Tuning method of radio frequency quadrupole field accelerator cavity and medium
By using gravity error compensation and electric field tuning models, the problem of non-uniform electric field distribution within the cavity of the radio frequency quadrupole accelerator was solved, achieving precise cavity tuning and improving manufacturing accuracy and tuning effect.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-12
- Publication Date
- 2026-04-07
AI Technical Summary
In the manufacturing process of radio frequency quadrupole accelerator cavities, existing technologies suffer from processing errors that lead to asymmetry and non-uniformity in the electric field distribution within the cavity, affecting subsequent applications. Furthermore, existing cold measurement methods are subject to gravity errors, which affect tuning accuracy.
By obtaining the initial electric field distribution based on the perturbation, calculating the maximum sag for gravity error compensation, fitting the movement trajectory of the perturbation, and combining the catenary equation and boundary conditions, gravity error compensation is performed to obtain the correction measurement results. Precise tuning is then achieved through the electric field tuning model and frequency tuning.
The manufacturing precision of the radio frequency quadrupole accelerator cavity has been improved, the influence of gravity error has been reduced, and more accurate electric field and frequency tuning has been achieved to meet the needs of a wide range of applications.
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Figure CN121815535A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of accelerator technology and relates to a tuning method and medium for a radio frequency quadrupole accelerator cavity. Background Technology
[0002] The Radio Frequency Quadrupole (RFQ) accelerator is a compact, high-current, low-energy ion linear accelerator that cleverly utilizes a single radio frequency electric field to achieve lateral matching focusing, longitudinal matching beam focusing, and acceleration of the beam.
[0003] During the manufacturing process of RFQ accelerators, processing errors can lead to asymmetry and non-uniformity in the electric field distribution within the cavity, thus affecting subsequent applications. Therefore, manufacturers need to correct the resonant frequency and electric field distribution within the RFQ accelerator cavity through cold testing and tuning. A commonly used cold testing method is the perturbation method, which involves introducing a perturbation body into the RFQ accelerator cavity and moving it along the cavity axis. By measuring the frequency / phase shift caused by the perturbation body, the electric field distribution within the RFQ accelerator cavity can be measured. Tuning is then performed based on these measurements to correct the resonant frequency and electric field distribution within the RFQ accelerator cavity. Therefore, how to accurately tune the RFQ accelerator cavity is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0004] This application provides a tuning method and medium for a radio frequency quadrupole accelerator cavity, which solves the technical problem of how to accurately tune an RFQ accelerator cavity.
[0005] In a first aspect, this application provides a tuning method for a radio frequency quadrupole accelerator cavity, the method comprising:
[0006] Initial measurement results of the four-quadrant electric field distribution within the cavity of a radio frequency quadrupole accelerator were obtained based on perturbations.
[0007] Gravity error compensation is applied to the initial measurement results to obtain corrected measurement results;
[0008] Based on the calibration measurement results, the dipole field component and the quadrupole field component inside the radio frequency quadrupole accelerator cavity are obtained;
[0009] Based on the two-pole field component and the four-pole field component, it is determined whether the radio frequency quadrupole accelerator cavity meets the tuning target. If it does not meet the target, a tuning operation is performed until the tuning target is met.
[0010] In some embodiments of the first aspect of this application, the initial measurement results of obtaining the four-quadrant electric field distribution within the cavity of a radio frequency quadrupole accelerator based on a perturbation body include:
[0011] The perturbation quantity of the four-quadrant electric field is obtained based on the perturbation body;
[0012] The distribution of the four-quadrant electric field along the axial direction is obtained based on the perturbation as an initial measurement result; the axial direction is the particle acceleration direction inside the radio frequency quadrupole accelerator cavity.
[0013] In some embodiments of the first aspect of this application, the method further includes:
[0014] The perturbation body is placed at the starting point of movement in each quadrant electric field, and the perturbation body is moved along the axial direction to the ending point of movement in the quadrant electric field.
[0015] The phase change of the perturbation body at each axial position point during the movement process is measured, and the phase change is used as the perturbation quantity at the corresponding axial position point.
[0016] The distribution of the electric field along the axial direction of the corresponding quadrant is obtained based on the perturbation at each of the axial position points within each quadrant electric field.
[0017] In some embodiments of the first aspect of this application, gravity error compensation for the initial measurement results includes:
[0018] Calculate the maximum sag of the traction line during the movement of the perturbation; the traction line is suspended between the starting point and the ending point of the movement.
[0019] The movement trajectory of the perturbation is fitted based on the maximum sag and boundary conditions;
[0020] The electric field distribution of the moving trajectory is simulated based on the moving trajectory;
[0021] The change in gravity is obtained based on the electric field distribution of the moving trajectory;
[0022] The initial measurement results are compensated for gravity error based on the change in gravity to obtain the corrected measurement results.
[0023] In some embodiments of the first aspect of this application, calculating the maximum sag of the traction rope during the movement of the perturbation includes:
[0024] Obtain a tension-sag relationship model;
[0025] The maximum sag of the traction rope under a fixed tension is obtained based on the tension-sag relationship model.
[0026] In some embodiments of the first aspect of this application, fitting the movement trajectory of the perturbation body based on the maximum sag and boundary conditions includes:
[0027] The maximum droop point is determined based on the maximum droop amount;
[0028] An initial fitting curve is obtained based on the maximum droop point, the starting point of the movement, and the ending point of the movement of the perturbation.
[0029] The initial fitting curve is corrected based on the boundary conditions to obtain the movement trajectory of the perturbation; the boundary conditions include the length boundary and endplate boundary of the radio frequency quadrupole accelerator cavity.
[0030] In some embodiments of the first aspect of this application, obtaining the dipole field component and the quadrupole field component based on the calibration measurement result includes:
[0031] Based on the corrected measurement results, the average axial distribution of the four-quadrant electric field along the axial direction is obtained;
[0032] Obtain the average value of the average axial distribution;
[0033] The quadrupole field components are obtained based on the average axial distribution and the average value of the average axial distribution;
[0034] The second-order field components are obtained based on the corrected measurement results and the average axial distribution.
[0035] In some embodiments of the first aspect of this application, performing the tuning operation includes:
[0036] The first depth change corresponding to electric field tuning is calculated based on a pre-built electric field tuning model.
[0037] Calculate the second depth change corresponding to frequency tuning based on the current cavity frequency and the target tuning frequency;
[0038] The total depth change of the tuner is obtained based on the first depth change and the second depth change;
[0039] The tuning operation is performed based on the total depth change of the tuner.
[0040] In some embodiments of the first aspect of this application, calculating the change in the first depth of the tuner corresponding to electric field tuning based on a pre-built electric field tuning model includes:
[0041] The required inductance change of the tuner in the quadrant electric field is obtained based on the pre-built electric field tuning model.
[0042] The first depth is obtained based on the response relationship between the change in inductance and the change in tuner depth.
[0043] Secondly, this application provides a computer storage medium in which the computer program, when executed by a processor, implements the method described above.
[0044] As described above, the tuning method and medium for the radio frequency quadrupole accelerator cavity provided in this application have the following beneficial effects:
[0045] This application innovatively proposes a tension-sag relationship model to calculate the maximum sag of the traction wire. By fitting the actual motion trajectory of the perturbation body using the maximum sag and boundary conditions, it compensates for errors caused by gravity during cold testing, obtaining a more accurate electric field distribution within the RFQ accelerator cavity, thus enabling precise tuning. Furthermore, based on gravity-compensated errors, this application performs cavity electric field tuning and frequency tuning, achieving better tuning results, improving the manufacturing precision of the RFQ accelerator cavity, and meeting a wide range of application needs. Attached Figure Description
[0046] Figure 1 The diagram shows a flowchart illustrating the tuning method for a radio frequency quadrupole accelerator cavity provided in an embodiment of this application.
[0047] Figure 2 The diagram shown is a schematic representation of the process for gravity error compensation of the initial measurement results provided in an embodiment of this application.
[0048] Figure 3 The diagram shows the stress state of a micro-element of an elastic rope provided in an embodiment of this application.
[0049] Figure 4 The diagram shows the sag of the traction line with ceramic balls of different radii under different tensions, as provided in the embodiments of this application.
[0050] Figure 5 The diagram shown is a flowchart illustrating the process of fitting the movement trajectory of the micro-perturbation body based on the maximum droop amount, as provided in an embodiment of this application.
[0051] Figure 6 The diagram shows a comparison of the static trajectories of a 7m span traction line provided in this embodiment of the application under a tension of 20N, without a small ball and with a 5mm ceramic ball suspended in the middle of the rope.
[0052] Figure 7 The diagram shows a comparison of the electric field distribution before and after data smoothing, as provided in the embodiments of this application.
[0053] Figure 8a The diagram shown is a schematic diagram of the four-quadrant electric field distribution after gravity error compensation, provided in an embodiment of this application.
[0054] Figure 8b The diagram shown is a schematic representation of the four-quadrant electric field distribution without gravity error compensation, provided in an embodiment of this application.
[0055] Figure 9 The diagram shown is a flowchart illustrating the execution of a tuning operation as provided in an embodiment of this application.
[0056] Figure 10a The diagram shows the changes in the quadrupole field components during the tuning process provided in this embodiment of the application.
[0057] Figure 10b and Figure 10c The diagram shows the change of the diode field component during the tuning process provided in the embodiment of this application. Detailed Implementation
[0058] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.
[0059] It should be noted that in the following description, reference is made to the accompanying drawings, which illustrate several embodiments of this application. It should be understood that other embodiments may also be used, and changes in mechanical composition, structure, electrical system, and operation may be made without departing from the spirit and scope of this application. The following detailed description should not be considered limiting, and the scope of the embodiments of this application is defined only by the claims of the published patent. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application. Spatial terms such as “upper,” “lower,” “left,” “right,” “below,” “below,” “lower part,” “above,” “upper part,” etc., may be used herein to illustrate the relationship between one element or feature shown in the figures and another element or feature.
[0060] Furthermore, as used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context indicates otherwise. It should be further understood that the terms “comprising,” “including,” indicate the presence of the stated feature, operation, element, component, item, kind, and / or group, but do not preclude the presence, occurrence, or addition of one or more other features, operations, elements, components, items, kinds, and / or groups. The terms “or” and “and / or” as used herein are to be interpreted inclusively, or mean any one or any combination thereof.
[0061] The core of a radio frequency quadrupole accelerator (RFQ accelerator) lies in a special high-frequency oscillating electric field generated within its cavity. This electric field is generated by four precisely machined pole electrodes (usually wave-shaped or modulated) inside the cavity. In other words, the electric field distribution within the RFQ accelerator cavity actually includes the distribution of electric fields in four quadrants, and the purpose of tuning is to make the distribution of electric fields in the four quadrants uniform and symmetrical.
[0062] Before tuning, existing techniques often employ perturbation methods for cold testing to obtain the electric field distribution inside the RFQ accelerator cavity, and then perform tuning based on this. However, for long RFQ cavities, cold testing using perturbation methods often introduces gravity errors. This is because the perturbator and traction wire sag under gravity during movement, causing the perturbator's trajectory to deviate from the ideal path. The longer the cavity, the more pronounced the gravity effect, impacting the accuracy of cold testing and subsequent tuning performance.
[0063] To address the impact of gravity on cold measurements in long cavities, existing solutions typically fall into two categories. One approach involves allowing a perturbation body to slide along the electrode surface, constraining its trajectory with the electrodes to prevent sagging. This method has been used in cold measurements of long-cavity RFQs such as CMIF-RFQ (Compact Medium-current Ion injector Facility) and LEAF-RFQ (Low Energy Accelerator Facility with High intensityion beams). However, this method has drawbacks: the electrode surface is easily scratched by the perturbation body, and it requires a large perturbation body, potentially exceeding the linear response conditions of perturbation theory, thus affecting measurement accuracy. The other approach involves measuring the magnetic field distribution using a small metal sphere near the cavity of the RFQ. This method has been used in cold measurements of RFQs such as XiPAF (Xi'an Proton Accelerator Facility), but because the magnetic field distribution is insensitive to positional errors, this method often underestimates the actual electric field distribution error.
[0064] To at least address the aforementioned technical problems, this application proposes a tuning method and medium for a radio frequency quadrupole accelerator cavity, which can fit the actual motion trajectory of a perturbation body through gravity error compensation, thereby obtaining more accurate electric field distribution results and providing a solid foundation for tuning.
[0065] Figure 1 The diagram shows a flowchart illustrating the tuning method for a radio frequency quadrupole accelerator cavity provided in an embodiment of this application. Figure 1 As shown, the tuning method of the radio frequency quadrupole accelerator cavity includes steps S1 to S4.
[0066] S1. Initial measurement results of the four-quadrant electric field distribution within the cavity of the radio frequency quadrupole accelerator based on perturbation.
[0067] In some embodiments, obtaining the initial measurement result of the four-quadrant electric field distribution within the cavity of a radio frequency quadrupole accelerator based on the perturbation body includes: obtaining the perturbation amount of the four-quadrant electric field based on the perturbation body; and obtaining the axial distribution of the four-quadrant electric field based on the perturbation amount as the initial measurement result.
[0068] In some embodiments, the perturbation used includes tetrafluoroethylene microspheres, ceramic microspheres, metal microspheres, etc., and this application does not limit this.
[0069] Specifically, a perturbation body is placed at the starting point of movement in the electric field of each quadrant within the RFQ accelerator cavity, and the perturbation body is moved axially to the ending point of movement in the electric field of each quadrant; the phase change of the perturbation body at each axial position point during the movement is measured, and the phase change is used as the perturbation quantity at the corresponding axial position point; the distribution of the electric field along the axial direction of the corresponding quadrant is obtained based on the perturbation quantity at each axial position point in each quadrant electric field.
[0070] Here, the axial direction refers to the direction of particle acceleration within the RF quadrupole accelerator cavity. In other words, in RFQ, the axial direction refers to the direction along the central axis of the particle beam, which is the length direction of the RFQ cavity from the inlet to the outlet, and is usually represented by the coordinate z.
[0071] Using a small ball as a perturbation, taking quadrant 1 as an example, a fixed lateral position in quadrant 1 is designated as the endpoint of the movement. The ball is placed at this position, and then, using a traction line, it is moved at a constant speed along the axis (z-direction) of the RFQ accelerator from the starting point to the endpoint at the other end. In reality, for each axial position point during the movement, the perturbation will disturb the electromagnetic field at that point, causing a small shift Δφ in the resonant phase of the entire cavity of the RFQ accelerator. This phase change... The tangent of the electric field is proportional to the square of the electric field intensity at the axial position of the perturbation, |E1(z)|². This yields a curve showing the variation of Δφ with z. This curve directly reflects the distribution of the electric field intensity in quadrant 1 along the length of the RFQ at a fixed lateral position. By measuring the electric field distribution in the four quadrants, the initial measurement results of the electric field distribution in the four quadrants within the RFQ cavity can be obtained.
[0072] S2. Perform gravity error compensation on the initial measurement results to obtain corrected measurement results.
[0073] As mentioned earlier, during cold measurement using the perturbation method, errors in the trajectory can occur due to the gravity of the perturbation body and the traction wire, resulting in an erroneous electric field distribution. Therefore, this application compensates for gravity errors in the initial measurement results to obtain a corrected electric field distribution as the rectified measurement result. Figure 2 The diagram shown is a schematic representation of the process for compensating for gravity errors in the initial measurement results, as provided in an embodiment of this application. Figure 2 As shown, gravity error compensation for the initial measurement results includes steps S21 to S25.
[0074] S21. Calculate the maximum sag of the traction line during the movement of the micro-perturbation; the traction line is suspended between the starting point and the ending point of the movement.
[0075] In some embodiments, a tension-sag relationship model is obtained; based on the tension-sag relationship model, the maximum sag of the traction rope under a fixed tension is obtained.
[0076] In some embodiments, the traction line is considered as an elastic rope suspended between the starting point (0, 0) and the ending point (0, 0). Between 0 and 0, where Let W be the span of the catenary within the RFQ cavity. Assume the elastic rope has: weight W, original length L0, cross-sectional area A0, and elastic modulus E. Then, the sag model of the elastic rope can be abstracted as a catenary model with elastic force.
[0077] Let p be the coordinate of the arc length of the rope. According to the mechanical properties of continuous media, the elastic rope should satisfy the following constraints:
[0078] (1)
[0079] Furthermore, the force situation of the infinitesimal element of the elastic rope is as follows: Figure 3 As shown. Based on the force balance relationship, the force balance equations for the elastic rope in the x and y directions are as follows:
[0080] (2)
[0081] Where V is the vertical tension component at the starting point (s=0), H is the horizontal component, and s is the Lagrange coordinate of the rope. Then, according to the constitutive relation of elastic materials, there is tension... Elongation ratio of elastic rope The relationship is:
[0082] (3)
[0083] EA0 is the axial stiffness, which represents the rope's ability to resist axial tension.
[0084] Squaring both sides of equation (2) and substituting them into equation (1), we get:
[0085] (4)
[0086] Further transformation of equation (3) yields:
[0087] (5)
[0088] Substituting into equation (4) and integrating both sides, the displacement distribution of the elastic rope in the x-direction can be obtained as follows:
[0089] (6)
[0090] This formula is actually a linear superposition of the geometric deformation and elastic deformation of the elastic rope. Further derivation yields:
[0091] (7)
[0092] Similarly, the displacement distribution of the elastic rope in the y-direction can be obtained as follows:
[0093] (8)
[0094] According to boundary conditions , This allows us to solve for the equation of the elastic catenary. When the rope has no elastic force, the elastic modulus E is infinite, and the equation degenerates into the classic catenary equation.
[0095] However, when a perturbation is suspended on the elastic rope, the derivative of the tension T at the load point is discontinuous, so the expressions of equations (7) and (8) cannot be directly extended to the case of an elastic rope with a load. Therefore, to solve the problem of a catenary with a load in the middle, it is necessary to divide the rope into two segments with the load point as the boundary, apply the original equation (Equation 8) separately to each segment, and add the connection condition of the load point in the middle.
[0096] When the rope is loaded in the middle, the midpoint of the catenary is the point of maximum sag. At this point, the left and right halves of the rope are symmetrical and experience the same force conditions. Therefore, the following example only analyzes the left half. Let the weight of the perturbation be G. ball After introducing a perturbation load, it can be assumed that the perturbation introduces an additional vertical force on the elastic rope. Therefore, analyzing the left half, the force balance condition for the left half is transformed into:
[0097] (9)
[0098] The tension in the left half can then be obtained as:
[0099] (10)
[0100] Since the maximum sag occurs at the midpoint of the catenary, according to the constraints... S0 can be solved:
[0101] (11)
[0102] Then the sag at the middle of the elastic rope can be calculated. Represented as:
[0103] (12)
[0104] Furthermore, if equation (12) is used as the tension-sag relationship model, then when the tension is fixed, the sag of the middle part of the traction line can be obtained according to the tension-sag relationship model, which is the maximum sag of the traction line under a fixed tension.
[0105] Figure 4 The diagram shows the sag of the traction wire containing ceramic balls of different radii under different tensions, as provided in the embodiments of this application. Figure 4 As shown, when the ball is located at the center of the traction line, the sag of the traction line gradually decreases as the tension T increases. Furthermore, under the same tension error, the greater the tension, the smaller the sag error (i.e., the gradient decreases as the tension increases). In actual testing, the tension T of the traction line has a significant impact on the measurement process: a large tension causes the fixed pulley to experience a large lateral force, leading to eccentric rotation and unstable motion of the perturbation; conversely, too small a tension results in excessive sag, increasing the compensation error accordingly. Therefore, in some embodiments, a traction line tension of 20N-25N can be selected for actual cold testing of the RFQ cavity.
[0106] S22. Fit the movement trajectory of the perturbation body based on the maximum droop and boundary conditions.
[0107] Figure 5 The diagram shown is a flowchart illustrating the process of fitting the movement trajectory of the micro-perturbation body based on the maximum droop amount, as provided in an embodiment of this application. Figure 5 As shown, fitting the movement trajectory of the micro-perturbation body based on the maximum droop includes steps S221 to S223.
[0108] S221. Determine the maximum droop point based on the maximum droop amount.
[0109] As mentioned above, according to formula (12), the sag in the middle of the rope should be the maximum sag, and the midpoint of the rope is the maximum sag point.
[0110] S222. Obtain an initial fitting curve based on the maximum droop point, the starting point of the movement, and the ending point of the movement of the micro-perturbation.
[0111] In some embodiments, the starting point of movement is set to point A, the maximum downward point to point B, and the ending point to point C, with a distance of 7m between points A and C. To completely determine the trajectory of the perturbation, it is necessary to solve the force balance equations at each point during the ball's motion. However, in CST (CST Studio Suite), overly complex equations cannot be introduced during calculation. To simplify the calculation, this application uses the catenary equation combined with the coordinates of points A, B, and C to fit the ball's trajectory to obtain an initial fitting curve. The fitting equation is:
[0112] (13)
[0113] Figure 6 This diagram illustrates a comparison of the static trajectories of a 7m span traction line provided in this application under a tension of 20N, without a small ball and with a 5mm ceramic ball suspended in the middle of the rope. Figure 6 As shown, the initial fitting curve fitted by equation (13) is as follows (e.g.) Figure 6 The solid green line in the image) and the static trajectory when a 5mm ceramic ball is suspended in the middle of the rope (e.g., the trajectory of the ball). Figure 6 The error (the red dashed line in the image) is less than 0.03 mm.
[0114] In some other embodiments, the same boundary conditions (S(0)=0, S( )=0,S( The trajectory of the ball is fitted by the parabolic equation (S0) to obtain the initial fitted curve. The curve fitted by the parabolic variance and the curve fitted by the catenary equation basically coincide.
[0115] S223. Based on the boundary conditions, the initial fitted curve is corrected to obtain the movement trajectory of the perturbation.
[0116] The boundary conditions include the length boundary of the radio frequency quadrupole accelerator cavity and the endplate boundary.
[0117] In some embodiments, since the cavity length is 5756.55 mm and the distance between points A and C at both ends of the traction line is 7 m, the initial fitting curve within the cavity fitted by the catenary equation (Equation 13) is only a part of the total catenary. Therefore, in order to ensure that the maximum sag point is located at the exact center of the cavity and that the intersection of the catenary and the end plate is 20 mm from the center of the electrode, it is necessary to further modify the initial fitting curve based on the length boundary of the cavity and the boundary of the end plate, and obtain the movement trajectory of the micro-perturbation through the catenary equation.
[0118] In some embodiments, the trajectory finally fitted by the catenary equation in CST-MWS is represented as:
[0119] (14)
[0120] Where t is a free parameter, taking values of to , Given the total length of the cavity, ensure that the equation of the catenary within the cavity is obtained.
[0121] S23. Simulate the electric field distribution of the moving trajectory based on the moving trajectory.
[0122] In some embodiments, the electric field on the trajectory described by equation (14) is simulated in CST. Due to the mesh generation, the CST calculation results contain noise, with the noise amplitude being approximately 4% of the signal amplitude. To reduce the impact of noise on the calculation results, the Loss smoothing method is used to smooth the data during the calculation. Taking quadrants 1 and 4 as examples, the electric field distribution data before and after smoothing are as follows: Figure 7 As shown.
[0123] S24. Obtain the change in gravity based on the electric field distribution of the moving trajectory.
[0124] In some embodiments, the electric field distribution of the moving trajectory obtained based on the moving trajectory simulation is denoted as E. seg Let E(z) be the electric field distribution of the non-drooping curve. We can calculate E... seg The change in electric field E(z) relative to the non-drooping curve is:
[0125] (15)
[0126] S25. Based on the change in gravity, perform gravity error compensation on the initial measurement result to obtain the corrected measurement result.
[0127] Let the initial measurement result be E. n (z), then based on the change in electric field By performing gravity error compensation on the initial measurement results, the corrected measurement results can be obtained as follows:
[0128] (16)
[0129] S3. Based on the calibration measurement results, obtain the dipole field component and the quadrupole field component inside the radio frequency quadrupole accelerator cavity.
[0130] To characterize the difference between the electric field distribution and the ideal situation, dipole voltage and quadrupole voltage are introduced to represent the lateral asymmetry and axial unevenness of the electric field distribution within the RFQ accelerator cavity, respectively. Obtaining the dipole and quadrupole voltage components based on the corrected measurement results includes: obtaining the average axial distribution of the average value of the four quadrant electric fields along the axial direction based on the corrected measurement results; obtaining the average value of the average axial distribution; obtaining the quadrupole voltage component based on the average axial distribution and its average value; and obtaining the second-order field component based on the corrected measurement results and the average axial distribution.
[0131] In some embodiments, the quadrupole field component is defined as:
[0132] (17)
[0133] in, It is a uniform axial distribution. This represents the average value of the average axial distribution.
[0134] The polar field component is defined as:
[0135] (18)
[0136] (19)
[0137] in, , , and Equation (18) represents the electric field distribution along the axial direction in quadrants 1-4. Equation (19) represents the polar component in the vertical direction (assuming quadrant 1 is at the top and quadrant 3 is at the bottom), and Equation (19) represents the polar component in the vertical direction (assuming quadrant 2 is at the top and quadrant 4 is at the bottom).
[0138] Figure 8a and Figure 8b The diagrams shown are schematic representations of the four-quadrant electric field distribution after gravity error compensation and without gravity error compensation, respectively, provided in the embodiments of this application. Figure 8a and Figure 8b As shown, after gravity error compensation, the maximum value of the dipolar field component decreased from 4% to 2%, and the quadrupole field component decreased from 4% to 2.5%, and there was no obvious separation in the four quadrants. Therefore, the gravity compensation can be considered appropriate.
[0139] S4. Based on the two-pole field component and the four-pole field component, determine whether the radio frequency four-pole accelerator cavity meets the tuning target. If it does not meet the target, perform a tuning operation until the tuning target is met.
[0140] In some embodiments, after calculating the dipole and quadrupole components based on equations (17) to (19) of the corrected electric field distribution, it can be determined whether the dipole and quadrupole components are within the target range. If they are not within the target range, it indicates that the electric field in the RFQ accelerator cavity has not yet reached the target uniform and symmetrical state, that is, the tuning target has not yet been achieved. Therefore, tuning operations still need to be performed until the tuning target is met.
[0141] Figure 9 The diagram shown is a flowchart illustrating the performance of a tuning operation as provided in an embodiment of this application. Figure 9 As shown, performing the tuning operation includes steps S41 to S44.
[0142] S41. Calculate the first depth change corresponding to electric field tuning based on the pre-built electric field tuning model.
[0143] In some embodiments, calculating the first depth change corresponding to electric field tuning based on a pre-built electric field tuning model includes: obtaining the inductance change required by the tuner in the quadrant electric field based on the pre-built electric field tuning model; and obtaining the first depth based on the response relationship between the inductance change and the tuner depth change.
[0144] In an RFQ accelerator, when measuring the electric field distribution using the perturbation method, the voltage of the perturbation can be expressed as:
[0145] (20)
[0146] in, It is the normalized, perturbation-free voltage of the lowest quadrupole mode of the RFQ accelerator. and These are the normalized unperturbed voltages for the nth-order quadrupole mode and the bipolar mode, respectively. Represents a four-pole mode unit vector. The unit vector representing the bipolar pattern in quadrant 1 and quadrant 3. The unit vector representing the two-quadrant and four-quadrant bipolar modes.
[0147] Furthermore, when n equals 0, When n>0, l is the length of the RFQ accelerator cavity.
[0148] Furthermore, , and Here are the mode mixing coefficients, representing the contributions of the higher-order quadrupole mode and the bipolar mode to the disturbance voltage of the operating mode, respectively:
[0149]
[0150]
[0151]
[0152] in, , , , This can be obtained by measuring the electric field distribution in the four quadrants, and at the same time satisfy .
[0153] in, This refers to the RF voltage amplitude (usually the peak voltage) on the four terminals of the RFQ accelerator. This is the nominal quadrupole field voltage. It refers to the voltage imbalance of the quadrupole field. and It refers to the imbalance of the diode field voltage.
[0154] Furthermore, according to perturbation theory, the mode mixing coefficients can also be expressed using unit-length capacitance and integral inductance:
[0155]
[0156]
[0157]
[0158] in, This represents the coupling between the RFQ quadrants. The cavity resonant angular frequency, The angular frequency of the nth order quadrupole mode; It is the angular frequency of the nth order bipolar mode; For capacitance error, This is the inductance error.
[0159] Assuming the undesirable electric field distribution after perturbation is caused by capacitance error, the capacitance error can be compensated by changing the tuner's insertion depth, i.e., introducing "inductance error". Based on this, an electric field tuning model can be constructed to obtain the inductance change that can compensate for the capacitance error.
[0160] In some embodiments, the capacitance error in the RFQ accelerator cavity is expressed as:
[0161]
[0162]
[0163]
[0164] in , and It refers to the harmonic number used. and These are the capacitance error coefficients for the four-pole and two-pole modes, respectively. The choice of harmonic number should ensure that the mode mixing coefficients... , and For n>( , and It doesn't matter at all.
[0165] Furthermore, the capacitance error coefficient and This means:
[0166]
[0167]
[0168] To eliminate capacitance error, the inductance distribution along the RFQ accelerator cavity axis should be as follows:
[0169]
[0170] As can be seen from equation (32), the inductance is a continuous function that varies with axial position, but the change in inductance can only be achieved by using a discrete tuner. Therefore, this application defines a function... as follows:
[0171]
[0172] Where a is the radius of the tuner, and z is the axial position point. Let be the axial position point where the t-th tuner is located. Therefore, the required inductance change for the t-th tuner in quadrant J is... It can be represented as:
[0173]
[0174] Equation (34) above is the electric field tuning model. By solving this model, the required inductance change of the tuner in the quadrant electric field can be obtained.
[0175] Furthermore, the change in inductance produced by each tuner The amount of change in the depth of the tuner insertion in response The response relationship between them is as follows:
[0176]
[0177] in The inductance sensitivity of the tuner can be obtained through experimental measurement or simulation.
[0178] Based on the response relationship between the inductance change and the tuner depth change, the first depth required for each tuner is obtained as follows:
[0179]
[0180] S42. Calculate the second depth change corresponding to frequency tuning based on the current cavity frequency and the target tuning frequency.
[0181] In addition to electric field tuning, this application introduces frequency tuning. Let the target frequency be f0 / kHz and the current cavity frequency be f / kHz, then the second depth change required for each tuner can be expressed as:
[0182]
[0183] Where d is the tuning coefficient of each tuner, obtained through actual measurement, and the average value of all tuning coefficients is taken in the calculation.
[0184] S43. Obtain the total depth change of the tuner based on the first depth change and the second depth change.
[0185] The total depth change required for each tuner is:
[0186]
[0187] S44. Perform the tuning operation based on the total depth change of the tuner.
[0188] The total depth change obtained according to equation (38) is used to adjust the t-th regulator in the limit J to perform the tuning operation.
[0189] Figure 10aThe diagram shows the changes in the quadrupole field components during the tuning process provided in this embodiment of the application. Figure 10b and Figure 10c The diagram shows the change of the diode field components during the tuning process provided in the embodiments of this application. Figures 10a to 10c As shown, this application is used to tune the RFQ accelerator cavity. Initially, the tuner insertion depth is 21 mm, the cavity frequency is 164.7567 MHz, the quadrupole field component is -1.77% to 2.16%, and the diode field component is -0.68% to 2.20%. After four tunings, the frequency is adjusted to 164.9682 MHz (target frequency is 164.95 MHz), the quadrupole field component is -0.68% to 1.15%, and the diode field component is -1.33% to 1.12%. It can be seen that this application can achieve better tuning results with fewer tuning iterations, ensuring that the electric field distribution and frequency of the RFQ accelerator cavity meet the tuning target.
[0190] This application uses the catenary equation to fit the motion curve of a small ball under the influence of gravity, thereby compensating for gravity errors. Actual measurements show that for a 5.8m long RFQ accelerator cavity, the uncompensated dipole field error reaches 4%, and the quadrupole field error reaches 4%. After gravity compensation, both the dipole and quadrupole field errors are less than 2.5%, and the normalized electric field distribution in the four quadrants does not show significant deviation. Therefore, the compensation amount can be considered appropriate, and the gravity compensation algorithm has achieved good results.
[0191] Furthermore, based on gravity compensation, this application develops an electric field tuning algorithm based on transmission line perturbation theory and incorporates frequency tuning functionality into the electric field tuning process. Applying this application, the dipole and quadrupole field components of the RFQ accelerator can be reduced to less than ±1.2% and the frequency error to less than 0.02MHz within four tuning operations, achieving excellent tuning results.
[0192] The scope of protection of the tuning method for the radio frequency quadrupole accelerator cavity described in this application is not limited to the order of steps listed in this embodiment. Any solution implemented by adding, subtracting, or replacing steps in the prior art based on the principles of this application is included within the scope of protection of this application.
[0193] This application also provides a computer-readable storage medium storing a computer program thereon, which, when called by a processor, implements the tuning method of the radio frequency quadrupole accelerator cavity provided in this application.
[0194] Computer-readable storage media can be tangible devices capable of holding and storing instructions used by an instruction execution device. Computer-readable storage media can be, for example, (but not limited to) electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, and mechanical encoding devices.
[0195] The computer-readable program represented herein can be downloaded from a computer-readable storage medium to various computing / processing devices, or downloaded via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network, to an external computer or external storage device. A network adapter card or network interface in each computing / processing device receives computer-readable program instructions from the network and forwards these instructions to the computer-readable storage medium in the respective computing / processing device.
[0196] The above embodiments are merely illustrative of the principles and effects of this application and are not intended to limit this application. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of this application. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this application should still be covered by the claims of this application.
Claims
1. A tuning method for a radio frequency quadrupole accelerator cavity, characterized in that, The method includes: Initial measurement results of the four-quadrant electric field distribution within the cavity of a radio frequency quadrupole accelerator were obtained based on perturbations. Gravity error compensation is applied to the initial measurement results to obtain corrected measurement results; Based on the calibration measurement results, the dipole field component and the quadrupole field component inside the radio frequency quadrupole accelerator cavity are obtained; Based on the two-pole field component and the four-pole field component, it is determined whether the radio frequency quadrupole accelerator cavity meets the tuning target. If it does not meet the target, a tuning operation is performed until the tuning target is met.
2. The tuning method for the radio frequency quadrupole accelerator cavity according to claim 1, characterized in that, The initial measurement results of obtaining the four-quadrant electric field distribution within the cavity of the radio frequency quadrupole accelerator based on perturbations include: The perturbation quantity of the four-quadrant electric field is obtained based on the perturbation body; The distribution of the four-quadrant electric field along the axial direction is obtained based on the perturbation as an initial measurement result; the axial direction is the particle acceleration direction inside the radio frequency quadrupole accelerator cavity.
3. The tuning method for the radio frequency quadrupole accelerator cavity according to claim 2, characterized in that, The method further includes: The perturbation body is placed at the starting point of movement in each quadrant electric field, and the perturbation body is moved along the axial direction to the ending point of movement in the quadrant electric field. The phase change of the perturbation body at each axial position point during the movement process is measured, and the phase change is used as the perturbation quantity at the corresponding axial position point. The distribution of the electric field along the axial direction of the corresponding quadrant is obtained based on the perturbation at each of the axial position points within each quadrant electric field.
4. The tuning method for the radio frequency quadrupole accelerator cavity according to claim 1, characterized in that, Gravity error compensation for the initial measurement results includes: Calculate the maximum sag of the traction line during the movement of the perturbation; the traction line is suspended between the starting point and the ending point of the movement. The movement trajectory of the perturbation is fitted based on the maximum sag and boundary conditions; The electric field distribution of the moving trajectory is simulated based on the moving trajectory; The change in gravity is obtained based on the electric field distribution of the moving trajectory; The initial measurement results are compensated for gravity error based on the change in gravity to obtain the corrected measurement results.
5. The tuning method for the radio frequency quadrupole accelerator cavity according to claim 4, characterized in that, The calculation of the maximum sag of the traction rope during the movement of the perturbation includes: Obtain a tension-sag relationship model; The maximum sag of the traction rope under a fixed tension is obtained based on the tension-sag relationship model.
6. The tuning method for the radio frequency quadrupole accelerator cavity according to claim 4, characterized in that, Fitting the movement trajectory of the perturbation body based on the maximum sag and boundary conditions includes: The maximum droop point is determined based on the maximum droop amount; An initial fitting curve is obtained based on the maximum droop point, the starting point of the movement, and the ending point of the movement of the perturbation. The initial fitting curve is corrected based on the boundary conditions to obtain the movement trajectory of the perturbation; the boundary conditions include the length boundary and endplate boundary of the radio frequency quadrupole accelerator cavity.
7. The tuning method for the radio frequency quadrupole accelerator cavity according to claim 1, characterized in that, The acquisition of the dipole and quadrupole components based on the calibration measurement results includes: Based on the corrected measurement results, the average axial distribution of the four-quadrant electric field along the axial direction is obtained; Obtain the average value of the average axial distribution; The quadrupole field components are obtained based on the average axial distribution and the average value of the average axial distribution; The second-order field components are obtained based on the corrected measurement results and the average axial distribution.
8. The tuning method for the radio frequency quadrupole accelerator cavity according to claim 1, characterized in that, Performing tuning operations includes: The first depth change corresponding to electric field tuning is calculated based on a pre-built electric field tuning model. Calculate the second depth change corresponding to frequency tuning based on the current cavity frequency and the target tuning frequency; The total depth change of the tuner is obtained based on the first depth change and the second depth change; The tuning operation is performed based on the total depth change of the tuner.
9. The tuning method for a radio frequency quadrupole accelerator cavity according to claim 8, characterized in that, The calculation of the first depth change of the tuner corresponding to electric field tuning based on the pre-built electric field tuning model includes: The required inductance change of the tuner in the quadrant electric field is obtained based on the pre-built electric field tuning model. The first depth is obtained based on the response relationship between the change in inductance and the change in tuner depth.
10. A computer storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 9.