Method for improving longitudinal focusing force of central area of accelerator based on negative particle phase

Abstract

The invention discloses a method for improving longitudinal focusing force of a central area of an accelerator based on a negative particle phase. 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; the rotation angle of the head structure of the radio frequency cavity generating the energy difference is adjusted clockwise, so that the energy of particles at different longitudinal positions of a beam cluster has a certain energy difference; the rotation angle of the head structure of the radio frequency cavity with the energy difference eliminated is adjusted anticlockwise, the energy difference is eliminated at the position with the minimum beam bunch width, particles are compressed from the current radio frequency period to the middle received and accelerated area with the minimum phase width, and therefore the longitudinal focusing force of the particles in the track direction is improved. Longitudinal focusing is achieved in a negative phase adjusting mode, and defocusing in the height direction is avoided 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 based on the negative particle phase. 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 particles that arrive at the acceleration gap first at the front end of the bunch have a low energy gain and a slow speed after passing through the acceleration gap; the particles that arrive at the acceleration gap later at the back end of the bunch have a high energy gain and a fast speed after passing through the acceleration gap, realizing the 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), during the focusing stage when the particles pass through the acceleration gap, since the beam current that arrives first has a large energy gain and the beam current that arrives later has a small energy gain, 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 take into account the requirements of focusing and defocusing, for the situation where the beam current that arrives first has a small energy gain and the beam current that arrives later has a large energy gain, 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 for 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 for 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 an accelerator based on the negative particle phase, aiming to solve the problem that the traditional method for providing longitudinal focusing force in the central region has the side effect of defocusing in the height direction.

[0007] A method for improving the longitudinal focusing force in the central region of an accelerator based on the negative particle phase is characterized by including the following steps:

[0008] Step 1: Divide the radio frequency cavity into a radio frequency cavity for generating energy difference and a radio frequency cavity for eliminating 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.

[0009] Step 2: By clockwise adjusting the rotation angle of the head structure of the radio frequency cavity for generating energy difference, make the particle energies at different longitudinal positions of the bunch show a certain energy difference; by counterclockwise adjusting the rotation angle of the head structure of the radio frequency cavity for eliminating energy difference, eliminate the energy difference at the position where the bunch width is the smallest, and compress the particles from the non-receiving and non-accelerating regions on both sides of the current radio frequency cycle to the region with the smallest phase width in the middle that is received and accelerated, thereby improving the longitudinal focusing force of the particles along the trajectory direction. This region with the smallest width is the region where the wide phase is compressed to the narrow phase.

[0010] Further, the presented certain energy difference includes energy differences in monotonic and non-monotonic situations; making the particle energies at different longitudinal positions of the bunch show a certain energy difference means that the particles at different positions of the head and tail of the bunch corresponding to one radio frequency cycle show a certain energy difference.

[0011] Further, on the current turn of the beam in the central region, when it is set to clockwise adjust the rotation angle of the beam head structure, the cavities for generating energy difference and eliminating 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 radio frequency cavity 4 and the position of the radio frequency cavity 1 for the next turn of the beam.

[0012] Further, on the current circle of the beam in the central region, when setting the rotation angle of the beam head structure in the clockwise direction, the radio frequency cavities 1 and 2 that generate energy differences and eliminate energy differences are rotated counterclockwise by 90 degrees. The cavities that generate energy differences and eliminate energy differences are radio frequency cavity 2 and radio frequency cavity 3 respectively; the radio frequency cavities 1 and 2 that generate energy differences and eliminate energy differences are rotated counterclockwise by 180 degrees. The cavities that generate energy differences and eliminate energy differences are radio frequency cavity 3 and radio frequency cavity 4 respectively; the radio frequency cavities 1 and 2 that generate energy differences and eliminate energy differences are rotated counterclockwise by 270 degrees. The cavities that generate energy differences and eliminate energy differences are radio frequency cavity 4 and the position of the beam in the next circle of the beam passing through radio frequency cavity 1.

[0013] Further, when setting the rotation angle of the beam head structure in the clockwise direction, 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 in the counterclockwise direction, 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.

[0014] Further, when setting the rotation angle of the beam head structure in the clockwise direction, 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 small circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a large circle relative to the center point of the accelerator: Let the radius of the particles moving in a large circle at the tail of the bunch be r1, and the radius of the particles moving in a small circle at the head of the bunch be (1 - k)r1, where k < 1.

[0015] Further, when setting the rotation angle of the radio frequency cavity head structure in the clockwise direction, for the radio frequency cavity 1 that generates energy differences, when the beam head rotates counterclockwise by 90 degrees from the radio frequency cavity 1 to the radio frequency cavity 2, the particles at the head of the beam with low energy rotate by an angle exceeding 90 degrees relative to their own center point (1 - k)r1, where k < 1, and the rotation angle of the particles at the tail of the bunch 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 slowly, while the particles at the tail of the beam move relatively fast, so that the phase width is compressed to the minimum, and the particles at the head and tail of the beam are compressed from the non-receiving and non-accelerating regions of the current radio frequency cycle to the intermediate receiving and accelerating regions, improving the longitudinal focusing force of the particles along the trajectory direction; at this time, the radio frequency cavity 2 serves as the cavity to eliminate energy differences, and the radio frequency cavity 2 is rotated counterclockwise by a set angle to eliminate energy differences.

[0016] Further, when setting the rotation angle of the head structure of the radio frequency cavity in the clockwise direction and using the radio frequency cavity 2 as the radio frequency cavity for generating energy difference, when the beam head rotates counterclockwise by 90 degrees from the radio frequency cavity 2 to reach the radio frequency 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 of the beam head move relatively the slowest, while the particles of the beam tail move relatively the fastest, so that the phase width is compressed to the minimum, and the particles of the beam head and the beam tail are compressed from the non-receiving and non-accelerating regions of the current radio frequency cycle to the middle receiving and accelerating regions, thereby increasing the longitudinal focusing force of the particles along the trajectory direction; at this time, the radio frequency cavity 3 serves as the cavity for eliminating energy difference, and the radio frequency cavity 3 is rotated counterclockwise by a set angle to eliminate the energy difference.

[0017] Further, when setting the rotation angle of the head structure of the radio frequency cavity in the clockwise direction and using the radio frequency cavity 3 as the radio frequency cavity for generating energy difference, when the beam head rotates counterclockwise by 90 degrees from the radio frequency cavity 3 to reach the radio frequency 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 of the beam head move relatively the slowest, while the particles of the beam tail move relatively the fastest, so that the phase width is compressed to the minimum, and the particles of the beam head and the beam tail are compressed from the non-receiving and non-accelerating regions of the current radio frequency cycle to the middle receiving and accelerating regions, thereby increasing the longitudinal focusing force of the particles along the trajectory direction; at this time, the radio frequency cavity 4 serves as the cavity for eliminating energy difference, and the radio frequency cavity 4 is rotated counterclockwise by a set angle to eliminate the energy difference.

[0018] Advantages and Effects of the Invention

[0019] 1. The present invention realizes longitudinal focusing by adopting the negative phase method. 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.

[0020] 2. The present invention eliminates the energy difference at the radio frequency cavity 2 where the phase width is compressed to the minimum, solving the problem that in one revolution 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. Description of the Drawings

[0021] Figure 1 Schematic diagram of the central area of the cyclotron;

[0022] Figure 2 Radio frequency voltage curve;

[0023] Figure 3Energy gain of particles with different phases;

[0024] Figure 4 Trajectories of particles with different energies;

[0025] Figure 5 Difference in particle angle change at different speeds;

[0026] Figure 6 For the first method of clockwise adjusting the rotation angle of the head structure of the present invention;

[0027] Figure 7 For the second method of clockwise adjusting the rotation angle of the head structure of the present invention;

[0028] Figure 8 For the third method of clockwise adjusting the rotation angle of the head structure of the present invention;

[0029] Figure 9 For the fourth method of clockwise adjusting the rotation angle of the head structure of the present invention;

[0030] Figure 10 Schematic diagram of the present invention being accepted and accelerated;

[0031] Figure 11 Flowchart of the method for improving the longitudinal focusing force in the central region of the accelerator based on the negative particle phase of the present invention. Detailed implementation method

[0032] 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, while providing longitudinal focusing force and taking into account that it will not cause defocusing in the height direction. Another innovation point is: eliminating the energy difference 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, some quadrants move slowly and some quadrants move fast. 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.

[0033] 2. Theoretical basis

[0034] Figure 1 It 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:

[0035] 3. V(t) = V0 sinτ (1)

[0036] Where V0 is the amplitude of the radio frequency voltage and τ is the radio frequency time. An accelerating gap with a radio frequency electric field is formed between the radio frequency cavity and the ground electrode. The accelerating gaps are numbered from accelerating gap 1 to accelerating gap 8 in the order of particle passage. Particles are accelerated when passing through the accelerating gaps.

[0037] In order for particles to have an accelerating voltage when passing through the accelerating 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 accelerating 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 Figure 2 so that the particles can gain energy; at accelerating 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

[0038] 0° to 180° in

[0039] Let the radio frequency times when the particles pass through accelerating gap 1 and accelerating gap 2 be τ1 and τ2 respectively, and the charge of the negative ion be -q. Then the energy gain of the particle from accelerating gap 1 and accelerating gap 2 is:

[0040] ΔE = qV0(sinτ2 - sinτ1)(2)

[0041] Equation (2) shows that particles arriving at the radio frequency cavity at different times obtain different energy gains. For the same radio frequency cavity structure, the time lengths required for particles arriving at different times to pass through the radio frequency cavity, that is, the difference between τ1 and τ2, are the same:

[0042]

[0043] τ2 - τ1 = hα(3)

[0044]

[0045] h is the harmonic number of the accelerator and α is the opening angle of the radio frequency cavity. Define the particle phase: Figure 3 It is the average radio frequency time when the particle enters and leaves the radio frequency cavity, and it is also the radio frequency time when the particle arrives at the center line of the radio frequency cavity. Substituting Equation (3) and Equation (4) into Equation (2), we get:

[0046] 3. Invention Principle

[0047] As can be seen from Equation (5), 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 partial phases are accelerated in each radio frequency 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.

[0048] 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 is:

[0049]

[0050] 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:

[0051]

[0052] As can be seen from Equation (7), the angular velocities of particles with 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. Taking the position (r1, 0) at the azimuth angle of 0° as the starting time, the azimuth angle of particle 1 changes with time t: Figure 4 As shown by the solid line part. Taking the position (r1, 0) at the azimuth angle of 0° as the starting time, the azimuth angle of particle 1 changes with time t:

[0053] θ1 = ωt (8)

[0054] The coordinates of particle 1 changing with time can be expressed as:

[0055]

[0056] Particle 2 also starts from the position (r1, 0). There is a difference in energy from particle 1, making its rotation radius:

[0057] r2 = k·r1 (10)

[0058] When the energy of particle 2 is less than that of particle 1, k < 1, and vice versa 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:

[0059]

[0060] The azimuth angle of particle 2 is:

[0061]

[0062] Substitute Equation (8) and Equation (11) into Equation (12), solve, and obtain:

[0063]

[0064] 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's rotation is the same as that of Particle 1, which is ω, 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 A negative ordinate in [reference] indicates that the angle by which Particle 2 rotates less than Particle 1 from the starting point to that moment, and a positive ordinate indicates a larger rotation angle; a decrease in the ordinate indicates that the angular velocity of Particle 2's rotation at that moment is less than that of Particle 1, and an increase indicates that the angular velocity is greater than that of Particle 1. It and Figure 4 The corresponding relationship is:

[0065] (1) Particle 1 rotates 90° in each of the first to fourth quadrants, and the angular velocity is a constant value 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 in [reference], and reaches the minimum value near the abscissa of 90°.

[0066] (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 an increase in the ordinate in [reference]. When the abscissa is 180°, both Particle 1 and Particle 2 have rotated half a circle, so the ordinate is 0.

[0067] (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 an increase in the ordinate in [reference], and reaches the maximum value near the abscissa of 270°.

[0068] (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 a decrease in the ordinate in [reference]. When the abscissa is 360°, both Particle 1 and Particle 2 have rotated one full circle, so the ordinate is 0.

[0069] When the energy of Particle 2 is greater than that of Particle 1, that is, when k is greater than 1, the above variation law is opposite.

[0070] 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 RF 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 dispersion is eliminated at the position where the bunch width is the smallest, realizing longitudinal focusing of the bunch.

[0071] 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 partial 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 that the bunch crosses a certain position. By reasonably designing the structure of the central region, providing longitudinal focusing force and reducing the longitudinal length of the beam are beneficial to improving the beam transmission efficiency.

[0072] 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:

[0073]

[0074] 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:

[0075]

[0076] It can be seen from Equation (7) that the angular velocities of particles with 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. Taking the position (r1, 0) at the azimuth angle of 0° as the starting time, the azimuth angle where the particle 1 is located changes with time t: Figure 4 θ1 = ωt (8)

[0077] θ1 = ωt (8)

[0078] The coordinates of particle 1 changing with time can be expressed as:

[0079]

[0080] Particle 2 also starts from the position (r1, 0). Due to the difference in energy from particle 1, its rotation radius:

[0081] r2 = k·r1 (10)

[0082] When the energy of particle 2 is less than that of particle 1, k < 1, and vice versa k > 1. Particle 2 also rotates at an angular velocity of ω, and its center of rotation is ((1 - k)r1, 0). The coordinates of particle 2 changing with time can be expressed as:

[0083]

[0084] The azimuth angle of particle 2 is:

[0085]

[0086] Substitute equations (8) and (11) into equation (12), solve, and obtain:

[0087]

[0088] 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, 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 [], a negative ordinate indicates that the angle rotated by particle 2 from the starting point to this moment is smaller than that of particle 1, and a positive value indicates a larger rotated 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:

[0089] (1) Particle 1 rotates 90° in each of the first to fourth quadrants, and the angular velocity is a constant value ω1. The angle θ1 rotated by particle 2 in the first quadrant is greater than 90°, and the angular velocity ω2 relative to the accelerator center is greater than that of particle 1, corresponding to Figure 5 in which the ordinate decreases and reaches the minimum value near the abscissa of 90°.

[0090] (2) The angle θ2 rotated by particle 2 in the second quadrant is less than 90°, and the angular velocity ω2 relative to the accelerator center is less than that of particle 1, corresponding to Figure 5 in which the ordinate increases. When the abscissa is 180°, both particle 1 and particle 2 have rotated half a circle, so the ordinate is 0.

[0091] (3) The angle θ2 rotated by particle 2 in the third quadrant is less than 90°, and the angular velocity ω2 relative to the accelerator center is less than ω1 of particle 1, corresponding to Figure 5 in which the ordinate increases and reaches the maximum value near the abscissa of 270°.

[0092] (4) The angle θ2 rotated by particle 2 in the fourth quadrant is greater than 90°, and the angular velocity ω2 relative to the accelerator center is greater than that of particle 1, corresponding to Figure 5The ordinate in the middle decreases. When the abscissa is 360°, both particle 1 and particle 2 have rotated one circle, so the ordinate is 0.

[0093] When the energy of particle 2 is greater than that of particle 1, that is, when k is greater than 1, the above variation law is opposite. 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 a certain angle of rotation, the energy dispersion is eliminated at the position where the bunch width is the smallest, realizing longitudinal focusing of the bunch.

[0094] 4. Design principle of realizing longitudinal focusing by negative phase adjustment method: The Figure 6 of the present invention realizes longitudinal focusing by using a negative phase method to realize longitudinal focusing, Figure 8 、 9 is a derivative result of realizing longitudinal focusing by a negative phase method.

[0095] First, the method of realizing longitudinal focusing by a negative 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 clockwise. Adjusting the head structure clockwise means that the head of the beam reaches the center line of the radio frequency cavity in advance. The particle phase is the average value of the time of passing through the two acceleration 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 the -10-degree phase 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 acceleration gap but also to the average value of the time of passing through the entrance and exit acceleration gaps. For example, the average value of -80 degrees and +60 degrees in the Figure 2 radio frequency period is -10 degrees, and the -10 degrees of this radio frequency period corresponds to Figure 3 the -10° phase. Assuming φ is selected as -10°, in the Figure 2 radio frequency voltage period, the passing times τ1 and τ2 of acceleration gap 1 and acceleration gap 2 can be selected as -80° and 60°. The passing time of acceleration gap 1 meets the focusing requirements in the height direction. Although acceleration gap 2 is a defocusing phase in the height direction, it has high energy and low influence, and overall shows a focusing effect.

[0096] 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 it is focused overall. 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 it is focused overall in the height direction. In short, because the focusing in the height direction is satisfied at the first accelerating gap, the defocusing in the height direction at the second accelerating gap has less impact than the accelerating gap 1, and the average phases of the accelerating gap 1 and the accelerating gap 2 meet the conditions for longitudinal focusing. Therefore, the method of negative phase realizes longitudinal focusing while providing longitudinal focusing force and avoiding defocusing in the height direction.

[0097] Second, the method of negative phase realizes longitudinal focusing and eliminates energy differences 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 RF voltage is 50 kV when the beam head 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, because 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. It is equivalent to the beam head moving slowly and the tail beam moving fast, and the fast in the front and the slow in the back realizes 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 chromatic dispersion at the RF 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 the 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 beam moves fast and the back moves slowly. 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, so the fourth quadrant is also focusing. 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, making 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 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.

[0098] Based on the above principle, the present invention designs a method for improving the longitudinal focusing force in the central region of an accelerator based on the negative particle phase, as Figure 11 shown, which is characterized by including the following steps:

[0099] 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;

[0100] Step 2: By clockwise adjusting the rotation angle of the head structure of the RF cavity that generates energy difference and counterclockwise adjusting the rotation angle of the head structure of the RF cavity that eliminates energy difference, compress the particles from the non-receiving and non-accelerating regions on both sides of the current RF cycle to the region with the smallest phase width that is received and accelerated in the middle, thereby improving the longitudinal focusing force of the particles along the trajectory direction. The region with the smallest width is the region where the wide phase is compressed to the narrow phase;

[0101] Further, the specific steps of Step 2 are as follows:

[0102] 1) By clockwise adjusting the rotation angle of the head structure of the RF cavity that generates energy difference, make the energies of the particles at different longitudinal positions of the bunch present a certain energy difference; the presenting of a certain energy difference includes the energy difference in monotonic and non-monotonic cases; the different longitudinal positions refer to the different positions of the head and tail of the bunch corresponding to one RF cycle; the presenting of a certain energy difference of the particle energy means that the energies of the bunch head and the bunch tail generate a difference;

[0103] 2) By counterclockwise adjusting the rotation angle of the head structure of the radio frequency cavity that eliminates the energy difference, the energy difference is eliminated at the position where the bunch width is the smallest, achieving longitudinal focusing of the bunch; this area with the smallest width is the area where the wide phase is compressed to the narrow phase.

[0104] As Figure 6 shown, on the current bunch of the beam in the central region, 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, as Figure 7 shown, or radio frequency cavity 2 and radio frequency cavity 3 respectively; as Figure 8 shown, or radio frequency cavity 3 and radio frequency cavity 4 respectively; as Figure 9 shown, or the positions of radio frequency cavity 4 and radio frequency cavity 1 for the next bunch of the beam.

[0105] As Figure 7 shown, when setting the rotation angle of the beam head structure to be adjusted clockwise, rotate radio frequency cavity 1 and radio frequency cavity 2 that generate the energy difference and eliminate the energy difference counterclockwise by 90 degrees. At this time, the cavities that generate the energy difference and eliminate the energy difference are radio frequency cavity 2 and radio frequency cavity 3 respectively; as Figure 8 shown, rotate radio frequency cavity 1 and radio frequency cavity 2 that 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 that 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 radio frequency cavity 4 and the position of the second bunch (not drawn in the figure) where the beam of radio frequency cavity 1 passes through.

[0106] When setting the rotation angle of the beam head structure to be adjusted clockwise, the voltage at the position where the bunch head particles are located is relatively small and the energy gain obtained is relatively small, while the voltage at the position where the tail particles 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 bunch head particles are located is relatively large and the energy gain obtained is relatively large, while the voltage at the position where the tail particles are located is relatively small and the energy gain obtained is relatively small.

[0107] As Figure 6 、 7 、8 shown, when setting the rotation angle of the beam head structure to be adjusted clockwise, since the energy gain of the bunch head particles is lower than that of the bunch tail particles, the bunch head particles move in a small circle relative to the accelerator center point and the bunch tail particles move in a large circle relative to the accelerator center point: Let the radius of the particles moving in the large circle of the bunch tail be r1, and the radius of the particles moving in the small circle of the bunch head be (1 - k)r1, k < 1.

[0108] AsFigure 6 As shown, 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 particles at the beam head and with lower energy rotate by an angle exceeding 90 degrees relative to their own central point (1 - k)r1, k < 1, and the particles at the beam tail and with higher energy rotate by 90 degrees relative to their own central 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, so that the phase width is compressed to the minimum, and the particles at the beam head and tail are compressed from the non-receiving and non-accelerating regions of the current RF cycle to the middle receiving and accelerating regions, improving the longitudinal focusing force of the particles along the trajectory direction; 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.

[0109] As Figure 7 shown, 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 particles at the beam head rotate by an angle exceeding 90 degrees relative to their own central point (1 - k)r1, k < 1, and the particles at the beam tail rotate by 90 degrees relative to their own central 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, so that the phase width is compressed to the minimum, and the particles at the beam head and tail are compressed 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; 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.

[0110] As Figure 8 shown, 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 particles at the beam head rotate by an angle exceeding 90 degrees relative to their own central point (1 - k)r1, k < 1, and the particles at the beam tail rotate by 90 degrees relative to their own central 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, so that the phase width is compressed to the minimum, and the particles at the beam head and tail are compressed 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; 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.

[0111] Embodiment 1: Achieving longitudinal focusing by means of negative phase adjustment

[0112] As Figure 6 shown, in the present invention, ① the entry and exit of particles from a single radio frequency cavity are regarded as a whole, and ② the time for particles to pass through the center line of the radio frequency cavity is adjusted by angularly moving the position of the radio frequency cavity, that is, the particle phase φ in Equation (4), to change the energy gain obtained by the particles. The longitudinal focusing is achieved in the way of negative phase. Taking the radio frequency cavity 1 in Figure 1 as an example, assuming that the center phase of the current bunch is 0°, the head region of the radio frequency cavity 1 corresponding to the first-turn particle trajectory is rotated clockwise, so that the whole bunch arrives at the radio frequency cavity 1 earlier, φ < 0, as in the range of -90° to 0° in Figure 3 . 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. It can be seen from Figure 5 that near the angle of 90°, at the position corresponding to the radio frequency cavity 2, the particles in the bunch head with low energy rotate the smallest angle, and the particles in the bunch tail 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 in the range of 0° to 90° in Figure 3 . The particles in the bunch head obtain the highest energy gain in the radio frequency cavity 2, and the lowest in the tail. After the bunch is accelerated through the radio frequency cavity 1 and the radio frequency 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.

[0113] Embodiment 2

[0114] As Figure 8 shown, the present invention does not limit the cavity that generates a monotonically changing energy dispersion to the radio frequency cavity 1. For example, for the way of achieving longitudinal focusing in the negative phase, it is modified to rotate the head of the radio frequency cavity 2 clockwise and the head of the radio frequency cavity 3 counterclockwise.

[0115] It should be emphasized that the above specific embodiments are only explanations of the present invention, and they are not limitations to the present invention. After reading this specification, those skilled in the art can make modifications without creative contributions to the above embodiments 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 based on the phase of negative particles, 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; Step 2: By clockwise adjusting the rotation angle of the head structure of the radio frequency cavity that generates energy difference, make the particle energies at different longitudinal positions of the bunch present a certain energy difference; by counterclockwise adjusting the rotation angle of the head structure of the radio frequency cavity that eliminates energy difference, eliminate the energy difference at the position where the bunch width is the smallest, and compress the particles from the non-receiving and non-accelerating regions on both sides of the current radio frequency cycle to the region with the smallest phase width that is received and accelerated in the middle, thereby increasing the longitudinal focusing force of the particles along the trajectory direction. 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 an accelerator based on the phase of negative particles according to claim 1, wherein: The presenting of a certain energy difference includes the energy difference in the monotonic case and the non-monotonic case; the making of the particle energies at different longitudinal positions of the bunch present a certain energy difference means that the particles at different positions of the head and tail of the bunch corresponding to one radio frequency cycle present a certain energy difference.

3. The method for enhancing the longitudinal focusing force in the central region of an accelerator based on the phase of negative particles according to claim 2, wherein: On the current turn of the beam in the central region, when setting to clockwise adjust the rotation angle of the beam head structure, the cavities that generate energy difference and eliminate energy difference are respectively radio frequency cavity 1 and radio frequency cavity 2, or respectively radio frequency cavity 2 and radio frequency cavity 3, or respectively radio frequency cavity 3 and radio frequency cavity 4, or respectively radio frequency cavity 4 and the position of the next turn of the beam of radio frequency cavity 1.

4. The method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of negative particles according to claim 3, wherein: On the current turn of the beam in the central region, when setting to clockwise adjust the rotation angle of the beam head structure, rotate radio frequency cavity 1 and 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 radio frequency cavity 2 and radio frequency cavity 3; Rotate radio frequency cavity 1 and radio frequency cavity 2 that generate energy difference and eliminate energy difference counterclockwise by 180 degrees, and the cavities that generate energy difference and eliminate energy difference are respectively radio frequency cavity 3 and radio frequency cavity 4; rotate radio frequency cavity 1 and radio frequency cavity 2 that generate energy difference and eliminate energy difference counterclockwise by 270 degrees, and the cavities that generate energy difference and eliminate energy difference are respectively radio frequency cavity 4 and the position of the next turn of the beam passed by radio frequency cavity 1.

5. The method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of negative particles according to claim 1, wherein: When setting 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 setting 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.

6. The method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of negative particles according to claim 5, characterized in that: When setting the rotation angle of the beam head structure for clockwise adjustment, 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.

7. A method for enhancing the longitudinal focusing force in the central region of an accelerator based on the phase of negative particles according to claim 4, characterized in that: When setting the rotation angle of the radio frequency cavity head structure for clockwise adjustment, for the radio frequency cavity 1 that generates energy differences, when the beam head rotates counterclockwise by 90 degrees from the radio frequency cavity 1 to reach the radio frequency cavity 2, the beam head and the particles with lower energy rotate by an angle exceeding 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 with higher 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, and the particles at the head and tail of the beam are compressed from the non-receiving and non-accelerating regions of the current radio frequency cycle to the middle receiving and accelerating regions, improving the longitudinal focusing force of the particles along the trajectory direction; At this time, the radio frequency cavity 2 serves as the cavity to eliminate energy differences, and the radio frequency cavity 2 is rotated counterclockwise by a set angle to eliminate energy differences.

8. The method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of negative particles according to claim 4, wherein: When setting the rotation angle of the radio frequency cavity head structure for clockwise adjustment and using the radio frequency cavity 2 as the radio frequency cavity that generates energy differences, when the beam head rotates counterclockwise by 90 degrees from the radio frequency cavity 2 to reach the radio frequency cavity 3, the beam head rotates by an angle exceeding 90 degrees relative to its own center point (1 - k)r1, k < 1, and the rotation angle of the particles at the tail of the beam 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, and the particles at the head and tail of the beam are compressed 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; At this time, the radio frequency cavity 3 serves as the cavity to eliminate energy differences, and the radio frequency cavity 3 is rotated counterclockwise by a set angle to eliminate energy differences.

9. The method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of negative particles according to claim 4, characterized in that: When setting the rotation angle of the radio frequency cavity head structure for clockwise adjustment and using the radio frequency cavity 3 as the radio frequency cavity that generates energy differences, when the beam head rotates counterclockwise by 90 degrees from the radio frequency cavity 3 to reach the radio frequency cavity 4, the beam head rotates by an angle exceeding 90 degrees relative to its own center point (1 - k)r1, k < 1, and the rotation angle of the particles at the tail of the beam 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, and the particles at the head and tail of the beam are compressed 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; At this time, the radio frequency cavity 4 serves to eliminate energy differences, and the radio frequency cavity 4 is rotated counterclockwise by a set angle to eliminate energy differences.

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