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

Abstract

The invention discloses a positive particle phase-based method for improving longitudinal focusing force of a central area of an accelerator. The method comprises the following steps of: dividing a radio frequency cavity into a radio frequency cavity for generating energy difference and a radio frequency cavity for eliminating the energy difference; the energy gain of beam head particles is set to be high, and the energy of beam tail particles is set to be low; the rotation angle of the head structure of the radio frequency cavity generating the energy difference is adjusted anticlockwise, 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 clockwise, the energy difference is eliminated at the position with the minimum beam bunch width, and particles are compressed from non-receiving and non-acceleration areas on the two sides of the current radio frequency period to the middle received and accelerated area with the minimum phase width. Longitudinal focusing is achieved in a positive phase mode, and the focusing effect in the height direction is better while longitudinal focusing is achieved in the positive phase mode.

Description

Technical Field

[0001] The present invention belongs to the technical field of the central region of a cyclotron, and particularly relates to a method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of positive particles. 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 rear 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] In order to provide stronger focusing force in the height direction, the traditional method needs to select Figure 2 in the region of -90° to 0°. 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 first-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 simultaneously take into account the requirements of focusing and defocusing, for the situation where the energy gain of the first-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 in the height direction, select an accelerator with a relatively strong magnetic field focusing force to make up for the deficiency of the poor longitudinal focusing effect when selecting Figure 2 in the region of -90° to 0°. If there is no accelerator with a relatively strong magnetic field focusing force to make up for the 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 the radio frequency voltage range of -180 to -90 is selected; the traditional method of providing focusing force in the height direction in the central region has the side effect of inability to focus longitudinally when the radio frequency voltage range of -90° to 0° is selected. Summary of the Invention

[0006] To solve the deficiencies of the prior art, the present invention proposes a method for improving the longitudinal focusing force in the central region of an accelerator based on the positive particle phase, aiming to solve the problem that the traditional method of providing focusing force in the height direction in the central region has the side effect of inability to focus longitudinally.

[0007] A method for improving the longitudinal focusing force in the central region of an accelerator based on the positive particle phase, 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; set that the energy gain of the beam head particles reaching the acceleration gap first is high, and the energy of the beam tail particles reaching the acceleration gap later is low.

[0009] Step 2: By counterclockwise adjusting the rotation angle of the head structure of the radio frequency cavity for generating energy difference, make the energies of particles at different longitudinal positions in the bunch show a certain energy difference; by clockwise 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 that is received and accelerated in the middle, 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 presenting of a certain energy difference includes energy differences in monotonic and non-monotonic cases; the making of the energies of particles at different longitudinal positions in the bunch show a certain energy difference means that the particles at different positions at the head and tail of the bunch corresponding to one radio frequency cycle show a certain energy difference.

[0011] Further, when setting the counterclockwise adjustment of the rotation angle of the beam head structure, the cavities for generating energy difference and eliminating energy difference are radio frequency cavity 1 and radio frequency cavity 4 respectively.

[0012] Further, when setting the counterclockwise adjustment of the rotation angle of the beam head structure, rotate radio frequency cavity 1 and radio frequency cavity 4 for generating energy difference and eliminating energy difference counterclockwise by 90 degrees, and the cavities for generating energy gain and eliminating energy difference are at the second turn positions of radio frequency cavity 2 and radio frequency cavity 1 respectively.

[0013] Furthermore, when setting the rotation angle of the radio frequency cavity head structure to be adjusted counterclockwise, since the particles at the head of the bunch have a higher energy gain than those at the tail of the bunch, the particles at the head of the bunch move in a larger circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a smaller circle relative to the center point of the accelerator: Let the radius of the particles at the head of the bunch moving in the larger circle relative to the center point of the accelerator be r1, and the radius of the particles at the tail of the bunch moving in the smaller circle be (1 - k)r1, where k < 1.

[0014] Furthermore, when setting the rotation angle of the radio frequency cavity head structure to be adjusted counterclockwise, for the radio frequency cavity 1 that generates energy differences, when the particles at the tail of the beam rotate 270 degrees counterclockwise 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 relative to its own center (1 - k)r1, where k > 1 do not reach 270 degrees, and the rotation angle of the particles at the head of the beam relative to its own center point r1 is 270 degrees. At this time, the particles at the tail of the beam move relatively fastest, while the particles at the head of the beam move relatively slowest, thereby compressing the phase width to the minimum, and compressing the particles at the head and tail of the beam from the non-receiving and non-accelerating regions of the current radio frequency cycle to the intermediate 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 is used to eliminate the energy difference, and the radio frequency cavity 4 is rotated clockwise by a set angle to eliminate the energy difference.

[0015] Furthermore, when setting the rotation angle of the radio frequency cavity head structure to be adjusted counterclockwise, and using the radio frequency cavity 2 as the cavity that generates energy differences, for the radio frequency cavity 2 that generates energy differences, when the particles at the tail of the beam rotate 270 degrees counterclockwise from the radio frequency cavity 2 to reach the second circle of the radio frequency cavity 1, in the fourth quadrant, the particles at the tail of the beam relative to its own center (1 - k)r1, where k < 1 do not reach 270 degrees, and the rotation angle of the particles at the head of the beam relative to its own center point r1 is 270 degrees. In the fourth quadrant, the particles at the tail of the beam represented by the dotted line move relatively fastest, while the particles at the head of the beam represented by the solid line move relatively slowest, thereby compressing the phase width to the minimum, and thus improving the longitudinal focusing force of the particles along the trajectory direction; at this time, the radio frequency cavity 1 is used as the cavity to eliminate the energy difference, and the position of the second circle of the radio frequency cavity 1 where the beam passes through is rotated clockwise by a set angle to eliminate the energy difference.

[0016] Advantages and effects of the present invention

[0017] 1. The present invention realizes longitudinal focusing in a positive-phase manner. By regarding the two accelerations of a radio-frequency cavity as an overall adjustment, while providing longitudinal focusing force, it also ensures that there is no defocusing in the height direction. At the same time, since the positive-phase method is used to realize longitudinal focusing and the positive phase φ is selected, and the positive phase is greater than the negative phase. As can be seen from formula (4), the phase φ is related to the inlet and outlet gap times τ1 and τ2. The larger the phase φ, the larger τ1 and τ2, and the stronger the axial focusing when τ1 and τ2 are large. Therefore, when the positive-phase method is used to realize longitudinal focusing, the focusing effect in the height direction is better.

[0018] 2. The present invention eliminates the energy difference at the radio-frequency cavity 4 where the phase width compression is the smallest, solving the problem that in one turn of the tail particles, some quadrants move slowly and some quadrants move fast, resulting in the re-occurrence of longitudinal defocusing in the quadrants where the tail particles move slowly after eliminating the energy difference. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the central area of the cyclotron;

[0020] Figure 2 Radio-frequency voltage curve;

[0021] Figure 3 Energy gain of particles with different phases;

[0022] Figure 4 Trajectories of particles with different energies;

[0023] Figure 5 Difference in particle angle changes at different speeds;

[0024] Figure 6 For the first method of counterclockwise adjusting the rotation angle of the head structure of the present invention;

[0025] Figure 7 For the second method of counterclockwise adjusting the rotation angle of the head structure of the present invention;

[0026] Figure 8 For the schematic diagram of the present invention being accepted and accelerated;

[0027] Figure 9 For the flowchart of the method for improving the longitudinal focusing force in the central area of the accelerator based on the positive particle phase of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0028] 1. Innovation points of the present invention: One of the innovation points lies in regarding the two - stage acceleration of a radio - frequency cavity as an overall adjustment, which can provide longitudinal focusing force while avoiding defocusing in the height direction. The second innovation point is that the energy difference is eliminated 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 slower in some quadrants and faster 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.

[0029] 2. Theoretical basis

[0030] Figure 1 It is a schematic diagram of the central area 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:

[0031] 3. V(t) = V0 sinτ (1)

[0032] Where V0 is the amplitude of the radio - frequency voltage and τ is the radio - frequency time. An acceleration gap with a radio - frequency electric field is formed between the radio - frequency cavity and the ground electrode. According to the order of particle passage, they are acceleration gap 1 to acceleration gap 8, and the particles are accelerated when passing through the acceleration gap.

[0033] In order to enable the particles to have an accelerating voltage when passing through the acceleration gap, 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) so that the particles can obtain energy; at acceleration gap 2, it enters the ground electrode from the radio - frequency cavity, and at this time, the 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 gain of the particle from acceleration gap 1 and acceleration gap 2 is:

[0034] ΔE = qV0(sinτ2 - sinτ1) (2)

[0035] 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:

[0036] τ2 - τ1 = hα (3)

[0037] h is the harmonic number of the accelerator, and α is the opening angle of the radio - frequency cavity. Define the particle phase:

[0038]

[0039] It is the radio frequency time average value of the particles entering and leaving the radio frequency cavity, and also the radio frequency time when the particles reach the center line of the radio frequency cavity. Substituting Equation (3) and Equation (4) into Equation (2), we get:

[0040]

[0041] Equation (5) shows that particles with a phase of 0, that is, particles that exactly reach the center line of the radio frequency cavity when the radio frequency time is 0, obtain the highest energy gain, as Figure 3 shown.

[0042] 3. Principle of the Invention

[0043] 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 radio frequency cycle, forming periodic particle bunches. Longitudinal refers to the direction in which the particle bunches advance, manifested as the length of the bunches or the time length spanned by the bunches passing through a certain position. By reasonably designing the structure of the central region, providing longitudinal focusing force, and reducing the longitudinal length of the beam, it is beneficial to improve the beam transmission efficiency.

[0044] 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 charged particles in the cyclotron:

[0045]

[0046] 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:

[0047]

[0048] 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 Figure 4 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:

[0049] θ1 = ωt (8)

[0050] The coordinates of particle 1 changing with time can be expressed as:

[0051]

[0052] Particle 2 also starts at the position (r1, 0) and has a different energy from Particle 1, resulting in its rotation radius:

[0053] r2 = k·r1 (10)

[0054] 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 center of rotation is ((1 - k)r1, 0). The coordinates of Particle 2 changing with time can be expressed as:

[0055]

[0056] The azimuth angle of Particle 2 is:

[0057]

[0058] Substitute Equation (8) and Equation (11) into Equation (12), solve, and obtain:

[0059]

[0060] Figure 5 Taking k = 0.8 as an example, the angular difference between Particle 2 and Particle 1 at the same moment is shown. The relationship between the abscissa 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 the [graph], a negative ordinate indicates that the angle by which Particle 2 rotates less than Particle 1 from the starting point to this moment, and a positive ordinate indicates a larger rotation angle; a decreasing ordinate indicates that the angular velocity of Particle 2 at this moment is less than that of Particle 1, and an increasing ordinate indicates a greater angular velocity than that of Particle 1. Its correspondence with Figure 4 is as follows:

[0061] (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 center of rotation 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 decreasing ordinate in the [graph], and reaching the minimum value near the abscissa of 90°.

[0062] (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 increasing ordinate in the [graph]. When the abscissa is 180°, both Particle 1 and Particle 2 have rotated half a circle, so the ordinate is 0.

[0063] (3) The rotation angle θ2 of particle 2 in the third quadrant is less than 90°, and its angular velocity ω2 relative to the accelerator center is greater than ω1 of particle 1, corresponding to Figure 5 the increase in the ordinate in the figure, and it reaches the maximum value near the abscissa of 270°.

[0064] (4) The rotation angle θ2 of particle 2 in the fourth quadrant is greater than 90°, and its angular velocity ω2 relative to the accelerator center is less than that of particle 1, corresponding to Figure 5 the decrease in the ordinate in the figure. When the abscissa is 360°, both particle 1 and particle 2 have rotated one circle, so the ordinate is 0.

[0065] When the energy of particle 2 is greater than that of particle 1, that is, k > 1, the above variation law is reversed.

[0066] Taking the center of the cyclotron as the origin of the coordinate system, the angular velocities of particles with different energies are variable. 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.

[0067] It can be seen from Equation (5) that not all particles injected into the accelerator at all times can be accelerated. The phase φ can be accelerated only between -90° and 90°. In fact, the ability of the accelerator to receive and accelerate the beam is much smaller than this range. Therefore, even if the particle beam is continuously injected into the accelerator, only particles with certain phases are accelerated in each RF cycle, forming a periodic particle bunch. Longitudinal refers to the direction in which the particle bunch advances, manifested as the length of the bunch or the time length that the bunch spans through a certain position. By reasonably designing the structure of the central region, providing longitudinal focusing force and reducing the longitudinal length of the beam are beneficial to improving the beam transmission efficiency.

[0068] 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:

[0069]

[0070] 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:

[0071]

[0072] 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 Figure 4As shown by the solid line part. 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:

[0073] θ1 = ωt (8)

[0074] The coordinates of particle 1 changing with time can be expressed as:

[0075]

[0076] Particle 2 also starts from the position (r1, 0). Due to the difference in energy from particle 1, its rotation radius is:

[0077] r2 = k·r1 (10)

[0078] When the energy of particle 2 is less than that of particle 1, k < 1; otherwise, 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:

[0079]

[0080] The azimuth angle of particle 2 is:

[0081]

[0082] Substitute equations (8) and (11) into equation (12) and solve to obtain:

[0083]

[0084] Figure 5 Taking k as 0.8 as an example, it shows the angle difference between particle 2 and particle 1 at the same moment. 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 [the figure], the negative ordinate indicates that the angle θ2 of particle 2 rotating from the starting point to this moment is smaller than that of particle 1, and the positive indicates a larger rotation angle; the decrease in the ordinate indicates that the angular velocity of particle 2 rotating at this moment is less than that of particle 1, and the increase indicates a greater angular velocity than that of particle 1. Its correspondence with Figure 4 is as follows:

[0085] (1) Particle 1 rotates 90° in each of the first to fourth quadrants, and the angular velocity is a constant value ω1. The angle θ2 of particle 2 rotating 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°.

[0086] (2) The rotation angle θ2 of particle 2 in the second quadrant is less than 90°, and its angular velocity ω2 relative to the accelerator center is less 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.

[0087] (3) The rotation angle θ2 of particle 2 in the third quadrant is less than 90°, and its angular velocity ω2 relative to the accelerator center is less than ω1 of particle 1, corresponding to Figure 5 The ordinate increases and reaches the maximum value near the abscissa of 270°.

[0088] (4) The rotation angle θ2 of particle 2 in the fourth quadrant is greater than 90°, and its angular velocity ω2 relative to the accelerator center is greater 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 circle, so the ordinate is 0.

[0089] When the energy of particle 2 is greater than that of particle 1, i.e., k > 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 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.

[0090] 5. The design principle of realizing longitudinal focusing by the positive phase adjustment method. First, the Figure 6 of the present invention is to realize longitudinal focusing by the positive phase method, Figure 7 which is a derivative result of realizing longitudinal focusing by the positive phase method. Realizing longitudinal focusing by the positive phase method takes into account not causing defocusing in the height direction while providing longitudinal focusing force. The method it adopts is to adjust the head structure counterclockwise. Adjusting the head structure counterclockwise means that the head of the beam arrives at the center line of the radio frequency cavity later. The particle phase is the average value of the time passing through the two acceleration gaps when entering and leaving the radio frequency cavity, that is, the radio frequency time when the particle arrives at the center line of the radio frequency cavity. Arriving at the center line of the radio frequency cavity later means choosing a phase such as Figure 3 +10 degrees in Figure 2 Here, +10 degrees is an example rather than a limitation, and other positive phases are also acceptable. Using the phase of +10 degrees 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 to the average value of the time passing through the entrance acceleration gap and the two time intervals when entering and leaving, for example, corresponding to Figure 3 the average value of -60 degrees and +80 degrees in the radio frequency cycle is +10 degrees, and the +10 degrees of this radio frequency cycle corresponds to Figure 2In the radio frequency voltage cycle, the transit times τ1 and τ2 of acceleration gaps 1 and 2 can be selected as -60° and +80°. The transit time of acceleration gap 1 meets the focusing requirements in the height direction. Although acceleration gap 2 is in a defocusing phase in the height direction, it has high energy and low influence, presenting an overall focusing effect. The reason why the transit time of acceleration gap 1 meets the focusing requirements in the height direction is that -60 is in the voltage rising region from -90 to 0 rather than the voltage falling region. In this region, the condition for longitudinal focusing cannot be met, but the condition for focusing in the height direction can be met because when the voltage decreases with time, the influence on focusing in the height direction is small. The voltage of accelerator gap 2 is in the voltage rising interval from 0 to 90 degrees. The voltage rising interval meets the condition for longitudinal focusing but does not meet the condition for focusing in the height direction. However, because the voltage at 80 degrees is relatively high at this time, the higher the energy, the faster the particles rotate, and the faster the particles rotate, the smaller the defocusing influence on the height direction. On the contrary, if the particles rotate slowly or the energy of the particles is relatively low, the defocusing influence on the height direction will be large. In short, because focusing in the height direction is achieved at the first acceleration gap, and the condition for longitudinal focusing is met at the second acceleration gap, and at the same time, the influence on focusing in the height direction is very small. Therefore, the longitudinal focusing achieved by the positive phase method can provide longitudinal focusing force while avoiding defocusing in the height direction.

[0091] Second, the longitudinal focusing achieved by the positive phase method eliminates the energy difference where the phase width is compressed to the minimum. ① The prerequisite for longitudinal compression is that the energy gain of the beam tail is small and the energy gain of the beam head is large, so that the tail moves in a small circle and the head moves in a large circle. The reason why the energy gain of the beam tail is small and the energy gain of the beam head is large is that the voltage decreases with time. Suppose the radio frequency voltage is 60 kV when the beam head passes through point A. When the particles at the tail pass through point A, the radio frequency voltage has dropped to 50 kV. Therefore, the energy gain of the head is large and the energy gain of the tail is small. ② As Figure 6 shown, because the particles at the head have a large energy gain and move in a large circle. When reaching the radio frequency cavity 4, the dotted-line tail particles do not exceed 270 degrees relative to their own center point, while the solid-line head particles rotate by 270 degrees. It is equivalent to the head of the beam moving slowly and the tail of the beam moving fast. The fast in the front and the slow in the back achieve the compression of the phase width. That is, the phase width is compressed to the minimum at the radio frequency cavity 4. Therefore, the energy difference is eliminated by rotating the cavity 4 clockwise at the radio frequency cavity 4. ③ The reason for eliminating the energy difference at the radio frequency cavity 4 is that the particles at the beam tail do not move fast in each of the four quadrants 1, 2, 3, and 4. From Figure 6Look, it moves slowly at the tails in the 1st and 4th quadrants, and moves fast at the tails in the 2nd and 3rd quadrants. The beam in the front moves fast while the one in the back moves slow. In the 1st and 4th quadrants, it is equivalent to stretching the beam. Stretching the beam is not focusing but defocusing. It can be seen that if the energy difference is not eliminated at the RF cavity 4, the particles at the head of the beam in the four quadrants are: defocusing, focusing, focusing, defocusing, causing the particles in a circle in the current central region to be focused for half of the time and defocused for half of the time. When the energy difference is eliminated at the RF cavity 4, the energy gain of the head and the tail at the RF cavity 4 is the same, so the defocusing situation in the 4th quadrant will no longer occur.

[0092] 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 positive particle phase. As Figure 9 shown, its characteristics include the following steps:

[0093] Step 1: Divide the RF cavity into an RF cavity that generates energy difference and an RF cavity that eliminates energy difference; set that the energy gain of the beam head particles that reach the acceleration gap first is high, and the energy of the beam tail particles that reach the acceleration gap later is low.

[0094] Step 2: By counterclockwise adjusting the rotation angle of the head structure of the RF cavity that generates energy difference, make the particles at different longitudinal positions of the bunch present a certain energy difference; by clockwise adjusting the rotation angle of the head structure of the RF 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 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. This region with the smallest width is the region where the wide phase is compressed to the narrow phase.

[0095] The presented certain energy difference includes the energy difference in the monotonic case and the non-monotonic case; making the particles at different longitudinal positions of the bunch present a certain energy difference means that the particles at different positions of the head and the tail of the bunch corresponding to one RF cycle present a certain energy difference.

[0096] As Figure 6 shown, when counterclockwise adjusting the rotation angle of the beam head structure of the RF cavity that generates energy difference, the cavities that generate energy difference and eliminate energy difference are the RF cavity 1 and the RF cavity 4 respectively.

[0097] As Figure 7 shown, when setting the counterclockwise adjustment of the rotation angle of the beam head structure, rotate the RF cavities 1 and 4 that generate energy difference and eliminate energy difference counterclockwise by 90 degrees, and the cavities that generate energy gain and eliminate energy difference are the RF cavity 2 and the second turn position of the RF cavity 1 respectively.

[0098] As Figure 6 , 7 shown, when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise, since the particles at the head of the bunch have a higher energy gain than the particles at the tail of the bunch, the particles at the head of the bunch move in a larger circle relative to the center point of the accelerator, and the particles at the tail of the bunch move in a smaller circle relative to the center point of the accelerator: Let the radius of the particles moving in a larger circle at the head of the bunch relative to the center point of the accelerator be r1, and the radius of the particles moving in a smaller circle at the tail of the bunch be (1 - k)r1, where k < 1.

[0099] As Figure 6 shown; when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise, for the RF cavity 1 that generates energy difference, when the particles at the tail of the beam current rotate counterclockwise by 270 degrees from the RF cavity 1 to reach the RF cavity 4, in the third quadrant, the particles at the tail of the beam current do not reach 270 degrees relative to its own center (1 - k)r1, where k > 1, and the rotation angle of the particles at the head of the beam current relative to its own center point r1 is 270 degrees. At this time, the particles at the tail of the beam current move relatively fastest, while the particles at the head of the beam current move relatively slowest, thereby compressing the phase width to the minimum, and compressing the particles at the head and tail of the beam current from the non-receiving and non-accelerating regions of the current RF cycle to the intermediate receiving and accelerating regions, thereby increasing the longitudinal focusing force of the particles along the trajectory direction; at this time, the RF cavity 4 is used to eliminate the energy difference, and the RF cavity 4 is rotated clockwise by a set angle to eliminate the energy difference.

[0100] As Figure 7 shown; when setting the rotation angle of the head structure of the RF cavity to be adjusted counterclockwise, and using the RF cavity 2 as the cavity that generates energy difference, for the RF cavity 2 that generates energy difference, when the particles at the tail of the beam current rotate counterclockwise by 270 degrees from the RF cavity 2 to reach the second circle of the RF cavity 1, in the fourth quadrant, the particles at the tail of the beam current do not reach 270 degrees relative to its own center (1 - k)r1, where k < 1, and the rotation angle of the particles at the head of the beam current relative to its own center point r1 is 270 degrees. In the fourth quadrant, the particles at the tail of the beam current represented by the dotted line move relatively fastest, while the particles at the head of the beam current represented by the solid line move relatively slowest, thereby compressing the phase width to the minimum, thereby increasing the longitudinal focusing force of the particles along the trajectory direction; at this time, the RF cavity 1 is used as the cavity to eliminate the energy difference, and the position of the second circle where the beam current passes through the RF cavity 1 is rotated clockwise by a set angle to eliminate the energy difference.

[0101] Example 1: Achieving longitudinal focusing by using the positive phase adjustment method. As Figure 6 shown, achieving longitudinal focusing by the positive phase method is that the head region of the RF cavity 1 rotates counterclockwise, making the entire bunch reach the RF cavity 1 later, φ > 0, as Figure 3The range from 0° to 90°. At this time, the head of the bunch has the smallest φ and the highest energy gain; the tail of the bunch has the largest φ and the lowest energy gain. From Figure 5 it can be seen that near the angle of 270°, corresponding to the position of the radio frequency cavity 4, the particles with high energy at the head of the bunch rotate by the smallest angle, and the particles with low energy at the tail of the bunch rotate by the largest angle. The difference between the two reaches the minimum value, that is, the bunch is compressed to the smallest width. Adjust the position of the radio frequency cavity 4 and rotate it clockwise so that the bunch phase is located in Figure 3 the range from -90° to 0°. The particles at the head of the bunch obtain the lowest energy gain in the radio frequency cavity 4, and the highest at the tail. The phase of the central particles of the bunch at the radio frequency cavities 2 and 3 is set to 0°, without generating additional energy dispersion. After the bunch is accelerated through the radio frequency 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 tail.

[0102] Embodiment 2

[0103] As Figure 7 shown, for the way of positive phase to achieve longitudinal focusing, by modifying to rotate the head of the radio frequency cavity 2 counterclockwise and the head of the radio frequency cavity 4 clockwise, longitudinal focusing can be achieved. The lower the energy, the more significant the focusing effect.

[0104] 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. Those skilled in the art can make modifications to the above embodiments without creative contributions according to needs after reading this specification, but as long as they are within the scope of the claims of the present invention, they are protected by the patent law.

Claims

1. A method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of positive 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; it is set that the energy gain of the beam head particles that reach the acceleration gap first is high, and the energy of the beam tail particles that reach the acceleration gap later is low; Step 2: By counterclockwise 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 show a certain energy difference; by clockwise 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 of being received and accelerated in the middle, so as to improve 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 positive particles according to claim 1, wherein: The presenting a certain energy difference includes the energy difference in the monotonic case and the non-monotonic case; the 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.

3. The method for enhancing the longitudinal focusing force in the central region of an accelerator based on the phase of positive particles according to claim 2, wherein: When it is set to counterclockwise adjust the rotation angle of the beam head structure, the cavities that generate energy difference and eliminate energy difference are radio frequency cavity 1 and radio frequency cavity 4 respectively.

4. The method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of positive particles according to claim 3, wherein: When it is set to counterclockwise adjust the rotation angle of the beam head structure, rotate radio frequency cavity 1 and radio frequency cavity 4 that generate energy difference and eliminate energy difference counterclockwise by 90 degrees, and the cavities that generate energy gain and generate chromatic dispersion elimination are at the second turn positions of radio frequency cavity 2 and radio frequency cavity 1 respectively.

5. The method for improving the longitudinal focusing force in the central region of an accelerator based on the phase of positive particles according to claim 4, wherein: When it is set to counterclockwise adjust the rotation angle of the radio frequency cavity head structure, since the beam head particles have a higher energy gain than the beam tail particles, the beam head particles move in a large circle relative to the accelerator center point, and the beam tail particles move in a small circle relative to the accelerator center point: Let the radius of the particles of the beam head moving in a large circle relative to the accelerator center point be r1, and the radius of the particles of the beam tail moving in a small circle be (1 - k)r1, where k < 1.

6. A method for enhancing the longitudinal focusing force in the central region of an accelerator based on the phase of positive particles according to claim 5, characterized in that: When it is set to counterclockwise adjust the rotation angle of the radio frequency cavity head structure, for radio frequency cavity 1 that generates energy difference, when the particles at the beam tail rotate counterclockwise by 270 degrees from radio frequency cavity 1 to reach radio frequency cavity 4, in the third quadrant, the particles at the beam tail do not reach 270 degrees relative to its own center (1 - k)r1, where k > 1, and the rotation angle of the beam head relative to its own center point r1 is 270 degrees. At this time, the particles at the beam tail move relatively fastest, while the particles at the beam head move relatively slowest, so as to compress the phase width to the minimum, and compress the particles at the beam head and tail from the non-receiving and non-accelerating regions of the current radio frequency cycle to the middle region of being received and accelerated, so as to improve the longitudinal focusing force of the particles along the trajectory direction; At this time, radio frequency cavity 4 is used to eliminate energy difference, and radio frequency cavity 4 is rotated clockwise by a set angle to eliminate energy difference.

7. A method for enhancing the longitudinal focusing force in the central region of an accelerator based on the phase of positive particles according to claim 6, characterized in that: When setting the rotation angle of the head structure of the radio frequency cavity in the counterclockwise direction and using the radio frequency cavity 2 as the cavity for generating energy difference, for the radio frequency cavity 2 that generates energy difference, when the particles at the tail of the beam rotate counterclockwise by 270 degrees from the radio frequency cavity 2 to reach the second turn of the radio frequency cavity 1, in the fourth 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. The rotation angle of the head of the beam relative to its own center point r1 is 270 degrees. In the fourth quadrant, the particles at the tail of the beam represented by the dashed line move relatively fastest, while the particles at the head of the beam represented by the solid line move relatively slowest, thereby compressing the phase width to the minimum, and thus improving the longitudinal focusing force of the particles along the trajectory direction; At this time, the radio frequency cavity 1 is used as the cavity for eliminating energy difference, and the position of the second turn of the beam passing through the radio frequency cavity 1 is rotated clockwise by a set angle to eliminate the energy difference.

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