Method, device and equipment for online measurement of loaded quality factor of radio frequency superconducting cavity

Abstract

The method, device and equipment for online measuring the loaded quality factor of a radio frequency superconducting cavity provided by the present invention include: obtaining the cavity pressure of the radio frequency superconducting cavity; V c , forward voltage V f And low level output signal V LLRF ; For low level output signal V LLRF Correction is performed to obtain the corrected signal V 1; Based on cavity pressure V c , forward voltage V f and signal V 1. Construct a generalized cavity system differential equation in polar coordinates; solve the zero-state step response and zero-input response of the generalized cavity system differential equation in polar coordinates to obtain the half-bandwidth of the generalized cavity system; obtain the loaded quality factor of the radio frequency superconducting cavity according to the half-bandwidth of the generalized cavity system. Therefore, the present invention can realize the online accurate measurement of the loaded quality factor of the radio frequency superconducting cavity.

Description

Technical Field

[0001] The invention relates to a method, a device and equipment for online measuring the loaded quality factor of a radio frequency superconducting cavity under the condition of power source impedance mismatch, 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 or long pulse mode due to their low loss and high gradient characteristics. In recent years, many major accelerator projects at home and abroad have chosen superconducting technology as the preferred solution. In the field of RF superconductivity, the loaded quality factor of RF superconducting cavities is Q L is a very important physical quantity. First, the loaded quality factor Q L It is an important indicator to determine whether the cavity has thermal quench; secondly, the loaded quality factor Q L It is the key parameter for calibrating the cavity acceleration gradient using the cavity incident power; secondly, the loaded quality factor Q L or cavity half bandwidth f 0.5 is the core parameter of the cavity mathematical model; finally, when the cavity is operating with a beam, the loaded quality factor of the cavity is Q L It also needs to be matched with the beam current to achieve optimal acceleration efficiency.

[0003] Loaded quality factor of the cavity Q L It can be measured based on the cavity field attenuation curve after turning off the RF power source. This is also the mainstream technical solution adopted by international accelerator laboratories such as the European Synchrotron Radiation Laboratory (DESY) and the Japan High Energy Accelerator Research Institute. However, the above method is derived from the zero input response of the cavity differential equation, which requires the cavity incident signal (also called the forward signal) to be V f ) is 0 after the RF power is turned off. In practice, since the impedance of the power source or high-power circulator cannot completely match the impedance of the transmission line, the cavity reflection signal (also called reverse signal) V r ) will be reflected back from the power source and mixed into V f , resulting in a loaded quality factor Q L Inaccurate measurement.

[0004] In summary, the existing technology can achieve a loaded quality factor Q LThe method of measuring the cavity quality factor under the condition of power source impedance mismatch is urgent. Summary of the invention

[0005] 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 a method, device and equipment for online measurement of the loaded quality factor of a radio frequency superconducting cavity, which can calculate the loaded quality factor of the cavity regardless of whether the impedance of the source end is well matched with the transmission line. Q L .

[0006] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is:

[0007] In a first aspect, the present invention provides a method for online measuring the loaded quality factor of a radio frequency superconducting cavity, the method comprising: obtaining a cavity pressure of the radio frequency superconducting cavity; V c , forward voltage V f And low level output signal V LLRF ; For low level output signal V LLRF Process the signal V 1, where V 1= V LLRF , g is a complex constant coefficient; based on the cavity pressure V c , forward voltage V f and signal V 1. Construct the differential equation of the generalized cavity system in polar coordinates; solve the zero-state step response and zero-input response of the differential equation of the generalized cavity system in polar coordinates to obtain the half-bandwidth of the generalized cavity system; obtain the loaded quality factor of the RF superconducting cavity based on the half-bandwidth of the generalized cavity system.

[0008] In some possible embodiments, based on the cavity pressure V c , forward voltage V f and signal V 1 The specific process of constructing the differential equation of the generalized cavity system in polar coordinates is as follows: Based on the cavity pressure V c and forward voltage V fConstruct the cavity differential equation, and obtain the cavity transfer function model from the cavity differential equation through the Latten transformation; introduce the feedback loop, and establish the transfer function model of the generalized cavity system based on the cavity transfer function model; establish the generalized cavity system differential equation through the Latten inverse transformation based on the transfer function model of the generalized cavity system; convert the cavity pressure V c and signal V 1 According to the amplitude and phase angle decomposition, the differential equation of the generalized cavity system in polar coordinates is obtained.

[0009] In some possible embodiments, the differential equation of the generalized cavity system is:

[0010] ;

[0011] in, Cavity pressure V c The differential of Ω 0.5 is the half bandwidth of the generalized cavity system, ΔΩ is the detuning of the generalized cavity system, is a constant, j Is an imaginary unit.

[0012] In some possible embodiments, the differential equation of the generalized cavity system in polar coordinates is:

[0013] ;

[0014] in, is the input signal, r Cavity pressure V c The amplitude, is the differential of r.

[0015] In some possible embodiments, the zero-state step response of the generalized cavity system differential equation in polar coordinates is solved based on the RF field establishment time after the solid-state power source is turned on, based on the cavity pressure V c Amplitude r The rising process of the generalized cavity system is obtained as 0.5, rise .

[0016] In some possible embodiments, the half bandwidth Ω of the generalized cavity system is 0.5, rise The calculation process is:

[0017] t = 0, the input signal suddenly jumps to the given value, the cavity pressure V c The amplitude gradually increases from 0, and the whole process is similar to the step response under zero-state conditions. The differential equation of the generalized cavity system becomes:

[0018] ;

[0019] in, u ( t ) is a unit step signal, 0 ≤ t < t OFF ,constant h 0 is signal h ( t ) exist t = 0 time to t = t OFF The average value between moments;

[0020] The solution to the above differential equation is:

[0021] ;

[0022] make:

[0023] ;

[0024] Taking the logarithm of the above formula, we get:

[0025] ;

[0026] in, R 1( t ) vs. time t There is a linear relationship, through ln[ R 1( t )] The linear fitting of the signal can calculate Ω 0.5, rise .

[0027] In some possible embodiments, the zero input response of the generalized cavity system differential equation in polar coordinates is solved based on the cavity field decay time after the solid-state power source is turned off, based on the cavity pressure V c Amplitude r The decreasing process of the generalized cavity system gives the half bandwidth Ω 0.5, decay , the specific process is:

[0028] t = t OFF At this moment, the input signal suddenly jumps to 0, and the cavity pressure V c The amplitude gradually decays to 0. t > t OFF , the whole process is similar to the zero input response, and the differential equation of the generalized cavity system becomes:

[0029] ;

[0030] The solution to the above zero input equation is:

[0031] ;

[0032] Among them, the constant r 0= r(t OFF - );

[0033] make:

[0034] ;

[0035] Taking the logarithm of the above formula, we get:

[0036] ;

[0037] in, R 2( t ) vs. time t There is a linear relationship, through ln[ R 2( t )] Linear fitting of the signal can calculate Ω 0.5, decay .

[0038] In some possible embodiments, the loaded quality factor of the radio frequency superconducting cavity, including the loaded quality factor during the cavity pressure increase phase, is Q L, rise and the loaded quality factor during the cavity pressure decay phase Q L, rise , the specific calculation formula is:

[0039] ;

[0040] In the formula, f 0.5, rise and f 0.5, decay is the half bandwidth obtained based on the rise period and decay period, f RF is the RF operating frequency.

[0041] In a second aspect, the present invention also provides an apparatus for online measuring the loaded quality factor of a radio frequency superconducting cavity, comprising: a signal acquisition module configured to acquire the cavity pressure of the radio frequency superconducting cavity; V c , forward voltage V f And low level output signal V LLRF ; The signal processing module is configured to output a low level signal V LLRF Process the signal V 1, whereV 1= V LLRF , g are complex constant coefficients; differential equation building blocks are configured based on the cavity pressure V c , forward voltage V f and signal V 1. Constructing a differential equation of the generalized cavity system in polar coordinates; a differential equation solving module is configured to solve the zero-state step response and zero-input response of the differential equation of the generalized cavity system in polar coordinates to obtain the half-bandwidth of the generalized cavity system; a loaded quality factor solving module is configured to obtain the loaded quality factor of the radio frequency superconducting cavity according to the half-bandwidth of the generalized cavity system.

[0042] 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.

[0043] The present invention adopts the above technical solution, and has the following characteristics:

[0044] 1. The present invention proposes an online solution for the cavity loaded quality factor Q L The new method can calculate the loaded quality factor of the cavity regardless of whether the impedance of the source end is well matched with the transmission line. Q L , and its calculation results are consistent with those measured by precision instruments.

[0045] 2. The present invention can detect the loaded quality factor online Q L Dynamic changes over time, during the RF training process of the RF superconducting cavity pulse operation mode, the present invention can be directly used to identify thermal quench events, and high-precision loaded quality factor Q L The measurement results can also be used to calibrate the acceleration gradient of the radio frequency superconducting cavity.

[0046] In summary, the present invention can be widely used in particle accelerators. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] 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:

[0048] Figure 1 The present invention is a flowchart of a method for online measurement of a radio frequency superconducting cavity loaded quality factor according to an embodiment of the present invention.

[0049] Figure 2 The system block diagram of online measurement of loaded quality factor of a radio frequency superconducting cavity according to an embodiment of the present invention is shown.

[0050] Figure 3 : is an equivalent block diagram of the cavity transfer function under impedance matching and mismatch in an embodiment of the present invention, wherein a is a block diagram under ideal conditions (i.e., when the impedance is completely matched), b is a schematic diagram of the reverse signal being reflected from the source end and re-mixed into the forward signal when the impedance is mismatched; c is an equivalent block diagram of a real RF superconducting cavity system when the impedance is mismatched in practice, and d is a simplified block diagram of c after equivalent transformation.

[0051] Figure 4 : is a waveform diagram of the cavity pressure, forward and reverse signals of the radio frequency superconducting cavity in the embodiment of the present invention, wherein a is a waveform diagram of the cavity pressure, forward and reverse signals of the radio frequency superconducting cavity in the self-excited working mode (SEL), and b is a low-level output signal of the radio frequency superconducting cavity in the self-excited working mode (SEL) after incident and amplified by the power source V 1 and the reverse signal mixed into the forward signal V 2.

[0052] Figure 5 is the cavity pressure in the embodiment of the present invention V c With signal V 1 is a schematic diagram of the phase difference between .

[0053] Figure 6 Ω is calculated according to the cavity pressure rising process and falling process in the embodiment of the present invention. 0.5 An example of the process of calculating the chamber pressure rise process is shown in Figure 2, where a is the calculation of Ω during the chamber pressure rise process. 0.5 The process example diagram of b is the calculation of Ω during the cavity pressure drop process. 0.5 is an example diagram of the process, and c is an enlarged view of the box in a.

[0054] Figure 7 Schematic diagram of the measurement results of the cavity half bandwidth of the cavity system in the embodiment of the present invention, where a is the half bandwidth of the cavity system F 0.5 Long-term measurement results at the rising and falling edges, b is the cavity half bandwidth f 0.5 Long-term measurement results at rising and falling edges. DETAILED DESCRIPTION

[0055] 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.

[0056] Since existing technology can achieve loaded quality factor Q L The present invention provides a method, device, equipment and medium for online measurement of the loaded quality factor of a radio frequency superconducting cavity, including: obtaining the cavity pressure of the radio frequency superconducting cavity; V c , forward voltage V f And low level output signal V LLRF ; For low level output signal V LLRF Process the signal V 1, where V 1= V LLRF , g is a complex constant coefficient; based on the cavity pressure V c , forward voltage V f and signal V 1. Construct a generalized cavity system differential equation in polar coordinates; solve the zero-state step response and zero-input response of the generalized cavity system differential equation in polar coordinates to obtain the half-bandwidth of the generalized cavity system; obtain the loaded quality factor of the radio frequency superconducting cavity according to the half-bandwidth of the generalized cavity system. Therefore, the present invention can realize the online accurate measurement of the loaded quality factor of the radio frequency superconducting cavity.

[0057] 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.

[0058] Embodiment 1: Figure 1 As shown, the method for online measuring the loaded quality factor of a radio frequency superconducting cavity under the condition of power source impedance mismatch provided by this embodiment includes:

[0059] S1. Baseband signal reading: obtaining the cavity pressure of the RF superconducting cavity V c , original forward voltage V f * , original reverse voltage V r * and low level output signal V LLRF .

[0060] In this embodiment, Figure 2 As shown, a system for online measurement of the loaded quality factor 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, a host computer 8 and a coaxial feed tube 9. 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 through the coaxial feed tube 9, the output end (through port) of the directional coupler 3 is fed into the radio frequency superconducting cavity through the input coupler 4, and the directional coupler 3 extracts the cavity incident signal. P f and reflected signal P r The signal extraction coupler 6 is used to connect the radio frequency superconducting cavity 5 to extract the cavity sampling signal. P t , the above signals ( P f , P r and P t ) is received by the digital low-level system 1 after being down-converted by the down-conversion module 7. The digital low-level system 1 receives the radio frequency signal ( P f , P r and P t ) to demodulate the corresponding digital baseband in-phase and quadrature (I / Q) components, and finally upload them to the host computer 8 through the data bus. The power source impedance mismatch of this embodiment refers to the mismatch between the output impedance of the solid-state power source and the characteristic impedance of the transmission line (coaxial feed tube), which usually causes the RF signal on the transmission line to be reflected again from the solid-state power source.

[0061] Furthermore, the digital low-level system 1 is provided with a field programmable gate array (FPGA for short), and the FPGA is provided with a digital signal processing module, which converts the cavity sampling signal of the radio frequency superconducting cavity P t , cavity incident signal P f and reflected signal P r The corresponding three-way original voltage signals are processed and down-converted into intermediate frequency signals. Three groups of original digital baseband signals are obtained by sampling the intermediate frequency signals and performing I / Q demodulation, namely: the cavity pressure of the RF superconducting cavity V c , original forward voltage V f * and the original reverse voltage V r * Unless otherwise specified, the parameters involved in this embodiment, such as V c * , V f * , V r * , V LLRF , V f , V r , V 1 and V 2, etc. are all complex numbers, 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).

[0062] S2, signal calibration: original forward voltage V f * and the original reverse voltage V r * Calibrate to get the calibrated forward voltage V f and reverse voltage V r , and the low-level output signal of the digital low-level system output V LLRF (Right now Figure 2 The signal output from the digital low-level system 1 to the solid-state power source 2 is the input signal of the solid-state power source 2) and the cavity pressure V c Calibration signal V 1 and V 2.

[0063] In this embodiment, the formula V f = XV f * Get the forward voltage after calibration V f , where the correction factor X is plural, X Mainly used to compensate for the influence of RF signal transmission cables and high-power RF devices on measurement results. Complex coefficients X The existing technology can be used to solve it. Similarly, using the formula V r = YV r * Get the reverse voltage after calibration V r .

[0064] Theoretically, the forward / reverse voltage after calibration is V f / V r and cavity pressure V c The following relationship should be satisfied:

[0065] .

[0066] like Figure 4 As shown in a, the cavity pressure V c and the forward / reverse voltage after calibration V f / V r It can satisfy formula (1), further verifying the parameter X and Y reliability.

[0067] like Figure 3 As shown in a in the figure, when the solid-state power source impedance matches the transmission line (such as a coaxial feed tube) (that is, the output impedance of the solid-state power source is equal to the characteristic impedance of the coaxial feed tube, and the RF signal on the coaxial feed tube will not be reflected by the power source), the rectangular low-level output signal V LLRF After the solid-state power source 2 outputs, a rectangular forward signal is obtainedV f On the contrary, if Figure 3 As shown in b, when the solid-state power source impedance does not match the transmission line, part of the reverse signal V r Will be reflected back by solid-state power source 2 and mixed into the forward signal V f Therefore, the measured forward signal V f In addition to the contribution from the power source, it also includes a part of the reverse signal V r Therefore, the forward signal V f It will no longer be a rectangular pulse. The above process can be expressed as:

[0068] ;

[0069] Using formula (1) V r = V c ─ V f Substituting into formula (2) we get:

[0070]

[0071] Further:

[0072] ;

[0073] Among them, the complex constant coefficient g = c 1 / (1+ c 2), k = c 2 / (1+ c 2) With X and Y Same, c 1 and c 1 can be solved using existing technology. Complex constant coefficients g Mainly used to characterize V f The gain from the power source, the complex constant coefficient k Mainly used to characterize V f The gain of the cavity pressure signal due to impedance mismatch.

[0074] like Figure 4 As shown in b, V f and V LLRF andV c Satisfying formula (3) further verifies the complex constant coefficient g and k The reliability of V 1= V LLRF , V 2= kV LLRF ,in, V 1 is the low-level output signal after being amplified by the power source. V 2 is the reverse signal mixed into the forward signal.

[0075] S3. Establish differential equations: Establish differential equations for a generalized cavity system consisting of an RF transmission line, a directional coupler, an input coupler, and an RF superconducting cavity.

[0076] In this embodiment, since the generalized cavity system includes the reflection process of the power source, it is relatively complicated to directly analyze its derivation process from the perspective of differential equations. This embodiment will draw on the idea of ​​the feedback loop of the control system and establish the differential equation of the generalized cavity system from the perspective of the transfer function, which is divided into four steps: first, obtain its transfer function model from the cavity differential equation through the Lapse transformation; then, introduce the feedback loop to establish the transfer function model of the generalized cavity system; third, through the Lapse inverse transformation, return from the transfer function of the generalized cavity system to the differential equation of the generalized cavity system. Finally, in order to facilitate finding the solution of the differential equation, the amplitude and phase are separated from the differential equation of the generalized cavity system, and the differential equation in polar coordinate form is established. The specific process is as follows, including:

[0077] S31. Obtain the transfer function model from the cavity differential equation through Lapland transformation.

[0078] In this embodiment, based on the cavity pressure V c and forward voltage V f Construct the cavity differential equation as follows:

[0079] ;

[0080] in, Cavity pressure V c The differential, parameter β is the coupling coefficient, for the RF superconducting cavity β >>1; ω 0.5 is the cavity half bandwidth, Δ ω is the dynamic cavity detuning. Note that f 0.5 With Δ fAlso used to express the half-bandwidth and detuning of a cavity, but they are not related to ω 0.5 and Δω The units are different. f 0.5 With Δ f The units of are all Hertz, and the corresponding relationships of the above physical quantities are as follows:

[0081] .

[0082] In this embodiment, Figure 3 As shown in b, the above differential equation (4) is transformed into V f arrive V c The transfer function model of the time domain signal is as follows: V ( t ) in the complex frequency domain corresponds to V ( s ), time domain signal V ( t )differential In the complex frequency domain, the Lassen transform corresponds to sV ( s ). According to the above rules, the La-type transformation of formula (4) is:

[0083] .

[0084] The above formula can be further simplified to obtain:

[0085] .

[0086] Note that due to β >>1, in formula (5), 2 β / (1+ β ) simplifies to the constant 2. That is from V f arrive V c The transfer function is abbreviated as H 1( s ).

[0087] S32. Introduce a feedback loop to establish a transfer function model of the generalized cavity system.

[0088] In this embodiment, when the source impedance does not match, a portion of the reflected signal on the transmission line will be reflected by the source, re-enter the transmission line and mix into the incident signal. V fFrom the perspective of signal and system, it can be considered that the generalized cavity system has a feedback path. Figure 2 The invention discloses a generalized RF system from the output end of the solid-state power source to the output end of the RF superconducting cavity, including a transmission line (i.e., a coaxial feed pipe), a directional coupler, an input coupler and a superconducting cavity.

[0089] like Figure 3 As shown in c, part of the feedback signal will be sent from the output end ( V c ) is fed back to the input terminal ( V f ), considering the cavity including the feedback loop as a whole, the signal V 1 to V c The transfer function model is:

[0090] ;

[0091] Notice: That is from V 1 to V c The transfer function is abbreviated as H 2( s ), the above formula is simplified to:

[0092] ;

[0093] in, k I is a complex constant coefficient k The real part of k Q is a complex constant coefficient k The imaginary part of .

[0094] Further, let Among them, Ω 0.5 It can also be considered as the half bandwidth of the generalized cavity system, and ΔΩ is recorded as the detuning of the generalized cavity system, both of which are in radians per second. Under the above conditions, if Figure 3 As shown in d, formula (6) can be further simplified as:

[0095] .

[0096] S33. By using the inverse Latent transformation, the differential equation of the generalized cavity system is established according to the transfer function in equation (7).

[0097] In this embodiment, formula (7) can be converted into:

[0098] .

[0099] According to the inverse Lagrange transform, the above formula is converted into the time domain form. The conversion rule is: sV ( s ) is converted into the time domain through the inverse Lapland transform , in the complex frequency domain V ( s ) is converted into the time domain through the inverse Lapland transform V ( t ), according to the above rules, transform the above formula into differential equation form:

[0100] .

[0101] The above differential equation (8) is the differential equation of the generalized cavity system, which includes the RF transmission line, directional coupler, input coupler and RF superconducting cavity. Note that this equation already includes the feedback path (i.e., the reflection process at the power source end), which is also the key difference between equation (8) and the cavity differential equation (which does not include the reflection process at the source end).

[0102] S34. Establish the differential equation of the generalized cavity system in polar coordinates.

[0103] In this embodiment, the cavity pressure V c and signal V 1 is decomposed into polar coordinates according to the amplitude and phase angle as follows:

[0104] .

[0105] In the formula, r and They are V c Amplitude and phase angle, 0.5 μ and ε Signal V 1In terms of amplitude and phase angle.

[0106] Note that the parameter " μ The coefficient 0.5 in front is to offset the 2 in equation (8). Substituting the above equation into the differential equation (8) of the cavity system, we get:

[0107] .

[0108] Furthermore, the above equation can be separated into real and imaginary parts:

[0109] .

[0110] The real part of the above equation can be further expressed as:

[0111] .

[0112] in, , formula (9) is the differential equation of the generalized cavity system in polar coordinates.

[0113] S4. Solve the zero-step response and zero-input response of the differential equation of the generalized cavity system in polar coordinates.

[0114] In this embodiment, Figure 4 and Figure 5 The waveform diagram of each signal when the cavity works in the self-excitation mode. t = 0 time when the RF power is fed in, V 1 and V f Jump from 0 to a given value, V c The magnitude of t = t OFF Time (approximately t = 5 milliseconds position), turn off the solid-state power source power, V The amplitude of 1 immediately jumps to 0. V c The amplitude decays exponentially. It can be seen that due to the mismatch of the source impedance, V f Due to mixing with some V c And includes a slow rise and decay process, such as Figure 4 As shown in a. Figure 4 As shown in b, V 1Amplitude 0.5 μ Approximately rectangular. In the self-excited (SEL) working mode, V c and V The phase difference of 1 is approximately constant ( Figure 5 ),because b= 1 / (1-2 k I ) is a constant; then Figure 6 As shown, the input signal on the left side of differential equation (9) It is approximately a rectangle. Note that in the embodiments of the present invention, the cavities all work in the SEL mode.

[0115] S41. Solve the zero-state step response of the differential equation. The process is as follows:

[0116] like Figure 6 As shown in a and c, t = 0, the input signal of differential equation (9) suddenly jumps to a given value (about 900), V cThe amplitude gradually rises from 0, and the whole process is similar to the step response under zero state conditions (0 ≤ t < t OFF ), the differential equation (9) becomes:

[0117] .

[0118] in, u ( t ) is a unit step signal. Constant h 0 is signal h ( t ) exist t = 0 time t = t OFF The average value between moments (such as Figure 6 As shown, the embodiment of the present invention h 0≈900), then the solution of the differential equation (10) is:

[0119] .

[0120] Moving the exponential term in (11) to the left side of the equation yields:

[0121] .

[0122] definition , then the above formula becomes:

[0123] .

[0124] then Taking the logarithm we get:

[0125] .

[0126] Among them, Ω 0.5, rise According to the rise time (0 ≤ t < t OFF ) is the half bandwidth of the generalized cavity system, which is generally a constant. It is not difficult to see from formula (13) that R 1( t ) vs. time t There is a linear relationship, through ln[ R 1( t )] The linear fitting of the signal can calculate Ω 0.5, rise .

[0127] S42. Solve the zero input response of the differential equation. The process is as follows:

[0128] like Figure 6 As shown in b,t = t OFF At the moment when the input signal of the differential equation (9) suddenly jumps to 0, V c The amplitude gradually decays to 0 ( t > t OFF ), the whole process is similar to the zero input response, and the differential equation (9) becomes:

[0129] .

[0130] The above differential equation is a classical first-order linear differential equation, and its solution has the following general form:

[0131] ;

[0132] Among them, the constant C can be obtained from the initial conditions.

[0133] like Figure 6 As shown in b, t = t OFF At this moment, the left side of formula (15) is r 2( t OFF ), which is the signal r 2( t )exist t = t OFF The value at the moment (at Figure 6 In r 0≈800. ), let this value be written as r 0; the right side of formula (15) is a constant C , easy to get C = r 2( t OFF )= r 0.

[0134] Move the exponential term in equation (15) to the left side of the equation to obtain:

[0135] .

[0136] definition , then the above formula can be further converted to

[0137] .

[0138] Taking the logarithm of the above formula, we get:

[0139] .

[0140] Among them, Ω 0.5, decay According to the decay time ( t > t OFF ) is the half bandwidth of the generalized cavity system, which is generally a constant. It is not difficult to see from formula (17) that R 2( t ) vs. time t Linear relationship ( t > t OFF ), by ln[ R 2( t )] Linear fitting of the signal can calculate Ω 0.5, decay .

[0141] S5. Solve the loaded quality factor Q L .

[0142] In this embodiment, the loaded quality factor Q L and half bandwidth ω 0.5 and f 0.5 The following relationship is satisfied:

[0143]

[0144] Notice, ω 0.5 and f 0.5 Both represent the cavity half bandwidth, and their units are radians per second and Hertz, respectively. f RF is the resonant frequency of the cavity.

[0145] According to formula (7), ω 0.5 = b· Ω 0.5 , b =1 / (1-2 k I ). For Ω 0.5, rise and Ω 0.5, decay , first calculate the half bandwidth of the cavity pressure rising stage ω 0.5, rise and f 0.5, rise , and the half bandwidth of the cavity pressure decay phase ω 0.5, decay and f 0.5, decay , and further, the loaded quality factor of the cavity pressure rising stage is obtained respectively QL, rise and the loaded quality factor during the cavity pressure decay phase Q L, rise , the formula is summarized as follows:

[0146] ;

[0147] In the formula, f 0.5, rise and f 0.5, decay It is based on the half bandwidth of the rise period and decay period, and its unit is Hertz.

[0148] The specific application of the method for online measuring the loaded quality factor of a radio frequency superconducting cavity of the present invention is described in detail below through specific embodiments.

[0149] The solid-state power source 2 used in this embodiment is manufactured by Chengdu Kaiteng Company. Each power source includes 24 inserts, and the saturated output power of a single insert is about 1.4 kW. The radio frequency superconducting cavity 5 adopts a half-wavelength radio frequency superconducting cavity, the resonant frequency of the cavity is 162.5 MHz, and the half bandwidth is about 120 Hz.

[0150] Based on the above parameter settings, the method for online measuring the loaded quality factor of a radio frequency superconducting cavity provided in this embodiment includes:

[0151] 1. Voltage signal measurement.

[0152] like Figure 1 As shown, the cavity pressure of the radio frequency superconducting cavity 5 is measured. V c , original forward voltage V f * and the original reverse voltage V r * ,include:

[0153] 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 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.

[0154] 2. After the above RF signal is down-converted, digitized and I / Q demodulated in sequence, the digitized original baseband voltage signal, i.e., the cavity pressure V c , original forward voltage V f * and the original reverse voltage V r * .

[0155] 2. Signal calibration.

[0156] According to the original forward voltage V f * and the original reverse voltage V r * Perform signal calibration, including:

[0157] 1. Original forward voltage signal V f * calibration.

[0158] according to V f = XV f * Solve for the calibrated forward signal. Note: The cavity pressure signal is usually used as a reference signal and does not require calibration. The complex multiplication operation can be performed as follows:

[0159] ;

[0160] In the formula, V fI and V fQ They are V f 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 the original reverse voltage V r * The calibration and original forward voltage signal V f* The calibration principle is the same as that of , so I will not go into details here.

[0161] 2. Signal V 1 calibration process.

[0162] and V f Similar to the calibration, read the current low level output signal online V LLRF ,according to V 1= V LLRF Get the signal V 1. Complex number multiplication operations can be performed as follows:

[0163] ;

[0164] In the formula, V 1I and V 1Q They are V The real and imaginary parts of 1; V LLRFI and V LLRFQ They are V LLRF The real and imaginary parts of g I and g Q are complex constant coefficients g The real and imaginary parts of .

[0165] 3. Construct differential equations.

[0166] The cavity pressure V c and signal V 1 is decomposed into polar coordinates according to the amplitude and phase angle as follows:

[0167] ;

[0168] Evaluate the input signal of the differential equation h ( t ), the formula is as follows:

[0169] ;

[0170] The differential equation of the cavity system is constructed as follows:

[0171] .

[0172] It should be noted that the low level output signal V LLRFThe waveform can be selected independently. In this embodiment, a rectangular wave is selected. Since the radio frequency superconducting cavity needs a sufficiently long time to achieve field building, the pulse width of the rectangular wave can generally be selected to be 5 to 10 milliseconds. In this embodiment of the present invention, the pulse width of the rectangular wave is selected to be 5 milliseconds. V 1= V LLRF ,Depend on Figure 4 As can be seen from b, V The pulse width of 1 is also 5 milliseconds.

[0173] 4. Solve differential equations.

[0174] 1. Solve the step response of the differential equation.

[0175] like Figure 6 As shown in a, t = 0 time, h ( t ) suddenly jumps to a given value (about 900), V c The amplitude gradually rises from 0, and the whole process is similar to the step response under zero state conditions (0 ≤ t < t OFF ), the solution of the differential equation is:

[0176] ;

[0177] in, h 0 can be selected h ( t )exist t = t 1 and t = t The average value between 2. t 2 can be selected as t OFF The previous 0.1~0.2 milliseconds, t 1 Relative t 2 1~2 milliseconds in advance, the average calculation process can directly call Python numpy.mean function.

[0178] like Figure 6 As shown in a, r 1( t ) can be further converted to:

[0179] ;

[0180] Taking the logarithm of the above formula, we get: ;

[0181] Among them, Ω 0.5, rise According to the rise time (0 <t < t OFF ) is the half bandwidth of the generalized cavity system, which is generally a constant. It is not difficult to see that R 1( t ) vs. time t There is a linear relationship. By ln[ R 1( t )] The linear fitting of the signal can calculate Ω 0.5, rise . It should be noted that in the case of ln[ R 1( t )]When linear fitting is performed, t The value should be between 0 and t OFF Within the range. t Minimum value of t a >0, i.e. t The maximum value of t b < t OFF Preferably, t a Optional so that R 1( t a ) is in the range of 0.9 to 1. R 1( t a )=0.95. t b Optional so that R 1( t b ) is in the range of 0.5 to 0.75. R 1( t b )=0.5. On this basis, x = t , y =ln[ R 1( t )]Linear fitting, t The value range is t a < t < t b . Linear fitting can be done using Python's numpy.polyfit Functions, for example: P 1= numpy.polyfit ( x , y , 1), where Ω 0.5, rise =- P1(0), Python subscripts start at 0.

[0182] 2. Solve the zero input response of the differential equation.

[0183] like Figure 6 As shown, the above sub-figure corresponds to the RF superconducting cavity in the self-excited working mode (SEL), the signal h ( t ) and the cavity pressure amplitude when it rises and falls r 1( t )and r 2( t ). The two middle sub-pictures are signals r 1( t )and r 2( t )The result after linear transformation and normalization R 1( t )and R 2( t ). The two sub-pictures at the bottom are for the signal R 1( t )and R 2( t ) After obtaining the logarithm, the half bandwidth Ω of the generalized cavity system can be obtained according to the rising process and the falling process through linear fitting. 0.5, rise and Ω 0.5, decay The measurement results.

[0184] Specifically, Figure 6 As shown in b, t = t OFF time V 1 jumps to 0, V c The amplitude gradually decays to 0 ( t > t OFF ), the whole process is similar to the zero input response, and the solution of the differential equation is:

[0185] ;

[0186] Among them, the constant r 0= r 2 (t OFF - ), in the embodiment of the present invention, as Figure 6 As shown in b, r 0≈800.

[0187] The above formula can be further converted into:

[0188]

[0189] Taking the logarithm of the above formula, we get:

[0190] ;

[0191] Among them, Ω 0.5, decay According to the decay time ( t > t OFF ) is the half bandwidth of the generalized cavity system calculated, which is generally a constant. It is not difficult to see from formula (17) that R 2( t ) vs. time t There is a linear relationship, through ln[ R 2( t )] Linear fitting of the signal can calculate Ω 0.5, decay . As with the step response of the differential equation, in the case of ln[ R 1( t )]When linear fitting is performed, t The value of should be t c < t < t d . t Minimum value of t c > t OFF Preferably, t c Optional so that R 2( t a ) is in the range of 0.9 to 1. R 1( t a )=0.95. t d Optional so that R 2( t d ) is in the range of 0.5 to 0.75. R 2( t d )=0.5. On this basis, x = t , y ln[ R 2( t )]Linear fitting, t The value range is t c < t < t d. Linear fitting can be done using Python's numpy.polyfit Functions, for example: P 2= numpy.polyfit ( x , y , 1), where Ω 0.5, decay =- P 2(0), Python subscripts start at 0.

[0192] 5. Calculate the loaded quality factor of the generalized cavity system.

[0193] Calculate the cavity half bandwidth ω 0.5, rise and ω 0.5, decay , the formula is as follows:

[0194] ;

[0195] It is worth noting that in principle, the calculated values ​​in both cases ( ω 0.5, rise , ω 0.5, decay ),( Q L, rise , Q L, decay ) should be equal. However, in practice, the measurement results may be affected by environmental drift. In addition, in the embodiment of the present invention, ( ω 0.5, rise , ω 0.5, decay )and( f 0.5, rise , f 0.5, decay ) refers to the half bandwidth of the cavity. (Ω 0.5, rise ,Ω 0.5, decay )and( F 0.5, rise , F 0.5, decay ) refers to the half bandwidth of the generalized cavity system. F 0.5, rise =Ω 0.5, rise / (2π) , F 0.5, decay =Ω 0.5, decay / (2π), its unit is Hertz.

[0196] 6. Online experimental verification.

[0197] The experiment of this embodiment has been carried out in TM 010 Experimental verification on a radio frequency superconducting cavity shows that the working frequency of the cavity f RF =162.5 MHz. Figure 7 a in the figure is the half bandwidth of the cavity system measured based on the cavity pressure rise time (rising edge, black) and decay time (falling edge, red) of the 9# RF superconducting cavity. Figure 7 b in the figure is the half bandwidth of the cavity obtained by measuring the cavity pressure rise time (black) and decay time (red) in the embodiment of the present invention. It can be seen that the measurement results obtained by the two methods are less than 1 Hz.

[0198] In order to further verify the effectiveness of the present invention, this embodiment uses a network analyzer to measure the bandwidth and Q L The input and output ports of the network analyzer are directly connected to the RF superconducting cavity through the input coupler and the signal extraction coupler. The measurement results of the network analyzer are: Q L =647811, corresponding to half bandwidth f 0.5,网分 =162.5×10 6 / 2 / 647811≈125.4 Hz. It can be seen that the measurement results of the network are consistent with Figure 7 The measured results are very consistent, further proving the effectiveness of the present invention. It is worth noting that solving the step response requires the system to work in SEL mode, while solving the zero input response generally does not have this requirement. Therefore, after turning off the RF power, the bandwidth and Q L Finally, Table 1 compares the cavity measured by the traditional method, the method of the present invention and the network analyzer. Q L It can be seen that the measurement results of the present invention (attenuation process) are basically consistent with the measurement results of the network division, which verifies the effectiveness of the present invention.

[0199]

[0200] Embodiment 2: Embodiment 1 above provides a method for online measurement of the loaded quality factor of a radio frequency superconducting cavity. Correspondingly, this embodiment provides a device for online measurement of the loaded quality factor of a radio frequency superconducting cavity. The device provided in this embodiment can implement the method for online measurement of the loaded quality factor of a radio frequency superconducting cavity of Embodiment 1, and the device can be implemented by software, hardware, or a combination of software and hardware. For the convenience of description, this embodiment is described in various units according to their functions. Of course, the functions of each unit can be implemented in the same or multiple software and / or hardware during implementation. For example, the device may include integrated or separate functional modules or functional units to perform the corresponding steps in each method of Embodiment 1. Since the device of this embodiment is basically similar to the method embodiment, the description process of this embodiment is relatively simple, and the relevant parts can refer to the partial description of Embodiment 1. The embodiment of the device for online measurement of the loaded quality factor of a radio frequency superconducting cavity provided by the present invention is merely schematic.

[0201] Specifically, the device for online measuring the loaded quality factor of a radio frequency superconducting cavity provided in this embodiment includes:

[0202] The signal acquisition module is configured to obtain the cavity pressure of the radio frequency superconducting cavity. V c , forward voltage V f And low level output signal V LLRF ;

[0203] The signal processing module is configured to output a low level signal V LLRF Process the signal V 1, where V 1= V LLRF , g is a complex constant coefficient;

[0204] Differential equation building blocks are configured based on the cavity pressure V c , forward voltage V f and signal V 1. Construct the differential equation of the generalized cavity system in polar coordinates;

[0205] A differential equation solving module is configured to solve a zero-state step response and a zero-input response of a differential equation of the generalized cavity system in polar coordinates to obtain a half bandwidth of the generalized cavity system;

[0206] The loaded quality factor solving module is configured to obtain the loaded quality factor of the radio frequency superconducting cavity according to the half bandwidth of the generalized cavity system.

[0207] Embodiment 3: This embodiment provides an electronic device corresponding to the method for online measuring the loaded quality factor of a 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.

[0208] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In the description of this specification, the description of reference terms such as "a preferred embodiment", "further", "specifically", "in the present embodiment", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiments of this specification. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example.

[0209] 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. A method for online measurement of the loaded quality factor of a radio frequency superconducting cavity, characterized in that: The method includes: Obtaining the cavity pressure of a radio frequency superconducting cavity V c , forward voltage V f And low level output signal V LLRF ; For low level output signal V LLRF Process the signal V 1, where V 1= V LLRF , g is a complex constant coefficient. The specific process is: when the solid-state power source impedance matches the transmission line, the low-level output signal V LLRF After the solid-state power source output, a rectangular forward signal is obtained V f On the contrary, when the solid-state power source impedance does not match the transmission line, a portion of the reverse signal V r will be reflected back by the solid-state power source and mixed into the forward signal V f : ； Will V r = V c ─ V f Substituting into the above formula we get: Further: ； Among them, the complex constant coefficient g = c 1 / (1+ c 2), k = c 2 / (1+ c 2), and is the coefficient; make V 1= V LLRF , V 2= kV LLRF ,in, V 1 is the low-level output signal after being amplified by the solid-state power source. V 2 is the reverse signal mixed into the forward signal; Based on cavity pressure V c , forward voltage V f and signal V 1Construct the differential equation of the generalized cavity system in polar coordinates, including: based on the cavity pressure V c and forward voltage V f Construct the cavity differential equation, and obtain the cavity transfer function model from the cavity differential equation through the Latten transformation; introduce the feedback loop, and establish the transfer function model of the generalized cavity system based on the cavity transfer function model; establish the generalized cavity system differential equation through the Latten inverse transformation based on the transfer function model of the generalized cavity system; convert the cavity pressure V c and signal V 1. Decompose according to amplitude and phase angle to obtain the differential equation of the generalized cavity system in polar coordinates; Solve the zero-state step response and zero-input response of the differential equation of the generalized cavity system in polar coordinates to obtain the half-bandwidth of the generalized cavity system. The loaded quality factor of the radio frequency superconducting cavity is obtained according to the half bandwidth of the generalized cavity system.

2. The method for online measurement of the loaded quality factor of a radio frequency superconducting cavity according to claim 1, characterized in that: The differential equation of the generalized cavity system is: ； in, Cavity pressure V c The differential of is the half bandwidth of the generalized cavity system, is the detuning of the generalized cavity system, is a constant, j Is an imaginary unit.

3. The method for online measurement of the loaded quality factor of a radio frequency superconducting cavity according to claim 2, characterized in that: The differential equation of the generalized cavity system in polar coordinates is: ； in, is the input signal, r Cavity pressure V c The amplitude, is the differential of r.

4. The method for online measuring the loaded quality factor of a radio frequency superconducting cavity according to claim 2, characterized in that: The zero-state step response of the differential equation of the generalized cavity system in polar coordinates is solved based on the RF field establishment time after turning on the solid-state power source and the cavity pressure. V c Amplitude r The half bandwidth of the generalized cavity system is obtained by .

5. The method for online measurement of the loaded quality factor of a radio frequency superconducting cavity according to claim 4, characterized in that: Half-Bandwidth of Generalized Cavity Systems The calculation process is: t = 0, the input signal suddenly jumps to the given value, the cavity pressure V c The amplitude gradually increases from 0, and the whole process is similar to the step response under zero-state conditions. The differential equation of the generalized cavity system becomes: ； in, u ( t ) is a unit step signal, 0 ≤ t < t OFF ,constant h 0 is signal h ( t ) exist t = 0 time to t = t OFF The average value between moments; The solution to the above differential equation is: ； make: ； Taking the logarithm of the above formula, we get: ； in, R 1( t ) vs. time t There is a linear relationship, through ln[ R 1( t )] The linear fitting of the signal can be used to calculate .

6. The method for online measurement of loaded quality factor of a radio frequency superconducting cavity according to claim 4, characterized in that: The zero input response of the differential equation of the generalized cavity system in polar coordinates is solved based on the cavity field decay time after turning off the solid-state power source and the cavity pressure V c Amplitude r The half bandwidth of the generalized cavity system is obtained by the decreasing process of , the specific process is: t = t OFF At this moment, the input signal suddenly jumps to 0, and the cavity pressure V c The amplitude gradually decays to 0. t > t OFF , the whole process is similar to the zero input response, and the differential equation of the generalized cavity system becomes: ； The solution to the zero input equation is: ； Among them, the constant r 0= r(t OFF - ); make: ； Taking the logarithm of the above formula, we get: ； in, R 2( t ) vs. time t There is a linear relationship, through ln[ R 2( t )] Linear fitting of the signal can calculate .

7. The method for online measurement of loaded quality factor of a radio frequency superconducting cavity according to claim 5, characterized in that: The loaded quality factor of the RF superconducting cavity, including the loaded quality factor during the cavity pressure increase stage Q L, rise and the loaded quality factor during the cavity pressure decay phase Q L, rise , the specific calculation formula is: ； In the formula, f 0.5, rise and f 0.5, decay is the half bandwidth obtained based on the rise period and decay period, f RF is the RF operating frequency.

8. A device for implementing the method for online measuring the loaded quality factor of a radio frequency superconducting cavity as described in any one of claims 1 to 7, characterized in that: include: The signal acquisition module is configured to obtain the cavity pressure of the radio frequency superconducting cavity. V c , forward voltage V f And low level output signal V LLRF ; The signal processing module is configured to output a low level signal V LLRF Process the signal V 1, where V 1= V LLRF , g is a complex constant coefficient; Differential equation building blocks are configured based on the cavity pressure V c , forward voltage V f and signal V 1. Construct the differential equation of the generalized cavity system in polar coordinates; A differential equation solving module is configured to solve a zero-state step response and a zero-input response of a differential equation of the generalized cavity system in polar coordinates to obtain a half bandwidth of the generalized cavity system; The loaded quality factor solving module is configured to obtain the loaded quality factor of the radio frequency superconducting cavity according to the half bandwidth of the generalized cavity system.

9. 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 1-7.

Images