Prediction method for operable region of conduction cooling superconducting cavity

Abstract

The invention discloses a prediction method for an operable domain of a conduction cooling superconducting cavity. The prediction method comprises the following steps: calculating field distribution under a target acceleration gradient according to electromagnetic characteristics of a real airspace of the superconducting cavity; calculating the surface loss power density and the dynamic thermal load under the target acceleration gradient based on the field distribution and the actual surface resistance; reversely calculating the temperature of a secondary cold head according to the total heat load of the superconducting cavity; solving a steady-state temperature field by taking the second-stage cold head temperature as a thermal boundary condition of a cold head mounting position to obtain temperature distribution of the cavity surface; updating parameters according to the temperature distribution until heat balance; constructing a constraint set according to the steady-state temperature field; inputting the measurement data of the superconducting cavity into the prediction model, and predicting the margin of each steady-state temperature point; correcting the prediction model according to the deviation between the prediction margin and the actual measurement margin to obtain an online prediction model; and inputting the operation data into an online prediction model to calculate the margin of each steady-state temperature point, predicting the operable region of the conduction cooling superconducting cavity and giving an action suggestion.

Description

Technical Field

[0001] This invention belongs to the field of radio frequency superconducting technology and cryogenic engineering, and relates to a method for predicting the operational domain of a conductive cooling superconducting cavity, which is applicable to the prediction and online evaluation of the operational domain of a conductive cooling superconducting cavity in vertical testing. Background Technology

[0002] The radio frequency (RF) accelerator module is a core component of the accelerator, responsible for powering the particle beam. Compared to room-temperature RF technology, superconducting RF technology offers advantages such as lower cost, less beam loss, and higher beam power. The superconducting cavity, as the core component of superconducting RF technology, must operate within the superconducting temperature range. To maintain the required cryogenic environment of the superconducting cavity, liquid helium immersion is typically used, requiring a complex and expensive liquid helium supply system, which hinders the widespread application of superconducting RF accelerators in medical, industrial, and other fields. With the continuous development of superconducting cavity technology, the quality factor (Q0 value) of the superconducting cavity has been continuously improved, and the dynamic heat load wattage of the superconducting cavity can be controlled to the single-digit order of magnitude. The improved Q0 value of the superconducting cavity makes it possible to abandon the traditional liquid helium immersion cooling scheme and adopt a new cooling scheme based on a small refrigerator that utilizes heat conduction to remove the heat load of the superconducting cavity. This solution does not require a liquid helium immersion environment or external helium compressors, cryogenic pipelines, and other supporting equipment, thus significantly reducing the system size and making the module structure more compact. It is also easier to maintain, reducing manufacturing and operating costs, and making it easier to promote and apply in industrial, medical, and other fields.

[0003] However, the following problems still exist in the vertical testing and engineering operation of conduction-cooled superconducting cavities: (1) The cooling capacity of the cold head changes significantly with temperature, and the thermal simulation of superconducting cavities with traditional constant wall temperature or constant heat flux boundaries is difficult to reflect the real operating point; (2) In the vertical testing of conduction-cooled cavities, there are many factors affecting the test system, such as various static heat loads and contact thermal resistance, which leads to deviations between the temperature measurement point distribution and the simulation prediction. Existing methods mostly regard the above deviations as fixed assumptions or empirical margins, and lack a mechanism for online identification and correction of key thermal parameters based on measured data during the vertical testing process, thus making it difficult to obtain high-precision prediction results of the superconducting cavity's operational domain boundary; (3) Existing methods mostly output a single superconducting cavity Eacc-Q0 curve, lacking a clear division of the operational / inoperable region and an explanation of limiting factors, making it difficult to guide test strategies and online operations; (4) There is a lack of online prediction tools that are linked with the real-time data of the vertical test system, making it impossible to adaptively correct the model and output an operable safety margin during the test process. Summary of the Invention

[0004] To address the problems existing in the prior art, the purpose of this invention is to provide a method for predicting the operational domain of conduction-cooled superconducting cavities. This method is for predicting the electromagnetic-thermal coupling performance of high-performance superconducting cavities such as Nb3Sn under conduction-cooled conditions. It is particularly suitable for vertical testing, operational domain assessment, instability risk determination, and online prediction and decision support during the testing process of conduction-cooled superconducting cavities.

[0005] This method, based on the cavity electromagnetic field scaling and surface resistance model, constructs a multi-physics coupled iterative solution of "electromagnetic loss—heat conduction—cold head cooling capacity / temperature characteristics." It incorporates the cable loss of the test antenna and the reflected power variation caused by coupling deviation into the overall system's thermal balance, using whether the cold head cooling capacity-system thermal load reaches thermal balance and whether other engineering constraints are met as the determining criteria. Furthermore, this invention proposes a fast scanning strategy of "interval search-interval contraction-boundary adaptive densification" for efficiently locating the achievable maximum acceleration gradient and the operational domain boundary. It also combines constraints such as cold head capacity, hot spot temperature margin, reflected power ratio, and test antenna loss to identify the dominant factors limiting the maximum acceleration gradient, thereby achieving "operable region division and explanation of limiting factors."

[0006] The technical solution of this invention is as follows: A method for predicting the operational domain of a conductively cooled superconducting cavity, comprising the following steps: Predictive model training phase: The field distribution under the target acceleration gradient is calculated based on the electromagnetic characteristics of the vacuum domain of the superconducting cavity; the surface loss power density and dynamic heat load under the target acceleration gradient are calculated based on the field distribution and the actual surface resistance of the superconducting cavity; the temperature of the secondary cold head is inversely calculated based on the cooling capacity-temperature characteristic function of the secondary cold head used in the vertical test system of the conductive cooling superconducting cavity, according to the total heat load of the superconducting cavity; the temperature of the secondary cold head is used as the thermal boundary condition of the cold head installation position to solve the steady-state temperature field and obtain the temperature distribution on the cavity surface; the actual surface resistance, dynamic heat load, and total heat load are updated according to the temperature distribution, and the above process is repeated until the thermal equilibrium convergence criterion is met; a constraint set is constructed based on the steady-state temperature field after thermal equilibrium convergence. Prediction model calibration stage: Input the measurement data of the superconducting cavity into the prediction model to predict the margin at each steady-state temperature point; determine the calibration parameter set based on the deviation between the predicted margin and the measured margin, calibrate the prediction model, and obtain the online prediction model of the superconducting cavity. Online prediction phase: Input the superconducting cavity's operating data into the online prediction model to calculate the margin at each steady-state temperature point, predict the operational domain of the conduction-cooled superconducting cavity, and provide action suggestions based on the constraint set.

[0007] Preferably, electromagnetic characteristic analysis is performed on the vacuum domain of the superconducting cavity to obtain the characteristic frequency and magnetic field distribution of the superconducting cavity, and the stored energy is extracted.U 0 and accelerating gradient E acc0 Calculate the target acceleration gradient as a baseline value. E acc Field distribution under [condition].

[0008] Preferably, based on the target acceleration gradient E acc Field distribution and actual surface resistance Calculate the surface loss power density under the target acceleration gradient. And obtain dynamic heat load .

[0009] Preferred, according to Calculate scaling factor According to the scaling factor Scaling the field distribution yields the target acceleration gradient. E acc Field distribution under; E acc It is the target acceleration gradient. L eff It is the effective acceleration length. R / Q These are the characteristic impedance parameters of the superconducting cavity. f It is the characteristic frequency of the superconducting cavity.

[0010] Preferably, the actual surface resistance Among them, C T It is the temperature factor, C Q It is the coating quality factor, R s This represents the theoretical surface resistance of the superconducting cavity.

[0011] Preferably, based on the incident power of the radio frequency line Reflection power The additional heat load entering the cryogenic end of the superconducting cavity is calculated based on the line attenuation coefficient. .

[0012] Preferably, based on the total heat load of the superconducting cavity The cooling capacity-temperature characteristic function of the two-stage cold head used in the vertical test system of the conductive cooling superconducting cavity. Calculate the temperature of the secondary cold head by reverse calculation ; to increase the temperature of the secondary cold head As the thermal boundary condition at the cold head mounting location, a steady-state temperature field solution is performed to obtain the temperature distribution on the cavity surface. T(x, y, z) ;according to T (x, y, z) Update actual surface resistance Dynamic heat load With total heat load Repeat the above process until the thermal equilibrium convergence criterion is met; total heat load , This is the static heat load.

[0013] Preferably, the constraint set includes: (1) Cold head capability constraints ; (2) Hot spot temperature margin constraint ;in, This represents the maximum temperature at critical locations within the superconducting cavity and heat conduction path. These are the temperature limits for superconducting materials within the superconducting temperature range; (3) Reflection power ratio constraint ;in, The reflection threshold is set by the test system itself. (4) Temperature difference constraint across the superconducting transition temperature region ;in This represents the maximum temperature difference across the superconducting cavity during the transition from superconducting to superconducting temperature. The design limit is set for the maximum allowable temperature difference of the cavity; (5) Frequency constraints ; This represents the frequency drift relative to the reference state.

[0014] Preferably, action suggestions are given based on the margin and constraint set for each steady-state temperature point: (1) For fixed coupling conditions Find the maximum reachable gradient at the current steady-state temperature. Output the maximum allowed gradient. or maximum permissible incident power And provide a step-by-step strategy; When the dominant limiting factor is the reflectance ratio When the output reflection warning threshold is reached, it is recommended to suspend power increase and prioritize checking coupling matching, antenna attenuation, and additional heat load at the low temperature end. When the dominant limiting factor is the cooling head capability or hot spot temperature At that time, the output cold head has an absolute margin, and it is recommended that if subsequent tests continue to stay at this operating point, the priority should be to reduce static heat load, reduce antenna dissipation, or improve contact thermal resistance. (2) For adjustable coupling conditions Find the maximum reachable gradient at the current steady-state temperature. Output the maximum allowed gradient. or maximum permissible incident power Give the direction of coupling adjustment, so that Maintaining within the preset range, thereby reducing And expand the operational boundaries; When the dominant limiting factor is When the dominant limiting factor is..., it is recommended to adjust the coupling to reduce reflection; when the dominant limiting factor is... or When this is the case, it is recommended to limit the power step or back to a safe operating point while maintaining low reflection. If the dominant limiting factor is the misharmonic constraint If detuning causes a significant increase in reflection, output a detuning warning and suggest taking tuning strategies, reducing the power step, or waiting for thermal stability to avoid an increase in reflection power caused by frequency drift. (3) Construct a quench risk criterion based on absolute margin; when the absolute margin of the cold head cold capacity rapidly approaches zero, or the absolute margin of the hot spot rapidly approaches zero, or the reflected power rapidly increases during the power / gradient increase process, it is determined that the quench risk zone has been entered and an early warning and power rollback suggestion are output.

[0015] Preferably, the constraint with the smallest margin is used as the dominant limiting factor to explain the reason for the boundary formation and to provide directions for test improvement.

[0016] The advantages of this invention are as follows: (1) The cooling capacity-temperature characteristics of the secondary cold head are directly incorporated into the electromagnetic-thermal coupling iteration, which can reflect the steady-state operating point of the conductive cooling superconducting cavity under the real cold head boundary, rather than using an idealized constant temperature or constant heat flux boundary.

[0017] (2) Integrate static heat load, heat load caused by radio frequency lines and thermal resistance of key interfaces into the overall thermal balance, so that the prediction results are closer to the actual working conditions of the conduction cooling vertical test system.

[0018] (3) The output format is expanded from a single performance curve to include the operable domain, non-operable domain, and operable domain boundary, which can directly provide the maximum achievable acceleration gradient, constraint margin, and dominant limiting factors, thereby improving the interpretability of the results.

[0019] (4) Real-time measurement data can be integrated into the model for online parameter adaptive correction, thereby improving the consistency between the prediction results and the assembly conditions of this test, and supporting online safety margin assessment and real-time action suggestion output.

[0020] (5) It can be applied to the vertical testing of superconducting cavities without liquid helium conduction cooling and the engineering design and operation assistance of related conduction cooling modules. Attached Figure Description

[0021] Figure 1 This is the overall flowchart of the present invention.

[0022] Figure 2This is a schematic diagram of the electromagnetic loss mechanism of a conductive cooling superconducting cavity.

[0023] Figure 3 This is a flowchart for multiphysics simulation of a conductive cooling superconducting cavity. Detailed Implementation

[0024] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0025] An optional embodiment of the present invention provides a method for predicting the performance of a conductively cooled superconducting cavity based on electromagnetic-thermal coupling. Through bidirectional coupling iteration of cold head cooling capacity and temperature, introduction of test system losses, rapid scanning and feasible domain output, and online adaptive parameter correction, the method achieves: (1) rapid determination of the maximum achievable acceleration gradient and the boundary of the feasible domain of the superconducting cavity; (2) construction of the feasible region and interpretation of limiting factors; and (3) online parameter correction and safety margin prediction in conjunction with real-time data from the vertical test system. This improves the predictability, interpretability, and operability of vertical testing of liquid helium-free conductively cooled superconducting cavities.

[0026] Runnable domain This refers to the set of all operating points that satisfy the "feasibility criterion" and the constraint set under given test parameters and operating conditions. The feasibility criterion is that when the cooling capacity of the cold head and the total heat load of the system reach thermal equilibrium convergence and satisfy the constraint set, the operating point is considered stable; otherwise, it is considered infeasible or at risk of instability / overrun. The operable domain boundary is the interface between the operable and inoperable domains. After a rapid scan of the operating points, a feasible maximum acceleration gradient is obtained. Satisfying Eacc≤ A feasible solution exists within the range and does not violate the constraints, while Eacc > Unreachable or in violation of constraints within the specified range.

[0027] An optional embodiment of this invention provides a method for predicting the performance and evaluating the online operational domain of a conductively cooled superconducting cavity based on electromagnetic-thermal coupling, including an offline prediction stage and an online correction and real-time evaluation stage. The overall process can be summarized as follows: electromagnetic field scaling → actual surface resistance modeling → surface loss and heat load calculation → iterative solution of the steady-state operating point using bidirectional coupling of the cold head → constraint and margin evaluation → online parameter correction → online prediction based on measured data and provision of action suggestions. The overall flowchart is shown below. Figure 1 As shown, the specific steps are as follows.

[0028] 1. Electromagnetic reference establishment and field scaling Electromagnetic characteristic analysis (eigenmode and frequency domain analysis) was performed on the vacuum domain of the superconducting cavity to obtain its characteristic frequencies. f Magnetic field distribution H and extract energy storage U 0 and accelerating gradient E acc0 As a baseline value; to establish the field scaling relationship for subsequent multi-condition reproduction: the field distribution under the target acceleration gradient is obtained by using a scaling factor, which is defined by equation (1): in SF It is a scaling factor. E acc It is the target acceleration gradient. L eff It is the effective acceleration length. R / Q It is the characteristic impedance parameter of the superconducting cavity.

[0029] 2. Modeling of actual surface resistance Under conductive cooling, the temperature of the superconducting cavity surface cannot maintain the same uniformity as when immersed in liquid helium. Therefore, the effect of temperature on surface resistivity must be fully considered. Rs(T) It is essential to understand the impact of surface wear.

[0030] Surface resistance R of superconducting cavity s Theoretically, it consists of two parts: one part is the residual resistance R0 of the material, which is usually related to impurities contained in the material and residual magnetism in the environment; the other part is the BCS resistance R. BCS This is given by BCS theory.

[0031] For Nb3Sn superconducting cavities, R BCS Resistance can be written as: As is a coefficient related to the material and model, ω is the angular frequency, Δ(T) is the superconducting band gap, and k is the voltage level. B is Boltzmann constant, Tc is the transition temperature of the superconducting material, and T is the local temperature of the cavity surface.

[0032] Under conductive cooling, the surface temperature of an Nb3Sn superconducting cavity cannot maintain the same uniformity as under liquid helium immersion, inevitably resulting in temperature differences. Particularly when crossing the superconducting transition temperature region (approximately 18K), these temperature differences drive thermocurrents and induce additional magnetic fields; magnetic flux trapping leads to an increase in residual resistance. Furthermore, the coating quality and spatial uniformity of the Nb3Sn superconducting cavity directly affect the surface resistivity. Therefore, the surface resistivity R of an Nb3Sn superconducting cavity in actual testing or operation is defined as follows: s,ac : Where C T It is a temperature factor used to describe the effect of the cavity temperature difference on the surface resistivity across the superconducting transition temperature; C Q It is the coating quality factor, used to describe the effect of the coating quality of the Nb3Sn superconducting cavity on the surface resistivity, and is mainly derived from liquid helium vertical testing calibration. C T The value is set as an identifiable parameter, which can be calibrated offline by historical vertical tests or updated online by measured data. It is used to correct the general model to an online prediction model consistent with the test.

[0033] 3. Calculation of surface loss and dynamic heat load Under the target acceleration gradient Eacc, the scaling field result from step one and the actual surface resistance obtained from step two are compared. The surface loss power density corresponding to the target acceleration gradient can be calculated using equation (6). and obtain dynamic heat load :

[0034] 4. Vertical test equivalent heat load modeling Under vertical testing conditions, in addition to cavity surface losses, the equivalent dissipation power of the RF circuitry (coaxial cable, test antenna attenuation, etc.) under the combined effect of incident and reflected power must also be considered, as it serves as an additional heat load entering the cryogenic end. The equivalent power dissipation can be calculated from the incident power. Reflection power The results are calculated using the line attenuation coefficient. Based on whether the length of the coupled antenna can maintain the critical coupling state of the cavity-coupled antenna with changes in cavity performance, the test conditions can be divided into two types: fixed coupling condition and adjustable coupling condition. Under the fixed coupling condition, coupling deviation may lead to… Rise, and thus change Under adjustable coupling conditions, the coupling can be maintained by adjusting the coupling. Within a preset range, thus suppressing .

[0035] 5. Cooling capacity-temperature bidirectional coupling and steady-state iterative solution (feasibility criterion) of the cold head Define total heat load: ,in Calculated from step three, This is the static heat load (online phase correction is allowed). Calculated from step four. The cooling capacity-temperature characteristic function of the two-stage cold head used in this conductive cooling superconducting cavity vertical test system is denoted as: . The performance curves can be obtained from the selected refrigeration equipment manufacturer or through calibration experiments, and can be input into the solution program in the form of fitting functions, interpolation functions or lookup tables.

[0036] For a given current total heat load ,exist Calculate the corresponding secondary cold head temperature by reverse calculation. That is, to find the solution that satisfies: The temperature value; subsequently, the temperature of the secondary cold head. As the thermal boundary condition at the cold head mounting location, the steady-state temperature field is solved to obtain the cavity surface temperature distribution. T(x, y, z) Then according to T(x, y, z) Update actual surface resistance Dynamic heat load With total heat load Repeat the above process until the thermal equilibrium convergence criterion is met: If the acceleration gradient converges within the superconducting temperature region, then the acceleration gradient is considered to be correct. Stability can be achieved; if the iteration does not converge or the critical temperature exceeds the limit, then the condition is considered stable. Unattainable. Flowchart as follows: Figure 3 As shown.

[0037] 6. Constraint and Margin Assessment To extend the prediction results from a single performance curve to the operational region The main limiting factors are identified. Based on the convergence of the steady-state temperature field and thermal equilibrium obtained in step five, a constraint set C is constructed, and a relative margin is simultaneously output at each steady-state temperature point. The constraint with the smallest margin is taken as the dominant limiting factor, thereby explaining the main reasons for boundary formation and proposing directions for test improvement. This constraint set can also be used to predict safety margins online and output action suggestions.

[0038] The constraint set C mainly includes: (1) Cold head capability constraints : To describe the infeasibility or instability risks caused by insufficient cold block capacity, based on the cold block's cooling capacity-temperature characteristics... and total heat load Define constraints on the cold head's capability. : (2) Hot spot temperature margin constraint : Maximum temperature at critical locations in the cavity and heat conduction path Upper limit constraint, defining hotspot temperature margin constraint : in It can be set as the temperature limit for superconducting materials within the superconducting temperature range to prevent local hot spots from triggering rapid performance deterioration or thermal runaway; (3) Reflection power ratio constraint : Under fixed coupling conditions, to suppress the significant increase in dissipation power caused by the increase in the reflected power ratio and the risk of quenching, a reflected power ratio constraint is defined. : in It is the maximum allowable reflection power ratio value, which can be set by the reflection threshold allowed by the test system itself; (4) Temperature difference constraint across the superconducting transition temperature region : To control the flux trapping effect induced by temperature difference across the superconducting transition temperature region (e.g., around 18 K), a temperature difference constraint across the superconducting transition temperature region is defined. : in It can be defined as the maximum temperature difference on the ellipsoidal cavity during the process of crossing the superconducting transition temperature range. The maximum allowable temperature difference for the cavity is designed as a limit. For Nb3Sn superconducting cavities, the upper limit can be given based on past liquid helium vertical tests, conductive cooling tests and process experience. Generally, it can be taken as 0.2K. (5) Frequency constraints : During the vertical test with conductive cooling, the temperature of the superconducting cavity changes, and the temperature rise, in particular, can cause frequency drift. Therefore, a frequency constraint is defined. : It represents the frequency drift relative to the reference state, and its source can be multiphysics simulation, experimental calibration relationship or real-time measurement; This represents the maximum permissible frequency drift limit, which is an engineering-defined threshold and can be determined by tuning capability and testing strategy.

[0039] To facilitate a unified comparison of constraints of different physical quantities, this invention defines a unified margin index for each constraint. The current value of the k-th constraint quantity in the above constraint set is defined as... The corresponding limit is denoted as For any of the constraints in (1) to (5) above. Its margin is defined as: in This indicates that the constraints are met and there is a margin. This indicates that the boundary has been reached. This indicates a violation of constraints; and it is considered that... The constraint corresponding to the minimum value is the dominant limiting factor at that working point.

[0040] Furthermore, this invention maps possible dominant limiting factors to suggested actions or optimization directions: Main recommendation: Reduce static heat load. Reduce antenna loss ; Recommendation: Optimize the heat conduction structure / interface in hotspot areas or optimize the heat conduction path; For fixed coupling, it is recommended to reduce the input power amplitude and set a reflection threshold warning; for adjustable coupling, it is recommended to adjust the coupling in a timely manner to reduce [the impact of the current]. ; Leading suggestion: Optimize cooling strategies to further control [the temperature]. and to Perform online calibration; Recommendation: It is suggested to correct the frequency value online, tune in a timely manner, or reduce the temperature rise to control frequency drift.

[0041] 7. Online parameter identification and adaptive correction During the vertical test, the measurement data is fed into the prediction model in real time, and the key uncertain parameters that cause experimental-simulation deviations are corrected and updated online. This allows the general prediction model to be adaptively corrected to an online prediction model that is consistent with the test setup, providing a reliable parameter set for subsequent online boundary and margin predictions.

[0042] During testing, temperature parameters (such as cold head temperature, critical cavity temperature, hot spot temperature, etc.) and radio frequency physical quantities (such as incident power, reflected power, frequency, VSWR, etc.) are acquired in real time. These quantities are then used as a set of calibration parameters. Equivalent contact thermal resistance of key heat-conducting surfaces Static heat load parameters (Can be further subdivided according to different locations and types), actual surface resistance temperature correction factor , antenna loss factor dB.

[0043] The objective function is constructed based on the deviation between the model's predicted output and the real-time measurement data, and the parameter set is... Online identification and updating are performed, and the objective function adopts a weighted least squares form: in, For the i-th real-time measurement, This is the output of the corresponding model obtained from steps 1 to 6 under the parameter set θ. The weights corresponding to each measurement quantity, These are offline calibration values ​​or empirical initial values. Here is the regularization coefficient. Further, under the constraints of upper and lower bounds in the physical parameters, the solution is: This yields a set of reliable parameters under the current test assembly conditions, which are then fed back into the prediction calculation processes corresponding to steps 1 through 6 to achieve online adaptive correction.

[0044] Step 7 does not reconstruct the operational domain, but rather, based on the offline predictions in step 6, performs online adaptive correction on the model, thereby adaptively correcting the general prediction model to an online prediction model consistent with the assembly used in this test.

[0045] 8. Online prediction and action suggestions This invention includes an online margin prediction and action suggestion module, used to quickly calculate the runnable domain boundary, constraint margin, and dominant limiting factors under the current test conditions. It further generates real-time executable action suggestions for vertical testing, forming the decision output of the entire offline-online prediction model. It is important to note that the suggestion in step 6 is an "offline interpretive suggestion," explaining the reasons for boundary constraints and providing directions for structural or test strategy optimization; the suggestion in step 8 is an "online execution suggestion," providing immediately executable actions for the current real-time test process, such as limiting power steps, adjusting coupling, tuning frequency, maintaining the current operating conditions, or rolling back to a safe operating point. The two are at different levels.

[0046] The input mainly includes the corrected parameter set. The system also includes real-time measurements of key temperature values ​​and radio frequency physical quantities. Based on these inputs, the state variables, constraint margins, and dominant limiting factors at the current operating point are calculated using the aforementioned solution method. Subsequently, a local fast scan is employed to solve for the maximum reachable gradient near the current operating point. First, obtain the feasible / infeasible large interval [E] L E U Then, use interval contraction to |E] U -E L |≤δ, thus we obtain ≈E L This outputs the online security margin: in and This is the corresponding value for the current working point. and It is the calculated maximum value.

[0047] Based on the predicted safety margins and dominant limiting factors, action suggestions for vertical testing will be generated, including action suggestions under different operating conditions: (1) Fixed coupling condition Output the maximum allowed gradient. or maximum permissible incident power And provide a recommended step strategy (such as when (Reduce power step size or stop boosting when power is below the threshold). When the dominant limiting factor is the reflectance ratio When the output reflection warning threshold is reached, it is recommended to suspend power increase and prioritize checking coupling matching, antenna attenuation, and additional heat load at the low temperature end. When the dominant limiting factor is the cooling head capability or hot spot temperature At this point, the output cold head has an absolute margin, and it is recommended that if subsequent tests continue to stay at this operating point, priority should be given to reducing static heat load, reducing antenna dissipation, or improving contact thermal resistance.

[0048] (2) Adjustable coupling condition In output or At the same time, the coupling adjustment direction is given, so that Maintaining within the preset range, thereby reducing And expand the boundaries of the operable domain; When the dominant limiting factor is When the dominant limiting factor is..., it is recommended to adjust the coupling to reduce reflection; when the dominant limiting factor is... or When this is the case, it is recommended to limit the power step or back to a safe operating point while maintaining low reflection. If the dominant limiting factor is the misharmonic constraint If detuning causes a significant increase in reflection, output a detuning warning and suggest taking tuning strategies, reducing the power step, or waiting for thermal stabilization to avoid an increase in reflection power caused by frequency drift.

[0049] Furthermore, to avoid localized quenching within the superconducting cavity due to a rapid increase in heat load during vertical conductive cooling tests, this invention constructs a quenching risk criterion based on absolute margin. When any of the following occurs during power / gradient ramp-up: the absolute margin of the cold head rapidly approaches zero, the absolute margin of the hot spot rapidly approaches zero, or the reflected power rapidly increases, it is determined that the system has entered a high-risk quenching zone, and a warning and power reduction suggestion are output.

[0050] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for predicting the operating region of a conductively cooled superconducting cavity, comprising the following steps: Prediction model training phase: Calculate the field distribution under the target acceleration gradient based on the electromagnetic characteristics of the vacuum domain of the superconducting cavity; The surface loss power density and dynamic heat load under the target acceleration gradient are calculated based on the field distribution and the actual surface resistance of the superconducting cavity. The temperature of the second-stage cold head is inversely calculated from the cooling capacity-temperature characteristic function of the second-stage cold head used in the vertical test system of the conduction cooling superconducting cavity based on the total heat load of the superconducting cavity. The temperature of the secondary cold head is used as the thermal boundary condition of the cold head installation position. The steady-state temperature field is solved to obtain the temperature distribution on the cavity surface. The actual surface resistance, dynamic heat load and total heat load are updated according to the temperature distribution. The above process is repeated until the thermal equilibrium convergence criterion is met. A constraint set is constructed based on the steady-state temperature field after thermal equilibrium convergence. Prediction model calibration stage: Input the measurement data of the superconducting cavity into the prediction model to predict the margin at each steady-state temperature point; determine the calibration parameter set based on the deviation between the predicted margin and the measured margin, calibrate the prediction model, and obtain the online prediction model of the superconducting cavity. Online prediction phase: Input the superconducting cavity's operating data into the online prediction model to calculate the margin at each steady-state temperature point, predict the operational domain of the conduction-cooled superconducting cavity, and provide action suggestions based on the constraint set.

2. The method according to claim 1, characterized in that, Electromagnetic characteristics of the vacuum domain of the superconducting cavity were analyzed to obtain its characteristic frequencies, magnetic field distribution, and energy storage. U 0 and accelerating gradient E acc0 Calculate the target acceleration gradient as a baseline value. E acc Field distribution under [condition].

3. The method according to claim 2, characterized in that, Based on the target acceleration gradient E acc Field distribution and actual surface resistance Calculate the surface loss power density under the target acceleration gradient. And obtain dynamic heat load .

4. The method according to claim 2, characterized in that, according to Calculate scaling factor According to the scaling factor Scaling the field distribution yields the target acceleration gradient. E acc Field distribution under; E acc It is the target acceleration gradient. L eff It is the effective acceleration length. R / Q These are the characteristic impedance parameters of the superconducting cavity. f It is the characteristic frequency of the superconducting cavity.

5. The method according to claim 1, 2, or 3, characterized in that, The actual surface resistance Among them, C T It is the temperature factor, C Q It is the coating quality factor, R s This represents the theoretical surface resistance of the superconducting cavity.

6. The method according to claim 1, characterized in that, Based on the incident power of the radio frequency circuit Reflection power The additional heat load entering the cryogenic end of the superconducting cavity is calculated based on the line attenuation coefficient. .

7. The method according to claim 6, characterized in that, Based on the total heat load of the superconducting cavity The cooling capacity-temperature characteristic function of the two-stage cold head used in the vertical test system of the conductive cooling superconducting cavity. Calculate the temperature of the secondary cold head by reverse calculation ; Temperature of the secondary cold head As the thermal boundary condition at the cold head mounting location, a steady-state temperature field solution is performed to obtain the temperature distribution on the cavity surface. T(x,y,z) ;according to T(x,y,z) Update actual surface resistance Dynamic heat load With total heat load Repeat the above process until the thermal equilibrium convergence criterion is met; total heat load , This is the static heat load.

8. The method according to claim 7, characterized in that, The constraint set includes: (1) Cold head capability constraints ; (2) Hot spot temperature margin constraint ;in, This represents the maximum temperature at critical locations within the superconducting cavity and heat conduction path. These are the temperature limits for superconducting materials within the superconducting temperature range; (3) Reflection power ratio constraint ;in, The reflection threshold is set by the test system itself. (4) Temperature difference constraint across the superconducting transition temperature region ;in This represents the maximum temperature difference across the superconducting cavity during the transition from superconducting to superconducting temperature. The design limit is set for the maximum allowable temperature difference of the cavity; (5) Frequency constraints ; This represents the frequency drift relative to the reference state.

9. The method according to claim 8, characterized in that, Based on the margin and constraint set at each steady-state temperature point, action suggestions are given: (1) For fixed coupling conditions Find the maximum reachable gradient at the current steady-state temperature. ; Output the maximum allowed gradient or maximum permissible incident power And provide a step-by-step strategy; When the dominant limiting factor is the reflectance ratio When the output reflection warning threshold is reached, it is recommended to suspend power increase and prioritize checking coupling matching, antenna attenuation, and additional heat load at the low temperature end. When the dominant limiting factor is the cooling head capability or hot spot temperature At that time, the output cold head has an absolute margin, and it is recommended that if subsequent tests continue to stay at this operating point, the priority should be to reduce static heat load, reduce antenna dissipation, or improve contact thermal resistance. (2) For adjustable coupling conditions Find the maximum reachable gradient at the current steady-state temperature. ; Output the maximum allowed gradient or maximum permissible incident power Give the direction of coupling adjustment, so that Maintaining within the preset range, thereby reducing And expand the operational boundaries; When the dominant limiting factor is When the dominant limiting factor is..., it is recommended to adjust the coupling to reduce reflection; when the dominant limiting factor is... or When this is the case, it is recommended to limit the power step or back to a safe operating point while maintaining low reflection. If the dominant limiting factor is the misharmonic constraint If detuning causes a significant increase in reflection, output a detuning warning and suggest taking tuning strategies, reducing the power step, or waiting for thermal stability to avoid an increase in reflection power caused by frequency drift. (3) Construct a criterion for loss of control risk based on absolute margin; When the absolute margin of the cooling head rapidly approaches zero, or the absolute margin of the hot spot rapidly approaches zero, or the reflected power rapidly increases during the power / gradient increase process, it is determined that the system has entered a high-risk zone for overload and an early warning and power rollback suggestion are issued.

10. The method according to claim 9, characterized in that, Using the constraint with the minimum margin as the dominant limiting factor, we explain the reasons for the boundary formation and provide directions for test improvement.

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