles is shown in Figs. 1 and 2, comprising a dual ECR ion source system 1, a dual-beam injection and transmission system 2 based on magnetic analyzer, a main magnet system 3, a high-frequency system 4 based on octupole harmonics, and a dual beam extraction system 5 for accurately controlling the energy of the extracted α particle beam based on the deflector.
The dual beam injection and transmission system 2 is located between the dual particle extraction ports of the dual ECR ion source system 1 and the lower surface of the main magnet system 3 of the cyclotron. The main magnet system 3 is divided into two layers and is symmetrically distributed on the upper and lower sides of the center plane of the cyclotron. Each side of the main magnet system 3 is composed of four magnet poles uniformly distributed in the circumferential direction and a main magnet cover plate outside the magnet pole. The magnetic field valley is between each magnet pole and between adjacent magnet poles. The high-frequency system 4 based on octupole harmonics is distributed in two layers and symmetrically arranged at 180 degrees on each side of the center plane of the cyclotron within the magnetic field valley. The dual-beam extraction system 5 includes a α particle extraction port and an H₂ ⁺ particle extraction port, both of which are located on the outermost track of the cyclotron beam trajectory.
The cyclotron for accelerating α particles and H₂ ⁺ particles is configured to share the same magnet and high-frequency parameters of the dual-beam injection and transmission system 2, achieving isochronous acceleration of both types of particles.
The double ECR ion source system 1 includes an α particle ion source injection system 1-1 and an H₂ ⁺ particle source injection system 1-2. The dual-beam extraction system 5 includes an α particle extraction port 5-1 and an H₂ ⁺ particle extraction port 5-2. The dual-beam extraction system 5 extracts α particles by electrostatic deflection and high-current proton beams through H₂ ⁺ stripping.

Supplementary description

For H₂ ⁺ particles, after the extraction design and selection of the stripper placement position, the particles become H⁺ particles after passing through the stripping membrane. The orbit's radius of gyration becomes smaller, and the particles are deflected one or more times in the cyclotron before being extracted from the cyclotron. The specific number of turns depends on the extraction energy and the requirements for the beam envelope size.
The dual-beam injection and transmission system 2 based on the magnetic analyzer, as shown in Fig. 2, is a system in which α particles and H₂ ⁺ particles use the same set of transmission lines. The beam passes through the ±30-degree dipole magnet of the 30-degree analysis magnet 2-2 of the dual-beam injection and transmission system 2, such that α particles and H₂ ⁺ particles with a normalized emission of 0.2π mm mrad are separated. After being normalized, the α particles and H₂ ⁺ particles are injected into the center of the cyclotron through the front solenoid 2-1, 30-degree analysis magnet 2-2, rear solenoid 2-3, x-y guiding magnet 2-4, and beam concentrator 2-5 for acceleration. The 30-degree analysis magnet 2-2 is used for impurity ion analysis.
During the cyclotron design phase, the dual-beam extraction system 5, which precisely controls the energy of the extracted α particle beam based on the deflector, strictly limits the particle phase space at the injection center to control the energy spread of the extracted α particles and reduce the beam loss in the extraction area. During the cyclotron tuning phase, the upper computer control system adjusts the deflector position and voltage in real-time to accurately control the beam extraction point by adjusting the deflector position and voltage.
The high-frequency system 4 based on the 8th harmonic, as shown in Figs. 5-1 and 5-2, adapts to the case of selecting the same type of λ/2 dual-gap coaxial cavity. The cavity height is reduced by less than half, the dees angle is reduced by half, and the inner rod diameter, cavity outer radius angle width, and dees thickness are adjusted accordingly.
To achieve isochronous acceleration of α particles and H₂ ⁺ particles, the particle's cyclotron frequency is given by: $f = \frac{qeB}{2 πm} \approx 15.2 \frac{q}{A} \cdot B [MHz]$
where B is the magnetic field strength in Tesla, q is the particle charge, A is the particle mass number. Since the charge to mass ratio q/A of α particles and H₂ ⁺ particles is the same, the cyclotron frequency f is almost equal, and the cyclotron can achieve isochronous acceleration of α particles and H₂ ⁺ particles without adjusting the magnet and high-frequency parameters.
The process of separating and normalizing α particles and H₂ ⁺ particles to an emitted normalized emittance of 0.2 π mm mrad is achieved by using the 30-degree analysis magnet 2-2. This is done by calculating the deflection angle and radius of α particles and H₂ ⁺ particles based on the difference in the deflection radius and angle of impurity particles and non-impurity particles in the secondary magnet. This allows for the filtering out of impurity particles that are not α particles or H₂ ⁺ particles.
The filtering out of impurity particles is achieved by calculating the deflection angle and radius of α particles and H₂ ⁺ particles in the dipole deflection magnet, based on the mass resolution m/Δm. The mass resolution can be expressed as: $\frac{m}{Δm} = \frac{M_{x} (1,3)}{2 [|Y_{x}| s_{1} + \frac{δW}{W} M_{x} (1,3) + s_{2}]}$
where m is the mass of the desired particle, Δm is the mass deviation, M_x is the transfer matrix of the dipole magnet, Y_x is the known radial magnification, δW/W is the known beam energy spread, s ₁ and s ₂ are the known aperture widths, and the transfer matrix M_x is calculated based on the above known conditions. Using the transfer matrix M_x, the motion of α particles and H₂ ⁺ particles after passing through the dipole deflection magnet can be calculated, which includes the deflection radius ρ ₀ and deflection angle Θ. This allows for the filtering out of particles that do not belong to the deflection radius ρ ₀ and deflection angle Θ. The mass resolution m/Δm in Equation (2) is shared by both α particles and H₂ ⁺ particles, with the higher of the two mass resolutions being used as a common mass resolution m/Δm.
The H₂ ⁺ particles can be stripped into two protons by a stripping foil, which doubles the beam current and achieves high production yields of commonly used medical isotopes. The α particles are extracted by an electrostatic deflector, and the electric field of the deflector can be calculated using the following equation: $E = \frac{2 E_{k} Δs}{qρ}$
where q and E_k are the charge and kinetic energy of the particles, ρ and η are the curvature radius and angular width of the deflector, and Δs is the radial deviation at the exit of the deflector.
After passing through the analysis system, the α and H₂ ⁺ particles enter the dual-beam merging injection line, which use the same injection line system to ensure consistent magnetic rigidity. The energy ratio of injection is 2: 1 for H₂ ⁺ and α particles.
The height of the cavity is reduced by half, and the included angle of the dees is also reduced by half, including the cavity height decreasing from 2.4 m to 0.9 m, and the dees included angle decreasing from 45 degrees to 22.5 degrees. The diameter of the inner rod, outer radius and angular width of the cavity, and thickness of the dees are adjusted adaptively, including a minimum inner rod diameter of 40 mm, a cavity angular width of 40 degrees, and dees thickness of 12 mm to 14 mm. The cavity angular width of 40 degrees refers to the angular width of the cavity at two-thirds of the cyclotron radius.

Supplementary description

The high frequency cavity angular width of the high-frequency system 4 based on the 8th harmonic 4 for the 8th harmonic is Θ, and the harmonic number of the cyclotron is h. When using two high frequency cavities, the energy gain per particle per revolution isΔw = 4qeV_a |sin(hθ)/2|. A maximum energy gain can be achieved when the angle θ is 22.5 degrees, ensuring high acceleration efficiency.
The phase width for the small phase space injection is 5 to 10 degrees.
The high current proton beam is extracted through the H₂ ⁺ stripping method. After passing through the stripping foil, the particles become H⁺ ions, with a smaller orbit radius, and then are extracted from the cyclotron after one or multiple revolutions, which depends on the extraction energy and the size of the beam envelope.
A method for achieving peak acceleration using a high-frequency system 4 based on the 8th harmonic, characterized by the following steps:

Step 1: set the height of the 8th harmonic high frequency cavity to 0.9 m and the deflection angle of the dees to 22.5 degrees.
Step 2: set the minimum inner rod diameter to 40 mm.
Step 3: increase the cavity angular width to 40 degrees to increase the vacuum area inside the cavity, leaving only enough space for water-cooled wiring between the cavity side and the main magnet system (3) of the cyclotron. Increasing the cavity angular width to 40 degrees means that the cavity angular width in the range of the outer 85% radius from the center of the cyclotron is increased.
Step 4: set the dees thickness to 12 mm to 14 mm to increase the distributed capacitance.
Step 5: use a tapered acceleration electrode design to reduce unnecessary electric field distribution and losses.

A method for precisely controlling the beam extraction point is shown in Fig. 4 and includes the following steps:
Step 1: design the amplitude and phase of the first harmonic to use the resonance excitation to increase the distance between turns, while determining the preset position of the deflector. The preset position of the deflector is between the outermost and second outermost beam tracks.

Supplementary description

Because particles are continuously accelerated, under normal circumstances, they will definitely reach the extraction point, which is the preset position of the deflector plate. If the beam cannot reach the extraction point or the preset position of the deflector plate, it means that the beam has already been lost before reaching the extraction point due to the influence of errors.
Step 2: obtaining the designed first harmonic distribution through magnetic field compensation.
Step 3: performing beam tuning to observe the radial target particle distribution.
Step 4: check whether the beam has reached the extraction point. If the beam has not reached the extraction point, proceed to Step 5. If the beam has reached the extraction point, proceed to Step 6. The extraction point is the preset position of the deflector.
Step 5: adjusting the deflector plate position and voltage in real time and return to Step 3.
Step 6: extracting the beam.

Implementation Example 1: Shared transmission system for α particles and H₂ ⁺ particles

In a cyclotron that accelerates 9 MeV/A α particles and 9 MeV/A H₂ ⁺ particles, a pre-analysis system is needed as an impurity ion analyzer because not all particles extracted from the ECR ion source are expected α particles or H₂ ⁺ particles. For example, for the H₂ ⁺ ion source, the particles extracted from its outlet include H₂ ⁺, H+, etc. As shown in Fig. 2, H⁺ is deflected by a 30-degree bending magnet and injected into the beam collector of the injection system. The angle and radius of the dipole bending magnet can be designed according to the mass resolution requirements, which can be expressed as: $\frac{m}{Δm} = \frac{M_{x} (1,3)}{2 [|Y_{x}| s_{1} + \frac{δW}{W} M_{x} (1,3) + s_{2}]}$
where M_x is the transfer matrix of the dipole magnet, Y_x is the radial magnification rate, δW/W is the energy spread of the beam, and s ₁ and s ₂ are the width of the object slit and the image slit, respectively. After determining the energy resolution, the matrix element M_x(1,3) can be obtained, and the specific magnetic field strength can be calculated accordingly.
After passing through the analysis system, α particles and H₂ ⁺ particles enter the dual-beam merge injection line. Since both particles use the same injection line system, the energy ratio of injection is 2:1 to ensure consistent magnetic rigidity. For example, for 40 keV α particles, their magnetic rigidity is 0.02888 T·m, and for 20 keV H₂ ⁺ particles, their magnetic rigidity is also 0.02888 T·m. For a quadrupole lens, its transfer matrix can be written as: $R = [\begin{matrix} \cos KL & \frac{1}{K} \sin KL & 0 & 0 \\ - Ksin KL & \cos KL & 0 & 0 \\ 0 & 0 & chKL & \frac{1}{2} shKL \\ 0 & 0 & KshKL & chKL \end{matrix}]$
where K ² = µ ₀ G/Bρ. Under the same magnetic rigidity, the focusing characteristics of the quadrupole lens are consistent for different particles, which realizes the effect of using the same injection line system for different particles.

Implementation Example 2: Testing the Integral Phase Slip of α Particles and H₂ ⁺ Particles

As shown in Fig. 3, after entering the central region, the α particles and H₂ ⁺ particles can be accelerated with isochronous acceleration without changing any high-frequency parameters due to their equal charge-to-mass ratios. The main magnet system uses a four-sector structure with a pole angle of 22.5 degrees, and the peak and valley magnetic fields are 1.7 T and 0.4 T, respectively. Eight harmonic RF cavities are used for acceleration. The integral phase slip during the acceleration process for 9 MeV/A α particles and 9 MeV/A H₂ ⁺ particles is shown in Fig. 3. It can be seen that the integral phase slip for both types of particles is less than ±10 degrees, achieving high-efficiency acceleration and entering the extraction region.
Implementation Example 3: Design of turn separation for α particle deflector in extraction region
Different types of particles enter the dual-beam extraction system for extraction. In the design process, the α particles are kept at a certain turn separation, which can be expressed by the following equation: $Δr = {Δr}_{0} + Δx \sin [2 πn (v_{r} - 1) + θ_{0}] + 2 π (ν_{r} - 1) x \cos [2 πn (v_{r} - 1) + θ_{0}]$
where the first term represents the natural turn separation caused by energy gain, the second term represents the turn separation caused by resonance, and the third term represents the turn separation caused by orbital motion. Taking 36 MeV α particles as an example, the extraction radius is about 0.8 m. The extraction voltage in the extraction region is 0.08 MeV, and the highest single-ring energy gain is estimated to be 0.32 MeV The extraction energy is ~ 36 MeV The radial oscillation frequency in the extraction region is ~1. By plugging in the formula, the turn separation obtained by acceleration is ~3.2 mm. The turn separation caused by energy gain is slightly smaller than the radial size of the beam in the extraction region. To further increase the turn separation of extraction, a first harmonic magnetic field error can be introduced, and the turn separation can be further increased by utilizing the v_r =1 resonance in the extraction region. It is estimated that a first harmonic magnetic field of 1 Gs can generate an additional turn separation of about 3 mm, which is easy to implement with magnetic field compensation. By maintaining a certain turn separation, the α particles enter the cutting plate and are deflected from their original trajectory by electrostatic high voltage. Afterwards, the beam envelope is controlled through a series of magnetic channels to extract the cyclotron.
It should be emphasized that the above specific implementation examples are only for the description of the present application, and are not limitations of the present application. Those skilled in the art can make modifications to the above implementation examples without creative contributions after reading the present specification, as long as they fall within the scope of the claims of the present application, which are protected by patent law.

Claims

A cyclotron for accelerating α particles and H₂ ⁺ particles, characterized by comprising: a dual Electron Cyclotron Resonance (ECR) ion source system (1), a dual-beam injection and transmission system (2) based on magnetic analyzers, a main magnet system (3), a high-frequency system based on 8th harmonics (4), and a dual-beam extraction system (5) for control of α particle beam energy using a deflector; wherein,
the dual-beam injection and transmission system (2) is arranged between dual particle extraction ports of the dual ECR ion source system (1) and a lower surface of the main magnet system (3); the main magnet system (3) is divided into an upper layer and a lower layer, which are arranged on an upper side and a lower side of a center plane of the cyclotron respectively; each side of the main magnet system (3) consists of four magnetic poles evenly distributed in an azimuthal direction and a main magnetic pole covers outside the four magnetic poles; a magnetic field valley is provided between two adjacent magnetic poles of the four magnetic poles; the high-frequency system (4) based on 8th harmonics is divided into an upper layer and a lower layer, which are symmetrically arranged within the magnetic field valleys on the upper side and the lower side of the center plane of the cyclotron, with each of the upper layer and the lower layer covering 180 degrees; the dual-beam extraction system (5) comprises a α particle extraction port and a H₂ ⁺ particle extraction port, which are respectively located on an outermost turn of a cyclotron beam trajectory;

the cyclotron is configured to share magnet parameters and high-frequency parameters of the dual-beam injection and transmission system (2) for achieving an isochronous acceleration of the α particles and the H₂ ⁺ particles;

the dual ECR ion source system (1) comprises a part-time injection system for α particle ion sources and a source injection system for the H₂ ⁺ particles; the dual-beam extraction system (5) comprises a part-time extraction port for the α particles and an extraction port for the H₂ ⁺ particles; the dual-beam extraction system (5) is configured to extract the α particles by electrostatic deflection and extract high-intensity proton beams by stripping the H₂ ⁺ particles;

the dual-beam injection and transmission system (2) based on magnetic analyzers is a system where the α particles and the H₂ ⁺ particles use a same set of transmission lines; a beam passes through ±30-degree dipole magnets of a 30-degree analysis magnet (2-2) in the dual-beam injection and transmission system (2) such that the α particles and the H₂ ⁺ particles with a normalized emittance of 0.2 π mm mrad are separated; normalized α particles and normalized H₂ ⁺ particles, after normalization, are injected into a central region of the cyclotron through a front solenoid (2-1), a 30-degree analysis magnet (2-2), a rear solenoid (2-3), a x-y guiding magnet (2-4), and a buncher (2-5) for accelerating beams injected into the central region of the cyclotron; the 30-degree analysis magnet (2-2) is configured for impurity ion analysis;

the dual-beam extraction system (5) for control of α beam energy using a deflector, during a cyclotron design phase, is configured to employ a phase selector to limit a phase width of particles injected into the central region for controlling energy dispersion of extracted α particles and minimizing beam losses in an extraction region; during a cyclotron commissioning phase, is configured to adjust a position and voltage of the deflector in real-time with an upper computer control system for control of a beam extraction point by adjusting the position and voltage of the deflector; and

the high-frequency system (4) based on 8th harmonics is configured to reduce a height of a cavity by less than half and decrease an angle of dees by half when selecting a same type of λ/2 dual-gap coaxial cavity, and adjust an inner rod diameter, a cavity outer radius angle width, and a dees thickness adaptively.
The cyclotron for accelerating α particles and H₂ ⁺ particles according to claim 1, characterized in that, the achieving an isochronous acceleration of the α particles and the H₂ ⁺ particles comprises calculating a particle cyclotron frequency f based on isochronous acceleration: $f = \frac{qeB}{2 πm} \approx 15.2 \frac{q}{A} \cdot B [MHz]$
where B is a magnetic field strength in Tesla, q is number of charges of the particle, and A is mass of the particle.
The cyclotron for accelerating α particles and H₂ ⁺ particles according to claim 1, characterized in that, separating the α particles and the H₂ ⁺ particles with the normalized emittance of 0.2 π mm mrad comprises: using the 30-degree analysis magnet (2-2), based on different deflection radius and angle for impurity particles and non-impurity particles in a dipole magnet, and calculating a deflection angle and a radius for the α particles and the H₂ ⁺ particles, to filter out impurities that are not the α particles or the H₂ ⁺ particles.
The cyclotron for accelerating α particles and H₂ ⁺ particles according to claim 3, characterized in that, the filtering out impurities that are not the α particles or the H₂ ⁺ particles comprises: calculating the deflection angle and the radius for the α particles and the H₂ ⁺ particles in the dipole deflection magnet according to a mass resolution m/Δm, the mass resolution m/Δm is expressed as: $\frac{m}{Δm} = \frac{M_{x} (1,3)}{2 [|Y_{x}| s_{1} + \frac{δW}{W} M_{x} (1,3) + s_{2}]}$
wherein m is a desired particle mass, Δm is a mass deviation, M_x is a transmission matrix of the dipole magnet, Y_x is a known radial amplification rate, δW/W is a known beam energy spread, s ₁ and s ₂ are known slit width and image slit width respectively; the transmission matrix M_x is calculated based on known conditions, and motion of the α particles and the H₂ ⁺ particles through the dipole deflection magnet, including the deflection radius ρ ₀ and deflection angle Θ, is calculated by using the transmission matrix M_x ; particles that do not belong to the deflection radius ρ ₀ and the deflection angle θ are filtered out as impurities; the mass resolution m/Δm in formula (2) is shared by both the α particles and the H₂ ⁺ particles, and a higher value of the mass resolution m/Δm for the two types of particles is taken as a common mass resolution m/Δm.
The cyclotron for accelerating α particles and H₂ ⁺ particles according to claim 1, characterized in that, the H₂ ⁺ particles are stripped to two protons to double a beam intensity before the stripping.
The cyclotron for accelerating α particles and H₂ ⁺ particles according to claim 5, characterized in that, after passing through the 30-degree analysis magnet (2-2), both the α particles and the H₂ ⁺ particles enter the dual-beam injection and transmission system; since the α particles and the H₂ ⁺ particles share a same set of the dual-beam injection and transmission system, an energy ratio of injection is set to 2: 1 to ensure consistent magnetic rigidity.
The cyclotron for accelerating α particles and H₂ ⁺ particles according to claim 6, characterized in that, reducing the height of the cavity by less than half and reducing the angle of a dees by half comprises: reducing the height of the cavity from 2.4 m to 0.9 m and reducing the angle of dees from 45 degrees to 22.5 degrees; and the adjusting an inner rod diameter, a cavity outer radius angle width, and a dees thickness adaptively comprises: setting a minimum inner rod diameter to 40 mm, setting a cavity outer radius angle width to 40 degrees, and setting the dees thickness to 12 mm to 14 mm; the cavity angular width of 40 degrees means that an angular width of the cavity in a range of an outer 85% radius from a center of the cyclotron is increased.
The cyclotron for accelerating α particles and H₂ ⁺ particles according to claim 1, characterized in that, a phase width of a small bunch injection is 5 to 10 degrees.
The cyclotron for accelerating α particles and H₂ ⁺ particles according to claim 1, characterized in that, extracting the high-intensity proton beams by stripping the H₂ ⁺ particles comprises: after stripping the H₂ ⁺ particles from a strip foil such that the H₂ ⁺ particles become H⁺ particles with a smaller orbit radius, deflecting the H₂ ⁺ particles one or more turns in the cyclotron and extracting the H₂ ⁺ particles out of the cyclotron; a number of turns is determined based on extraction energy and size of beam envelope.
A method for performing a peak acceleration by the high-frequency system (4) based on 8th harmonics of the cyclotron for accelerating the α particles and the H₂ ⁺ particles according to any one of claims 1-9, characterized by comprising:
Step 1: setting a height of the cavity of the high-frequency system based on 8th harmonics to 0.9 m and the angle of dees to 22.5 degrees;

Step 2: setting a minimum inner rod diameter to 40 mm;

Step 3: increasing the cavity outer radius angle width to 40 degrees to increase a vacuum area inside the cavity, leaving only enough space for water-cooled wiring between a cavity side and the main magnet system (3) of the cyclotron, increasing the cavity outer radius angle width to 40 degrees means that an angular width of the cavity in a range of an outer 85% radius from a center of the cyclotron is increased;

Step 4: setting the dees thickness to 12 mm to 14 mm to increase a distributed capacitance; and

Step 5: using a tapered acceleration electrode design to reduce unnecessary electric field distribution and losses.
A method for precise control of a beam extraction point in the cyclotron for accelerating the α particles and the H₂ ⁺ particles according to any one of claims 1-9, characterized by comprising:
Step 1: designing an amplitude and phase of a first harmonic, using resonance-induced precession to increase a turn separation of a beam trajectory, and determining a preset position of the deflector; the preset position of the deflector is set to place the deflector between an outermost beam trajectory and a second outermost beam trajectory;

Step 2: obtaining a designed first harmonic distribution through magnetic field compensation;

Step 3: beam commissioning and observing radial distribution particles;

Step 4: checking whether the beam reaches the beam extraction point, when the beam does not reach the beam extraction point, proceeding to step 5; when the beam reaches the beam extraction point, proceeding to step 6; the beam extraction point is the preset position of the deflector;

Step 5: adjusting, in real-time, the position of the deflector and the voltage of the deflector, and returning to step 3; and
Step 6: extracting the beam.