Dual beam position measurement method and apparatus for a vacuum chamber

Abstract

The application provides a double-beam position measurement method and device suitable for a vacuum chamber, comprising: establishing an electrode response function according to actual boundaries of the vacuum chamber and arrangement parameters of induction electrodes based on a boundary element method; constructing a radio frequency vector superposition model of the double-beam under narrowband detection conditions based on the electrode response function; constructing an objective function for quantifying matching degrees of model signals and measured signals of each induction electrode; obtaining double-beam induction signals of eight induction electrodes as the measured signals; and minimizing and solving the objective function by using a weighted nonlinear least square method to obtain position parameters of the double-beam. The method and device can be used for circular vacuum chambers and non-circular symmetric vacuum chambers such as runway type vacuum chambers, can improve double-beam signal decoupling capability and position reconstruction precision, and can provide reliable position measurement input for a fast orbit feedback system near a collision point, and has good engineering application value.

Description

Technical Field

[0001] This invention relates to the fields of accelerator beam diagnostic technology and feedback control technology, and in particular to a dual-beam position measurement method and device suitable for vacuum chambers. Background Technology

[0002] In electron-positron colliders, the stability of the beam position near the collision point directly affects the collision brightness. To suppress orbital deviations at the collision point caused by ground vibrations, mechanical vibrations, and other disturbances, it is typically necessary to deploy high-precision, high-bandwidth beam position monitors near the collision point and use the measurement results in a fast orbital feedback system.

[0003] However, in some regions near the collision point, the electron beam and positron beam remain within the same shared beam tube segment, and they are not yet completely separated spatially. In this scenario, a conventional four-electrode BPM can only provide the mixed coupling response, making it difficult to simultaneously obtain the independent positions of the two beams. Therefore, it cannot directly meet the requirements for dual-beam feedback and collision state diagnosis.

[0004] Existing dual-beam position measurement schemes are mostly based on multi-electrode structures and typically establish analytical models under circular vacuum chamber conditions to realize the mapping relationship between electrode signals and beam positions. For circular or near-circular vacuum chambers, these analytical models have good applicability and ease of implementation.

[0005] However, in practical engineering, the vacuum chamber near the collision point is often limited by the magnet aperture, mechanical installation space, and beam channel layout, and often adopts a racetrack-shaped or other non-circular symmetrical cross-section. In this case, the relationship between electrode response and beam position is no longer suitable for directly using the analytical formula under circular boundary conditions, which can easily lead to problems such as increased model error, difficulty in decoupling the two beams, and decreased position reconstruction accuracy.

[0006] Furthermore, under narrowband detection conditions, the RF responses of the two beams on the same electrode are not a simple algebraic sum, but rather a vector superposition relationship related to the relative intensity, phase difference, and installation position of the two beams. In particular, when there is an installation deviation in the longitudinal distance between the BPM and the collision point, the phase difference will deviate from the design value, thereby further affecting the dual-beam position fitting results.

[0007] Therefore, it is necessary to propose a dual-beam position measurement method and device suitable for vacuum chambers to establish an electrode response model that matches the actual boundary, thereby achieving effective decoupling of the dual-beam signals and high-precision position reconstruction. It should be noted that the method is also applicable to circular vacuum chambers and can be verified by comparing the results with analytical models. Furthermore, in non-circular symmetrical vacuum chambers such as racetrack-shaped chambers, the method avoids the problem of directly applying circular analytical models, thus possessing greater engineering significance. Summary of the Invention

[0008] The purpose of this invention is to provide a dual-beam position measurement method and device suitable for vacuum chambers, in order to solve the problem that existing dual-beam position measurement schemes can use analytical models under circular vacuum chamber conditions, but it is difficult to directly establish an accurate response model under non-circular symmetrical vacuum chamber conditions such as runway-shaped chambers, thus affecting dual-beam decoupling and high-precision position reconstruction.

[0009] To achieve the above objectives, the present invention provides a dual-beam position measurement method suitable for vacuum chambers, comprising:

[0010] Step S1: Based on the boundary element method, establish the electrode response function according to the actual boundary of the vacuum chamber and the arrangement parameters of the sensing electrodes. The vacuum chamber is equipped with a BPM probe and the BPM probe has eight sensing electrodes.

[0011] Step S2: Based on the electrode response function, construct a dual-beam RF vector superposition model under narrowband detection conditions;

[0012] Step S3: Construct an objective function to quantify the degree of matching between the model signal and the measured signal of each sensing electrode;

[0013] Step S4: Acquire the dual-beam sensing signal from the eight sensing electrodes as the measured signal;

[0014] Step S5: Minimize the objective function using the weighted nonlinear least squares method to reconstruct the position parameters of the dual-beam stream.

[0015] The cross-section of the vacuum chamber is circular or a closed boundary with non-circular symmetry.

[0016] The eight induction electrodes are arranged in sections along the cross-sectional boundary of the vacuum chamber. Two electrodes are provided in the upper and lower regions of the cross-sectional boundary, and two electrodes are provided in the transition regions on both sides of the cross-sectional boundary.

[0017] Step S1 further includes: pre-calculating and storing the mapping relationship of the electrode response function, wherein the mapping relationship of the electrode response function includes a response function lookup table or a response function interpolation function.

[0018] Step S2 specifically includes:

[0019] Step S21: Define the parameter set to be determined, wherein the parameter set θ to be determined includes at least the first beam position (x,y) and the second beam position (u,v);

[0020] Step S22: Obtain the stored position of the first beam for the i-th sensing electrode pair. Second beam position Electrode response function , And calculate the induced signal components generated by the two beams on the i-th induction electrode;

[0021] Step S23: Construct a radio frequency vector superposition model based on the induced signal components generated by the two beams on the i-th induction electrode.

[0022] In the The induced signal component generated by the first beam on each sensing electrode The induced signal component generated by the second beam They are represented as follows:

[0023] ,

[0024] ,

[0025] in, and The relative signal intensity parameters of the two beams. and These are the positions of the first and second beams, respectively. and They are the first One sensing electrode is positioned relative to the first beam. Second beam position The electrode response function;

[0026] In the radio frequency vector superposition model, the first The amplitude of the model signal of each sensing electrode satisfy:

[0027] ,

[0028] in, The induced signal component generated by the first beam. The induced signal component generated by the second beam. For the two beams in the first The radio frequency phase difference at each sensing electrode.

[0029] objective function for:

[0030] ,

[0031] in, For the parameter set to be determined, For the first The noise parameters or weighting parameters of each sensing electrode channel. is the ordinal number of the sensing electrode. For the first The amplitude of the model signal of each sensing electrode. For the first The amplitude of the measured signal of each sensing electrode.

[0032] Step S1 further includes: obtaining the phase difference correction parameters, nominal orbit, and beam left and right order corresponding to the installation deviation of the sensing electrode;

[0033] Step S2 further includes: correcting the phase difference term in the dual-beam radio frequency vector superposition model according to the phase difference correction parameter;

[0034] Step S5 further includes: before minimizing the objective function, introducing corresponding constraints based on the nominal orbit and the left-right order of the beam.

[0035] On the other hand, the present invention provides a dual-beam position measurement device suitable for a vacuum chamber, comprising:

[0036] The BPM probe, equipped with eight sensing electrodes and placed in a vacuum chamber, is used to collect dual-beam sensing signals as measured signals.

[0037] The signal extraction structure is used to extract the dual-beam sensing signals from the eight sensing electrodes.

[0038] Narrowband detection module, used to extract the signal amplitude of the measured signal of each sensing electrode at a predetermined radio frequency;

[0039] The sampling module is used to digitally sample the measured signal to obtain the sampling result of the measured signal;

[0040] A parameter storage module is used to store the electrode response function;

[0041] The position reconstruction module is used to execute the dual-beam position measurement method for vacuum chambers described above based on the sampling results of the measured signal to obtain the position parameters of the dual beams;

[0042] The output module is used to output the position parameters of the dual beams.

[0043] The dual-beam position measurement device also includes a clock and trigger synchronization module.

[0044] Compared with the prior art, the method of the present invention has at least the following beneficial effects:

[0045] (1) The boundary element method is used to establish the electrode response function that matches the actual vacuum chamber boundary. It can be used for both circular vacuum chambers and non-circular symmetric vacuum chambers such as racetrack-shaped chambers, and has a wider range of applications.

[0046] (2) In the scenario of dual beams sharing a beam tube, by combining the radio frequency vector superposition model under narrow band detection conditions with the weighted nonlinear least squares solution method, the joint reconstruction of the independent positions of the two beams can be realized, which can improve the decoupling capability of the dual beam signals and the position reconstruction accuracy, and can provide reliable position measurement input for the fast track feedback system near the collision point.

[0047] (3) By calculating the response function offline and storing it in the form of a lookup table, interpolation function or equivalent fast mapping, both model accuracy and real-time online reconstruction can be taken into account.

[0048] (4) By introducing measures such as phase correction and initial value constraints, the accuracy, stability and engineering feasibility of position reconstruction can be improved;

[0049] (5) The output results can be directly used as the input of the fast track feedback system, which has good engineering application value. Attached Figure Description

[0050] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0051] Figure 1 A flowchart of a dual-beam position measurement method for a vacuum chamber provided in an embodiment of the present invention;

[0052] Figure 2 A schematic diagram showing the cross-section of a non-circular symmetrical vacuum chamber and the arrangement of the BPM probe with eight induction electrodes, provided for an embodiment of the present invention.

[0053] Figure 3 A schematic diagram showing the nominal orbital positions of the electron beam and positron beam in the cross-section of a vacuum chamber, provided for an embodiment of the present invention;

[0054] Figure 4 The graph showing the effect of phase error on the horizontal position reconstruction error of the dual-beam system is provided for the embodiments of the present invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the following embodiments are only for illustrating the present invention and are not intended to limit the scope of protection of the present invention.

[0056] This invention provides a dual-beam position measurement method and device suitable for vacuum chambers, used to measure the independent lateral positions of the electron and positron beams when they are in the same shared beam tube segment and not yet completely spatially separated. The following embodiments are described using the current design parameters of the shared beam tube segment of the Y-shaped vacuum chamber near the collision zone of the Super Taumon Device (STCF). In this preferred embodiment, the cross-section of the vacuum chamber adopts a racetrack-shaped non-circular symmetric closed boundary, with eight sensing electrodes arranged in sections along the boundary. The detection frequency is the accelerating radio frequency of 499.7 MHz, and position reconstruction employs a weighted nonlinear least squares solution method based on the boundary element method response function and a narrowband detection vector superposition model.

[0057] like Figure 1 As shown, a dual-beam position measurement method for vacuum chambers according to the present invention mainly includes the following steps:

[0058] Step S1: Based on the boundary element method, establish the electrode response function according to the actual boundary of the vacuum chamber and the arrangement parameters of the sensing electrodes. The vacuum chamber is equipped with a BPM probe and the BPM probe has eight sensing electrodes.

[0059] The individual beam position monitor (BPM) probe has eight sensing electrodes arranged along the cross-section of the vacuum chamber to jointly acquire dual-beam signals and measure position. Thus, the BPM probe can acquire dual-beam sensing signals, which are high-frequency coupled signals formed on each sensing electrode as the charged beam passes through the vacuum chamber. After conversion by the signal extraction structure and terminal load, these signals are expressed as radio frequency voltage signals. The generation mechanism is as follows: when the charged beam moves within the vacuum chamber, it excites mirror currents and electromagnetic field distributions related to the beam position at the chamber boundary and on the electrode surfaces. Each sensing electrode generates a corresponding output signal through coupling with the beam's electromagnetic field. Therefore, the amplitude of the output signals from different electrodes varies with the beam position and can be used for beam position measurement.

[0060] Step S1 may further include: pre-calculating and storing the mapping relationship of the electrode response functions, wherein the mapping relationship of the electrode response functions includes a response function lookup table, a response function interpolation function, or other fast mapping forms. This reduces the computational load of subsequent calculations and improves the real-time performance of online position reconstruction. Preferably, the electrode response functions are obtained offline using the actual boundary of the vacuum chamber and the actual arrangement parameters of the eight sensing electrodes as input, and the mapping relationship of the electrode response functions is stored in the parameter storage module to meet the real-time requirements of online position reconstruction.

[0061] In this embodiment, the cross-section of the vacuum chamber can be circular, racetrack-shaped, or other non-circular symmetric closed boundaries. The method of this invention is equally applicable under circular vacuum chamber conditions and can be verified by comparison with analytical model results. Under non-circular symmetric vacuum chamber conditions such as racetrack-shaped ones, this invention, through response modeling based on actual boundaries, avoids the model mismatch problem caused by directly applying analytical expressions for circular boundaries, thereby improving the accuracy and applicability of dual-beam position reconstruction.

[0062] Step S1 may further include: acquiring phase difference correction parameters, nominal orbit, and beam left-right sequence corresponding to the installation deviation of the sensing electrode. Therefore, in the subsequent position reconstruction process, phase difference correction, nominal orbit constraints, and beam left-right sequence constraints can be further introduced as needed to improve the position reconstruction speed and stability.

[0063] Among them, the phase difference correction parameter corr corresponds to the installation deviation of the sensing electrode. It is preferably determined based on the measured signal and the actual boundary conditions of the vacuum chamber during the beam debugging or calibration stage, and is used to correct the phase difference term in the RF vector superposition model when constructing the RF vector superposition model in step S2. The nominal orbit constraint is determined by the nominal orbit or reference orbit and is used as the initial value input for the joint solution in step S5; the left-right order constraint of the beam can be determined by the beam channel layout and the nominal relative position relationship of the two beams in the BPM cross section, and is introduced into the joint solution in step S5 by limiting the order relationship of the lateral position parameters of the two beams.

[0064] like Figure 2 As shown, in one embodiment of the present invention, eight sensing electrodes are arranged in sections along the cross-sectional boundary of the vacuum chamber. Two electrodes are provided in both the upper and lower regions of the cross-sectional boundary, and two electrodes are provided in the transition regions on both sides of the cross-sectional boundary. It should be noted that the center position, tilt angle, length, coverage area, and offset relative to the geometric center of the vacuum chamber of each electrode are not fixed, but can be adjusted and optimized according to the cross-sectional shape of the vacuum chamber, the nominal orbit positions of the two beams, the target sensitivity distribution, and the engineering installation space.

[0065] The optimization of the arrangement parameters of the eight sensing electrodes is to meet the following optimization objectives in dual-beam position measurement:

[0066] First, improve the response sensitivity of each electrode output to changes in the lateral position of the dual beams, so that when the beams undergo minute position changes, the detection signals of each channel can produce sufficiently distinguishable changes, thereby improving the position resolution.

[0067] Second, improve the response difference of the two beams on the eight electrodes to avoid the mixed signal of the two beams exhibiting too similar distribution characteristics in each channel, thereby enhancing the decoupling capability of the dual beam signals;

[0068] Third, reduce the correlation between the parameters to be determined during the location reconstruction process, improve the numerical conditions of the reconstruction model, and enhance the convergence, stability and noise resistance of the weighted nonlinear least squares solution.

[0069] Fourth, keep the signal amplitude distribution of the eight channels within a reasonable range to avoid the signal-to-noise ratio dropping due to some electrode signals being too weak, or the dynamic range being unevenly utilized due to some electrode signals being too strong.

[0070] Fifth, while meeting the above measurement performance requirements, engineering constraints such as the cross-sectional dimensions of the vacuum chamber, the layout of the beam channel, signal extraction, and mechanical installation space should also be taken into account.

[0071] In summary, the center position, tilt angle, length, coverage area, and offset relative to the geometric center of the vacuum chamber of each electrode can be adjusted and optimized to improve the position response sensitivity of the dual-beam system, enhance the distinguishability of the dual-beam signal, improve the stability during the solution process, and meet the optimization objectives of engineering feasibility.

[0072] Step S2: Based on the electrode response function, construct a radio frequency vector superposition model of dual beams under narrowband detection conditions;

[0073] The dual-beam RF vector superposition model includes the nonlinear relationship between the signals from the eight sensing electrodes and the position parameters, relative intensity parameters, and phase difference of the two beams.

[0074] Step S2 specifically includes:

[0075] Step S21: Define the set of parameters to be determined;

[0076] In this embodiment, the parameter set to be determined includes the first beam position (x, y) and the second beam position (u, v), and the relative signal strength parameters p and q of the two beams. Therefore, in this embodiment, the parameter set to be determined is θ = (x, y, u, v, p, q). In other embodiments, the parameter set to be determined θ includes at least the first beam position (x, y) and the second beam position (u, v).

[0077] In this invention, the relative signal strength parameters p and q are introduced into the position reconstruction model as unknown parameters to be solved jointly. They are used to characterize the relative intensity contributions of the first and second beams to the signals of each sensing electrode, without requiring them to be precisely given in advance before position reconstruction.

[0078] In this embodiment, in step S2, p and q together with the position parameters of the two beams constitute the parameter set to be determined, and in step S5, they are obtained by joint inversion using a weighted nonlinear least squares method based on the measured signals of the eight electrodes.

[0079] In other embodiments, the initial values ​​of p and q may be provided by the nominal beam current, beam current measurement results, or historical measurement results to improve the solution speed and stability.

[0080] Step S22: Obtain the stored position of the first beam for the i-th sensing electrode pair. Second beam position Electrode response function , And calculate the induced signal components generated by the two beams on the i-th induction electrode;

[0081] In a preferred embodiment, in the first The induced signal component generated by the first beam on each sensing electrode The induced signal component generated by the second beam They are represented as follows:

[0082] ,

[0083] ,

[0084] in, and The relative signal intensity parameters of the two beams are... and These are the positions of the first and second beams, respectively. and They are the first One sensing electrode is positioned relative to the first beam. Second beam position The electrode response function.

[0085] The electrode response function is preferably obtained offline by the boundary element method and stored in the parameter storage module in the form of a response function lookup table, response function interpolation function or other fast mapping to meet the real-time requirements of online position reconstruction.

[0086] Step S23: Construct a radio frequency vector superposition model based on the induced signal components generated by the two beams on the i-th induction electrode.

[0087] Considering the vector superposition characteristics of dual-beam RF signals under narrowband detection conditions, in the RF vector superposition model, the first... The amplitude of the model signal of each sensing electrode satisfy:

[0088] ,

[0089] in, The induced signal component generated by the first beam. The induced signal component generated by the second beam. For the two beams in the first The radio frequency phase difference at each sensing electrode, where i is the ordinal number of the sensing electrode.

[0090] In a preferred embodiment, the two beams are in the... Radio frequency phase difference at each sensing electrode for:

[0091] ,

[0092] in, To detect the angular frequency corresponding to the frequency, This represents the longitudinal distance between the sensing electrode and the collision point. It is the speed of light.

[0093] Preferably, if there is an installation deviation in the sensing electrode, a phase difference correction parameter needs to be introduced. The phase difference correction parameter is obtained by pre-calibration in step S1 and is used to correct the phase difference term in the dual-beam radio frequency vector superposition model during position reconstruction, so that the phase difference used in the position reconstruction model is closer to the actual effective phase difference of the system, thereby reducing the systematic position reconstruction error caused by phase mismatch.

[0094] Before step S2, preferably, an offline simulation is performed to establish a mapping relationship between the phase deviation and the dual-beam position reconstruction error. Specifically, this includes: during the offline simulation phase, with the nominal positions of the dual beams fixed, performing discrete scans of the phase deviation; for each scan value, the first... The actual value of the radio frequency phase difference at each sensing electrode is set as follows:

[0095]

[0096] in, The design value for the radio frequency phase difference between the two beams at the sensing electrode. This represents the potential phase deviation of the system. Based on the above... Eight corresponding sensing electrode signals are generated; subsequently, the uncorrected RF phase difference design value is still used during position reconstruction. We construct an objective function and minimize it to obtain the reconstructed positions of the dual beams. Then, we compare these reconstructed positions with the nominal positions of the dual beams to obtain the current phase deviation. The corresponding dual-beam position reconstruction error.

[0097] The offline established mapping relationship is used to characterize the influence of phase deviation on position reconstruction error and to provide a basis for the scanning range, changing trend and optimization direction of phase difference correction parameters in the subsequent calibration stage, rather than to directly correct the error of the reconstructed position result after the position reconstruction is completed.

[0098] Before step S2, the phase difference correction parameters are calibrated. Corr specifically includes: during the beam commissioning or calibration phase, based on measured signals, the potential phase deviation of the system in the dual-beam RF vector superposition model. Perform a scan and construct different Corresponding position error evaluation quantity , It is calculated based on the reconstructed and nominal positions of the electron and positron beams. When taking the minimum value, select the optimal value at that time. The phase difference correction parameter obtained from the final calibration corr and store.

[0099] Therefore, in the process of constructing the dual-beam radio frequency vector superposition model in step S2, the phase difference correction parameters obtained from calibration are called. Corr corrects the phase difference term in the dual-beam RF vector superposition model, matching the phase difference in the model with the actual effective phase difference of the system, thereby reducing the systematic position reconstruction error caused by phase mismatch. Thus, phase compensation can be achieved by combining offline established response patterns with measured signals without directly measuring the actual effective phase difference of the system.

[0100] Therefore, by combining the offline stored electrode response functions, a radio frequency vector superposition model is constructed on each sensing electrode to accurately characterize the generation law of the two-beam mixed signal. Step S3: Construct an objective function to quantify the degree of matching between the model signal and the measured signal of each sensing electrode;

[0101] In step S3, the objective function for:

[0102] ,

[0103] in, For the parameter set to be determined, For the first The noise parameters or weighting parameters of each sensing electrode channel. is the ordinal number of the sensing electrode. For the first The amplitude of the model signal of each sensing electrode. For the first The amplitude of the measured signal of each sensing electrode.

[0104] Step S4: Acquire the dual-beam sensing signal from the eight sensing electrodes as the measured signal;

[0105] Step S5: Minimize the objective function using the weighted nonlinear least squares method to reconstruct the position parameters of the dual-beam stream.

[0106] The position parameters of the dual-beam system are extracted from the optimal solution of the parameter set θ=(x,y,u,v,p,q), where x,y,u,v are output as independent position results for the electron and positron beams. This achieves position reconstruction.

[0107] Step S5 may further include: before minimizing the objective function, introducing corresponding constraints according to actual engineering needs, namely, introducing at least one of nominal orbit constraints and beam left-right order constraints, to improve reconstruction speed, stability, and measurement accuracy. Corresponding to the nominal orbit constraint: using the nominal orbit position of the beam as the initial value for the solution reduces the number of iterations in the nonlinear solution;

[0108] Corresponding to the left-right order constraint of the beam: Based on the beam layout of the collider, the left-right position order of the electron beam and positron beam is limited to avoid confusion in the solution results.

[0109] Based on the dual-beam position measurement method for vacuum chambers described above, the realized dual-beam position measurement device for vacuum chambers includes: a BPM probe with eight sensing electrodes, a signal extraction structure, a narrowband detection module, a sampling module, a parameter storage module, a position reconstruction module, and an output module.

[0110] The BPM probe, signal extraction structure, narrowband detection module, sampling module, parameter storage module, position reconstruction module, and output module are connected in sequence.

[0111] The BPM probe has eight sensing electrodes and is located in the common bundle tube section of the vacuum chamber to collect dual-beam sensing signals as measured signals.

[0112] The signal extraction structure is used to extract the dual-beam sensing signals from the eight sensing electrodes;

[0113] The narrowband detection module is used to extract the signal amplitude of the measured signal of each sensing electrode at a predetermined radio frequency;

[0114] The sampling module is used to digitally sample the measured signal, and the sampling result of the measured signal;

[0115] The parameter storage module is used to store the electrode response function (optionally, it also stores the phase difference correction parameter); the phase difference correction parameter is preferably determined based on the measured electrode signal and reference orbit conditions during the beam debugging or calibration stage;

[0116] The position reconstruction module is used to execute the dual-beam position measurement method for vacuum chambers described above based on the sampling results of the measured signal to obtain the position parameters of the dual beams;

[0117] The output module is used to output the position parameters of the dual beams.

[0118] The position reconstruction module includes a processor and a memory. The memory stores a program for performing dual-beam position reconstruction. When the program is executed by the processor, it implements the method described above.

[0119] The dual-beam position measurement device suitable for vacuum chambers may also include a clock and trigger synchronization module to provide a unified time reference for narrowband detection, sampling and position reconstruction processes.

[0120] The output module is connected to a fast orbital feedback system near the collision point and is used to take the dual-beam position measurement results as input to the feedback system.

[0121] Example 1: A dual-beam position measurement method suitable for vacuum chambers

[0122] In this embodiment, the dual-beam position measurement method of the present invention for vacuum chambers is implemented based on the current design parameters of the Super Taumon Device (STCF).

[0123] In step S1, as Figure 2 As shown, the vacuum chamber has a racetrack-shaped, non-circular, symmetrical cross-section, preferably 60 mm × 30 mm. Eight induction electrodes are arranged along the racetrack-shaped boundary, with two electrodes in the upper and lower regions and two electrodes in the two arc-shaped transition regions on each side. As a set of preferred arrangement parameters, the centers of the electrodes in the upper and lower regions are symmetrically positioned at ±11 mm relative to the geometric center of the vacuum chamber in the horizontal direction, and the centerlines of the electrodes in the arc-shaped transition regions on both sides are inclined at 22.5° relative to the horizontal axis. It should be noted that the above-mentioned electrode center positions, inclination angles, and lateral offsets are a set of preferred parameters applicable to the current design conditions of STCF and do not constitute a limitation on the scope of protection of this invention; the electrode arrangement parameters can be adjusted and optimized for different vacuum chamber cross-sections, nominal beam separation amounts, and engineering installation conditions.

[0124] like Figure 3 As shown, in this embodiment, the nominal orbital positions of the negative electron beam and the positron beam in the BPM cross-section are respectively and (Unit: mm), the horizontal separation of the two beams at the BPM position is 30 mm. The radio frequency signals from each electrode are fed into the narrowband detection module via a signal extraction structure, where narrowband detection is performed at 499.7 MHz. The detected signals are then sent to the sampling module for digital processing. The parameter storage module pre-stores a lookup table of response functions calculated offline using the boundary element method. The position reconstruction module establishes response models of the two beams on each sensing electrode based on the lookup table, and constructs the aforementioned objective function by combining the radio frequency vector superposition relationship. The independent position results of the electron beam and positron beam are then solved using a weighted nonlinear least squares method.

[0125] In this embodiment, the radio frequency phase difference between the two beams at the BPM position can be determined based on the longitudinal distance between the BPM and the collision point, and a phase difference correction parameter can be further introduced in step S2 to compensate for the influence of BPM installation error on the position reconstruction result.

[0126] After the position parameters of the dual beams are reconstructed in step S5, the position parameters reconstructed by the method of the present invention are evaluated using a performance evaluation method to verify whether the method and equipment of the present invention meet the engineering measurement requirements of the fast orbital feedback system near the collision point.

[0127] In this embodiment, 15 typical dual-beam migration scenarios shown in Table 1 are first selected for analysis. These scenarios are set around the nominal orbit position, and the positions of the two beams are perturbed in the horizontal and vertical directions to examine the position reconstruction performance and model sensitivity under different migration conditions.

[0128] Table 1: Typical Dual-Beam Migration Conditions

[0129]

[0130] In a preferred embodiment, taking the STCF design operating point parameters as an example, the relationship between the allowable orbital offset at the collision point, the BPM installation position, and the required measurement resolution is evaluated. Specifically, the BPM is installed at a position 500mm from the collision point, and considering the design constraint that the brightness loss at the collision point does not exceed 1%, the allowable relative vertical offset tolerance of the two beams at the collision point is taken as 5% of the vertical beam size at the collision point, i.e., 0.05. .

[0131] Under the linear approximation of beam action, the relative vertical offset of the two beams at the collision point This will cause a change in the vertical deflection angle of the beam:

[0132]

[0133] The positional change corresponding to this deflection angle at the BPM installation location is:

[0134]

[0135] Where L is the longitudinal distance between the BPM and the collision point. Therefore, the offset tolerance at the collision point can be converted into the positional change at the BPM installation location, resulting in a BPM resolution requirement of approximately 3.534 μm at that location, as shown in Table 2.

[0136] Table 2: BPM resolution requirements based on the vertical offset tolerance of STCF collision points

[0137]

[0138] In Table 2, E represents the beam energy. Indicates the vertical direction at the point of collision. function, This indicates the beam size in the vertical direction at the collision point. Indicates vertical beam parameters, This indicates the allowable vertical offset tolerance at the collision point. This represents the change in vertical deflection angle caused by the beam effect of the aforementioned vertical offset. This indicates the change in position caused by the deflection angle at the BPM installation location, which is also the minimum displacement that the BPM needs to resolve. The symbol above... "" indicates that the parameter is taken at the collision point, not by a multiplication sign.

[0139] Among them, the beam energy E and the vertical direction at the collision point function Beam size and vertical beam parameters It can be obtained from the design operating point parameters of STCF.

[0140] After obtaining the engineering resolution requirements, the theoretical resolution of the calculation system based on the position reconstruction model under typical operating conditions is further calculated in Table 1, with a signal-to-noise ratio of 70 dB. By analyzing the sensitivity of the signals of each detection channel to the parameters to be determined, the theoretical resolution capability of the dual-beam position reconstruction can be obtained, as shown in Table 3.

[0141] Table 3: Theoretical resolution of STCF dual-beam position reconstruction

[0142]

[0143] In Table 3, the numbers represent different dual-beam offset conditions; σ_p and σ_q represent the reconstruction uncertainties of the two beams relative to the signal strength parameters p and q, respectively; σ_x and σ_y represent the position reconstruction resolution of the first beam in the horizontal and vertical directions, respectively; σ_u and σ_v represent the position reconstruction resolution of the second beam in the horizontal and vertical directions, respectively. These parameters characterize the system's ability to resolve small changes in the position of the dual beams under a given signal-to-noise ratio. Their values ​​can be obtained through covariance analysis of the Jacobian matrix of the weighted nonlinear least squares reconstruction model, and the square root of the diagonal elements of the parameter covariance matrix is ​​taken as the theoretical resolution of each parameter to be determined.

[0144] As shown in Tables 2 and 3, under the 15 typical operating conditions analyzed, the theoretical resolution of the dual-beam lateral position obtained by the method and equipment of this invention is approximately 1.5–2.6 μm, which is better than the engineering resolution requirement of 3.534 μm shown in Table 2. This indicates that, under the conditions of the STCF design operating point and a signal-to-noise ratio of 70 dB, the scheme of this invention can meet the engineering application requirements for dual-beam position measurement and rapid orbit feedback near the collision point.

[0145] Furthermore, the positions, relative intensity ratios, and phase differences of the two beams can be scanned in a simulation environment to analyze the stability and error propagation patterns of the position reconstruction results under different operating conditions. The relevant analysis results can be used to guide BPM layout optimization, detection frequency selection, installation tolerance design, and phase calibration scheme development.

[0146] Since the output signals of the two beams under narrowband detection conditions satisfy the aforementioned RF vector superposition relationship, the longitudinal deviation between the actual installation position and the designed position of the BPM will cause the phase difference to deviate from the design value, thus affecting the dual-beam position reconstruction result. Therefore, in this embodiment, the actual phase difference after installation is expressed as:

[0147]

[0148] in, This is the design value for the radio frequency phase difference between the two beams at the sensing electrode. This represents the potential phase deviation of the system.

[0149] In this embodiment, in step S1, an electrode response function is established based on the actual boundary of the vacuum chamber and the arrangement parameters of the sensing electrodes. For the structural parameters used in this embodiment, the lateral offset of the electrode center is 11.0 mm, and the tilt angle of the electrode centerline in the arc transition region is 22.5°. Based on these parameters, the corresponding electrode response function for the eight electrodes is established.

[0150] In step S1, during the offline simulation phase, with the nominal positions of the dual beams fixed, the phase deviation is... Perform discrete scanning; for phase deviation Each scan value will be the first The actual value of the radio frequency phase difference at each sensing electrode Let the design value be the radio frequency phase difference between the two beams at the sensing electrode. Phase deviation The sum of the scan values ​​is used to generate signals for the corresponding eight sensing electrodes; then, the design value of the uncorrected radio frequency phase difference between the two beams at the sensing electrodes is used. The objective function is obtained by combining the signals from the eight sensing electrodes. The deviations of the reconstructed positions of the electron beam and positron beam in the horizontal direction relative to their respective nominal orbital positions are obtained by solving the problem. The mapping relationship between phase deviation and position reconstruction error can then be obtained. Figure 4 Simulation results show that, under the current electrode arrangement and detection conditions, the horizontal position reconstruction error of the dual-beam system exhibits a stable, approximately monotonic relationship with the phase deviation, indicating that the phase mismatch error in the system can be corrected using a one-dimensional phase scanning method. The offline simulation aims to establish the response law between phase deviation and position reconstruction error, and to provide a basis for the scanning range and inversion method of the compensated phase during actual calibration, rather than directly providing the final compensation value in the actual system.

[0151] During the beam commissioning or calibration phase, the compensation phase in the reconstructed model is scanned based on the measured signal, and a position error evaluation quantity is constructed. .

[0152] Preferably, the position error evaluation quantity is defined as the sum of the absolute values ​​of the reconstructed position errors of the electron beam and the positron beam:

[0153]

[0154] in, and These are the horizontal reconstruction positions of the electron beam and the positron beam, respectively. and These are the nominal horizontal positions of the electron beam and the positron beam, respectively.

[0155] When the position error evaluation quantity When taking the minimum value, select the corresponding optimal value. The phase difference correction parameter obtained from the final calibration The phase difference is then corr and stored. Thus, during the vector model construction process in step S2, the calibrated phase difference correction parameters can be called to match the phase difference in the reconstructed model with the actual effective phase difference of the system, thereby reducing the systematic position reconstruction error caused by phase mismatch. Phase compensation can be completed by combining the offline established response law with the measured signal without directly measuring the actual effective phase difference of the system.

[0156] Example 2: A dual-beam position measurement device suitable for vacuum chambers

[0157] The dual-beam position measurement device for vacuum chambers of the present invention includes: an eight-electrode BPM probe, a signal extraction structure, a narrowband detection module, a sampling module, a parameter storage module, a position reconstruction module, and an output module. The eight-electrode BPM probe is positioned in the common beam tube section of a Y-shaped vacuum chamber near the STCF collision zone and is used to acquire dual-beam induction signals. The signal extraction structure is used to extract the radio frequency signals from the eight induction electrodes. The narrowband detection module is used to extract the detection amplitude of each induction electrode at the target radio frequency. The sampling module is used to convert the detected analog signals into digital signals. The parameter storage module is used to store boundary element offline modeling results, response function lookup tables, phase difference correction parameters, channel compensation parameters, and configuration parameters required for the reconstruction algorithm. The position reconstruction module is used to perform dual-beam signal modeling, objective function construction, and nonlinear fitting solution based on the sampling results. The output module is used to output the dual-beam position results.

[0158] In this embodiment, the position reconstruction module is preferably implemented collaboratively by an FPGA and a CPU. The FPGA is used to perform multi-channel signal preprocessing, fast lookup table retrieval, and partial parallel computation, while the CPU is used to implement parameter management, fitting control, and result output. The parameter storage module preferably uses onboard memory or external high-speed memory to store lookup tables and calibration parameters. The output module can output the dual-beam position results to a host computer or feedback system via a digital communication interface.

[0159] In this embodiment, the device also includes a clock and trigger synchronization module, which provides a unified time reference for the narrowband detection, sampling, and position reconstruction processes, thereby ensuring that multi-channel detection signals are processed under the same conditions at the same time. The output module is preferably connected to a fast orbital feedback system near the STCF collision point, and is used to input the dual-beam position measurement results as the feedback system input.

[0160] In summary, the above embodiments based on the current design parameters of STCF demonstrate that the dual-beam position measurement method and device proposed in this invention can achieve effective decoupling of dual-beam signals, accurate reconstruction of independent positions, and reliable support for fast feedback systems under the condition of a shared beam tube section in a runway-shaped non-circular symmetric vacuum chamber.

[0161] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. Various variations can be made to the above embodiments of the present invention. All simple and equivalent changes and modifications made in accordance with the claims and description of this application fall within the protection scope of the claims of this patent. All aspects not described in detail in this invention are conventional technical content.

Claims

1. A dual-beam position measurement method suitable for vacuum chambers, characterized in that, include: Step S1: Based on the boundary element method, establish the electrode response function according to the actual boundary of the vacuum chamber and the arrangement parameters of the sensing electrodes. The vacuum chamber is equipped with a BPM probe and the BPM probe has eight sensing electrodes. Step S2: Based on the electrode response function, construct a radio frequency vector superposition model of dual beams under narrowband detection conditions; Step S3: Construct an objective function to quantify the degree of matching between the model signal and the measured signal of each sensing electrode; Step S4: Acquire the dual-beam sensing signal from the eight sensing electrodes as the measured signal; Step S5: Minimize the objective function using the weighted nonlinear least squares method to reconstruct the position parameters of the dual-beam stream; Step S2 specifically includes: Step S21: Define the parameter set to be determined, wherein the parameter set θ to be determined includes at least the first beam position (x,y) and the second beam position (u,v); Step S22: Obtain the stored position of the first beam for the i-th sensing electrode pair. Second beam position Electrode response function , And calculate the induced signal components generated by the two beams on the i-th induction electrode; Step S23: Construct a radio frequency vector superposition model based on the induced signal components generated by the two beams on the i-th induction electrode; In the The induced signal component generated by the first beam on each sensing electrode The induced signal component generated by the second beam They are represented as follows: ， ， in, and The relative signal intensity parameters of the two beams are... and These are the positions of the first and second beams, respectively. and They are the first One sensing electrode is positioned relative to the first beam. Second beam position The electrode response function; In the radio frequency vector superposition model, the first The amplitude of the model signal of each sensing electrode satisfy: ， in, The induced signal component generated by the first beam. The induced signal component generated by the second beam. For the two beams in the first The radio frequency phase difference at each sensing electrode is the ordinal number of the sensing electrode.

2. The dual-beam position measurement method for vacuum chambers according to claim 1, characterized in that, The cross-section of the vacuum chamber is circular or a closed boundary with non-circular symmetry.

3. The dual-beam position measurement method for vacuum chambers according to claim 1, characterized in that, The eight induction electrodes are arranged in sections along the cross-sectional boundary of the vacuum chamber. Two electrodes are provided in the upper and lower regions of the cross-sectional boundary, and two electrodes are provided in the transition regions on both sides of the cross-sectional boundary.

4. The dual-beam position measurement method for vacuum chambers according to claim 1, characterized in that, Step S1 further includes: pre-calculating and storing the mapping relationship of the electrode response function, wherein the mapping relationship of the electrode response function includes a response function lookup table or a response function interpolation function.

5. The dual-beam position measurement method for vacuum chambers according to claim 1, characterized in that, objective function for: ， in, For the parameter set to be determined, For the first The noise parameters or weighting parameters of each sensing electrode channel. is the ordinal number of the sensing electrode. For the first The amplitude of the model signal of each sensing electrode. For the first The amplitude of the measured signal of each sensing electrode.

6. The dual-beam position measurement method for vacuum chambers according to claim 1, characterized in that, Step S1 further includes: obtaining the phase difference correction parameters, nominal orbit, and beam left and right order corresponding to the installation deviation of the sensing electrode; Step S2 further includes: correcting the phase difference term in the radio frequency vector superposition model of the dual beams according to the phase difference correction parameter; Step S5 also includes: before minimizing the objective function, introducing corresponding constraints based on the nominal orbit and the left-right order of the beam.

7. A dual-beam position measurement device suitable for vacuum chambers, characterized in that, include: The BPM probe, equipped with eight sensing electrodes and placed in a vacuum chamber, is used to collect dual-beam sensing signals as measured signals. The signal extraction structure is used to extract the dual-beam sensing signals from the eight sensing electrodes. Narrowband detection module, used to extract the signal amplitude of the measured signal of each sensing electrode at a predetermined radio frequency; The sampling module is used to digitally sample the measured signal to obtain the sampling result of the measured signal; The parameter storage module is used to store the electrode response function; The position reconstruction module is used to execute the dual-beam position measurement method for vacuum chambers as described in any one of claims 1-6 based on the sampling results of the measured signal, and obtain the position parameters of the dual beams; The output module is used to output the position parameters of the dual beams.

8. The dual-beam position measuring device for a vacuum chamber according to claim 7, characterized in that, It also includes a clock and trigger synchronization module.

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