Online suppression method, device, equipment and medium for electromechanical coupling effect of radio frequency superconducting cavity

Abstract

The present invention discloses an online suppression method, device, equipment and medium for electromechanical coupling effect of radio frequency superconducting cavity, including obtaining the original cavity pressure of radio frequency superconducting cavity V c * and the original forward voltage V f * ; The original cavity pressure V c * and the original forward voltage V f * Perform calibration and normalization processing; select the normalized cavity pressure when electromechanical oscillation occurs V c and forward voltage V f Establish differential equations to calculate the dynamic detuning Δ of the RF superconducting cavity when electromechanical oscillation occurs f ; Based on normalized cavity pressure V c and dynamic detuning Δ f , use the system identification method to identify the transfer function of the mechanical mode of the RF superconducting cavity; establish the characteristic equation of the coupling system according to the transfer function of the mechanical mode of the cavity, the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller, and solve the characteristic equation to find the stability boundary under different parameter conditions; optimize the closed-loop control parameters according to the stability boundary to achieve online suppression of the electromechanical coupling effect.

Description

Technical Field

[0001] The present invention relates to an online suppression method, device, equipment and medium for a radio frequency superconducting cavity electromechanical coupling (Ponderomotive) effect, and relates to the field of particle accelerators. Background Art

[0002] RF superconducting cavities are very suitable for accelerating high average current beams in continuous wave (CW) or long pulse mode due to their low loss and high gradient advantages. In recent years, many major accelerator frontier projects under construction, preparation and planning at home and abroad have chosen RF superconducting technology as the preferred option. The operating bandwidth of RF superconducting cavities is usually limited to tens to hundreds of hertz. The extremely narrow bandwidth makes the cavity prone to failure when it is detuned by interference (such as mechanical vibration of an external vacuum pump). Therefore, each RF superconducting cavity must be equipped with a real-time digital RF low-level feedback control system (hereinafter referred to as the low-level system) to maintain its operational stability.

[0003] The electromechanical coupling effect is a physical phenomenon caused by the nonlinear detuned coupling between the RF field and the mechanical eigenmode of the RF superconducting cavity through the Lorentz force. In RF superconducting accelerators, especially heavy ion accelerators, the electromechanical coupling effect may cause monotonic instability of the RF field (i.e., a sudden drop or rise of the RF field), and may also cause oscillation instability of the RF field (i.e., RF field oscillation divergence). In addition, the electromechanical coupling oscillation of a single cavity often resonates with adjacent cavities, causing collective oscillation instability of multiple cavities, and then causing large-scale cavity failures. It can be seen that the electromechanical coupling effect is one of the main physical mechanisms leading to operational failures of RF superconducting cavities.

[0004] Internationally, advanced laboratories such as the Argonne National Laboratory (ANL) in the United States, the Canadian National Accelerator and Particle Research Center (TRIUMF), and the German Electron Synchrotron Radiation Facility (DESY) have successively constructed differential equation models to describe the electromechanical coupling effect and proposed preliminary stability criteria and other related theories. However, these studies still lack systematic work in experimental verification. Due to the complexity of the RF system itself, RF experts often rely on personal experience to deal with the electromechanical coupling effect in actual accelerator engineering, and it is difficult to effectively apply advanced theoretical knowledge to guide practice, so a unified research paradigm has not yet been formed.

[0005] In summary, the electromechanical coupling effect is one of the main causes of RF superconducting cavity failure. The existing theoretical framework has not yet formed a mature research paradigm in practice, which to some extent restricts its promotion and application in the field of particle accelerators. Summary of the invention

[0006] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, in view of the above problems, the purpose of the present invention is to provide an online suppression method, device, equipment and medium for the electromechanical coupling effect of a radio frequency superconducting cavity, which can alleviate and suppress radio frequency superconducting cavity failures caused by electromechanical oscillations by optimizing the control parameters of the closed-loop system.

[0007] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is:

[0008] In a first aspect, the present invention provides an online method for suppressing the electromechanical coupling effect of a radio frequency superconducting cavity, comprising: obtaining an original cavity pressure of the radio frequency superconducting cavity; V c * and the original forward voltage V f * ; The original cavity pressure V c * and the original forward voltage V f * Calibrate and normalize to get the normalized cavity pressure V c and forward voltage V f ; Screen out the normalized cavity pressure when electromechanical oscillation occurs V c and forward voltage V f , according to the normalized cavity pressure V c and forward voltage V f The differential equation is established and solved to obtain the dynamic detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation f ; Based on the normalized cavity pressure V c and dynamic detuning Δ f , using system identification method to identify the transfer function of the mechanical mode of the radio frequency superconducting cavity M ( s );According to the transfer function of the mechanical mode of the RF superconducting cavity M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ), solve the characteristic equation D ( s ) Find the stability boundary under different parameter conditions; optimize the closed-loop control parameters according to the stability boundary to achieve online suppression of the electromechanical coupling effect.

[0009] In one possible embodiment, the normalized cavity pressure when the electromechanical oscillation occurs is screened. V c and forward voltage V f , according to the normalized cavity pressure V c and forward voltage V f The differential equation is established and solved to obtain the dynamic detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation f ,include:

[0010] Filter out electromechanical oscillation faults from fault data and obtain the normalized cavity pressure when electromechanical oscillation occurs. V c and forward voltage V f ;

[0011] Normalized cavity pressure based on electromechanical oscillation V c and forward voltage V f Establish the cavity differential equation:

[0012] ;

[0013] in, t is the sampling time, Cavity pressure V c The differential of oh 0 is the cavity resonance frequency, oh h is the cavity half bandwidth, Δ oh is the dynamic cavity detuning, The beam current intensity is approximately 0. Generally, before the electromechanical oscillation occurs, the beam has been cut off because the RF field does not meet the beam index requirements. r / Q is the geometric factor of the cavity, Q E is the external quality factor, j is an imaginary unit;

[0014] Normalized cavity pressure V c and forward voltage V f Decompose it into real and imaginary parts:

[0015] ;

[0016] Defining parameters oh E = oh 0 / Q E Substituting into the cavity differential equation, we get:

[0017] ;

[0018] Separating the real and imaginary parts of the above equation yields:

[0019] ;

[0020] By Δ f and Give The relationship is: , and obtain the dynamic detuning Δ when the RF superconducting cavity generates electromechanical oscillation f .

[0021] In one possible embodiment, based on the normalized cavity pressure V c and dynamic detuning Δ f , using system identification method to identify the transfer function of the mechanical mode of the radio frequency superconducting cavity M ( s ), including: based on the normalized cavity pressure V c and dynamic detuning Δ f The input quantities for constructing the cavity mechanical mode model are Output ,in, E peak is the peak field amplitude of the RF superconducting cavity, Δ f LFD is the Lorenz detuning, Δ f 0 is the static detuning of the RF superconducting cavity, | V c | is the normalized cavity pressure V c The amplitude of the input and output u and y， Using the system identification method, the transfer function model of the cavity mechanical mode is obtained M ( s ).

[0022] In one possible embodiment, based on the input and output u and y， Using the system identification method, the transfer function model of the cavity mechanical mode is obtained M ( s ), the specific process is:

[0023] Mechanical Mode Transfer Function Model of Radio Frequency Superconducting Cavity M ( s ) has the structure:

[0024] ;

[0025] in, s is a complex frequency domain variable, N is the number of mechanical modes, oh k , Q k and M k Respectively k The frequency, quality factor and gain of the mechanical mode are unknown. The system identification method is used to identify the input and output data ( u , y ) Identify unknown parameters oh k , Q k and M k .

[0026] In a possible embodiment, according to the transfer function of the mechanical mode of the radio frequency superconducting cavity M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ), solve the characteristic equation D ( s ) Find the stability boundary under different parameter conditions. The specific process is: perform Laplace transform on the cavity differential equation to obtain the transfer function of the RF superconducting cavity; obtain the transfer function of the low-level system PI controller; based on the transfer function of the mechanical mode of the RF superconducting cavity M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s );

[0027] Solving equations D ( s )=0Find all the solutions of the characteristic equation, namely the characteristic roots, specifically: when the equation D ( s )=0 has M characteristic roots, denoted by l 1, l 2… l M , expressed as l 1= l 1I + jl 1Q , l 2= l 2I + jl2Q , l M = l MI + jl MQ , to keep the system stable, the real parts of all characteristic roots need to be less than 0, l Imax is the maximum value of the real part of all characteristic roots, that is:

[0028] ;

[0029] like l Imax <0, then the real parts of all characteristic roots are less than 0, indicating that the system is stable; if l Imax >0, then the real part of at least one characteristic root is greater than 0, indicating that the system is unstable.

[0030] In one possible embodiment, the closed-loop control parameters are optimized according to the stability boundary to achieve online suppression of the electromechanical coupling effect, that is, given the cavity and low-level feedback parameters, find out the corresponding l Imax , draw the stability curve. The specific process is: determine the cavity parameters; when the system works in open-loop mode, scan Δ h / h h and E peak , and obtain the stable region l Imax <0 and unstable region l Imax >0 boundary curve, called stability boundary; when the system works in closed-loop mode, under each set of low-level feedback control parameters, scanning Δ h / h h and E peak ,calculate l Imax And determine the stable region and the unstable region, and obtain the corresponding stability boundary, where E peak is the peak cavity field amplitude of the RF superconducting cavity, oh h is the cavity half bandwidth, Δ oh is the dynamic cavity detuning; after determining the stability boundary, according to the current RF superconducting cavity peak cavity field amplitude E peak The maximum detuning that may occur with the RF superconducting cavity is determined, and appropriate closed-loop parameters are selected to ensure that the closed-loop system always operates in a stable state.

[0031] In a second aspect, the present invention provides an online suppression device for electromechanical coupling effect of a radio frequency superconducting cavity, comprising:

[0032] A voltage acquisition unit is configured to obtain an original cavity pressure of the radio frequency superconducting cavity. V c * and the original forward voltage V f * ;

[0033] The data processing unit is configured to convert the original cavity pressure V c * and the original forward voltage V f * Calibrate and normalize to get the normalized cavity pressure V c and forward voltage V f ;

[0034] A dynamic detuning calculation unit is configured to screen out the normalized cavity pressure when electromechanical oscillation occurs. V c and forward voltage V f , according to the normalized cavity pressure V c and forward voltage V f The differential equation is established and solved to obtain the dynamic detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation f ;

[0035] The system identification unit is configured to identify the normalized cavity pressure based on the selected V c and dynamic detuning Δ f , using system identification method to identify the transfer function of the mechanical mode of the radio frequency superconducting cavity M ( s );

[0036] The characteristic equation solver is configured to calculate the transfer function of the mechanical mode of the RF superconducting cavity. M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ), solve the characteristic equation D ( s ) Find the stability boundary under different parameter conditions;

[0037] The parameter optimization unit is configured to optimize the closed-loop control parameters according to the stability boundary to achieve online suppression of the electromechanical coupling effect.

[0038] In a third aspect, the present invention also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, and the instructions are executed by the processor so that the processor can execute any one of the methods described.

[0039] In a fourth aspect, the present invention further provides a computer-readable storage medium storing one or more programs, wherein the one or more programs include computer instructions, and the computer instructions are used to enable a computer to execute any one of the methods described.

[0040] Since the present invention adopts the above technical scheme, it has the following characteristics: 1. When electromechanical coupling oscillation occurs in the radio frequency superconducting cavity, the present invention can combine the control system theory to establish a research paradigm for analyzing the electromechanical coupling effect. It can not only effectively alleviate and suppress the electromechanical coupling effect, but also provide a new way to analyze and suppress the electromechanical coupling effect for systematically studying the physical mechanism behind the electromechanical coupling oscillation phenomenon of the radio frequency superconducting cavity. 2. The present invention is entirely based on accelerator operation data, and there is no need to design special measurement experiments, so there is no need to occupy additional machine operation time. 3. The coupling system model constructed by the present invention can also be widely used in the study of accelerator radio frequency loops, covering the following fields: the coupling relationship between microphonics and electromechanical oscillations, the coupling relationship between tuners and electromechanical oscillations, and the design of model-based radio frequency field feedback controllers and tuner feedback controllers. 4. The present invention establishes a coupling system model by reading the radio frequency fault signal to suppress the electromechanical coupling effect, wherein the acquisition, down-conversion and IQ demodulation of the radio frequency signal can be completed by a general low-level system, and the suppression of electromechanical coupling oscillation is achieved by optimizing the low-level feedback parameters. The core data processing, system identification and model analysis can be deployed on a general host computer, and the above applications do not require additional hardware equipment. In summary, the present invention can be widely used in particle accelerators. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Throughout the accompanying drawings, the same reference numerals are used to represent the same components. In the accompanying drawings:

[0042] Figure 1 The figure is a signal processing flow chart of an embodiment of the present invention.

[0043] Figure 24 is a block diagram of an online suppression system for electromechanical coupling effect in an embodiment of the present invention.

[0044] FIG3 (a) shows the original cavity pressure in the embodiment of the present invention. V c * Calculate the normalized cavity pressure V c 3 (b) is a schematic diagram of the total detuning Δ in the embodiment of the present invention. f Calculate the Lorenz detuning Δ f LFD 3 (c) is a schematic diagram of the principle of calculating numerical differentials using the four-point central difference method in an embodiment of the present invention.

[0045] FIG4 (a) is a radio frequency superconducting cavity CM of CAFe2 in an embodiment of the present invention. 4-1 Typical waveform diagram when electromechanical coupling oscillation occurs. The upper figure shows the normalized cavity pressure amplitude | V c |, the figure below is the Lorenz detuning Δ f LFD ; FIG4(b) is a diagram showing the mechanical mode of the cavity obtained by using the system identification method based on the data in FIG4(a) in an embodiment of the present invention. M ( s ), where the upper and lower parts of Figure 4(b) correspond to M ( s )’s amplitude-frequency and phase-frequency characteristic curves.

[0046] FIG5(a) is a comparison of the electromechanical coupling oscillation events in FIG4(a) according to an embodiment of the present invention; FIG5(b) is a comparison of the electromechanical coupling oscillation events in the same RF superconducting cavity CM according to an embodiment of the present invention. 4-1 Model output and measured results for other different types of electromechanical coupling events.

[0047] FIG6 (a) is a system block diagram of an embodiment of the present invention in open-loop mode, including a mechanical mode model M ( s ) and cavity model H c ( s ); FIG6 (b) is a system block diagram of the closed-loop mode in an embodiment of the present invention, including a mechanical mode model M ( s ), cavity model H c ( s ) and LLRF controller K ( s ).

[0048] FIG. 7 (a) is a schematic diagram of the principle of scanning the stability boundary in an embodiment of the present invention; FIG. 7 (b) is a schematic diagram of the characteristic equation in the open-loop mode in an embodiment of the present invention. D ( s ) calculated, the gray part is the unstable area; FIG7 (c) is an embodiment of the present invention according to the characteristic equation in the closed-loop mode D ( s ) calculated, the gray part is the unstable area, and the unstable area gradually shrinks with the increase of the closed-loop gain; FIG7 (d) is an embodiment of the present invention according to the characteristic equation in the closed-loop mode D ( s ) calculated by adjusting the amplitude controller K A ( s ) and phase controller K P ( s ) to adjust the PI parameters to obtain different stability boundaries.

[0049] FIG8 (a) is a diagram showing a comparison of the cavity CM in the present invention in an embodiment of the present invention. 4-1 The measured stability boundary (black circle) in the closed-loop operation mode and the characteristic equation of the closed-loop mode D ( s ) calculated stable boundary (grey dotted line); Figure 8 (b) is a comparison of another cavity CM on the CAFe2 device in the embodiment of the present invention. 4-2 The measured stability boundary (black square) in the closed-loop operation mode and the characteristic equation of the closed-loop mode D ( s ) calculated stability boundary (grey dotted line).

[0050] FIG9 (a) is a diagram showing a comparison of the radio frequency superconducting cavity CM in the embodiment of the present invention. 4-1 The triggering frequency of electromechanical oscillation fault before and after optimizing the low-level feedback parameters. The gray part is the result before optimization, and the black part is the result after optimization. FIG9 (b) compares the RF superconducting cavity CM in the present invention with the embodiment of the present invention. 4-2 The triggering frequency of electromechanical oscillation fault before and after optimizing the low-level feedback parameters. The gray part is the result before optimization, and the black part is the result after optimization. DETAILED DESCRIPTION

[0051] It should be understood that the terms used herein are only for the purpose of describing specific example embodiments and are not intended to be limiting. Unless the context clearly indicates otherwise, the singular forms "one", "an" and "said" as used herein may also be meant to include plural forms. The terms "include", "comprise", "contain", and "have" are inclusive, and therefore specify the existence of stated features, steps, operations, elements and / or parts, but do not exclude the existence or addition of one or more other features, steps, operations, elements, parts, and / or combinations thereof. The method steps, processes, and operations described herein are not interpreted as necessarily requiring them to be performed in the specific order described or illustrated, unless the execution order is clearly indicated. It should also be understood that additional or alternative steps may be used.

[0052] Since the existing methods mainly rely on expert experience to deal with the electromechanical coupling failure of the radio frequency superconducting cavity, its theoretical framework has not yet formed a mature research paradigm in practice. The online suppression method, device, equipment and medium of the electromechanical coupling effect of the radio frequency superconducting cavity provided by the present invention include: obtaining the original cavity pressure of the radio frequency superconducting cavity V c * and the original forward voltage V f * ; The original cavity pressure V c * and the original forward voltage V f * Calibrate and normalize to get the normalized cavity pressure V c and forward voltage V f ; Screen out the normalized cavity pressure when electromechanical oscillation occurs V c and forward voltage V f , according to the normalized cavity pressure V c and forward voltage V f The differential equation is established and solved to obtain the dynamic detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation f ; Based on the normalized cavity pressure V c and dynamic detuning Δ f , using system identification method to identify the transfer function of the mechanical mode of the radio frequency superconducting cavity M ( s );According to the transfer function of the mechanical mode of the RF superconducting cavity M ( s), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ), solve the characteristic equation D ( s ) Find the stability boundary under different parameter conditions; optimize the closed-loop control parameters according to the stability boundary to achieve online suppression of the electromechanical coupling effect. Therefore, the present invention provides a method for suppressing and alleviating the electromechanical coupling effect without taking up additional machine running time.

[0053] The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0054] Embodiment 1: Figure 1 As shown, the online suppression method of the electromechanical coupling effect of the radio frequency superconducting cavity provided in this embodiment includes:

[0055] S1. Online measurement of the cavity sampling signal of the RF superconducting cavity P t , cavity incident signal P f and cavity reflection signal P r , to obtain the original cavity pressure of the RF superconducting cavity V c * , original forward voltage V f * and the original reverse voltage V r * .

[0056] In this embodiment, Figure 2 As shown, an online suppression system for the electromechanical coupling effect of a radio frequency superconducting cavity is provided, including a digital low-level system 1, a solid-state power source 2, a directional coupler 3, an input coupler 4, a radio frequency superconducting cavity 5, a signal extraction coupler 6, a down-conversion module 7 and a host computer 8. Among them, the output end of the digital low-level system 1 is connected to the input end of the solid-state power source 2, the output end of the solid-state power source 2 is connected to the input end of the directional coupler 3, the output end (through port) of the directional coupler 3 is fed into the radio frequency superconducting cavity 5 through the input coupler 4, and the directional coupler 3 is used to extract the cavity incident signal of the radio frequency superconducting cavity 5. P f and cavity reflection signal P rThe signal extraction coupler 6 is connected to the radio frequency superconducting cavity 5 to extract the cavity sampling signal P t , cavity incident signal P f , cavity reflection signal P r and cavity sampling signal P t After down-conversion by down-conversion module 7, it is sent to digital low-level system 1. Digital low-level system 1 is based on cavity incident signal P f , cavity reflection signal P r and cavity sampling signal P t The corresponding digitized baseband in-phase and quadrature (I / Q) components are demodulated and uploaded to the host computer 8 via the data bus.

[0057] Furthermore, the digital low-level system 1 is provided with an FPGA (field programmable gate array), and the FPGA is provided with a digital signal processing module, which samples the cavity signal of the radio frequency superconducting cavity. P t , cavity incident signal P f and reflected signal P r Processing is performed to obtain the corresponding three-way original voltage signals, including the original cavity pressure V c * , original forward voltage V f * and the original reverse voltage V r * .

[0058] It should be noted that the parameters involved in this embodiment, such as V c * , V f * , V r * , V c , V c,ss * 、V f and etc. are all in complex form, which can be expressed in the form of amplitude and phase, for example: V =| V |e j∠V , where | V | is the amplitude or modulus, ∠ V is the phase or argument; it can also be expressed as the real part plus the imaginary part, for example: V = V I + jV Q ,in, V I is the real part or the in-phase component, V Q is the imaginary part or called the orthogonal component.

[0059] S2, the original cavity pressure V c * and forward voltage V f * Calibrate and normalize to get the normalized cavity pressure V c and forward voltage V f .

[0060] In this embodiment, the original cavity pressure V c * and forward voltage V f * You can use the formula: V f, cali = XV f * Get the forward voltage after calibration V f, cali , where the correction factor X is a complex number, which can be expressed as amplitude and phase (i.e. X =| X | e j∠X ) can also be expressed as the real part plus the imaginary part (i.e. X = X I + jX Q ) is not limited here.

[0061] Furthermore, as shown in Figure 3(a) and Figure 3(b), the original cavity pressure is calculated V c * The signal runs at the steady-state signal average value when no electromechanical coupling fault occurs to obtain the normalization coefficient V c, ss* , and use V c = V c * / V c, ss * Normalized cavity pressure V c Similarly, to ensure signal consistency, the forward voltage after calibration must be V f, cali Perform the exact same scaling to get the normalized forward voltage V f ,Right now V f = V f, cali / V c, ss * Generally speaking, P t represents the radio frequency signal, V c It means that the digitized baseband signal has no RF frequency components.

[0062] S3. Screen the fault data obtained by online measurement. When it is judged to be an electromechanical oscillation fault, the normalized cavity pressure during the electromechanical oscillation is used to determine the fault. V c and forward voltage V f Establish the cavity differential equation and calculate the dynamic detuning Δ of the RF superconducting cavity f .

[0063] In this embodiment, the specific implementation of the above process is as follows:

[0064] S31. Screen out the electromechanical oscillation fault from the fault data. The process is as follows:

[0065] As shown in Figure 4 (a), when the RF superconducting cavity undergoes electromechanical oscillation, its cavity pressure amplitude will oscillate violently. Usually, electromechanical oscillation will cause the cavity pressure amplitude to change by more than 10%, that is, the normalized cavity pressure amplitude | V c | will drop below 0.9. In addition, the cavity pressure amplitude | V c |The frequency spectrum of the oscillation signal can be obtained by taking FFT (Fast Fourier Transform). Since electromechanical oscillation occurs at several fixed frequency points, such as 120 Hz (corresponding to the higher peak in the figure) and 280 Hz (corresponding to the lower peak in the figure) in Figure 4 (b), the electromechanical coupling fault can be screened out from the fault data based on the above two principles.

[0066] S32, based on normalized cavity pressure V c and forward voltage V f The cavity differential equation is established as follows:

[0067] ;

[0068] in, Cavity pressure V c The differential of oh 0 is the cavity resonance frequency, oh h is the cavity half bandwidth, Δ oh is the dynamic cavity detuning, oh 0. oh h and Give The units are all radians per second. is the beam current intensity, parameter r / Q is the geometric factor of the cavity, which only depends on the shape of the cavity and is generally a constant. Q E is the external quality factor, which is related to the unloaded quality factor of the cavity Q 0. Load quality factor Q L The relationship between them is as follows:

[0069] .

[0070] Since the superconducting heavy ion accelerator device CAFE2 in this embodiment is a weak current accelerator, its beam current intensity is in the microampere level, that is, I b ( t )≈0. In this case, the influence of the beam on the cavity field (commonly known as the number loading effect) can be ignored. On the other hand, before the electromechanical oscillation occurs, the beam has been cut off because the RF field no longer meets the beam index requirements. Therefore, in this embodiment, the above formula is further modified to:

[0071] .

[0072] S33, normalized cavity pressure V c and forward voltage V f According to the real and imaginary parts, it is decomposed into I + jQ " is in the following form:

[0073] ;

[0074] Defining parameters oh E = oh 0 / Q E Substituting into the cavity differential equation, we get:

[0075] .

[0076] S34. Separate the real and imaginary parts of the above formula to obtain:

[0077] .

[0078] S35, oh h With Δ oh As an unknown variable, and other physical quantities as coefficients, solve the above two-variable linear equation to get:

[0079] .

[0080] S36, based on Δ f With Δ oh The relationship Δ f The solution.

[0081] In this embodiment, f 0. f h With Δ f It is also used to express the resonant frequency, half bandwidth, and detuning of a cavity, but they are not related to oh 0. oh h and Give The units are different. f 0. f h With Δ f The units of are all Hertz, and the corresponding relationships of the above physical quantities are as follows:

[0082] .

[0083] S4, according to the normalized cavity pressure V c and cavity dynamic detuning Δ f , the transfer function of the cavity mechanical mode is obtained by system identification method M ( s ).

[0084] In this embodiment, according to the normalized cavity pressure V c and cavity dynamic detuning Δ f , realize the cavity mechanical mode transfer function model M ( s ) including:

[0085] S41. Establish the input and output time series data required to complete the system identification.

[0086] In this embodiment, based on the normalized cavity pressure V c and dynamic detuning Δ f , respectively construct the input of the cavity mechanical mode model Output ,in, E peak is the peak field amplitude of the RF superconducting cavity, Δ f LFD is the Lorenz detuning, Δ f 0 is the static detuning of the RF superconducting cavity.

[0087] Furthermore, system identification generally requires deducting the steady-state part from the input and output data. f Deduct the steady-state part Δ f 0 (i.e. static detuning), we get the Lorenz detuning Δ f LFD As shown in Figure 3(b), the static detuning part Δ f 0 can be calculated by the steady-state time t 1 and t 2 Moment Δ f The average value is obtained. f LFD The unknown model M ( s ) output y , as shown in the lower figure of Figure 4 (a), the measured Δ f LFD result.

[0088] Normalized cavity pressure V c Convert it into field strength data, and square the two to get the unknown model M ( s ) u . Similarly, you need to | V c | 2 After deducting the steady-state part, due to V c It has been normalized to 1, and its steady-state part is 1, as shown in Figure 4(a).

[0089] S42, based on input and output u and y， Using modern system identification methods, the transfer function model of the cavity mechanical mode is obtained M ( s ), the specific process is:

[0090] Mechanical Mode Transfer Function Model of Radio Frequency Superconducting Cavity M ( s ) generally has a known structure as follows:

[0091] .

[0092] in, s is a complex frequency domain variable, usually expressed as s =Δ s + yes ,in, s is the real part, usually expressed as an attenuation factor, representing the attenuation or growth of the control signal. oh is the imaginary part, which represents the angular frequency and the oscillation frequency of the signal. j Is an imaginary unit. N is the number of mechanical modes. oh k , Q k and M k Respectively k The frequency, quality factor and gain of each mechanical mode are unknown. Using the existing system identification method, the input and output data ( u , y ) Identify unknown parameters oh k , Q k and M k . Because the object to be identified M ( s ) is known, here we can directly use the gray box identification model greyest method provided by Matlab system identification toolbox to identify the unknown parameters oh k , Q k and M k As shown in Figure 4 (b), when the above parameters are known, the mechanical mode transfer function model of the RF superconducting cavity can be obtained: M ( s ).

[0093] S5. Transfer function based on the cavity mechanical mode M ( s ), RF superconducting cavity H c ( s ) and low-level feedback controller models K ( s), establish the characteristic equations in open-loop and closed-loop modes D ( s ), solve the equation D ( s )=0, we get the characteristic root (i.e., the equation D ( s )=0), when the real part of the characteristic root is negative, the system is stable. Based on this, the stable boundary of the cavity under different parameters is drawn, that is, the boundary where the electromechanical coupling effect occurs and the boundary where the electromechanical coupling effect does not occur.

[0094] In this embodiment, based on the mechanical mode transfer function model of the radio frequency superconducting cavity M ( s ), the transfer function of the RF superconducting cavity H c ( s ) and the low-level system controller transfer function K ( s ) Establish the characteristic equation D ( s ) to find the characteristic root. The specific steps are as follows:

[0095] S51. By performing Laplace transform on the cavity differential equation, the transfer function of the RF superconducting cavity can be obtained as follows:

[0096] ;

[0097] Multiply the numerator and denominator of the above formula to get:

[0098] ;

[0099] S52, low-level systems mostly use proportional integral (PI) feedback control, and the transfer function model of the PI controller is as follows:

[0100] ;

[0101] Note that since the low-level system contains two loops of amplitude and phase (or two loops of I and Q), the controllers of the two loops of amplitude and phase are K A ( s )and K P ( s ), they are all PI controllers and have the following form:

[0102] ;

[0103] Among them, the feedback control parameter K pa , Kia The P and I parameters of the amplitude control loop and the feedback control parameters are K pp , K ip They are the P parameter and I parameter of the phase control loop respectively.

[0104] S53, establish characteristic equations in open-loop and closed-loop modes D ( s ), the specific process is as follows:

[0105] As shown in FIG6 (a), without introducing a low-level feedback loop, the system operates in an open-loop mode. According to the prior art, the characteristic equation of FIG6 (a) is:

[0106] ;

[0107] As shown in Figure 6 (b), when a low-level feedback loop is introduced, the system works in a closed-loop mode. According to the prior art, the characteristic equation of Figure 6 (b) is:

[0108] ;

[0109] S54, solve the equation D ( s )=0 to find all the solutions (i.e. characteristic roots) of the characteristic equation. The specific process is:

[0110] Assume equation D ( s )=0 has M characteristic roots, denoted by l 1, l 2… l M . In general, they are all complex numbers and can be expressed as l 1= l 1I + jl 1Q , l 2= l 2I + jl 2Q , l M = l MI + jl MQ To keep the system stable, the real parts of all characteristic roots must be less than 0. Assume l Imax is the maximum value of the real part of all characteristic roots, that is:

[0111] ;

[0112] like l Imax <0, the real parts of all characteristic roots are less than 0 and the system is stable.

[0113] like l Imax >0, then the real part of at least one characteristic root is greater than 0 and the system is unstable.

[0114] S6. Combined with the stability boundary, optimize the closed-loop system parameters to ensure the stability of the coupled system.

[0115] In this embodiment, given the cavity and low-level feedback parameters, find out the corresponding l Imax , draw the stability curve, the specific process is:

[0116] S61. Given cavity parameters, including: cavity half bandwidth oh h , dynamic cavity detuning Δ oh , the peak field amplitude of the RF superconducting cavity E peak ; At the same time, the low-level feedback control parameters are given, including: K pa , K ia , K pp , K ip , that is, the characteristic root can be calculated. In general, the half bandwidth of the cavity is oh h Does not change during operation (unless the cavity experiences thermal quenching) and can be tuned at detuned and half bandwidth oh h The ratio Δ h / h h The horizontal axis (X axis) is the peak field amplitude of the radio frequency superconducting cavity. E peak Scan the ordinate to get 2D l Imax image.

[0117] S62, as shown in Figure 7 (a), when the system works in open-loop mode, the Δ oh / oh h and E peak , and obtain the stable region ( l Imax <0) and unstable region ( l Imax>0) boundary curve is called the stability boundary. Shortening the step size can improve the accuracy of the stability boundary. Figure 7 (b) shows the scanning result after shortening the step size, and a smooth stability region boundary can be seen.

[0118] S63, when the system works in closed-loop mode, given each set of low-level feedback control parameters ( K pa , K ia , K pp , K ip ) and scan Δ h / h h and E peak ,calculate l Imax And determine the stable region and unstable region, and then get the corresponding stability boundary. As shown in Figure 7 (c) and Figure 7 (d), each set of low-level feedback control parameters ( K pa , K ia , K pp , K ip ) corresponds to a different stability boundary.

[0119] S64. After determining the stability boundary, according to the current peak cavity field amplitude of the RF superconducting cavity E peak The maximum detuning that may occur with the RF superconducting cavity is determined, and appropriate closed-loop parameters are selected to ensure that the closed-loop system always operates in a stable state.

[0120] The specific process of the online suppression method of the electromechanical coupling effect of the radio frequency superconducting cavity provided by the present invention is described in detail below through specific embodiments. The solid-state power source used in this embodiment is manufactured by Chengdu Kaiteng Company. Each power source contains 24 inserts (model: KFPA-162-1-1), and the saturated output power of a single insert is about 1.4 kW. The radio frequency superconducting cavity is a half-wavelength radio frequency superconducting cavity (HWR010, whose relativistic speed is 0.1). The resonant frequency of the cavity is 162.5 MHz, and the half bandwidth is about 100 Hz. The FPGA chip model is ZYNQ7100, and its data sampling rate is 100 MHz. Based on the above parameters, the online suppression method of the electromechanical coupling effect of the radio frequency superconducting cavity provided in this embodiment includes:

[0121] 1. Measure the voltage of the RF superconducting cavity.

[0122] like Figure 1 As shown, the original cavity pressure of the RF superconducting cavity is measured V c * , forward voltage V f * and reverse voltage V r * The specific process is:

[0123] 1. Use the signal extraction coupler 6 to extract the cavity pressure signal online P t , using directional coupler 3 to measure the cavity incident signal online P f and reflected signal P r , where the cavity pressure signal of this embodiment is P t , cavity incident signal P f and reflected signal P r All are 162.5 MHz radio frequency signals, and this is taken as an example but is not limited to this.

[0124] 2. After the above RF signal is down-converted, digitized and IQ demodulated in sequence, the digital low-level system 1 obtains the digitized original baseband voltage signal, i.e., the original cavity pressure V c * , original forward voltage V f * and the original reverse voltage V r * The digital low level system 1 uploads the above baseband signal to the data bus.

[0125] 2. Signal calibration and normalization.

[0126] According to the original cavity pressure V c * and the original forward voltage V f * The signal calibration and normalization are realized inside the host computer 8, including:

[0127] 1. Original forward voltage signal V f * calibration.

[0128] according to V f, cali = XV f * Solve for the calibrated forward signal. Note: The cavity pressure signal is usually used as a reference signal and does not need to be calibrated. The complex multiplication operation can be performed as follows:

[0129] ;

[0130] In the formula, V f, caliI and V f, caliQ They are V f, cali The real and imaginary parts of V fI * and V fQ * They are V f * The real and imaginary parts of X I and X Q The calibration coefficients are X The real and imaginary parts of .

[0131] 2. Normalization and standardization of original cavity pressure V c * and the original forward voltage V f * .

[0132] Original cavity pressure V c * The signal runs in a steady state when no electromechanical coupling fault occurs. When the electromechanical coupling fault is triggered, V c * The signal will undergo electromechanical coupling oscillation, and the RF superconducting cavity will no longer be in a steady state. Calculate the steady-state time of the RF superconducting cavity t 1 and t The average of the cavity pressure between the two moments was used as the normalization coefficient V c, ss * ,use V c = V c * / V c, ss * Get the normalized cavity pressure V c . Generally t2 Select a few points 2 to 2.5 seconds before the coupling fault occurs. t 1 Relative t 2 one second earlier. For example, the electromechanical oscillation in Figure 4 (a) occurs at 3.5 seconds, so we can choose t 2 = 1 second, t 1 = 0 seconds. As shown in Figure 4 (a), after normalization V c The amplitude of the steady-state average is 1 and the phase is 0 degrees. Taking this as an example, the calculation process of finding the average value can be directly called by Python numpy.mean function.

[0133] Original cavity pressure V c * and the original forward voltage V f * Normalization:

[0134] .

[0135] 3. According to cavity pressure V c and forward voltage V f Solving the dynamic detuning, the specific process is as follows:

[0136] 1. Calculate separately V c The real part of V cI With the imaginary part V cQ The numerical differentiation of .

[0137] In this embodiment, the numerical differential can be calculated using a two-point central difference method or a four-point central difference method, and the calculation formula is as follows:

[0138] ;

[0139] in, f ( t ) is the signal to be differentiated, t 0 The moment at which the differential needs to be calculated, T is the sampling time.

[0140] Amplitude signal r As an example, the method of calculating the differential using the four-point central difference method is shown in Figure 3 (c). V c Real part of signal V cI ( t )exist tThe differential at time 0 can be calculated from the values ​​of the two sampling points before and after. t The sampling point corresponding to time 0 is n 0, and the first two sampling points are n 0-2, n 0-1, and the next two sampling points are n 0+1, n 0+2. As shown in Figure 3(c), the signals corresponding to the above four sampling points are V c ( t ) are sampled values ​​of V c [ n 0-2], V c [ n 0-1], V c [ n 0+1] and V c [ n 0+2], then the sequence r At the sampling point n The numerical differential of 0 can be expressed as:

[0141] ;

[0142] In the formula, T is the sampling period, V cQ The differential and V cI The calculation process of differentiation is the same and will not be repeated here.

[0143] 2. According to each sampling point n Where V c [ n ], forward voltage and differential V cI ( n ), V cQ ( n ), calculate each sampling point n Dynamic detuning at Δ f [ n ].

[0144] 4. Based on the cavity pressure and dynamic detuning data, the cavity mechanical mode system is identified.

[0145] In this embodiment, the cavity mechanical mode system is identified based on the cavity pressure and dynamic detuning data, including:

[0146] 1. Establishment of system identification data.

[0147] In the overall detuning Δ f Deduct the steady-state part Δ f 0 (i.e. static detuning), we get the Lorenz detuning Δ f LFD As shown in Figure 3(b), the static detuning part Δ f 0 can be calculated by the steady-state time t 1 and t 2 Moment Δ f The average value is obtained. f LFD The unknown model M ( s ) output data y . Generally t 2 Select a few points 2 to 2.5 seconds before the coupling fault occurs. t 1 Relative t 2 one second earlier. For example, the electromechanical oscillation in Figure 4 (a) occurs at 3.5 seconds, so we can choose t 2 = 1 second, t 1 = 0 seconds. Figure 4 (a) shows the measured Δ f LFD As a result, the mean value of the steady-state part is 0, which meets the system identification requirements.

[0148] Normalized cavity pressure data V c Convert it into field strength data, and square the two to get the unknown model M ( s ) u . Similarly, you need to | V c | 2 After deducting the steady-state part, due to V c has been normalized to 1, then | V c | 2 The steady-state part of is also 1, as shown in Figure 4 (a). In summary, the above process can be expressed by the following formula:

[0149] .

[0150] 2. Cavity mechanical mode M ( s ) identification.

[0151] Based on the input time series u [ n ]and y [ n], the mechanical mode of the cavity is identified by using the greyest function of Matlab system identification toolbox M ( s ) transfer function model. Figure 4 (b) is a transfer function model obtained by using the system identification method. Figure 5 (a) is a comparison of the electromechanical coupling oscillation events in Figure 4 (a) in an embodiment of the present invention. Figure 5 (b) is a comparison of the same RF superconducting cavity CM in an embodiment of the present invention. 4-1 The model output results and measured results of other different types of electromechanical coupling events in the above-mentioned model are verified. M ( s )’s effectiveness.

[0152] 5. According to the mechanical mode of the cavity M ( s ), establish and solve the characteristic equation D ( s ), find the characteristic roots and stability curve.

[0153] In this embodiment, according to the cavity mechanical mode M ( s ), establish and solve the characteristic equation D ( s ), find the characteristic root and stability curve, the specific process is:

[0154] 1. Given cavity parameters, including: cavity half bandwidth oh h , dynamic cavity detuning Δ oh , the peak field amplitude of the RF superconducting cavity E peak ; At the same time, the low-level feedback control parameters are given, including: K pa , K ia , K pp , K ip , and establish the characteristic equations in open-loop mode and closed-loop mode respectively.

[0155] 2. Solve the characteristic equation and find the largest characteristic root of a real number l Imax , draw the boundary curve. As shown in Figure 7 (a), when the system works in open-loop mode, the Δ h / h h and E peak For each given set of coordinates (Δ h / h h , Epeak ), solve the equation D ( s )=0, find l Imax .like l Imax <0, then the coordinate (Δ h / h h , E peak ) is marked in white, indicating that the system is stable; if l Imax >0, then the coordinates (Δ h / h h , E peak ) is marked in black, indicating that the system is unstable. After the scan is completed, the boundary between the black and white areas is the stability boundary. h / h h and E peak The scanning step length can improve the accuracy of the scanned image. E peak The scanning step size is 0.1 mV / m, Δ h / h h The scanning step size is 0.02. Take this as an example, not limited to this. Figure 7 (b) shows the smooth stability region boundary obtained by scanning with the above step size.

[0156] When the system works in closed-loop mode, given each set of low-level feedback control parameters ( K pa , K ia , K pp , K ip ) and scan Δ h / h h and E peak , and a stability boundary is obtained. As shown in Figure 7 (c) and Figure 7 (d), each group ( K pa ,K ia , K pp , K ip ) corresponds to a stability boundary. In Figure 7 (c), assuming that the initial low-level feedback control parameter is K pa = K 0 ,Kia =0, K pp = K 0, K ip =0; by increasing in equal proportion at the same time K pa and K pp , can change the stability boundary, reduce the unstable region induced by the electromechanical coupling effect, and achieve the suppression of the electromechanical coupling effect. In Figure 7 (d), it is assumed that the initial low-level feedback control parameter is K pa = a, K ia =0, K pp = b , K ip =0; can be adjusted reasonably K pa and K pp , find the most suitable stability boundary. Note that the feedback control parameters of the closed-loop system are limited by the loop delay and cannot be increased indefinitely, otherwise the loop oscillation will occur due to excessive feedback gain. Under the premise of ensuring that electromechanical coupling is not caused, the feedback control parameters should be as small as possible. For example, suppose that the current cavity is required to operate under a peak electric field of 30 megavolts per meter, as shown in the black dotted straight line in Figure 7 (d). According to Figure 7 (d), you can choose K pa =5 a , K pp = b This ensures that the system always works in a stable state. Considering that a certain margin should be reserved for the system, it should be given priority K pa =5 a , K pp =2.5 b (or K pa =6 a , K pp = b ).

[0157] 6. Online experimental verification.

[0158] The experiment of this example was carried out in the radio frequency superconducting cavity CM of the superconducting heavy ion accelerator CAFe2. 4-1 and CM 4-2The above experiments verify that the RF parameters of the two cavities are shown in Table 1. Figure 8 (a) compares the CM of the cavity in this embodiment. 4-1 The experimentally measured stability boundary (black circle) in the closed-loop operation mode and the characteristic equation of the closed-loop mode D ( s ) calculated stability boundary (gray dotted line). Figure 8 (b) compares the CM 4-2 The measured stability boundary (black square) in the closed-loop operation mode and the characteristic equation of the closed-loop mode D ( s ) calculated by the stability boundary (gray dotted line). It can be seen that D ( s ) The calculated stability boundary is in good agreement with the experimental measurement results, which proves the effectiveness of the present invention. It should be noted that measuring the stability boundary by experimental means usually requires carefully designed special experiments and also takes up valuable machine running time, while the method of the present invention does not take up any machine time.

[0159] As shown in Figures 9(a) and 9(b), the radio frequency superconducting cavity CM in the embodiment of the present invention is compared respectively. 4-1 and CM 4-2 The triggering frequency of electromechanical oscillation fault before and after optimizing the low-level feedback parameters. The gray part is the result before optimization using the method of the present invention, and the black part is the result after optimization using the method of the present invention. It can be seen that before optimization, the RF superconducting cavity CM 4-1 and CM 4-2 The electromechanical oscillation fault is frequently triggered (more than 10 times per day on average). After optimization, the electromechanical oscillation fault is effectively alleviated (less than 1 time per day on average), which verifies the effectiveness of the method proposed in the embodiment of the present invention.

[0160]

[0161] Embodiment 2: Embodiment 1 above provides an online suppression method for the electromechanical coupling effect of a radio frequency superconducting cavity. Correspondingly, this embodiment provides an online suppression device for the electromechanical coupling effect of a radio frequency superconducting cavity. Since the device of this embodiment is basically similar to the method embodiment, the description process of this embodiment is relatively simple. For relevant parts, please refer to the partial description of Embodiment 1. The embodiment of the online suppression device for the electromechanical coupling effect of a radio frequency superconducting cavity provided by the present invention is only illustrative.

[0162] Specifically, the online suppression device for the electromechanical coupling effect of a radio frequency superconducting cavity provided by the present invention comprises:

[0163] A voltage acquisition unit is configured to obtain an original cavity pressure of the radio frequency superconducting cavity. V c * and the original forward voltageV f * ;

[0164] The data processing unit is configured to convert the original cavity pressure V c * and the original forward voltage V f * Calibrate and normalize to get the normalized cavity pressure V c and forward voltage V f ;

[0165] A dynamic detuning calculation unit is configured to screen out the normalized cavity pressure when electromechanical oscillation occurs. V c and forward voltage V f , according to the normalized cavity pressure V c and forward voltage V f The differential equation is established and solved to obtain the dynamic detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation f ;

[0166] The system identification unit is configured to identify the normalized cavity pressure based on the selected V c and dynamic detuning Δ f , using system identification method to identify the transfer function of the mechanical mode of the radio frequency superconducting cavity M ( s );

[0167] The characteristic equation solver is configured to calculate the transfer function of the mechanical mode of the RF superconducting cavity. M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ), solve the characteristic equation D ( s ) Find the stability boundary under different parameter conditions;

[0168] The parameter optimization unit is configured to optimize the closed-loop control parameters according to the stability boundary to achieve online suppression of the electromechanical coupling effect.

[0169] Embodiment 3: This embodiment provides an electronic device corresponding to the online suppression method of the electromechanical coupling effect of the radio frequency superconducting cavity provided in this embodiment 1. The electronic device may be an electronic device for a client, such as a mobile phone, a laptop computer, a tablet computer, a desktop computer, etc., to execute the method of embodiment 1.

[0170] Embodiment 4: This embodiment provides a computer-readable storage medium storing one or more programs, wherein the one or more programs include computer instructions. When the computer instructions are executed by a computer, the computer executes the method provided in the above-mentioned embodiment 1.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An online method for suppressing electromechanical coupling effect of a radio frequency superconducting cavity, characterized in that: include: Obtaining the original cavity pressure of the radio frequency superconducting cavity V c * and the original forward voltage V f * ; The original cavity pressure V c * and the original forward voltage V f * Calibrate and normalize to get the normalized cavity pressure V c and forward voltage V f ; Screen out the normalized cavity pressure when electromechanical oscillation occurs V c and forward voltage V f , according to the normalized cavity pressure V c and forward voltage V f The differential equation is established and solved to obtain the dynamic detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation f ; Based on the normalized cavity pressure V c and dynamic detuning Δ f , using system identification method to identify the transfer function of the mechanical mode of the radio frequency superconducting cavity M ( s ), the specific process is: based on the normalized cavity pressure V c and dynamic detuning Δ f The input quantities for constructing the cavity mechanical mode model are Output ,in, E peak is the peak cavity field amplitude of the RF superconducting cavity, Detuned for Lorenz, is the static detuning of the RF superconducting cavity, | V c | is the normalized cavity pressure V c the magnitude of Based on input and output u and y， Using the system identification method, the transfer function model of the cavity mechanical mode is obtained M ( s ), the specific process is: RF superconducting cavity mechanical mode transfer function model M ( s ) has the structure: ； in, s is a complex frequency domain variable, N is the number of mechanical modes, ω k , Q k and M k Respectively k The frequency, quality factor and gain of the mechanical mode are unknown. The system identification method is used to identify the input and output data ( u , y ) Identify unknown parameters ω k , Q k and M k ; According to the transfer function of the mechanical mode of the RF superconducting cavity M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ), solve the characteristic equation D ( s ) Find the stability boundary under different parameter conditions; The closed-loop control parameters are optimized according to the stability boundary to achieve online suppression of the electromechanical coupling effect.

2. The online suppression method of the electromechanical coupling effect of the radio frequency superconducting cavity according to claim 1 is characterized in that: Screen out the normalized cavity pressure when electromechanical oscillation occurs V c and forward voltage V f , according to the normalized cavity pressure V c and forward voltage V f The differential equation is established and solved to obtain the dynamic detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation f ,include: Filter out electromechanical oscillation faults from fault data and obtain the normalized cavity pressure when electromechanical oscillation occurs. V c and forward voltage V f ; Normalized cavity pressure based on electromechanical oscillation V c and forward voltage V f Establish the cavity differential equation: ； in, t is the sampling time, Cavity pressure V c The differential of ω 0 is the cavity resonance frequency, ω h is the cavity half bandwidth, Δ ω is the dynamic cavity detuning, The beam current intensity is approximately 0, r / Q is the geometric factor of the cavity, Q E is the external quality factor, j is an imaginary unit; Normalized cavity pressure V c and forward voltage V f Decompose it into real and imaginary parts: ； Defining parameters ω E = ω 0 / Q E Substituting into the cavity differential equation, we get: ； Separating the real and imaginary parts of the above equation yields: ； Solving the above two-variable linear equation, we can obtain the dynamic cavity detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation: ω : ； By Δ f and Δω The relationship is: , and obtain the dynamic detuning Δ when the RF superconducting cavity generates electromechanical oscillation f .

3. The online suppression method of the electromechanical coupling effect of the radio frequency superconducting cavity according to claim 1 is characterized in that: According to the transfer function of the mechanical mode of the RF superconducting cavity M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ), solve the characteristic equation D ( s ) to find the stability boundary under different parameter conditions. The specific process is: The transfer function of the RF superconducting cavity is obtained by Laplace transforming the cavity differential equation; Obtain the transfer function of the low-level system PI controller; Transfer function based on mechanical mode of radio frequency superconducting cavity M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ); Solving equations D ( s )=0Find all the solutions of the characteristic equation, namely the characteristic roots, specifically: when the equation D ( s )=0 has M characteristic roots, denoted by λ 1, λ 2… λ M , expressed as λ 1= λ 1I + jλ 1Q , λ 2= λ 2I + jλ 2Q , λ M = λ MI + jλ MQ , to keep the system stable, the real parts of all characteristic roots need to be less than 0, λ Imax is the maximum value of the real part of all characteristic roots, that is: ； like λ Imax < 0, then the real parts of all characteristic roots are less than 0, indicating that the system is stable; like λ Imax >0, then the real part of at least one characteristic root is greater than 0, indicating that the system is unstable.

4. The online suppression method of the electromechanical coupling effect of the radio frequency superconducting cavity according to claim 3 is characterized in that: According to the stability boundary, the closed-loop control parameters are optimized to achieve online suppression of the electromechanical coupling effect, that is, given the cavity and low-level feedback parameters, find the corresponding λ Imax , draw the stability curve, the specific process is: Determine cavity parameters; When the system works in open-loop mode, the Δ ω / ω h and E peak , and obtain the stable region λ Imax < 0 and unstable region λ Imax >0 boundary curve is called stability boundary, where E peak is the peak cavity field amplitude of the RF superconducting cavity, ω h is the cavity half bandwidth, Δ ω Detuning the dynamic cavity; When the system works in closed-loop mode, under each set of low-level feedback control parameters, the sweep Δ ω / ω h and E peak ,calculate λ Imax And determine the stable area and unstable area, and obtain the corresponding stability boundary; After determining the stability boundary, according to the current peak cavity field amplitude of the RF superconducting cavity E peak The maximum detuning that may be produced by the RF superconducting cavity is determined, and appropriate closed-loop parameters are selected to ensure that the closed-loop system always operates in a stable state.

5. An online suppression device for the electromechanical coupling effect of a radio frequency superconducting cavity based on the online suppression method according to any one of claims 1 to 4, characterized in that: include: A voltage acquisition unit is configured to obtain an original cavity pressure of the radio frequency superconducting cavity. V c * and the original forward voltage V f * ; The data processing unit is configured to convert the original cavity pressure V c * and the original forward voltage V f * Calibrate and normalize to get the normalized cavity pressure V c and forward voltage V f ; A dynamic detuning calculation unit is configured to screen out the normalized cavity pressure when electromechanical oscillation occurs. V c and forward voltage V f , according to the normalized cavity pressure V c and forward voltage V f The differential equation is established and solved to obtain the dynamic detuning Δ when the RF superconducting cavity undergoes electromechanical oscillation f ; The system identification unit is configured to identify the normalized cavity pressure based on the selected V c and dynamic detuning Δ f , using system identification method to identify the transfer function of the mechanical mode of the radio frequency superconducting cavity M ( s ); The characteristic equation solver is configured to calculate the transfer function of the mechanical mode of the RF superconducting cavity. M ( s ), the transfer function of the RF superconducting cavity and the transfer function of the low-level system controller to establish the characteristic equation of the coupled system D ( s ), solve the characteristic equation D ( s ) Find the stability boundary under different parameter conditions; The parameter optimization unit is configured to optimize the closed-loop control parameters according to the stability boundary to achieve online suppression of the electromechanical coupling effect.

6. An electronic device, characterized in that: include: at least one processor; and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, and the instructions are executed by the processor so that the processor can execute the method according to any one of claims 1-4.

7. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include computer instructions for causing a computer to execute the method according to any one of claims 1-4.

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