Method for improving longitudinal focusing force of central area of cyclotron

Abstract

The invention discloses a method for improving longitudinal focusing force of a central area of a cyclotron. The method comprises the following steps: dividing a radio frequency cavity into a radio frequency cavity for generating energy difference and a radio frequency cavity for eliminating energy difference; the energy gain of beam head particles is low, and the energy of beam tail particles is high; or the energy gain of the beam head particles is high, and the energy gain of the beam tail particles is low; the head structure of the radio frequency cavity generating the energy difference and the head structure of the radio frequency cavity eliminating the energy difference are rotated by angles in opposite directions, so that the energy of head particles and tail particles of a beam bunch has a certain energy difference, and the particles are converted from non-receiving and non-acceleration areas of a current radio frequency period to a non-acceleration area. And compressing into an intermediate received and accelerated area. Longitudinal focusing is achieved in a negative phase mode, and defocusing in the height direction cannot be caused while longitudinal focusing force is provided; according to the invention, the focusing effect in the height direction is better while longitudinal focusing is realized in a positive phase mode.

Description

Technical Field

[0001] The present invention belongs to the technical field of the central region of a cyclotron, and particularly relates to a method for improving the longitudinal focusing force in the central region of a cyclotron. Background Art

[0002] The traditional method for providing the longitudinal focusing force in the central region is to adjust the position of the acceleration gap so that the transit time of the particle, that is, the radio frequency time τ when passing through the acceleration gap, is in the region where the voltage rises with time, that is Figure 2 in the region of -180° to -90°. The energy gain of the particles that arrive at the acceleration gap first at the front end of the bunch is low, and the speed after passing through the acceleration gap is slow; the energy gain of the particles that arrive at the acceleration gap later at the back end of the bunch is high, and the speed after passing through the acceleration gap is fast, achieving longitudinal focusing on the bunch. This effect is only significant when the particle energy is low, that is Figure 1 the position where the particle trajectory first passes through the acceleration gap 1.

[0003] The defect of this traditional method is that although the selected transit time has good longitudinal focusing force, it is defocusing in the height direction. Because the particles are first focused and then defocused when passing through the acceleration gap. If the transit time is in the region where the voltage rises with time, then the electric field strength during focusing is less than the electric field strength during defocusing, resulting in defocusing in the height direction.

[0004] The traditional method needs to select Figure 2 in the region of -90° to 0° in order to provide stronger focusing force in the height direction. In this region, the transit time selects the region where the voltage decreases with time. For the situation where the particles are first focused and then defocused when passing through the acceleration gap, although the defocusing problem can be solved (the electric field strength during focusing is greater than the electric field strength during defocusing), but during the focusing stage when the particles pass through the acceleration gap, since the energy gain of the beam arriving first is large and the energy gain of the beam arriving later is small, the focusing effect is not ideal. Since the focusing force of the particles comes from the electric field focusing force and the magnetic field focusing force, in order to simultaneously meet the requirements of focusing and defocusing, for the situation where the energy gain of the beam arriving first is small and the energy gain of the beam arriving later is large, the solution is to ensure that while solving the defocusing in the height direction, select an accelerator with a relatively strong magnetic field focusing force to make up for the deficiency of the poor longitudinal focusing effect when selecting Figure 2 in the region of -90° to 0°. If there is no accelerator with a relatively strong magnetic field focusing force to make up for the deficiency of the longitudinal focusing, the transit time can only be selected Figure 2 in the region of -180° to -90°. Since the voltage in this region rises with time, the electric field strength during focusing is less than the electric field strength during defocusing, resulting in defocusing in the height direction.

[0005] In summary, the traditional method of providing longitudinal focusing force in the central region has the side effect of defocusing in the height direction when the radio frequency voltage range of -180 to -90 is selected; the traditional method of providing focusing force in the height direction in the central region has the side effect of inability to focus longitudinally when the radio frequency voltage range of -90° to 0° is selected. Summary of the Invention

[0006] To solve the deficiencies of the prior art, the present invention proposes a method for improving the longitudinal focusing force in the central region of a cyclotron. The first objective is to solve the problem that the traditional method of providing longitudinal focusing force in the central region has the side effect of defocusing in the height direction; the second objective is to solve the problem that the traditional method of providing focusing force in the height direction in the central region has the side effect of inability to focus longitudinally.

[0007] The present invention adopts the following technical solutions to solve its technical problems:

[0008] A method for improving the longitudinal focusing force in the central region of a cyclotron, characterized by including the following steps:

[0009] Step 1: Divide the radio frequency cavity into a radio frequency cavity that generates energy difference and a radio frequency cavity that eliminates energy difference; set the energy gain of the beam head particles that reach the acceleration gap first to be low, and the energy of the beam tail particles that reach the acceleration gap later to be high; or set the energy gain of the beam head particles that reach the acceleration gap first to be high, and the energy gain of the beam tail particles that reach the acceleration gap later to be low.

[0010] Step 2: By rotating the head structures of the radio frequency cavity that generates energy difference and the radio frequency cavity that eliminates energy difference in opposite directions respectively, make the energies of the head particles and tail particles of the beam bunch show a certain energy difference, and compress the particles from the non-receiving and non-accelerating regions of the current radio frequency cycle to the middle receiving and accelerating regions, thereby improving the longitudinal focusing force of the particles along the trajectory direction; by adjusting the rotation angle of the head structure of the radio frequency cavity that eliminates energy difference in the counterclockwise or clockwise direction in the opposite direction, eliminate the energy difference at the position where the beam bunch width is the smallest; this region with the smallest width is the region where the wide phase is compressed to the narrow phase.

[0011] Further, the step of rotating the head structures of the radio frequency cavity that generates energy difference and the radio frequency cavity that eliminates energy difference in opposite directions in Step 2 is as follows:

[0012] When the energy gain of the beam head particles is low and the energy gain of the beam tail particles is high, clockwise adjust the rotation angle of the head structure of the radio frequency cavity that generates energy difference, and counterclockwise adjust the rotation angle of the head structure of the radio frequency cavity that eliminates energy difference.

[0013] When the energy gain of the particles at the head of the beam is high and the energy gain of the particles at the tail of the beam is low, counterclockwise adjust the rotation angle of the head structure of the radio frequency cavity that generates the energy difference, and clockwise adjust the rotation angle of the head structure of the radio frequency cavity that eliminates the energy difference; the presence of a certain energy difference includes energy differences in monotonic and non-monotonic cases.

[0014] When setting the rotation angle of the beam head structure to be adjusted clockwise, the voltage at the position where the particles at the head of the bunch are located is relatively small, and the energy gain obtained is relatively small, while the voltage at the position where the particles at the tail are located is relatively large, and the energy gain obtained is relatively large; when setting the rotation angle of the beam head structure to be adjusted counterclockwise, the voltage at the position where the particles at the head of the bunch are located is relatively large, and the energy gain obtained is relatively large, while the voltage at the position where the particles at the tail are located is relatively small. The energy gain obtained is relatively small.

[0015] Furthermore, when setting the rotation angle of the beam head structure to be adjusted clockwise, the cavities that generate the energy difference and eliminate the energy difference are radio frequency cavity 1 and radio frequency cavity 2 respectively, or radio frequency cavity 2 and radio frequency cavity 3 respectively, or radio frequency cavity 3 and radio frequency cavity 4 respectively, or the positions of the next bunch of the radio frequency cavity 4 and radio frequency cavity 1.

[0016] Furthermore, on the current bunch of the beam in the central area, when setting the rotation angle of the beam head structure to be adjusted clockwise, rotate radio frequency cavity 1 and radio frequency cavity 2, which generate the energy difference and eliminate the energy difference, counterclockwise by 90 degrees, and the cavities that generate the energy difference and eliminate the energy difference are radio frequency cavity 2 and radio frequency cavity 3 respectively; rotate radio frequency cavity 1 and radio frequency cavity 2, which generate the energy difference and eliminate the energy difference, counterclockwise by 180 degrees, and the cavities that generate the energy difference and eliminate the energy difference are radio frequency cavity 3 and radio frequency cavity 4 respectively; rotate radio frequency cavity 1 and radio frequency cavity 2, which generate the energy difference and eliminate the energy difference, counterclockwise by 270 degrees, and the cavities that generate the energy difference and eliminate the energy difference are the positions of the next bunch of the radio frequency cavity 4 and radio frequency cavity 1.

[0017] Furthermore, on the current bunch of the beam in the central area, when setting the rotation angle of the beam head structure to be adjusted counterclockwise, the cavities that generate the energy difference and eliminate the energy difference are radio frequency cavity 1 and radio frequency cavity 4 respectively.

[0018] Furthermore, on the current bunch of the beam in the central area, when setting the rotation angle of the beam head structure to be adjusted counterclockwise, rotate radio frequency cavity 1 and radio frequency cavity 4, which generate the energy difference and eliminate the energy difference, counterclockwise by 90 degrees, and the cavities that generate the energy gain and generate the chromatic dispersion elimination are radio frequency cavity 2 and the position of the next bunch of radio frequency cavity 1 respectively.

[0019] Furthermore, on the current bunch of beam in the central region, when setting the rotation angle to adjust the beam head structure clockwise, since the energy gain of the particles at the head of the bunch is lower than that of the particles at the tail of the bunch, the particles at the head of the bunch move in a smaller circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a larger circle relative to the center point of the accelerator: Let the radius of the particles moving in the larger circle at the tail of the bunch be r1, and the radius of the particles moving in the smaller circle at the head of the bunch be (1 - k)r1, where k < 1.

[0020] Furthermore, on the current bunch of beam in the central region, when setting the rotation angle to adjust the head structure of the RF cavity counterclockwise, since the energy gain of the particles at the head of the bunch is higher than that of the particles at the tail of the bunch, the particles at the head of the bunch move in a larger circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a smaller circle relative to the center point of the accelerator: Let the radius of the particles moving in the larger circle at the head of the bunch relative to the center point of the accelerator be r1, and the radius of the particles moving in the smaller circle at the tail of the bunch be (1 - k)r1, where k < 1.

[0021] Furthermore, on the current bunch of beam in the central region, when setting the rotation angle to adjust the head structure of the RF cavity clockwise, for the RF cavity 1 that generates energy difference, when the beam head rotates counterclockwise 90 degrees from the RF cavity 1 to reach the RF cavity 2, the beam head, the particles with lower energy, rotate an angle exceeding 90 degrees relative to its own center point (1 - k)r1, k < 1, and the rotation angle of the beam tail, the particles with higher energy, relative to its own center point r1 is 90 degrees. At this time, the particles at the head of the beam move relatively the slowest, and the particles at the tail of the beam move relatively the fastest, so that the phase width is compressed to the minimum. At this time, the RF cavity 2 serves as the cavity to eliminate the energy difference, and the RF cavity 2 is rotated counterclockwise by a set angle to eliminate the energy difference;

[0022] On the current bunch of beam in the central region, when setting the rotation angle to adjust the head structure of the RF cavity clockwise and using the RF cavity 2 as the RF cavity that generates energy difference, when the beam head rotates counterclockwise 90 degrees from the RF cavity 2 to reach the RF cavity 3, the beam head rotates an angle exceeding 90 degrees relative to its own center point (1 - k)r1, k < 1, and the rotation angle of the beam tail relative to its own center point r1 is 90 degrees. At this time, the particles at the head of the beam move relatively the slowest, and the particles at the tail of the beam move relatively the fastest, so that the phase width is compressed to the minimum. At this time, the RF cavity 3 serves as the cavity to eliminate the energy difference, and the RF cavity 3 is rotated counterclockwise by a set angle to eliminate the energy difference.

[0023] On the current beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted clockwise and using the RF cavity 3 as the RF cavity that generates energy difference, when the beam head rotates counterclockwise by 90 degrees from the RF cavity 3 to reach the RF cavity 4, the rotation angle of the beam head relative to its own center point (1 - k)r1, k < 1 exceeds 90 degrees, and the rotation angle of the beam tail relative to its own center point r1 is 90 degrees. At this time, the particles at the beam head move relatively the slowest, while the particles at the beam tail move relatively the fastest, so that the phase width is compressed to the minimum. At this time, the RF cavity 4 is used to eliminate the energy difference, and the RF cavity 4 is rotated counterclockwise by a set angle to eliminate the energy difference.

[0024] Furthermore, on the current beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise, for the RF cavity 1 that generates energy difference, when the particles at the beam tail rotate counterclockwise by 270 degrees from the RF cavity 1 to reach the RF cavity 4, in the third quadrant, the rotation angle of the particles at the beam tail relative to its own center of the circle (1 - k)r1, k < 1 does not reach 270 degrees, and the rotation angle of the beam head relative to its own center point r1 is 270 degrees. At this time, the particles at the beam tail move relatively the fastest, while the particles at the beam head move relatively the slowest, so that the phase width is compressed to the minimum. At this time, the RF cavity 4 is used to eliminate the energy difference, and the RF cavity 4 is rotated clockwise by a set angle to eliminate the energy difference.

[0025] On the current beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise and using the RF cavity 2 as the cavity that generates energy difference, for the RF cavity 2 that generates energy difference, when the particles at the beam tail rotate counterclockwise by 270 degrees from the RF cavity 2 to reach the next circle of the RF cavity 1, in the fourth quadrant, the rotation angle of the particles at the beam tail relative to its own center of the circle (1 - k)r1, k < 1 does not reach 270 degrees, and the rotation angle of the beam head relative to its own center point r1 is 270 degrees. At this time, the particles at the beam tail move relatively the fastest, while the particles at the beam head move relatively the slowest, so that the phase width is compressed to the minimum. At this time, the RF cavity 1 is used as the cavity to eliminate the energy difference, and the position of the next circle where the beam of the RF cavity 1 passes is rotated clockwise by a set angle to eliminate the energy difference.

[0026] Advantages and effects of the present invention

[0027] 1. The present invention achieves longitudinal focusing in a negative phase manner. By considering the two accelerations of a radio frequency cavity as an overall adjustment, while providing longitudinal focusing force, it also ensures that there is no defocusing in the height direction. By eliminating the energy difference at the radio frequency cavity 2 where the phase width is compressed the least, it solves the problem that in one revolution of the head particles, some quadrants move slowly and some move quickly, resulting in the reappearance of longitudinal defocusing in the quadrants where the head particles move slowly after chromatic dispersion elimination.

[0028] 2. The present invention achieves longitudinal focusing in a positive phase manner. By considering the two accelerations of a radio frequency cavity as an overall adjustment, while providing longitudinal focusing force, it also ensures that there is no defocusing in the height direction. At the same time, since the positive phase is selected to achieve longitudinal focusing in the positive phase the positive phase is greater than the negative phase. As can be seen from formula (4), the phase is related to the inlet and outlet gap times τ1 and τ2. When the phase is large, τ1 and τ2 are also large. When τ1 and τ2 are large, the axial focusing is strong. Therefore, when the longitudinal focusing is achieved in the positive phase manner, the focusing effect in the height direction is better. By eliminating the energy difference at the radio frequency cavity 4 where the phase width is compressed the least, it solves the problem that in one revolution of the tail particles, some quadrants move slowly and some move quickly, resulting in the reappearance of longitudinal defocusing in the quadrants where the tail particles move slowly after chromatic dispersion elimination. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the central area of the cyclotron;

[0030] Figure 2 Radio frequency voltage curve;

[0031] Figure 3 Energy gain of particles with different phases;

[0032] Figure 4 Trajectories of particles with different energies;

[0033] Figure 5 Difference in angular change of particles with different speeds;

[0034] Figure 6 Schematic diagram of Embodiment 1 and Embodiment 5 of the present invention;

[0035] Figure 7 Schematic diagram of Embodiment 2 and Embodiment 5 of the present invention;

[0036] Figure 8 Schematic diagram of Embodiment 3 of the present invention;

[0037] Figure 9 Schematic diagram of Embodiment 4 and Embodiment 5 of the present invention;

[0038] Figure 10 Schematic diagram of Embodiment 5 of the present invention;

[0039] Figure 11 Schematic diagram of Embodiment 5 of the present invention;

[0040] Figure 12 Schematic diagram of the present invention being accepted and accelerated;

[0041] Figure 13 Flowchart of the method for the present invention to improve the longitudinal focusing force in the central region of the cyclotron. Detailed implementation manners

[0042] Design principle of the present invention

[0043] 1. Innovations of the present invention: One of the innovations is to regard the two accelerations of a radio frequency cavity as an overall adjustment, which can provide longitudinal focusing force while avoiding defocusing in the height direction. Another innovation is to eliminate the energy difference at the place where the phase width is compressed to the minimum. The reason for eliminating the energy difference is that among the head particles in one revolution, they move slowly in some quadrants and fast in some quadrants. If the energy difference is not eliminated in time when the phase width is compressed to the minimum, longitudinal defocusing will occur in the quadrants where the head particles move fast.

[0044] 2. Theoretical basis

[0045] Figure 1 is a schematic diagram of the central region of a typical cyclotron. This structure has 4 radio frequency cavities, and the principle of the present invention is also applicable to structures with other numbers of cavities. It consists of a radio frequency cavity and a ground electrode. The potential of the ground electrode is 0, and the radio frequency cavity provides a periodic radio frequency voltage V:

[0046] 3. V(t) = V0 sinτ (1)

[0047] where V0 is the amplitude of the radio frequency voltage and τ is the radio frequency time. An acceleration gap with a radio frequency electric field is formed between the radio frequency cavity and the ground electrode. According to the order of particle passage, they are acceleration gaps 1 to 8. Particles are accelerated when passing through the acceleration gaps.

[0048] In order to enable particles to have an accelerating voltage when passing through the acceleration gaps, the signs of the radio frequency voltages when the particles enter and leave should be opposite. For example, when a negative ion is accelerated by radio frequency cavity 1, at acceleration gap 1, it enters the radio frequency cavity from the ground electrode, and at this time, the voltage of the radio frequency cavity should be negative, corresponding to Figure 2 -180° to 0° in (1), so that the particles can obtain energy; at acceleration gap 2, it enters the ground electrode from the radio frequency cavity, and at this time, the voltage of the radio frequency cavity should be positive, corresponding to Figure 2From 0° to 180°. Let the RF times when the particle passes through acceleration gap 1 and acceleration gap 2 be τ1 and τ2 respectively, and the charge of the negative ion be -q. Then the energy gains obtained by the particle from acceleration gap 1 and acceleration gap 2 are:

[0049] ΔE = qV0(sinτ2 - sinτ1)(2)

[0050] Equation (2) shows that particles arriving at the RF cavity at different times obtain different energy gains. For the same RF cavity structure, the time lengths required for particles arriving at different times to pass through the RF cavity, that is, the difference between τ1 and τ2, are the same:

[0051] τ2 - τ1 = hα(3)

[0052] h is the harmonic number of the accelerator, and α is the opening angle of the RF cavity. Define the particle phase:

[0053]

[0054] It is the average RF time when the particle enters and leaves the RF cavity, and it is also the RF time when the particle arrives at the center line of the RF cavity. Substitute Equation (3) and Equation (4) into Equation (2) to get:

[0055]

[0056] Equation (5) shows that particles with a particle phase of 0, that is, particles that exactly arrive at the center line of the RF cavity when the RF time is 0, obtain the highest energy gain, as Figure 3 shown.

[0057] 3. Invention principle

[0058] It can be seen from Equation (5) that not all particles injected into the accelerator at all times can be accelerated. The phase φ can be accelerated only between -90° and 90°. In fact, the ability of the accelerator to receive and accelerate the beam is much smaller than this range. Therefore, even if the particle beam is continuously injected into the accelerator, only particles with certain phases are accelerated in each RF cycle, forming periodic particle bunches. Longitudinal refers to the direction in which the particle bunch advances, which is manifested as the length of the bunch or the time length spanned by the bunch passing through a certain position. By reasonably designing the central region structure, providing longitudinal focusing force, and reducing the longitudinal length of the beam, it is beneficial to improve the beam transmission efficiency.

[0059] The magnetic field modulation degree in the central region of the cyclotron is low and can be approximately regarded as a uniform magnetic field. The rotation radius of a charged particle in the cyclotron:

[0060]

[0061] where \(m\) is the mass of the particle, \(v\) is the velocity of the particle, \(q\) is the charge of the particle, and \(B\) is the magnetic induction intensity. The angular velocity of the particle rotating in the cyclotron is:

[0062]

[0063] It can be seen from Equation (7) that the angular velocities of particles with different velocities are the same. Suppose there is a particle 1 rotating around the center of the cyclotron with a radius \(r\), as Figure 4 shown by the solid line part. Taking the position \((r_1, 0)\) at the azimuth angle of \(0^{\circ}\) as the starting moment, the azimuth angle of particle 1 changes with time \(t\):

[0064] \(\theta_1=\omega t\) (8)

[0065] The coordinates of particle 1 changing with time can be expressed as:

[0066]

[0067] Particle 2 also starts from the position \((r_1, 0)\). Due to the difference in energy from particle 1, its rotation radius:

[0068] \(r_2 = k\cdot r_1\) (10)

[0069] When the energy of particle 2 is less than that of particle 1, \(k\lt1\); conversely, \(k\gt1\). Particle 2 also rotates with an angular velocity of \(\omega\), and its rotation center is \(((1 - k)r_1, 0)\). The coordinates of particle 2 changing with time can be expressed as:

[0070]

[0071] The azimuth angle of particle 2 is:

[0072]

[0073] Substitute Equation (8) and Equation (11) into Equation (12) and solve to obtain:

[0074]

[0075] Figure 5 Taking \(k = 0.8\) as an example, the angular difference between particle 2 and particle 1 at the same moment is shown. The relationship between the abscissa \(\theta_1\) and time is shown in Equation (8). The angular velocity of particle 2 rotating is the same as that of particle 1, which is \(\omega\), but the center of its rotation is not at the origin, resulting in a change in the angular velocity of particle 2 in the coordinate system centered at the origin. Figure 5 In it, the negative ordinate indicates that from the starting point to this moment, particle 2 rotates through a smaller angle than particle 1, and the positive ordinate indicates a larger rotation angle; the decrease in the ordinate indicates that the angular velocity of particle 2 at this moment is less than that of particle 1, and the increase indicates that the angular velocity is greater than that of particle 1. Its correspondence with Figure 4 is:

[0076] (1) Particle 1 rotates 90° in each of the first to fourth quadrants, with a constant angular velocity ω1. The angle θ1 by which Particle 2 rotates in the first quadrant is greater than 90°, the angular velocity relative to its own rotation center is the same as that of Particle 1, and the angular velocity ω2 relative to the accelerator center is less than that of Particle 1, corresponding to Figure 5 a decrease in the ordinate, reaching a minimum value near the abscissa of 90°.

[0077] (2) The angle θ2 by which Particle 2 rotates in the second quadrant is less than 90°, the angular velocity ω2 relative to the accelerator center is greater than that of Particle 1, corresponding to Figure 5 an increase in the ordinate. When the abscissa is 180°, both Particle 1 and Particle 2 have rotated half a circle, so the ordinate is 0.

[0078] (3) The angle θ2 by which Particle 2 rotates in the third quadrant is less than 90°, the angular velocity ω2 relative to the accelerator center is greater than ω1 of Particle 1, corresponding to Figure 5 an increase in the ordinate, reaching a maximum value near the abscissa of 270°.

[0079] (4) The angle θ2 by which Particle 2 rotates in the fourth quadrant is greater than 90°, the angular velocity ω2 relative to the accelerator center is less than that of Particle 1, corresponding to Figure 5 a decrease in the ordinate. When the abscissa is 360°, both Particle 1 and Particle 2 have rotated one full circle, so the ordinate is 0.

[0080] When the energy of Particle 2 is greater than that of Particle 1, i.e., k > 1, the above variation law is reversed.

[0081] Taking the center of the cyclotron as the origin of the coordinate system, the angular velocities of particles with different energies are variable, and the difference between them changes with the rotation angle and has maximum and minimum values. By adjusting the structure of the head of the radio frequency cavity in the present invention, the energy dispersion of particles at different longitudinal positions in the bunch shows a monotonic change. After rotating through a certain angle, the energy difference is eliminated at the position where the bunch width is the smallest, realizing longitudinal focusing of the bunch.

[0082] It can be seen from Equation (5) that not all particles injected into the accelerator at all times can be accelerated. The phase φ can be accelerated only between -90° and 90°. In fact, the ability of the accelerator to receive and accelerate the beam current is much smaller than this range. Therefore, even if the particle beam is continuously injected into the accelerator, only particles with certain phases are accelerated in each radio frequency cycle, forming a periodic particle bunch. Longitudinal refers to the direction in which the particle bunch advances, manifested as the length of the bunch or the time length spanned by the bunch passing through a certain position. By reasonably designing the structure of the central region, providing longitudinal focusing force, and reducing the longitudinal length of the beam current, it is beneficial to improve the transmission efficiency of the beam current.

[0083] 4. Design principle of realizing longitudinal focusing by negative phase adjustment method: In the present invention, Figure 6 the longitudinal focusing is realized by the method of negative phase, Figure 8 and 9 it is the derivative result of realizing longitudinal focusing by the method of negative phase.

[0084] First, the method of realizing longitudinal focusing by negative phase can provide longitudinal focusing force while avoiding defocusing in the height direction. The method adopted is to adjust the head structure clockwise. Adjusting the head structure clockwise means making the head of the beam reach the center line of the radio frequency cavity in advance. The particle phase is the average value of the time passing through the two accelerating gaps when entering and leaving the radio frequency cavity, that is, the radio frequency time when the particle reaches the center line of the radio frequency cavity. In Figure 3 it is when the phase has not reached 0 degrees, that is, in the negative phase interval such as Figure 3 -10 degrees of phase, which is used as the phase of the central particle of the bunch. Since the two accelerations of a radio frequency cavity are regarded as an overall adjustment, the -10 degree phase corresponds not only to the entrance accelerating gap but also to the average value of the time passing through the entrance and exit accelerating gaps. For example, the average value of -80 degrees and +60 degrees in a radio frequency cycle is -10 degrees, and the -10 degrees of this radio frequency cycle corresponds to Figure 2 -10° phase. Assuming φ is selected as -10°, in Figure 3 the radio frequency voltage cycle of Figure 2 , the time passing through accelerating gap 1 and accelerating gap 2, τ1 and τ2, can be selected as -80° and 60°. The time passing through accelerating gap 1 meets the focusing requirements in the height direction. Although accelerating gap 2 is a defocusing phase in the height direction, it has high energy and low influence, and overall shows a focusing effect.

[0085] The transit time of the accelerating gap 1 meets the focusing requirements in the height direction because -80 is in the voltage rising region from -90 to 0 rather than the voltage falling region. In this region, the conditions for longitudinal focusing of the traditional method cannot be met, but the conditions for focusing in the height direction can be met. Because when particles pass through the accelerating gap, they are first focused and then defocused. When the voltage decreases with time, the focusing electric force is greater than the defocusing force, so overall it is focused. This effect is related to the energy of the particles. The lower the particle energy, the more significant the focusing and defocusing effects of this effect. The voltage of the accelerator gap 2 is in the voltage rising interval from 0 to 90 degrees. The voltage rising interval meets the conditions for longitudinal focusing of the traditional method, but does not meet the conditions for focusing in the height direction. However, because the particles have been accelerated by the accelerating gap 1 and have higher energy, the defocusing effect in the height direction of the accelerating gap 2 is smaller than the focusing effect of the accelerating gap 1, and overall it is focused in the height direction. In summary, because the focusing in the height direction is met at the first accelerating gap, the defocusing in the height direction at the second accelerating gap has less impact than that of the accelerating gap 1, and at the same time, the average phases of the accelerating gap 1 and the accelerating gap 2 meet the conditions for longitudinal focusing. Therefore, the method of longitudinal focusing with a negative phase can provide longitudinal focusing force while avoiding defocusing in the height direction.

[0086] Second, the method of longitudinal focusing with a negative phase eliminates the energy difference where the phase width is compressed to the minimum. ①. The prerequisite for longitudinal compression is that the energy gain of the beam head is small and the energy gain of the beam tail is large, so that the head moves in a small circle and the tail moves in a large circle: The reason why the energy gain of the beam head is small and the energy gain of the beam tail is large is that the voltage rises with time. Suppose the radio frequency voltage is 50 kV when the beam head passes through point A, and when the particles at the tail pass through point A, the radio frequency voltage has risen to 60 kV. Therefore, the energy gain of the head is small and the energy gain of the tail is large. ②. As Figure 6 shown, because the energy gain of the head is small, it moves in a small circle. When it reaches the radio frequency cavity 2, the head of the dotted line exceeds 90 degrees relative to its own center point, while the solid line tail rotates by 90 degrees, which is equivalent to the beam head moving slowly and the beam tail moving fast. The fast in the front and the slow in the back achieve the compression of the phase width. That is, the phase width is compressed to the minimum at the radio frequency cavity 2. Therefore, at the radio frequency cavity 2, the energy difference is eliminated by rotating the cavity 2 counterclockwise. ③. The reason for eliminating chromatic dispersion at the radio frequency cavity 2 is that the beam head does not move slowly in each of the four quadrants of 1, 2, 3, and 4. When it moves faster than the beam tail in a certain interval, it is not longitudinally focused but longitudinally defocused. For example, from Figure 6Look, in the first quadrant, the head of the beam moves slowly while the tail moves fast. In the second and third quadrants, the head moves fast and the tail moves slowly. The front part of the beam moves fast and the back part moves slowly. In the second and third quadrants, it is equivalent to stretching the beam. Stretching the beam is not focusing but defocusing. In the fourth quadrant, the dotted line moves slowly and the solid line moves fast, so the fourth quadrant is also focusing. It can be seen that if the dispersion is not eliminated at the RF cavity 2, the particles at the head of the beam in the four quadrants are: focusing, defocusing, defocusing, focusing, which makes half of the particles in the current central region focus for half of the time and defocus for half of the time. When the energy difference is eliminated, the energy gain of the head and the tail at the RF cavity 2 is the same, so the longitudinal defocusing in the second and third quadrants will no longer occur. Assuming that the first compression meets the requirements of longitudinal focusing, then the fourth quadrant does not need to focus either. Therefore, eliminating the dispersion at the RF cavity 2 so that there is no defocusing or focusing in the second, third, and fourth quadrants meets the requirements.

[0087] 5. The design principle of realizing longitudinal focusing by the positive phase adjustment method. First, the Figure 7 present invention realizes longitudinal focusing by the method of using the positive phase to achieve longitudinal focusing. Figure 10 It is a derivative result of realizing longitudinal focusing by the positive phase method. The method of realizing longitudinal focusing by the positive phase takes into account not causing defocusing in the height direction while providing longitudinal focusing force. The method it adopts is to adjust the head structure counterclockwise. Adjusting the head structure counterclockwise means that the head of the beam arrives at the center line of the RF cavity later. The particle phase is the average value of the time passing through the two acceleration gaps when entering and leaving the RF cavity, that is, the RF time when the particle arrives at the center line of the RF cavity. Arriving at the center line of the RF cavity later means selecting a phase such as Figure 3 +10 degrees (here +10 degrees is an example rather than a limitation, and other positive phases are also possible), and using the +10-degree phase as the phase of the central particle of the bunch. Since the two accelerations of an RF cavity are regarded as an overall adjustment, the +10-degree phase corresponds to the average value of the entrance acceleration gap and the two time intervals of passing through the gaps at the entrance and the exit. For example, the average value of -60 degrees and +80 degrees in the RF cycle is +10 degrees, and the +10 degrees in this RF cycle corresponds to Figure 2 the +10° phase. Assuming that φ is selected as +10°, in Figure 3 the +10° phase. Figure 2During the radio frequency voltage cycle, the transit times τ1 and τ2 of acceleration gaps 1 and 2 can be selected as -60° and +80°. The transit time of acceleration gap 1 meets the focusing requirements in the height direction. Although acceleration gap 2 has a defocusing phase in the height direction, it has high energy and low influence, presenting an overall focusing effect. The transit time of the acceleration gap 1 meets the focusing requirements in the height direction because -60 is in the voltage rising region from -90 to 0 rather than the voltage falling region. In this region, the condition for longitudinal focusing cannot be met, but the condition for focusing in the height direction can be met because when the voltage decreases with time, the influence on focusing in the height direction is small. The voltage of accelerator gap 2 is in the voltage rising interval from 0 to 90 degrees. The voltage rising interval meets the condition for longitudinal focusing but does not meet the condition for focusing in the height direction. However, because the voltage at 80 degrees is relatively high at this time, the higher the energy, the faster the particles rotate, and the faster the particles rotate, the smaller the defocusing influence on the height direction. On the contrary, if the rotation speed of the particles is slow or the energy of the particles is low, the defocusing influence on the height direction is large. In short, since focusing in the height direction is achieved at the first acceleration gap and the condition for longitudinal focusing is met at the second acceleration gap, and at the same time, the influence on focusing in the height direction is very small, the longitudinal focusing achieved by the positive phase method can provide longitudinal focusing force while avoiding defocusing in the height direction.

[0088] Second, the longitudinal focusing achieved by the positive phase method eliminates the energy difference where the phase width is compressed to the minimum. ① The prerequisite for longitudinal compression is that the energy gain of the beam tail is small and the energy gain of the beam head is large, so that the tail moves in a small circle and the head moves in a large circle. The reason why the energy gain of the beam tail is small and the energy gain of the beam head is large is that the voltage decreases with time. Suppose the radio frequency voltage is 60 kV when the beam head passes through point A. When the particles at the tail pass through point A, the radio frequency voltage has dropped to 50 kV. Therefore, the energy gain of the head is large and the energy gain of the tail is small. ② As Figure 6 shown, because the particles at the head have a large energy gain and move in a large circle, when reaching the radio frequency cavity 4, the dotted-line tail particles do not exceed 270 degrees relative to their own center point, while the solid-line head particles rotate by 270 degrees. It is equivalent to the head of the beam moving slowly and the tail of the beam moving fast, and the fast in the front and the slow in the back achieve the compression of the phase width. That is, the phase width is compressed to the minimum at the radio frequency cavity 4. Therefore, the energy difference is eliminated by rotating the cavity 4 clockwise at the radio frequency cavity 4. ③ The reason for eliminating the energy difference at the radio frequency cavity 4 is that the particles at the beam tail do not move fast in each of the four quadrants of 1, 2, 3, and 4. From Figure 6Look, it moves slowly at the tails of the 1st and 4th quadrants, and moves fast at the tails of the 2nd and 3rd quadrants. The beam in the front moves fast while the one in the back moves slowly. In the 1st and 4th quadrants, it is equivalent to stretching the beam, and stretching the beam is not focusing but defocusing. It can be seen that if the energy difference is not eliminated at the RF cavity 4, the particles at the head of the beam in the 4 quadrants are: defocusing, focusing, focusing, defocusing, making the particles in a circle in the current central region focus for half of the time and defocus for half of the time. When the energy difference is eliminated at the RF cavity 4, the energy gains of the head and the tail at the RF cavity 4 are the same, so the defocusing situation in the 4th quadrant will no longer occur.

[0089] 3) Differences between positive phase adjustment and negative phase adjustment: To achieve longitudinal focusing in the negative phase mode, select the negative phase To achieve longitudinal focusing in the positive phase mode, select the positive phase The positive phase is greater than the negative phase. It can be seen from formula (4) that the phase is related to the inlet and outlet gap times τ1 and τ2. The larger the phase is, the larger τ1 and τ2 are. The larger τ1 and τ2 are, the stronger the axial focusing is. Therefore, the height-direction focusing effect of achieving longitudinal focusing in the negative phase mode in the inlet acceleration gap is better than that of achieving longitudinal focusing in the positive phase mode in the inlet acceleration gap.

[0090] Based on the above principles, the present invention designs a method for improving the longitudinal focusing force in the central region of a cyclotron, as Figure 13 shown, which is characterized by including the following steps:

[0091] Step 1: Divide the RF cavity into an RF cavity that generates energy difference and an RF cavity that eliminates energy difference; set the energy gain of the beam head particles that reach the acceleration gap first to be low, and the energy of the beam tail particles that reach the acceleration gap later to be high; or set the energy gain of the beam head particles that reach the acceleration gap first to be high, and the energy gain of the beam tail particles that reach the acceleration gap later to be low;

[0092] Step 2: By rotating the head structures of the RF cavity that generates energy difference and the RF cavity that eliminates energy difference in opposite directions respectively, make the energies of the head particles and tail particles of the beam bunch show a certain energy difference, compress the particles from the non-receiving and non-accelerating regions of the current RF cycle to the middle receiving and accelerating regions, thereby improving the longitudinal focusing force of the particles along the trajectory direction; by making a counterclockwise or clockwise adjustment of the rotation angle in the opposite direction to the head structure of the RF cavity that eliminates energy difference, eliminate the energy difference at the position where the beam bunch width is the smallest; this region with the smallest width is the region where the wide phase is compressed to the narrow phase;

[0093] Further, the head structures of the RF cavities that generate energy differences and the RF cavities that eliminate energy differences in Step 2 are rotated by angles in opposite directions, namely:

[0094] When the energy gain of the particles at the head of the beam is low and the energy gain of the particles at the tail of the beam is high, clockwise adjust the rotation angle of the head structure of the RF cavity that generates energy differences, and counterclockwise adjust the rotation angle of the head structure of the RF cavity that eliminates energy differences;

[0095] When the energy gain of the particles at the head of the beam is high and the energy gain of the particles at the tail of the beam is low, counterclockwise adjust the rotation angle of the head structure of the RF cavity that generates energy differences, and clockwise adjust the rotation angle of the head structure of the RF cavity that eliminates energy differences; The presented certain energy differences include energy differences in monotonic and non-monotonic cases;

[0096] When setting the clockwise adjustment of the rotation angle of the beam head structure, as Figure 6 、 8 、9 shown, the voltage at the position where the particles at the head of the bunch are located is relatively small, and the obtained energy gain is relatively small, while the voltage at the position where the particles at the tail are located is relatively large, and the obtained energy gain is relatively large; As Figure 7 、 10 shown, when setting the counterclockwise adjustment of the rotation angle of the beam head structure, the voltage at the position where the particles at the head of the bunch are located is relatively large, and the obtained energy gain is relatively large, while the voltage at the position where the particles at the tail are located is relatively small. The obtained energy gain is relatively small.

[0097] As Figure 6 、 8 、9 shown, when setting the clockwise adjustment of the rotation angle of the beam head structure, the cavities that generate energy differences and eliminate energy differences are RF cavity 1 and RF cavity 2 respectively, or RF cavity 2 and RF cavity 3 respectively, or RF cavity 3 and RF cavity 4 respectively, or the positions of the second circle of RF cavity 4 and RF cavity 1 respectively.

[0098] As Figure 6 、 8 、9's respective left figures shown, on the current circle of the beam in the central region, when setting the clockwise adjustment of the rotation angle of the beam head structure, as Figure 8 shown, rotate the RF cavity 1 and RF cavity 2 that generate energy differences and eliminate energy differences counterclockwise by 90 degrees, and the cavities that generate energy differences and eliminate energy differences are RF cavity 2 and RF cavity 3 respectively; As Figure 9 shown, rotate the RF cavity 1 and RF cavity 2 that generate energy differences and eliminate energy differences counterclockwise by 180 degrees, and the cavities that generate energy differences and eliminate energy differences are RF cavity 3 and RF cavity 4 respectively; As Figure 11As shown, the radio frequency cavities 1 and 2 that generate and eliminate energy differences are rotated counterclockwise by 270 degrees. The cavities that generate and eliminate energy differences are the next circle positions where the beam of radio frequency cavity 4 and radio frequency cavity 1 passes through.

[0099] As Figure 7 shown, on the current circle of the beam in the central region, when setting the rotation angle to adjust the beam head structure counterclockwise, the cavities that generate and eliminate energy differences are radio frequency cavity 1 and radio frequency cavity 4 respectively.

[0100] As Figure 10 shown, on the current circle of the beam in the central region, when setting the rotation angle to adjust the beam head structure counterclockwise, the radio frequency cavities 1 and 4 that generate and eliminate energy differences are rotated counterclockwise by 90 degrees. The cavities that generate and eliminate energy gain are the next circle positions of radio frequency cavity 2 and radio frequency cavity 1 respectively.

[0101] As Figure 6 、 8 、9 as shown in their respective right figures, on the current circle of the beam in the central region, when setting the rotation angle to adjust the beam head structure clockwise, since the energy gain of the particles at the head of the bunch is lower than that of the particles at the tail of the bunch, the particles at the head of the bunch move in a smaller circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a larger circle relative to the center point of the accelerator: Let the radius of the particles moving in the larger circle at the tail of the bunch be r1, and the radius of the particles moving in the smaller circle at the head of the bunch be (1 - k)r1, where k < 1.

[0102] As Figure 7 、 10 shown in their respective right figures, on the current circle of the beam in the central region, when setting the rotation angle to adjust the radio frequency cavity head structure counterclockwise, since the energy gain of the particles at the head of the bunch is higher than that of the particles at the head of the bunch, the particles at the head of the bunch move in a larger circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a smaller circle relative to the center point of the accelerator: Let the radius of the particles moving in the larger circle at the head of the bunch relative to the center point of the accelerator be r1, and the radius of the particles moving in the smaller circle at the tail of the bunch be (1 - k)r1, where k < 1.

[0103] As Figure 6As shown, on the current bunch of beam in the central area, when setting the rotation angle of the head structure of the RF cavity in the clockwise direction, for the RF cavity 1 that generates energy difference, when the beam head rotates counterclockwise by 90 degrees from the RF cavity 1 to reach the RF cavity 2, the rotation angle of the beam head and the particles with lower energy relative to their own center point (1-k)r1, k < 1, exceeds 90 degrees, and the rotation angle of the bunch tail and the particles with higher energy relative to their own center point r1 is 90 degrees. At this time, the particles at the beam head move relatively the slowest, while the particles at the beam tail move relatively the fastest, thus the phase width is compressed to the minimum. At this time, the RF cavity 2 serves as the cavity to eliminate the energy difference, and the RF cavity 2 is rotated counterclockwise by a set angle to eliminate the energy difference;

[0104] As Figure 8 shown, on the current bunch of beam in the central area, when setting the rotation angle of the head structure of the RF cavity in the clockwise direction and using the RF cavity 2 as the RF cavity that generates energy difference, when the beam head rotates counterclockwise by 90 degrees from the RF cavity 2 to reach the RF cavity 3, the rotation angle of the beam head relative to its own center point (1-k)r1, k < 1, exceeds 90 degrees, and the rotation angle of the beam tail relative to its own center point r1 is 90 degrees. At this time, the particles at the beam head move relatively the slowest, while the particles at the beam tail move relatively the fastest, thus the phase width is compressed to the minimum. At this time, the RF cavity 3 serves as the cavity to eliminate the energy difference, and the RF cavity 3 is rotated counterclockwise by a set angle to eliminate the energy difference.

[0105] As Figure 9 shown, on the current bunch of beam in the central area, when setting the rotation angle of the head structure of the RF cavity in the clockwise direction and using the RF cavity 3 as the RF cavity that generates energy difference, when the beam head rotates counterclockwise by 90 degrees from the RF cavity 3 to reach the RF cavity 4, the rotation angle of the beam head relative to its own center point (1-k)r1, k < 1, exceeds 90 degrees, and the rotation angle of the beam tail relative to its own center point r1 is 90 degrees. At this time, the particles at the beam head move relatively the slowest, while the particles at the beam tail move relatively the fastest, thus the phase width is compressed to the minimum. At this time, the RF cavity 4 serves to eliminate the energy difference, and the RF cavity 4 is rotated counterclockwise by a set angle to eliminate the energy difference.

[0106] As Figure 7As shown in the figure, on the current bunch of beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise, for the RF cavity 1 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise by 270 degrees from the RF cavity 1 to reach the RF cavity 4, in the third quadrant, the particles at the tail of the beam do not reach 270 degrees relative to the center of its own circle (1 - k)r1, k < 1, and the rotation angle of the head of the beam relative to its own center point r1 is 90 degrees. At this time, the particles at the tail of the beam move relatively fastest, while the particles at the head of the beam move relatively slowest, thus compressing the phase width to the minimum. At this time, the RF cavity 4 is used to eliminate the energy difference, and the RF cavity 4 is rotated clockwise by a set angle to eliminate the energy difference.

[0107] As Figure 10 shown in the figure, on the current bunch of beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise, and taking the RF cavity 2 as the cavity that generates energy difference, for the RF cavity 2 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise by 270 degrees from the RF cavity 2 to reach the next circle of the RF cavity 1, in the fourth quadrant, the particles at the tail of the beam do not reach 270 degrees relative to the center of its own circle (1 - k)r1, k < 1, and the rotation angle of the head of the beam relative to its own center point r1 is 270 degrees. At this time, the particles at the tail of the beam move relatively fastest, while the particles at the head of the beam move relatively slowest, thus compressing the phase width to the minimum. At this time, the RF cavity 1 is used as the cavity to eliminate the energy difference, and the position of the next circle where the beam of the RF cavity 1 passes through is rotated clockwise by a set angle to eliminate the energy difference.

[0108] Example 1: Achieving longitudinal focusing by using the negative phase adjustment method

[0109] As Figure 6 shown in the figure, in the present invention, ① regarding the entry and exit of particles from an RF cavity as a whole, ② adjusting the time for particles to pass through the center line of the RF cavity by angularly moving the position of the RF cavity, that is, the particle phase φ in Equation (4), to change the energy gain obtained by the particles. The negative phase method is used to achieve longitudinal focusing. Taking the RF cavity 1 in Figure 1 as an example, assuming that the current bunch center phase is 0°, rotating the head region of the RF cavity 1 corresponding to the first - circle particle trajectory clockwise, so that the whole bunch reaches the RF cavity 1 earlier, φ is less than 0, as in Figure 3 the range from - 90° to 0° in the figure. At this time, the φ of the bunch head is the smallest and the energy gain is the lowest; the φ of the bunch tail is the largest and the energy gain is the highest. From Figure 5It can be seen that near the angle of 90°, corresponding to the position of the radio frequency cavity 2, the particles at the head of the bunch with lower energy rotate by the smallest angle, and the particles at the tail of the bunch with higher energy rotate by the largest angle. The difference between the two reaches the minimum value, that is, the bunch is compressed to the smallest width. Adjust the position of the radio frequency cavity 2 and rotate it counterclockwise so that the bunch phase is located in Figure 3 the range of 0° to 90° in

[0110] Example 2: Achieving longitudinal focusing by using the positive phase adjustment method. As Figure 7 shown, achieving longitudinal focusing by the positive phase method is that the head region of the radio frequency cavity 1 rotates counterclockwise, making the whole bunch reach the radio frequency cavity 1 later, φ > 0, as Figure 3 in the range of 0° to 90° in Figure 5 It can be seen that near the angle of 270°, corresponding to the position of the radio frequency cavity 4, the particles at the head of the bunch with higher energy rotate by the smallest angle, and the particles at the tail of the bunch with lower energy rotate by the largest angle. The difference between the two reaches the minimum value, that is, the bunch is compressed to the smallest width. Adjust the position of the radio frequency cavity 4 and rotate it clockwise so that the bunch phase is located in Figure 3 the range of -90° to 0° in

[0111] Example 3

[0112] As Figure 8 shown, the cavity for generating a monotonically changing energy dispersion in the present invention is not limited to the radio frequency cavity 1. For example, for achieving longitudinal focusing by the negative phase method, modify it to rotate the head of the radio frequency cavity 2 clockwise and the head of the radio frequency cavity 3 counterclockwise;

[0113] Example 4

[0114] As Figure 10 shown, for achieving longitudinal focusing by the positive phase method, modify it to rotate the head of the radio frequency cavity 2 counterclockwise and the head of the radio frequency cavity 4 clockwise, and both can achieve longitudinal focusing. The lower the energy, the more significant the focusing effect.

[0115] Example 5:

[0116] The present invention can be implemented in combination, including but not limited to:

[0117] (1) As in the combination of Figure 6 and Figure 9 , on the basis of realizing longitudinal focusing by rotating the head of RF cavity 1 clockwise and the head of RF cavity 2 counterclockwise in a negative phase manner, the head of RF cavity 3 can be rotated clockwise and the head of RF cavity 4 can be rotated counterclockwise.

[0118] (2) As in the combination of Figure 6 and Figure 10 : On the basis of realizing longitudinal focusing by rotating the head of RF cavity 1 clockwise and the head of RF cavity 2 counterclockwise in a negative phase manner, further rotate the head of RF cavity 2 counterclockwise so that the head energy of the bunch is the highest and the tail energy is the lowest after passing through RF cavity 2. Then adjust the part of RF cavity 1 corresponding to the second turn of the particle trajectory and rotate it clockwise to eliminate the energy dispersion.

[0119] (3) As in the combination of Figure 7 and Figure 11 , on the basis of realizing longitudinal focusing by rotating the head of RF cavity 1 counterclockwise and the head of RF cavity 4 clockwise in a positive phase manner, further rotate the head of RF cavity 4 clockwise so that the head energy of the bunch is the lowest and the tail energy is the highest after passing through RF cavity 4. Then adjust the part of RF cavity 1 corresponding to the second turn of the particle trajectory and rotate it counterclockwise to eliminate the energy dispersion.

[0120] It should be emphasized that the above specific embodiments are merely explanations of the present invention and are not limitations thereto. Those skilled in the art can make modifications to the above embodiments without creative contributions according to needs after reading this specification, but as long as they are within the scope of the claims of the present invention, they are protected by the patent law.

Claims

1. A method for improving the longitudinal focusing force in the central region of a cyclotron, characterized in that, It includes the following steps: Step 1: Divide the radio frequency cavity into a radio frequency cavity that generates energy difference and a radio frequency cavity that eliminates energy difference; set the energy gain of the beam head particles that reach the acceleration gap first to be low, and the energy of the beam tail particles that reach the acceleration gap later to be high; or set the energy gain of the beam head particles that reach the acceleration gap first to be high, and the energy gain of the beam tail particles that reach the acceleration gap later to be low; Step 2: By rotating the head structures of the radio frequency cavity that generates energy difference and the radio frequency cavity that eliminates energy difference in opposite directions respectively, make the energies of the head particles and tail particles of the bunch present a certain energy difference, and compress the particles from the non-receiving and non-accelerating regions of the current radio frequency cycle to the middle receiving and accelerating regions, so as to improve the longitudinal focusing force of the particles along the trajectory direction; By adjusting the rotation angle of the head structure of the radio frequency cavity that eliminates energy difference in the counterclockwise or clockwise direction in the opposite direction, eliminate the energy difference at the position where the bunch width is the smallest; this region with the smallest width is the region where the wide phase is compressed to the narrow phase.

2. The method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 1, characterized in that: The step 2 of rotating the head structures of the radio frequency cavity that generates energy difference and the radio frequency cavity that eliminates energy difference in opposite directions respectively means: When the energy gain of the beam head particles is low and the energy gain of the beam tail particles is high, clockwise adjust the rotation angle of the head structure of the radio frequency cavity that generates energy difference, and counterclockwise adjust the rotation angle of the head structure of the radio frequency cavity that eliminates energy difference; When the energy gain of the beam head particles is high and the energy gain of the beam tail particles is low, counterclockwise adjust the rotation angle of the head structure of the radio frequency cavity that generates energy difference, and clockwise adjust the rotation angle of the head structure of the radio frequency cavity that eliminates energy difference; the so-called presenting a certain energy difference includes the energy differences in monotonic and non-monotonic cases; When it is set to clockwise adjust the rotation angle of the beam head structure, the voltage at the position where the bunch head particles are located is relatively small and the obtained energy gain is relatively small, while the voltage at the position where the tail particles are located is relatively large and the obtained energy gain is relatively large; when it is set to counterclockwise adjust the rotation angle of the beam head structure, the voltage at the position where the bunch head particles are located is relatively large and the obtained energy gain is relatively large, while the voltage at the position where the tail particles are located is relatively small and the obtained energy gain is relatively small.

3. The method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 2, wherein: When it is set to clockwise adjust the rotation angle of the beam head structure, the cavities that generate energy difference and eliminate energy difference are respectively the radio frequency cavity 1 and the radio frequency cavity 2, or respectively the radio frequency cavity 2 and the radio frequency cavity 3, or respectively the radio frequency cavity 3 and the radio frequency cavity 4, or respectively the positions of the radio frequency cavity 4 and the radio frequency cavity 1 for the next bunch of beams.

4. A method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 3, characterized in that: On the current bunch of beams in the central region, when it is set to clockwise adjust the rotation angle of the beam head structure, rotate the radio frequency cavity 1 and the radio frequency cavity 2 that generate energy difference and eliminate energy difference counterclockwise by 90 degrees, and the cavities that generate energy difference and eliminate energy difference are respectively the radio frequency cavity 2 and the radio frequency cavity 3; Rotate the RF cavities 1 and 2 that generate and eliminate energy differences counterclockwise by 180 degrees. The cavities that generate and eliminate energy differences are RF cavity 3 and RF cavity 4 respectively; Rotate the RF cavities 1 and 2 that generate and eliminate energy differences counterclockwise by 270 degrees. The cavities that generate and eliminate energy differences are RF cavity 4 and the next turn position where the beam of RF cavity 1 passes through.

5. The method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 2, wherein: On the current turn of the beam in the central region, when setting the rotation angle of the beam head structure to be adjusted counterclockwise, the cavities that generate and eliminate energy differences are RF cavity 1 and RF cavity 4 respectively.

6. The method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 5, wherein: On the current turn of the beam in the central region, when setting the rotation angle of the beam head structure to be adjusted counterclockwise, rotate the RF cavities 1 and 4 that generate and eliminate energy differences counterclockwise by 90 degrees. The cavities that generate energy gain and eliminate energy differences are RF cavity 2 and the next turn position of RF cavity 1 respectively.

7. The method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 2, characterized in that: On the current turn of the beam in the central region, when setting the rotation angle of the beam head structure to be adjusted clockwise, since the energy gain of the particles at the head of the bunch is lower than that of the particles at the tail of the bunch, the particles at the head of the bunch move in a smaller circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a larger circle relative to the center point of the accelerator: Let the radius of the particles moving in the larger circle at the tail of the bunch be r1, and the radius of the particles moving in the smaller circle at the head of the bunch be (1 - k)r1, where k < 1.

8. The method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 2, wherein: On the current turn of the beam in the central region, when setting the rotation angle of the RF cavity head structure to be adjusted counterclockwise, since the energy gain of the particles at the head of the bunch is higher than that of the particles at the tail of the bunch, the particles at the head of the bunch move in a larger circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a smaller circle relative to the center point of the accelerator: Let the radius of the particles moving in the larger circle at the head of the bunch relative to the center point of the accelerator be r1, and the radius of the particles moving in the smaller circle at the tail of the bunch be (1 - k)r1, where k < 1.

9. The method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 2, characterized in that: On the current turn of the beam in the central region, when setting the rotation angle of the RF cavity head structure to be adjusted clockwise, for RF cavity 1 that generates energy differences, when the beam head rotates counterclockwise by 90 degrees from RF cavity 1 to RF cavity 2, the particles at the beam head with lower energy rotate by an angle exceeding 90 degrees relative to their own center point (1 - k)r1, where k < 1, and the particles at the beam tail with higher energy rotate by an angle of 90 degrees relative to their own center point r1. At this time, the particles at the beam head move relatively the slowest, and the particles at the beam tail move relatively the fastest, thus the phase width is compressed to the minimum. At this time, RF cavity 2 is used as the cavity to eliminate energy differences, and rotate RF cavity 2 counterclockwise by a set angle to eliminate energy differences; On the current bunch of beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted clockwise and using the RF cavity 2 as the RF cavity for generating energy difference, when the head of the beam rotates counterclockwise by 90 degrees from the RF cavity 2 to reach the RF cavity 3, the rotation angle of the head of the beam relative to its own center point (1 - k)r1, k < 1 exceeds 90 degrees, and the rotation angle of the tail of the beam relative to its own center point r1 is 90 degrees. At this time, the particles at the head of the beam move relatively the slowest, while the particles at the tail of the beam move relatively the fastest, so that the phase width is compressed to the minimum. At this time, the RF cavity 3 serves as the cavity for eliminating energy difference, and the RF cavity 3 is rotated counterclockwise by a set angle to eliminate the energy difference; On the current bunch of beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted clockwise and using the RF cavity 3 as the RF cavity for generating energy difference, when the head of the beam rotates counterclockwise by 90 degrees from the RF cavity 3 to reach the RF cavity 4, the rotation angle of the head of the beam relative to its own center point (1 - k)r1, k < 1 exceeds 90 degrees, and the rotation angle of the tail of the beam relative to its own center point r1 is 90 degrees. At this time, the particles at the head of the beam move relatively the slowest, while the particles at the tail of the beam move relatively the fastest, so that the phase width is compressed to the minimum. At this time, the RF cavity 4 serves as the cavity for eliminating energy difference, and the RF cavity 4 is rotated counterclockwise by a set angle to eliminate the energy difference.

10. The method for improving the longitudinal focusing force in the central region of a cyclotron according to claim 2, wherein: On the current bunch of beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise, for the RF cavity 1 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise by 270 degrees from the RF cavity 1 to reach the RF cavity 4, in the third quadrant, the particles at the tail of the beam do not reach 270 degrees relative to their own center of the circle (1 - k)r1, k < 1, and the rotation angle of the head of the beam relative to its own center point r1 is 270 degrees. At this time, the particles at the tail of the beam move relatively the fastest, while the particles at the head of the beam move relatively the slowest, so that the phase width is compressed to the minimum. At this time, the RF cavity 4 serves as the cavity for eliminating energy difference, and the RF cavity 4 is rotated clockwise by a set angle to eliminate the energy difference; On the current bunch of beam in the central region, when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise and using the RF cavity 2 as the cavity for generating energy difference, for the RF cavity 2 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise by 270 degrees from the RF cavity 2 to reach the next turn of the RF cavity 1, in the fourth quadrant, the particles at the tail of the beam do not reach 270 degrees relative to their own center of the circle (1 - k)r1, k < 1, and the rotation angle of the head of the beam relative to its own center point r1 is 270 degrees. At this time, the particles at the tail of the beam move relatively the fastest, while the particles at the head of the beam move relatively the slowest, so that the phase width is compressed to the minimum. At this time, the RF cavity 1 serves as the cavity for eliminating energy difference, and the position of the next turn of the beam passing through the RF cavity 1 is rotated clockwise by a set angle to eliminate the energy difference.

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