Method for improving longitudinal focusing force of central area of accelerator through positive and negative phase combined adjustment

Abstract

The invention discloses a method for improving longitudinal focusing force of a central area of an accelerator through positive and negative phase combined adjustment. 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; setting the energy gain of beam head particles to be low and the energy of beam tail particles to be high; or setting that the energy gain of the beam head particle which firstly reaches the acceleration gap is high and the energy gain of the beam tail particle which then reaches the acceleration gap is low; a primary phase width compression method and a secondary phase width compression method are adopted on the current circle of beam current in the central area: the phase width of the particles is compressed to be minimum by adjusting the rotation angles of head structures of a plurality of radio frequency cavities, so that the longitudinal focusing force and the height-direction focusing force of the particles are improved; according to the invention, two-time acceleration of one radio frequency cavity is regarded as overall adjustment, and defocusing in the height direction is not caused while longitudinal focusing force is provided.

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 an accelerator by combining positive and negative phase adjustments. Background Art

[0002] The traditional method for providing 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, realizing longitudinal focusing of 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 earlier-arriving beam is large and the energy gain of the later-arriving beam 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 balance the requirements of focusing and defocusing at the same time, for the situation where the energy gain of the earlier-arriving beam is small and the energy gain of the later-arriving beam is large, the solution is to ensure that while solving the defocusing problem in the height direction, select an accelerator with a relatively strong magnetic field focusing force to make up for the Figure 2 deficiency of the poor longitudinal focusing effect when selecting the region of -90° to 0°. If there is no accelerator with a relatively strong magnetic field focusing force to make up for the defect of insufficient 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 selecting the radio frequency voltage range from -180 to -90; 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 selecting the radio frequency voltage range from -90° to 0°. Moreover, the traditional methods of providing longitudinal focusing force or providing focusing force in the height direction in the central region both adopt the method of single-phase width compression in the radio frequency voltage range from -180 to -90 or from -90° to 0°, that is, in the radio frequency voltage range from -180 to -90, longitudinal focusing is completed by compressing the phase width once, and in the radio frequency voltage range from -90 or from -90° to 0°, height direction focusing is completed by compressing the phase width once. Single compression often has the problem that the phase width cannot be compressed to the minimum value. 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 an accelerator by combining positive and negative phase adjustments. 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. The third objective is to solve the problem that in the traditional method of providing longitudinal focusing force or providing focusing force in the height direction in the central region, the phase width is only compressed once, and single compression often cannot compress the phase width to the minimum value.

[0007] To solve its technical problems, the present invention proposes the following technical solutions:

[0008] A method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments, 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 that the energy gain of the beam head particles that reach the acceleration gap first is low, and the energy of the beam tail particles that reach the acceleration gap later is high; or set that the energy gain of the beam head particles that reach the acceleration gap first is high, and the energy gain of the beam tail particles that reach the acceleration gap later is low;

[0010] Step 2: In the current turn of the beam in the central region, adopt the method of compressing the phase width once: by adjusting the rotation angle of the head structure of a single radio frequency cavity, compress the particles from the non-receiving and non-accelerating regions of the current radio frequency cycle into the middle receiving and accelerating regions, thereby improving the longitudinal focusing force of the particles along the trajectory direction;

[0011] Step 3. On the current bunch of beam in the central region, adopt the method of secondarily compressing the phase width: By adjusting the rotation angles of the head structures of multiple RF cavities, the particles are compressed from the non-receiving and non-accelerating regions of the current RF cycle to the intermediate receiving and accelerating regions, thereby enhancing the longitudinal focusing force of the particles along the trajectory direction.

[0012] Further, the specific process of Step 2 is as follows:

[0013] 1) On the current bunch of beam in the central region, adopt the method of primarily compressing the phase. By rotating the head structure of a single RF cavity that generates an energy difference clockwise or counterclockwise, an energy difference is presented between the particles at the head and tail of the bunch. This certain energy difference compresses the bunch width to the minimum region. When the rotation angle of the head structure of a single RF cavity is adjusted clockwise, 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. When the rotation angle of the head structure of a single RF cavity is adjusted counterclockwise, the energy gain of the particles at the tail of the beam is low, and the energy gain of the particles at the head of the beam is high.

[0014] 2) On the current bunch of beam in the central region, adopt the method of primarily eliminating the energy difference. By adjusting the rotation angle of the head structure of a single RF cavity that eliminates the energy difference in the opposite direction (counterclockwise or clockwise), the energy difference is eliminated at the position where the bunch width is the smallest, achieving the longitudinal focusing of the bunch. This region with the smallest width is the region where the wide phase is compressed to the narrow phase.

[0015] Further, when it is set to adjust the rotation angle of the head structure of a single RF cavity clockwise, the cavities for generating the energy difference and eliminating the energy difference are respectively at the positions of RF cavity 1 and RF cavity 2, or respectively at the positions of RF cavity 3 and RF cavity 4, or respectively at the positions of RF cavity 4 and the next bunch of beam of RF cavity 1. When it is set to adjust the rotation angle of the head structure of a single RF cavity counterclockwise, the cavities for generating the energy difference and eliminating the energy difference are respectively RF cavity 1 and RF cavity 4.

[0016] Furthermore, the specific process of step three is as follows: 1) on the current circle of beam in the central area, a secondary compression phase method is adopted, by time-sharing the head structures of two RF cavities at different positions that produce energy differences or time-sharing the RF cavity at the same position to rotate clockwise or counterclockwise, so that the particle energies at different longitudinal positions of the bunch show a certain energy difference, and the certain energy difference compresses the width of the bunch to the minimum area; 2) on the current circle of beam in the central area, a secondary elimination of energy difference method is adopted, by time-sharing the head structures of the RF cavities at two different positions that eliminate the energy difference to rotate counterclockwise or clockwise in the opposite direction, so as to eliminate the energy difference at the position where the width of the bunch is the smallest, and realize longitudinal focusing of the bunch; the area with the smallest width is the area where the wide phase is compressed to the narrow phase.

[0017] Furthermore, in the step three process 1), a method of secondary compression of the phase width is adopted on the current circle of beam in the central area, which is as follows: on the basis of rotating the head of RF cavity 1 clockwise and the head of RF cavity 2 counterclockwise, the head of RF cavity 3 is rotated clockwise and the head of RF cavity 4 is rotated counterclockwise.

[0018] Further, on the current circle of beam in the central area, the clockwise rotating head of the RF cavity 1 and the counterclockwise rotating head of the RF cavity 2 are used as the first compression phase: for the RF cavity 1 that generates energy difference, when the beam head rotates 90 degrees counterclockwise from the RF cavity 1 to the RF cavity 2, the beam head and the low-energy particles rotate at an angle of more than 90 degrees relative to their own center point (1-k)r1, k<1, and the rotation angle of the particles at the tail of the bunch and the high-energy particles relative to their 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 2 is used as a cavity for eliminating energy difference, and the RF cavity 2 is rotated counterclockwise by a set angle to eliminate the energy difference;

[0019] On the current circle of beam in the central area, the clockwise rotating head of the RF cavity 3 and the counterclockwise rotating head of the RF cavity 4 are used as the second compression phase: when the beam head rotates 90 degrees counterclockwise 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, and 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.

[0020] Further, in the current bunch of beam in the central region in step 3, process 1), the method of secondarily compressing the phase width is as follows: On the basis of clockwise rotating the head of radio frequency cavity 1 and counterclockwise rotating the head of radio frequency cavity 2, further counterclockwise rotate the head of radio frequency cavity 2 so that the head of the bunch has the highest energy and the tail has the lowest energy after passing through radio frequency cavity 2, and then adjust the part of the second circle of the corresponding particle trajectory of radio frequency cavity 1 to rotate clockwise to eliminate the energy dispersion.

[0021] Further, on the current bunch of beam in the central region, taking the clockwise rotation of the head of radio frequency cavity 1 and the counterclockwise rotation of the head of radio frequency cavity 2 as the first compression of the phase: For radio frequency cavity 1 that generates energy difference, when the head of the beam rotates counterclockwise 90 degrees from radio frequency cavity 1 to radio frequency cavity 2, for the head of the beam and the particles with low energy, the rotation angle relative to its own center point (1 - k)r1, k < 1, exceeds 90 degrees, and for the tail of the bunch and the particles with high energy, the rotation angle 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, radio frequency cavity 2 is used as the cavity to eliminate the energy difference, and radio frequency 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, taking the further counterclockwise rotation of the head of radio frequency cavity 2 so that the head of the bunch has the highest energy and the tail has the lowest energy after passing through radio frequency cavity 2 as the cavity that generates energy difference, as the second compression of the phase: For radio frequency cavity 2 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise 270 degrees from radio frequency cavity 2 to the next bunch of beam of radio frequency cavity 1, in the fourth quadrant, for the particles at the tail of the beam, the rotation angle relative to its own center of the circle (1 - k)r1, k < 1, does not reach 270 degrees, 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 the fastest, and 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, radio frequency cavity 1 is used as the cavity to eliminate the energy difference, and the position of the next bunch of beam passed by radio frequency cavity 1 is rotated clockwise by a set angle to eliminate the energy difference.

[0023] Further, in the current bunch of beam in the central region in step 3, process 1), the method of secondarily compressing the phase width is as follows: On the basis of counterclockwise rotating the head of radio frequency cavity 1 and clockwise rotating the head of radio frequency cavity 4, for the next bunch of beam, further clockwise rotate the head of radio frequency cavity 4 so that the head of the bunch has the lowest energy and the tail has the highest energy after passing through radio frequency cavity 4, and then adjust the part of the second circle of the corresponding particle trajectory of radio frequency cavity 1 to rotate counterclockwise to eliminate the energy dispersion.

[0024] Furthermore, taking the counterclockwise rotation of the head of the radio frequency cavity 1 and the clockwise rotation of the head of the radio frequency cavity 4 as the first phase compression: on the current bunch of beam in the central region, for the radio frequency cavity 1 that generates energy difference, when the particles at the tail of the beam reach the radio frequency cavity 4 after rotating 270 degrees counterclockwise from the radio frequency cavity 1, in the third quadrant, the particles at the tail of the beam do not reach 270 degrees relative to its 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 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.

[0025] On the next bunch of beam in the central region, further rotating the head of the radio frequency cavity 4 clockwise so that the head energy of the bunch is the lowest and the tail energy is the highest after passing through the radio frequency cavity 4 is taken as the second phase compression; for the radio frequency cavity 4 that generates energy difference, when the particles at the head of the beam reach the radio frequency cavity 1 after rotating 90 degrees counterclockwise from the radio frequency cavity 4, in the fourth quadrant, the particles at the head of the beam do not reach 90 degrees relative to its own center of the circle (1 - k)r1, k < 1, 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 fastest, while the particles at the tail of the beam move relatively slowest, thus compressing the phase width to the minimum; then adjust the part of the second circle of the particle trajectory corresponding to the radio frequency cavity 1 and rotate it counterclockwise to eliminate the energy dispersion.

[0026] Advantages and effects of the present invention

[0027] 1. The present invention realizes longitudinal focusing by means of negative phase. By regarding the two accelerations of a radio frequency cavity as an overall adjustment, while providing longitudinal focusing force, it also takes into account that it will not cause defocusing in the height direction. The present invention solves the problem that in one circle of the head particles, in some quadrants they move slowly and in some quadrants they move fast, resulting in the reappearance of longitudinal defocusing in the quadrants where the head particles move slowly after eliminating the energy difference, by eliminating the energy difference at the radio frequency cavity 2 where the phase width is compressed to the minimum.

[0028] 2. The present invention realizes longitudinal focusing by means of positive phase. By regarding the two accelerations of a radio frequency cavity as an overall adjustment, while providing longitudinal focusing force, it also takes into account that it will not cause defocusing in the height direction. At the same time, since the positive phase is used to realize longitudinal focusing and the positive phase is selected 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, and the phase When it is large, τ1 and τ2 are also large. When τ1 and τ2 are large, the axial focusing is strong. Therefore, while achieving longitudinal focusing in the positive phase mode, the focusing effect in the height direction is better. The present invention eliminates the energy difference at the radio frequency cavity 4 where the phase width is compressed to the minimum, solving the problem that in one turn of the tail particles, in some quadrants they move slowly and in some quadrants they move quickly, resulting in the reappearance of longitudinal defocusing in the quadrants where the tail particles move slowly after chromatic dispersion elimination.

[0029] 3. The present invention adopts a combined method of positive phase and negative phase adjustment to achieve longitudinal focusing, enabling the phase width of the particles in the current turn of the beam in the central region to be compressed twice. The phase after the second compression is closer to the energy gain peak at the 0-phase as shown in Figure 3 Therefore, the longitudinal focusing effect is better. At the same time, because it is an overall adjustment, while ensuring longitudinal focusing, it also takes into account the focusing in the height direction. When the positive phase adjustment of the particles is adopted, due to the large phase value, while ensuring longitudinal focusing, the focusing in the height direction is enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Schematic diagram of the central region of the cyclotron;

[0031] Figure 2 Radio frequency voltage curve;

[0032] Figure 3 Energy gain of particles with different phases;

[0033] Figure 4 Trajectories of particles with different energies;

[0034] Figure 5 Difference in particle angle change at different speeds;

[0035] Figure 6 One of the schematic diagrams of Embodiment 1 and Embodiment 5 of the present invention;

[0036] Figure 7 One of the schematic diagrams of Embodiment 2 and Embodiment 5 of the present invention;

[0037] Figure 8 Schematic diagram of Embodiment 3 of the present invention;

[0038] Figure 9 Schematic diagram of Embodiment 4 and Embodiment 5 of the present invention;

[0039] Figure 10 One of the schematic diagrams of Embodiment 5 of the present invention;

[0040] Figure 11 One of the schematic diagrams of Embodiment 5 of the present invention;

[0041] Figure 12 Schematic diagram of the present invention being accepted and accelerated;

[0042] Figure 13 This is the flow chart of the method for adjusting the longitudinal focusing force in the central region of the accelerator by combining positive and negative phases in the present invention. Detailed implementation manners

[0043] 1. Innovation points of the present invention: One of the innovation points 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 point 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 turn, 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 This 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. The acceleration gaps are numbered from 1 to 8 in the order of particle passage. 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 radio frequency cavity voltage should be negative, corresponding to Figure 2 from -180° to 0° in (1) to enable the particles to obtain energy; at acceleration gap 2, it enters the ground electrode from the radio frequency cavity, and at this time the radio frequency cavity voltage should be positive, corresponding to Figure 2 from 0° to 180° in (1). Let the radio frequency times when the particles pass 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 of 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 that particles arriving at different times need 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 Equations (3) and (4) into Equation (2) to obtain:

[0055]

[0056] Equation (5) shows that particles with a particle phase of 0, that is, particles that exactly reach 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, and the phase 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 partial phases are accelerated in each RF cycle, forming periodic particle bunches. Longitudinal refers to the direction in which the particle bunch advances, manifested as the length of the bunch or the time length that the bunch spans when 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 a cyclotron:

[0060]

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

[0062]

[0063] As can be seen from Equation (7), the angular velocities of particles rotating at different speeds are the same. Suppose there is a particle 1 rotating around the center of the cyclotron with a radius r, as shown by the solid line part in Figure 4 . Taking the position (r1, 0) at the azimuth angle of 0° as the starting moment, the azimuth angle of particle 1 changes with time t:

[0064] θ1 = ωt (8)

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

[0066]

[0067] Particle 2 also starts from the position (r1, 0). Due to the difference in energy from particle 1, its rotation radius is:

[0068] r2 = k·r1 (10)

[0069] When the energy of particle 2 is less than that of particle 1, k < 1; conversely, k > 1. Particle 2 also rotates at an angular velocity of ω, and its rotation center is ((1 - k)r1, 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 as 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 θ1 and time is shown in Equation (8). The angular velocity of particle 2 rotating is the same as that of particle 1, which is ω. However, its rotation center 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 [the figure], a negative ordinate indicates that from the starting point to this moment, particle 2 rotates at a smaller angle than particle 1; a positive ordinate indicates a larger rotation angle. A decrease in the ordinate indicates that the angular velocity of particle 2 at this moment is less than that of particle 1, and an 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 the ordinate decreases and reaches a minimum near the abscissa of 90°.

[0077] (2) The angle θ2 by which Particle 2 rotates in the second quadrant is less than 90°, and the angular velocity ω2 relative to the accelerator center is greater than that of Particle 1, corresponding to Figure 5 the ordinate increases. 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°, and the angular velocity ω2 relative to the accelerator center is greater than ω1 of Particle 1, corresponding to Figure 5 the ordinate increases and reaches a maximum near the abscissa of 270°.

[0079] (4) The angle θ2 by which Particle 2 rotates in the fourth quadrant is greater than 90°, and the angular velocity ω2 relative to the accelerator center is less than that of Particle 1, corresponding to Figure 5 the ordinate decreases. 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. The present invention adjusts the structure of the head of the radio frequency cavity so that the energies of particles at different longitudinal positions in the bunch show a monotonically changing energy dispersion. 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] 4. Design principle of improving the longitudinal focusing force in the central region of the accelerator by positive and negative phase combination adjustment. The positive and negative phase combination adjustment of the present invention is achieved by combining single-phase adjustment and single-phase adjustment. Single-phase adjustment includes negative phase adjustment and positive phase adjustment. The positive and negative phase combination adjustment of the present invention includes three combinations: combination method one of negative phase adjustment and negative phase adjustment, combination method two of negative phase adjustment and negative phase adjustment, combination method three of positive phase adjustment and negative phase adjustment

[0083] 5. Design principle of realizing longitudinal focusing by negative phase adjustment method: The Figure 6 of the present invention realizes longitudinal focusing by means of negative phase to achieve longitudinal focusing, Figure 8 、 9It is a derivative result of achieving longitudinal focusing in a negative phase manner.

[0084] First, achieving longitudinal focusing in a negative phase manner not only provides longitudinal focusing force but also avoids 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 RF cavity in advance. The particle phase is the average of the transit times through the two acceleration gaps when entering and leaving the RF cavity, that is, the RF time when the particle reaches the center line of the RF 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 bunch center particle. Since the two accelerations in one RF cavity are regarded as an overall adjustment, the -10-degree phase corresponds not only to the entrance acceleration gap but also to the average of the transit times through the entrance and exit acceleration gaps. For example, the average of -80 degrees and +60 degrees in a RF cycle is -10 degrees, and the -10 degrees in this RF cycle corresponds to Figure 2 the -10° phase. Assuming Figure 3 -10° is selected, in the RF voltage cycle, the transit times τ1 and τ2 of acceleration gap 1 and acceleration gap 2 can be selected as -80° and 60°. The transit time of acceleration gap 1 meets the focusing requirements in the height direction. Although the acceleration gap 2 is in a defocusing phase in the height direction, its energy is high and the influence is low, and overall it shows a focusing effect. Figure 2 The transit time of the acceleration 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 by traditional methods cannot be met, but the conditions for focusing in the height direction can be met. Because the particles are first focused and then defocused when passing through the acceleration gap, and when the voltage decreases with time, the focusing electric field 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 accelerator gap 2 is in the voltage rising interval from 0 to 90 degrees. The voltage rising interval meets the conditions for longitudinal focusing by traditional methods, but does not meet the conditions for focusing in the height direction. However, because the particles have been accelerated by acceleration gap 1 and have a higher energy, the defocusing effect of acceleration gap 2 in the height direction is less than the focusing effect of acceleration gap 1, and overall it is focused in the height direction. In short, because the focusing in the height direction is satisfied at the first acceleration gap, the defocusing in the height direction at the second acceleration gap has less influence than that of acceleration gap 1, and at the same time, the average phase of acceleration gap 1 and acceleration gap 2 meets the conditions for longitudinal focusing. Therefore, achieving longitudinal focusing in a negative phase manner not only provides longitudinal focusing force but also avoids defocusing in the height direction.

[0085] The transit time of the acceleration 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 by traditional methods cannot be met, but the conditions for focusing in the height direction can be met. Because the particles are first focused and then defocused when passing through the acceleration gap, and when the voltage decreases with time, the focusing electric field 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 accelerator gap 2 is in the voltage rising interval from 0 to 90 degrees. The voltage rising interval meets the conditions for longitudinal focusing by traditional methods, but does not meet the conditions for focusing in the height direction. However, because the particles have been accelerated by acceleration gap 1 and have a higher energy, the defocusing effect of acceleration gap 2 in the height direction is less than the focusing effect of acceleration gap 1, and overall it is focused in the height direction. In short, because the focusing in the height direction is satisfied at the first acceleration gap, the defocusing in the height direction at the second acceleration gap has less influence than that of acceleration gap 1, and at the same time, the average phase of acceleration gap 1 and acceleration gap 2 meets the conditions for longitudinal focusing. Therefore, achieving longitudinal focusing in a negative phase manner not only provides longitudinal focusing force but also avoids defocusing in the height direction.

[0086] Second, the longitudinal focusing is achieved in the negative phase mode by eliminating the energy difference at the place 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 increases with time. Suppose the RF voltage is 50 kV when the head of the bunch passes through point A, and when the particles at the tail pass through point A, the RF 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, since the energy gain of the head is small, it moves in a small circle. When it reaches the RF 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. This is equivalent to the head of the beam moving slowly and the tail moving fast, and the fast in front and the slow behind achieve the compression of the phase width. That is, the phase width is compressed to the minimum at the RF cavity 2. Therefore, at the RF cavity 2, the energy difference is eliminated by rotating the cavity 2 counterclockwise. ③ The reason for eliminating the chromatic dispersion at the RF cavity 2 is that the head of the beam does not move slowly in each of the four quadrants 1, 2, 3, and 4. When it moves faster than the tail of the beam in a certain interval, it is not longitudinal focusing but longitudinal defocusing. For example, from Figure 6 viewpoint, in the first quadrant, the head moves slowly and the tail moves fast, in the second and third quadrants, the head moves fast and the tail moves slow, and the beam in front moves fast and the beam behind moves slow. In the second and third quadrants, it is equivalent to stretching the beam, and stretching the beam is defocusing rather than focusing. In the fourth quadrant, the dotted line moves slowly and the solid line moves fast again, so the fourth quadrant is also in focus. It can be seen that if the chromatic 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, so that half of the particles in the current central region are focused for half of the time and defocused for half of the time. When the energy difference is eliminated, the energy gains of the head and the tail at the RF cavity 2 are the same, so there will no longer be longitudinal defocusing in the second and third quadrants. Assuming that one-time compression meets the requirements of longitudinal focusing, then the fourth quadrant does not need to be focused either. Therefore, eliminating the chromatic 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 achieving longitudinal focusing by the positive phase adjustment method. First, the Figure 7 of the present invention is to achieve longitudinal focusing by the positive phase method to achieve longitudinal focusing, Figure 10It is a derivative result of achieving longitudinal focusing in the positive phase mode. Achieving longitudinal focusing in the positive phase mode takes into account not causing defocusing in the height direction while providing longitudinal focusing force. The method adopted 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 of the time gaps of the two accelerating 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 choosing a phase such as Figure 3 +10 degrees in Figure 3 (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 one RF cavity are regarded as an overall adjustment, the +10 degree phase corresponds to the average of the time gaps of the entrance accelerating gap and the two time gaps of entering and exiting, for example, corresponding to Figure 2 the average of -60 degrees and +80 degrees in the RF cycle is +10 degrees, and the +10 degrees of this RF cycle corresponds to Figure 3 the +10° phase. Assuming +10° is selected, in the Figure 2 RF voltage cycle, the time gaps τ1 and τ2 of accelerating gap 1 and accelerating gap 2 can be selected as -60° and +80°. The time gap of accelerating gap 1 meets the focusing requirements in the height direction. Although the accelerating gap 2 is in a defocusing phase in the height direction, it has high energy and low influence, and overall shows a focusing effect. The time gap of the accelerating 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 of longitudinal focusing cannot be met, but the condition of focusing in the height direction can be met because as 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 of longitudinal focusing, but does not meet the condition of 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 particle rotates, and the faster the particle rotates, the smaller the defocusing influence on the height direction. On the contrary, if the particle rotates slowly or the particle energy is low, the defocusing influence on the height direction is large. In short, since the focusing in the height direction is satisfied at the first accelerating slit, and the condition of longitudinal focusing is satisfied at the second accelerating slit, and at the same time, the influence on the focusing in the height direction is very small, so, achieving longitudinal focusing in the positive phase mode takes into account not causing defocusing in the height direction while providing longitudinal focusing force.

[0088] Second, the longitudinal focusing is achieved in the positive-phase mode by eliminating 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 travels in a small circle and the head travels in a large circle. The reasons for the small energy gain of the beam tail and the large energy gain of the beam head are that the voltage decreases over time. Assuming that the RF voltage is 60 kV when the beam head passes through point A, when the particles at the tail pass through point A, the RF 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, since the particles at the head have a large energy gain and travel in a large circle, when reaching the RF cavity 4, the tail particles on the dotted line do not exceed 270 degrees relative to their own center point, while the head particles on the solid line rotate by 270 degrees. It is equivalent that the beam head travels slowly and the beam tail travels fast, and the front is fast and the back is slow, which realizes the compression of the phase width. That is, the phase width is compressed to the minimum at the RF cavity 4. Therefore, the energy difference is eliminated by rotating the cavity 4 clockwise at the RF cavity 4. ③ The reason for eliminating the energy difference at the RF cavity 4 is that the particles at the beam tail do not travel fast in each of the four quadrants 1, 2, 3, and 4. From Figure 6 the view, the tail travels slowly in the 1st and 4th quadrants and fast in the 2nd and 3rd quadrants. The front beam travels fast and the back travels slow. 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 beam head in the four quadrants are: defocusing, focusing, focusing, defocusing, so that half of the particles in a circle in the current central region are focused and half of the time is defocused. 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) The difference between positive-phase adjustment and negative-phase adjustment: The negative-phase mode for achieving longitudinal focusing selects the negative phase The positive-phase mode for achieving longitudinal focusing selects 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. The larger the phase , the larger τ1 and τ2 are, and the stronger the axial focusing is when τ1 and τ2 are large. Therefore, the focusing effect in the height direction in the inlet acceleration gap of the negative-phase mode for achieving longitudinal focusing is better than that in the height direction in the inlet acceleration gap of the positive-phase mode for achieving longitudinal focusing.

[0090] 4) The design principles of the three combination modes:

[0091] A. The design principle of the combination mode 1 of negative-phase adjustment and negative-phase adjustment: As Figure 6 . 9As shown, when the beam current in the current circle of the central region is compressed twice; on the basis of clockwise rotating the head of RF cavity 1 and counterclockwise rotating the head of RF cavity 2, the head of RF cavity 3 is rotated clockwise and the head of RF cavity 4 is rotated counterclockwise. The first compression reaches the minimum phase width in cavity 2, and the second compression reaches the minimum phase width in cavity 4; both the first compression and the second compression are compressions with low energy at the head and high energy at the tail.

[0092] B. Design principle of the second combination method of negative phase adjustment and positive phase adjustment: As Figure 6 , 10 shown, when the beam current in the current circle of the central region is compressed twice; on the basis of clockwise rotating the head of RF cavity 1 and counterclockwise rotating the head of RF cavity 2, the head of RF cavity 2 is further rotated counterclockwise so that the energy at the head is the highest and the energy at the tail is the lowest after the bunch passes through RF cavity 2, and then the part of the second circle of the corresponding particle trajectory of RF cavity 1 is adjusted to rotate clockwise to eliminate the energy difference. The first compression reaches the minimum phase width in cavity 2, and the second compression reaches the minimum phase width at the position of the second circle of the corresponding particle trajectory of RF cavity 1; the first compression is a compression with low energy at the head and high energy at the tail, and the second compression is a compression with high energy at the head and low energy at the tail.

[0093] C. Design principle of the third combination method of positive phase adjustment and negative phase adjustment: As Figure 7 , 11 shown, when the beam current in the current circle of the central region is compressed twice; as Figure 7 shown, on the basis of counterclockwise rotating the head of RF cavity 1 and clockwise rotating the head of RF cavity 4, as Figure 11 shown, for the next beam current, the head of RF cavity 4 is further rotated clockwise so that the energy at the head is the lowest and the energy at the tail is the highest after the bunch head passes through RF cavity 4, and then the part of the second circle of the corresponding particle trajectory of RF cavity 1 is adjusted to rotate counterclockwise to eliminate the energy difference. The first compression reaches the minimum phase width in cavity 4, and the second compression reaches the minimum phase width in cavity 1; the first compression uses the method of high energy at the head and low energy at the tail, and the second compression uses the method of low energy at the head and high energy at the tail. The first compression realizes longitudinal compression by the tail moving fast and the head moving slower than the tail; the second compression realizes longitudinal compression by the head moving slowly and the tail moving faster than the head; the first is to adjust the fast movement of the tail to realize phase compression, and the second is to adjust the slow movement of the head to realize phase compression. Both of these two methods can realize longitudinal compression. The difference is that: when using the fast movement of the tail to realize phase compression, the phase with the highest gain is the positive phase on the right of the 0 phase of Figure 3 , the positive phase is larger than the negative phase in value, and the positive phase is related to the inlet and outlet gap times τ1 and τ2, and the phase The larger τ1 and τ2 are, the stronger the axial focusing is. Therefore, the height-direction focusing effect of achieving longitudinal focusing by the negative-phase method for the second time in the entrance acceleration gap is better than that of achieving longitudinal focusing by the negative-phase method in the height direction of the entrance acceleration gap.

[0094] Based on the above principle, the present invention designs a method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments, as Figure 13 shown, which is characterized by including the following steps:

[0095] Step 1: Divide the radio-frequency cavity into a radio-frequency cavity that generates energy differences and a radio-frequency cavity that eliminates energy differences; set that the energy gain of the beam head particles that reach the acceleration gap first is low, and the energy of the beam tail particles that reach the acceleration gap later is high; or set that the energy gain of the beam head particles that reach the acceleration gap first is high, and the energy gain of the beam tail particles that reach the acceleration gap later is low;

[0096] Step 2: On the current turn of the beam in the central region, adopt the method of compressing the phase width once: by adjusting the rotation angle of the head structure of a single radio-frequency cavity, compress the particles from the non-receiving and non-accelerating regions of the current radio-frequency cycle into the middle receiving and accelerating regions, thereby increasing the longitudinal focusing force of the particles along the trajectory direction;

[0097] Step 3: On the current turn of the beam in the central region, adopt the method of compressing the phase width twice: by adjusting the rotation angles of the head structures of multiple radio-frequency cavities, compress the particles from the non-receiving and non-accelerating regions of the current radio-frequency cycle into the middle receiving and accelerating regions, thereby increasing the longitudinal focusing force of the particles along the trajectory direction;

[0098] Further, the specific process of the above Step 2 is as follows:

[0099] 1) On the current turn of the beam in the central region, adopt the method of compressing the phase once. By rotating the head structure of a single radio-frequency cavity that generates energy differences clockwise or counterclockwise, make the particle energies of the beam head and the beam tail show a certain energy difference, and this certain energy difference compresses the beam width to the smallest region; when the rotation angle of the head structure of a single radio-frequency cavity is adjusted clockwise, the energy gain of the beam head particles is low, and the energy gain of the beam tail particles is high; when the rotation angle of the head structure of a single radio-frequency cavity is adjusted counterclockwise, the energy gain of the beam tail particles is low, and the energy gain of the beam head particles is high;

[0100] 2) On the current circle of beam in the central area, a method of eliminating energy differences once is adopted. By adjusting the rotation angle of the head structure of a single RF cavity that eliminates energy differences in the opposite direction counterclockwise or clockwise, the energy differences are eliminated at the position where the width of the bunch is the smallest, thereby achieving longitudinal focusing of the bunch; the area with the smallest width is the area where the wide phase is compressed to the narrow phase.

[0101] Furthermore, when the rotation angle of the head structure of a single RF cavity is set to be adjusted clockwise, the cavities that generate energy differences and eliminate energy differences are RF cavity 1 and RF cavity 2, or RF cavity 3 and RF cavity 4, or RF cavity 4 and the position of the next circle of beam of RF cavity 1; when the rotation angle of the head structure of a single RF cavity is set to be adjusted counterclockwise, the cavities that generate energy differences and eliminate energy differences are RF cavity 1 and RF cavity 4, respectively.

[0102] The specific process of step three is as follows: 1) On the current circle of beam in the center area, a secondary compression phase method is adopted, and the head structures of two RF cavities at different positions that produce energy differences are rotated clockwise or counterclockwise by time-sharing, or the RF cavity at the same position is rotated clockwise or counterclockwise by time-sharing, so that the particle energies at different longitudinal positions of the bunch show a certain energy difference, and the certain energy difference compresses the width of the bunch to the minimum area; 2) On the current circle of beam in the center area, a secondary elimination of energy difference method is adopted, and the head structures of two RF cavities at different positions that eliminate energy differences are rotated counterclockwise or clockwise in the opposite direction by time-sharing, so that the energy difference is eliminated at the position where the width of the bunch is the smallest, thereby achieving longitudinal focusing of the bunch; the area with the smallest width is the area where the wide phase is compressed to the narrow phase.

[0103] like Figure 6 , 9 As shown, in the process 1) of step 3, a method of secondary compression of the phase width is adopted on the current beam in the central area, which is specifically as follows: Figure 6 As shown, on the basis of rotating the head of RF cavity 1 clockwise and the head of RF cavity 2 counterclockwise, as shown in Figure 9 As shown, the head of the RF cavity 3 is rotated clockwise, and the head of the RF cavity 4 is rotated counterclockwise.

[0104] like Figure 6 , 9 As shown, in the current beam in the central area, the method of secondary compression phase width is adopted, as follows: Figure 6 As shown, the clockwise rotation of the head of the RF cavity 1 and the counterclockwise rotation of the head of the RF cavity 2 are taken as the first compression phase: Figure 8As shown, for the RF cavity 1 that generates energy differences, when the beam head rotates counterclockwise by 90 degrees from the RF cavity 1 to reach the RF cavity 2, the particles at the beam head and 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 and 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, while the particles at the beam tail move relatively the fastest, thus compressing the phase width to the minimum. At this time, the RF cavity 2 serves as the cavity to eliminate energy differences, and the RF cavity 2 is rotated counterclockwise by a set angle to eliminate energy differences;

[0105] As Figure 6 、 9 shown, on the current bunch of beam in the central region, taking the clockwise rotation of the head of the RF cavity 2 and the counterclockwise rotation of the head of the RF cavity 3 as the second phase compression: when the beam head rotates counterclockwise by 90 degrees from the RF cavity 3 to reach the RF cavity 4, the beam head rotates by an angle exceeding 90 degrees relative to its own center point (1 - k)r1, where k < 1, and the beam tail rotates by an angle of 90 degrees relative to its own center point r1. 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 compressing the phase width to the minimum. At this time, the RF cavity 4 serves to eliminate energy differences, and the RF cavity 4 is rotated counterclockwise by a set angle to eliminate energy differences.

[0106] As Figure 6 、 10 shown, in the process 1) of step three, on the current bunch of beam in the central region, the method of secondary compression of the phase width is adopted as follows: As Figure 6 shown, on the basis of the clockwise rotation of the head of the RF cavity 1 and the counterclockwise rotation of the head of the RF cavity 2, as Figure 10 shown, further rotate the head of the RF cavity 2 counterclockwise so that the energy of the head is the highest and the energy of the tail is the lowest after the bunch passes through the RF cavity 2, and then adjust the part of the corresponding particle trajectory of the second circle of the RF cavity 1 to rotate clockwise to eliminate the energy dispersion.

[0107] As Figure 6As shown in the figure, on the current bunch of beam in the central area, rotating the head of the clockwise-rotating RF cavity 1 and the head of the counterclockwise-rotating RF cavity 2 is taken as the first phase compression: For the RF cavity 1 that generates energy difference, when the head of the beam rotates counterclockwise by 90 degrees from the RF cavity 1 to reach the RF cavity 2, for the particles at the head of the beam with lower energy, the rotation angle relative to its own center point (1 - k)r1, k < 1, exceeds 90 degrees, and for the particles at the tail of the bunch with higher energy, the rotation angle 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 2 is used 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;

[0108] As Figure 10 shown in the figure, on the current bunch of beam in the central area, further rotating the head of the RF cavity 2 counterclockwise so that the energy of the head is the highest and the energy of the tail is the lowest after the bunch passes through the RF cavity 2 is taken as the cavity that generates energy difference and is used as the second phase compression: 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 bunch of beam in the RF cavity 1, in the fourth quadrant, the particles at the tail of the beam do not reach a rotation of 270 degrees relative to its 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 is used as the cavity to eliminate the energy difference, and the position of the next bunch of beam through which the beam in the RF cavity 1 passes is rotated clockwise by a set angle to eliminate the energy difference.

[0109] As Figure 7 、 Figure 11 shown in the figure, in the process 1) of step three on the current bunch of beam in the central area, the method of compressing the phase width twice is specifically as follows: On the basis of rotating the head of the RF cavity 1 counterclockwise and the head of the RF cavity 4 clockwise, for the next bunch of beam, further rotate the head of the RF cavity 4 clockwise so that the energy of the head is the lowest and the energy of the tail is the highest after the bunch passes through the RF cavity 4, and then adjust the part of the next bunch of the particle trajectory corresponding to the RF cavity 1 to rotate counterclockwise to eliminate the energy dispersion.

[0110] As Figure 7As shown in the figure, rotating the head of the counterclockwise rotating radio frequency cavity 1 and the head of the clockwise rotating radio frequency cavity 4 is taken as the first compression phase: On the current bunch of beam in the central region, for the radio frequency cavity 1 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise by 270 degrees from the radio frequency cavity 1 to reach the radio frequency cavity 4, in the third quadrant, the particles at the tail of the beam do not reach 270 degrees relative to its 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 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;

[0111] As Figure 11 shown in the figure, on the next bunch of beam in the central region, further rotating the head of the radio frequency cavity 4 clockwise so that the head energy of the bunch is the lowest and the tail energy is the highest after passing through the radio frequency cavity 4 is taken as the second compression phase. Specifically: For the radio frequency cavity 4 that generates energy difference, when the particles at the head of the beam rotate counterclockwise by 90 degrees from the radio frequency cavity 4 to reach the radio frequency cavity 1, in the fourth quadrant, the particles at the head of the beam do not reach 90 degrees relative to its own center of the circle (1 - k)r1, k < 1, 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 fastest, while the particles at the tail of the beam move relatively slowest, thus compressing the phase width to the minimum; Then adjust the part of the next circle of the particle trajectory corresponding to the radio frequency cavity 1 and rotate it counterclockwise to eliminate the energy dispersion.

[0112] Embodiment 1. Achieving longitudinal focusing by using the negative phase adjustment method

[0113] As Figure 6 shown in the figure, in the present invention, ① regarding the entry and exit of particles from a radio frequency cavity as a whole, ② adjusting the time for particles to pass through the center line of the radio frequency cavity by angularly moving the position of the radio frequency cavity, that is, the particle phase in formula (4) changes the energy gain obtained by the particles. The negative phase method is used to achieve longitudinal focusing. Taking Figure 1 the radio frequency cavity 1 in the figure as an example, assuming that the current bunch center phase is 0°, rotating the head region of the radio frequency cavity 1 corresponding to the first circle of particle trajectory clockwise so that the whole bunch reaches the radio frequency cavity 1 earlier, φ < 0, as Figure 3 in the range of -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. As Figure 5 can be seen, near the angle of 90°, at the position corresponding to the radio frequency cavity 2, the particles at the head of the bunch with low energy rotate the smallest angle, and the particles at the tail of the bunch with high energy rotate the largest angle, and 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 at Figure 3The range is from 0° to 90°. The particles at the head of the bunch obtain the highest energy gain in the RF cavity 2, and the lowest at the tail. After the bunch is accelerated through the RF cavity 1 and the RF cavity 2, the energy at the center of the bunch is the highest, gradually decreasing towards both sides, and reaching the minimum value at the head and the tail.

[0114] Embodiment 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 RF cavity 1 rotates counterclockwise, causing the entire bunch to reach the RF cavity 1 later, φ > 0, as Figure 3 in the range of 0° to 90°. At this time, the φ of the bunch head is the smallest and the energy gain is the highest; the φ of the bunch tail is the largest and the energy gain is the lowest. From Figure 5 it can be seen that near the angle of 270°, corresponding to the position of the RF cavity 4, the particles at the head of the bunch with high energy rotate the smallest angle, and the particles at the tail of the bunch with low energy rotate the largest angle, and the difference between the two reaches the minimum value, that is, the bunch is compressed to the smallest width. Adjust the position of the RF cavity 4, rotate it clockwise, so that the bunch phase is in the Figure 3 range of -90° to 0°. The particles at the head of the bunch obtain the lowest energy gain in the RF cavity 4, and the highest at the tail. The phase of the particles at the center of the bunch at the RF cavities 2 and 3 is set to 0°, without generating additional energy dispersion. After the bunch is accelerated through the RF cavities 1 to 4, the energy at the center of the bunch is the highest, gradually decreasing towards both sides, and reaching the minimum value at the head and the tail.

[0115] Embodiment 3

[0116] As Figure 8 shown, the cavity for generating a monotonically changing energy dispersion in the present invention is not limited to the RF cavity 1. For example, for achieving longitudinal focusing by the negative phase method, modify it to rotate the head of the RF cavity 2 clockwise and the head of the RF cavity 3 counterclockwise;

[0117] Embodiment 4

[0118] As Figure 10 shown, for achieving longitudinal focusing by the positive phase method, modify it to rotate the head of the RF cavity 2 counterclockwise and the head of the RF cavity 4 clockwise, both can achieve longitudinal focusing. The lower the energy, the more significant the focusing effect.

[0119] Embodiment 5:

[0120] The present invention can be implemented in combination, including but not limited to:

[0121] (1) As Figure 6 and Figure 9For the combination, 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 the negative phase mode, the head of RF cavity 3 can be rotated clockwise and the head of RF cavity 4 can be rotated counterclockwise.

[0122] (2) For the combination as 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 the negative phase mode, 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.

[0123] (3) For the combination as 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 the positive phase mode, 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.

[0124] It should be emphasized that the above specific embodiments are only explanations of the present invention, and they are not limitations of the present invention. After reading this specification, those skilled in the art can make modifications to the above embodiments without creative contributions as needed, 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 an accelerator by combining positive and negative phase adjustments, characterized in that, Including 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; it is set that the energy gain of the beam head particles arriving at the acceleration gap first is low, and the energy of the beam tail particles arriving at the acceleration gap later is high; or it is set that the energy gain of the beam head particles arriving at the acceleration gap first is high, and the energy gain of the beam tail particles arriving at the acceleration gap later is low. Step 2: On the current turn of the beam in the central region, adopt the method of compressing the phase width once: by adjusting the rotation angle of the head structure of a single radio frequency cavity, compress the particles from the non-receiving and non-accelerating regions of the current radio frequency cycle into the middle receiving and accelerating regions, thereby increasing the longitudinal focusing force of the particles along the trajectory direction. Step 3: On the current turn of the beam in the central region, adopt the method of compressing the phase width twice: by adjusting the rotation angles of the head structures of multiple radio frequency cavities, compress the particles from the non-receiving and non-accelerating regions of the current radio frequency cycle into the middle receiving and accelerating regions, thereby increasing the longitudinal focusing force of the particles along the trajectory direction.

2. The method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments according to claim 1, characterized in that: The specific process of the above Step 2 is as follows: 1) On the current turn of the beam in the central region, adopt the method of compressing the phase once. By rotating the head structure of a single radio frequency cavity that generates energy difference clockwise or counterclockwise, make the particle energies of the beam head and the beam tail show a certain energy difference. This certain energy difference compresses the beam width to the smallest region; when the rotation angle of the head structure of a single radio frequency cavity is adjusted clockwise, the energy gain of the beam head particles is low, and the energy gain of the beam tail particles is high. When the rotation angle of the head structure of a single radio frequency cavity is adjusted counterclockwise, the energy gain of the beam tail particles is low, and the energy gain of the beam head particles is high. 2) On the current turn of the beam in the central region, adopt the method of eliminating energy difference once. By adjusting the rotation angle of the head structure of a single radio frequency cavity that eliminates energy difference in the opposite direction (counterclockwise or clockwise), eliminate the energy difference at the position where the beam width is the smallest, and achieve longitudinal focusing of the beam; this region with the smallest width is the region where the wide phase is compressed to the narrow phase.

3. The method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments according to claim 2, characterized in that: When it is set to adjust the rotation angle of the head structure of a single radio frequency cavity clockwise, the cavities that generate energy difference and eliminate energy difference are respectively the positions of the next turn of the beam of radio frequency cavity 1 and radio frequency cavity 2, or radio frequency cavity 3 and radio frequency cavity 4, or radio frequency cavity 4 and radio frequency cavity 1; when it is set to adjust the rotation angle of the head structure of a single radio frequency cavity counterclockwise, the cavities that generate energy difference and eliminate energy difference are respectively radio frequency cavity 1 and radio frequency cavity 4.

4. The method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments according to claim 2, wherein: The specific process of Step 3 is as follows: 1) On the current bunch of beam in the central region, by using the method of secondary compression of phase, through time-sharing adjustment of the head structures of two RF cavities at different positions that generate energy differences or time-sharing adjustment of the clockwise or counterclockwise rotation angle of the RF cavity at the same position, the particle energies at different longitudinal positions of the bunch present a certain energy difference. This certain energy difference compresses the bunch width to the minimum region; 2) On the current bunch of beam in the central region, by using the method of secondary elimination of energy difference, through time-sharing adjustment of the counterclockwise or clockwise rotation angles in the opposite direction of the head structures of two RF cavities at different positions for eliminating energy differences, the energy difference is eliminated at the position where the bunch width is the smallest, realizing the longitudinal focusing of the bunch; this region with the smallest width is the region where the wide phase is compressed to the narrow phase.

5. A method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments, characterized in that: On the current bunch of beam in the central region in Process 1) of Step 3, the method of secondary compression of phase width is specifically as follows: On the basis of clockwise rotation of the head of RF cavity 1 and counterclockwise rotation of the head of RF cavity 2, clockwise rotation of the head of RF cavity 3 and counterclockwise rotation of the head of RF cavity 4 are carried out.

6. A method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments, characterized in that: On the current bunch of beam in the central region, taking the clockwise rotation of the head of RF cavity 1 and counterclockwise rotation of the head of RF cavity 2 as the first compression of phase: For RF cavity 1 that generates energy difference, when the beam head rotates counterclockwise 90 degrees from RF cavity 1 to RF cavity 2, the rotation angle of the beam head and the particles with low energy relative to its own center point (1 - k)r1, k < 1, exceeds 90 degrees, and the rotation angle of the bunch tail and the particles with high energy 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, RF cavity 2 is used as the cavity for eliminating energy difference, and RF cavity 2 is rotated counterclockwise by a set angle to eliminate the energy difference. On the current bunch of beam in the central region, taking the clockwise rotation of the head of RF cavity 3 and counterclockwise rotation of the head of RF cavity 4 as the second compression of phase: When the beam head rotates counterclockwise 90 degrees from RF cavity 3 to 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 bunch 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, RF cavity 4 is used for eliminating energy difference, and RF cavity 4 is rotated counterclockwise by a set angle to eliminate the energy difference.

7. A method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments, as claimed in claim 4, wherein: In the current bunch of beam in the central area during process 1) of step 3), the method of secondarily compressing the phase width is adopted, specifically as follows: On the basis of clockwise rotating the head of RF cavity 1 and counterclockwise rotating the head of RF cavity 2, further counterclockwise rotate the head of RF cavity 2 so that the energy of the head of the bunch is the highest and the energy of the tail is the lowest after passing through RF cavity 2, and then adjust the part of the second turn of the particle trajectory corresponding to RF cavity 1 to rotate clockwise to eliminate the energy dispersion.

8. A method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments, characterized in that: In the current bunch of beam in the central area, taking the clockwise rotation of the head of RF cavity 1 and the counterclockwise rotation of the head of RF cavity 2 as the first phase compression: For RF cavity 1 that generates energy difference, when the head of the beam rotates counterclockwise 90 degrees from RF cavity 1 to RF cavity 2, the head of the beam and the particles with low energy rotate more than 90 degrees relative to their own center point (1 - k)r1, k < 1, and the rotation angle of the tail of the bunch and the particles with high energy relative to their 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, RF cavity 2 is used as the cavity to eliminate the energy difference, and RF cavity 2 is rotated counterclockwise by a set angle to eliminate the energy difference. In the current bunch of beam in the central area, taking the further counterclockwise rotation of the head of RF cavity 2 so that the energy of the head of the bunch is the highest and the energy of the tail is the lowest after passing through RF cavity 2 as the cavity that generates energy difference, as the second phase compression: For RF cavity 2 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise 270 degrees from RF cavity 2 to the next bunch of beam in RF cavity 1, in the fourth quadrant, the particles at the tail of the beam do not reach a rotation of 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 90 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, RF cavity 1 is used as the cavity to eliminate the energy difference, and the position of the next bunch of beam passing through RF cavity 1 is rotated clockwise by a set angle to eliminate the energy difference.

9. A method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments, as claimed in claim 4, wherein: In the current bunch of beam in the central area during process 1) of step 3), the method of secondarily compressing the phase width is adopted. On the basis of counterclockwise rotating the head of RF cavity 1 and clockwise rotating the head of RF cavity 4, for the next bunch of beam, further clockwise rotate the head of RF cavity 4 so that the energy of the head of the bunch is the lowest and the energy of the tail is the highest after passing through RF cavity 4, and then adjust the part of the second turn of the particle trajectory corresponding to RF cavity 1 to rotate counterclockwise to eliminate the energy dispersion.

10. A method for improving the longitudinal focusing force in the central region of an accelerator by combining positive and negative phase adjustments, characterized in that: Taking the counterclockwise rotation of the head of the radio frequency cavity 1 and the clockwise rotation of the head of the radio frequency cavity 4 as the first phase compression: On the current bunch of beam in the central region, for the radio frequency cavity 1 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise by 270 degrees from the radio frequency cavity 1 and reach the radio frequency cavity 4, in the third quadrant, the particles at the tail of the beam do not reach 270 degrees relative to its 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 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; On the next bunch of beam in the central region, taking the further clockwise rotation of the head of the radio frequency cavity 4 so that the head energy of the bunch is the lowest and the tail energy is the highest after passing through the radio frequency cavity 4 as the second phase compression; For the radio frequency cavity 4 that generates energy difference, when the particles at the head of the beam rotate counterclockwise by 90 degrees from the radio frequency cavity 4 and reach the radio frequency cavity 1, in the fourth quadrant, the particles at the head of the beam do not reach 90 degrees relative to its own center of the circle (1 - k)r1, k < 1, 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 fastest, while the particles at the tail of the beam move relatively slowest, thus compressing the phase width to the minimum; Then adjust the part of the second circle of the particle trajectory corresponding to the radio frequency cavity 1 and rotate it counterclockwise to eliminate the energy dispersion.

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