A method for measuring beam arrival time using an electro-optic method

Abstract

This invention provides a method for measuring the arrival time of a particle accelerator beam using an electro-optic method, comprising: determining the cavity radius and cavity length of a cavity probe that meet the resolution requirements for arrival time measurement; fabricating the cavity probe based on the cavity radius and cavity length, and using it as an electrical signal pickup probe to construct a beam arrival time measurement device based on the electro-optic method; simultaneously acquiring the output signal from the cavity probe and the electro-optic interaction signal from the photodetector using the data acquisition and processing system of the beam arrival time measurement device; and determining the beam arrival time using the output signal from the cavity probe and the electro-optic interaction signal. The method of this invention utilizes a phase cavity as the electrical signal pickup probe for the electro-optic method. Compared to the traditional high-bandwidth button electrode scheme, the cavity probe scheme has a lower frequency, significantly reducing the difficulty of fabrication and signal transmission processing, and is unaffected by the beam position on the measurement results.

Description

Technical Field

[0001] This invention relates to the field of accelerator physics beam diagnostics, and more particularly to an electro-optic method for measuring the arrival time of a particle accelerator beam. Background Technology

[0002] The beam arrival time is one of the important parameters of linear particle accelerators, especially free electron laser devices. There are two main methods for measuring it: the radio frequency phase cavity method and the electro-optic method.

[0003] The radio frequency phase cavity method mixes the radio frequency beam signal coupled to the phase cavity probe with the local oscillator signal phase-locked with the accelerator master clock, down-converts it to an intermediate frequency signal, and then performs synchronous digital sampling and processing on the intermediate frequency signal to extract the phase of the beam signal and calculate the beam arrival time.

[0004] like Figure 1 As shown, the electro-optic method utilizes a beam bipolar pulse electrical signal sensed by a broadband probe to modulate a reference laser pulse (i.e., a reference optical signal) that is phase-locked with the accelerator's master clock, thereby outputting a modulated laser pulse. For example... Figure 2 As shown, when the zero-crossing point of the electrical signal is aligned with the output laser pulse, the amplitude of the output laser pulse remains unchanged. When the zero-crossing point of the electrical signal is earlier than the arrival time of the laser pulse, the amplitude of the output laser pulse decreases. When the zero-crossing point of the electrical signal is later than the arrival time of the laser pulse, the amplitude of the output laser pulse increases. Thus, the beam arrival time can be obtained by detecting the change in the amplitude of the laser pulse signal.

[0005] Radio frequency phase cavity method systems are relatively simple and more reliable, but their resolution is generally limited to tens of femtoseconds. Electro-optic method systems are relatively complex because they involve laser signals, resulting in higher costs and lower reliability, but their resolution can reach below ten femtoseconds. Therefore, the electro-optic beam arrival time measurement method is used in hard X-ray free-electron laser devices where high resolution is required.

[0006] Button-type electrodes have a large output signal bandwidth, and their peak voltage is inversely proportional to the square of the bundle length. Therefore, button electrodes are generally used as the electrical signal pickup probes in electro-optic methods in free-electron laser devices. The formula for the resolution of the arrival time measurement system in an electro-optic method is as follows:

[0007]

[0008] Among them, t resolution It is the time of arrival measurement resolution, σ A'norm This is the accuracy of the reference optical pulse amplitude detection, which is determined by both the reference optical pulse amplitude jitter and the system detection error. This value can be obtained by detecting unmodulated optical pulses. σ A'norm The typical value is 0.2%. π.RFThe EOM half-wave voltage is fixed at 5V. S slope This represents the zero-crossing slope of the probe signal, i.e., the rising slope of the button electrode's induced signal. It can be seen that the resolution is inversely proportional to the slope of the RF signal output by the button electrode; the larger the slope, the higher the resolution.

[0009] The greater the slope of the output signal from the button electrode, the greater the modulation of the laser pulse by the change in beam arrival time, and the greater the amplitude change of the modulated laser pulse, thus resulting in a more accurate arrival time measurement. The signal slope is determined by two conditions: first, the probe bandwidth, as a larger bandwidth results in a steeper output signal; and second, the beam charge, which has a linear relationship with the slope, allowing the influence of charge on the measurement results to be corrected using a charge measurement system.

[0010] The Shanghai hard X-ray free-electron laser requires a time resolution of 20 fs at a beam current of 100 pC. Therefore, the rising slope of the zero-crossing output signal of the button electrode must be at least 318 mV / ps, and to allow for margin, the zero-crossing slope must reach 400 mV / ps. To achieve this slope, based on simulations and typical designs, the button electrode probe bandwidth needs to be above 30 GHz. Such a high-bandwidth probe places high demands on the fabrication process, and the transmission and processing of high-bandwidth RF signals are very difficult and costly. At the same time, the beam position dependence of the button electrode output signal amplitude is difficult to eliminate, thus affecting the measurement results.

[0011] Cavity probes are commonly used for high-precision position measurement of the undulator section in free-electron laser devices due to their strong coupling signal and high sensitivity. The coupled TM010 mode is unaffected by beam position, and through design, it can output a signal that meets the zero-crossing slope requirements at a lower cavity center frequency. Compared to traditional high-bandwidth button electrode solutions, cavity probe solutions have lower frequencies, significantly reducing fabrication and signal transmission processing difficulties, while remaining unaffected by beam position. Therefore, using cavity probes for electro-optic beam arrival time measurement would greatly enhance the measurement system.

[0012] However, cavity probes appeared later than button electrode probes. Currently, cavity probes are mainly used for position measurement and radio frequency cavity time-of-arrival (TOA) measurement, with applications in other fields still under research. Electro-optic TOA measurement is a novel measurement method based on the interaction between laser and beam electrical signals. The key to system performance lies in how to make the slope of the beam electrical signal sufficiently large. Currently, button electrodes output broadband signals, while cavity probes output single-frequency narrowband signals. Therefore, the key is how to design a cavity probe that can output a beam signal with a sufficiently large slope. Summary of the Invention

[0013] The present invention aims to design a method for measuring beam arrival time using an electro-optic method with a phase cavity to reduce the difficulty and cost of probe fabrication, while avoiding beam position dependence.

[0014] To achieve the above objectives, the present invention provides a method for measuring the arrival time of a particle accelerator beam using an electro-optic method, comprising:

[0015] S1: Determine the cavity radius and cavity length of the cavity probe that meet the resolution requirements for time of arrival measurement;

[0016] S2: Based on the cavity radius and cavity length of the cavity probe, a cavity probe is made, and it is used as an electrical signal pickup probe to build a beam arrival time measurement device based on the electro-optic method.

[0017] S3: The data acquisition and processing system of the beam arrival time measurement device simultaneously acquires the output signal from the cavity probe of the electrical signal pickup probe and the electro-optic signal from the photodetector, and uses the output signal of the cavity probe and the electro-optic signal to determine the beam arrival time.

[0018] Step S1 specifically includes:

[0019] S11: Determine the required zero-crossing slope of the cavity probe's output signal based on the required resolution of the arrival time measurement;

[0020] S12: Set the charge amount of the beam current, the center frequency and bandwidth of the cavity probe's output signal; use the TM010 mode signal of the cavity probe as its output signal, and determine the voltage peak value requirement of the cavity probe's output signal when the zero-crossing slope requirement is met based on the center frequency of the output signal.

[0021] S13: Based on the charge amount of the beam, the center frequency and bandwidth of the output signal set in step S12, determine the cavity radius and cavity length of the cavity probe to meet the voltage peak requirements.

[0022] In step S11, the requirement for the zero-crossing slope means that the zero-crossing slope of the output signal of the cavity probe is greater than the required value for the zero-crossing slope.

[0023] The required value S of the zero-crossing slope of the probe's output signal slope for:

[0024]

[0025] Among them, t resolution This is the required value for the time of arrival measurement resolution, σ. A'norm It is the accuracy of the reference optical pulse amplitude detection; V π.RF This is the half-wave voltage of the electro-optic modulator.

[0026] In step S12, the requirement for the peak voltage of the output signal of the cavity probe means that the peak voltage of the output signal of the cavity probe is greater than the required value of the peak voltage of the output signal of the cavity probe.

[0027] The required peak voltage of the output signal of the cavity probe must meet the zero-crossing slope requirement, specifically including:

[0028] S121: Determine the relationship between the zero-crossing slope and peak value of the output signal of the cavity probe when the TM010 mode signal of the cavity probe is used as its output signal.

[0029] S122: Determine the required value of the peak value of the output signal of the cavity probe based on the required value of the zero-crossing slope and the relationship between the zero-crossing slope and the peak value of the cavity probe output signal in step S121.

[0030] The relationship between the zero-crossing slope and peak value of the output signal of the cavity probe is as follows:

[0031] k = 0.995·V p ·ω,

[0032] Where k is the zero-crossing slope, ω is the angular frequency of the output signal, ω = 2πf, and f is the center frequency of the output signal, V p It is the peak value of the output signal.

[0033] In step S13, the cavity radius and cavity length of the cavity probe are obtained by solving the following formula:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] R = j 01 ·c / ω,

[0041] Among them, V p Let L be the peak value of the output signal of the cavity probe, L be the cavity length of the cavity probe, R be the cavity radius of the cavity probe, and j be the peak value of the output signal of the cavity probe. 01 R is the first root of the zeroth-order Bessel equation. s Let α be the surface resistance, ∈0 be the vacuum permittivity, and α be the t-resistivity. tThis is the transit time factor, J1 is the first-order Bessel equation, Z is the characteristic impedance of the signal transmission line, q is the charge of the beam current, ω is the angular frequency of the output signal, ω = 2πf, f is the center frequency of the output signal, τ is the decay time of the output signal, which is related to the bandwidth of the output signal, Q0 is the intrinsic quality factor, and Q... ext It is the external quality factor, Q load R / Q is the load quality factor, and R / Q is the normalized shunt impedance. The superscript 010 indicates the TM010 mode.

[0042] The beam arrival time measurement device based on the electro-optic method includes:

[0043] An electrical signal pickup probe is configured to receive the beam current under test and output the output signal of a cavity probe.

[0044] An electro-optic modulator is configured to receive a reference optical pulse and the output signal of a cavity probe, and to modulate the reference optical pulse using the output signal of the cavity probe to output an electro-optic signal.

[0045] A photodetector, configured to receive and measure electro-optic signals; and

[0046] The data acquisition and processing system is configured to simultaneously acquire the output signal from the cavity probe of the electrical signal pickup probe and the electro-optic signal from the photodetector.

[0047] The arrival time of the beam is determined using the output signal of the cavity probe and the electro-optic interaction signal. Specifically, when determining the arrival time of the beam, the electro-optic interaction signal is normalized using the output signal of the cavity probe to remove the influence of beam charge jitter on the measurement results of the beam arrival time.

[0048] The electro-optic method for measuring the beam arrival time of a particle accelerator in this invention utilizes a phase cavity as the electrical signal pickup probe for electro-optic measurement. Compared to the traditional high-bandwidth button electrode scheme, the cavity probe scheme has a lower frequency, significantly reducing the difficulty of fabrication and signal transmission processing. Furthermore, it is unaffected by the beam position on the measurement results. Therefore, using a cavity probe for electro-optic beam arrival time measurement will greatly enhance the measurement system. This invention combines the advantages of both phase cavity and electro-optic beam arrival time measurement methods. Attached Figure Description

[0049] Figure 1 This is a block diagram illustrating the existing electro-optic method for measuring beam arrival time.

[0050] Figure 2 The jitter in the arrival time of the bundle affects the amplitude of the modulator output signal.

[0051] Figure 3This is a flowchart of the electro-optic method for measuring beam arrival time according to the present invention.

[0052] Figure 4 This is a waveform diagram of the output signal of a cavity probe with a cavity length of 10mm. Detailed Implementation

[0053] The preferred embodiments of the present invention are given below with reference to the accompanying drawings and described in detail.

[0054] The electro-optic method for measuring beam arrival time of the present invention is based on a cavity probe and specifically includes the following steps:

[0055] Step S1: Determine the cavity radius and cavity length of the cavity probe that meet the resolution requirements for time of arrival measurement;

[0056] Among them, the requirement for arrival time measurement resolution is an existing specification requirement.

[0057] Step S1 specifically includes:

[0058] Step S11: Determine the required zero-crossing slope of the cavity probe's output signal based on the required resolution of the arrival time measurement;

[0059] The relationship between the required resolution for arrival time measurement and the required zero-crossing slope of the cavity probe's output signal is as follows:

[0060]

[0061] Among them, t resolution This is the required value for the time of arrival measurement resolution, σ. A'norm This is the accuracy of the reference optical pulse amplitude detection, which is determined by both the reference optical pulse amplitude jitter and the system detection error. This value can be obtained by detecting unmodulated optical pulses. σ A'norm The typical value is 0.2%. π.RF The half-wave voltage of the electro-optic modulator (EOM) is fixed at 5V. slope This represents the required slope of the probe signal at its zero-crossing point. It is evident that resolution is inversely proportional to the slope of the RF signal output by the probe; a larger slope results in higher resolution.

[0062] Therefore, the required value S of the zero-crossing slope of the probe's output signal is... slope for:

[0063]

[0064] Accordingly, the requirement for the zero-crossing slope of the output signal of the cavity probe means that the zero-crossing slope of the output signal of the cavity probe is greater than the aforementioned required value for the zero-crossing slope.

[0065] Step S12: Set the charge amount of the beam, the center frequency and bandwidth of the cavity probe's output signal; then, use the TM010 mode signal of the cavity probe as its output signal, and determine the voltage peak value requirement of the cavity probe's output signal when the zero-crossing slope requirement is met based on the center frequency of the output signal.

[0066] Among these parameters, beam charge is a beam parameter of the accelerator. The center frequency and bandwidth of the output signal of the cavity probe are set empirically based on the manufacturing difficulty and back-end electronic processing requirements.

[0067] In this invention, the output signal of the cavity probe requires the TM010 mode signal; if other mode signals are present, they need to be filtered out.

[0068] The required peak voltage of the output signal of the cavity probe must meet the zero-crossing slope requirement, specifically including:

[0069] Step S121: Determine the relationship between the zero-crossing slope and peak value of the cavity probe's output signal when the TM010 mode signal of the cavity probe is used as its output signal.

[0070] Among them, the output signal V of the cavity probe ref The expression is:

[0071] V ref =V p cos(ωt)·e -t / τ (3)

[0072] Among them, V p ω is the peak value of the output signal, ω is the angular frequency of the output signal, ω = 2πf, f is the center frequency of the output signal, and τ is the decay time of the output signal.

[0073] Based on this, the output signal V of the cavity probe can be analyzed. ref The slope at the zero point is calculated by taking the derivative.

[0074] The slope k at the zero point is:

[0075]

[0076] Therefore, the relationship between the zero-crossing slope and the peak value of the output signal of the cavity probe is as follows:

[0077] k = 0.995·V p ·ω,

[0078] Where k is the zero-crossing slope, ω is the angular frequency of the output signal, ω = 2πf, and f is the center frequency of the output signal, V p It is the peak value of the output signal.

[0079] Step S122: Determine the required value of the peak value of the output signal of the cavity probe based on the required value of the zero-crossing slope and the relationship between the zero-crossing slope and the peak value of the output signal of the cavity probe in step S121.

[0080] Considering that the zero-crossing slope of the output signal of the cavity probe needs to meet the zero-crossing slope requirement, this means that the zero-crossing slope of the output signal of the cavity probe is greater than the aforementioned required value S. slope (k>S slope Therefore, the required value S of the slope at the zero-crossing point can be used as a reference. slope The peak voltage V of the cavity probe's output signal can be calculated using the relationship between step S121 and the equation. p The required value to be achieved.

[0081] Correspondingly, the voltage peak requirement of the output signal of a cavity probe refers to the requirement that the voltage peak of the output signal of the cavity probe be greater than the required value of the voltage peak of the output signal of the cavity probe.

[0082] Step S13: Based on the beam charge, output signal center frequency, and bandwidth set in step S12, determine the voltage peak value V. p The requirement is to meet the cavity radius and cavity length of the cavity probe;

[0083] Specifically, a required peak voltage can be determined, and then the cavity radius and length can be determined based on the peak voltage. For example, if the peak voltage is determined to be 8.0V, the corresponding cavity radius and length of the cavity probe can be deduced.

[0084] The output signal V of the cavity probe HC for:

[0085]

[0086] Where ω is the angular frequency of the output signal, ω=2πf, f is the center frequency of the output signal, τ is the decay time of the output signal, q is the charge of the beam, and Z is the characteristic impedance of the signal transmission line, which is typically 50Ω.

[0087] Among them, the peak value V of the output signal of the cavity probe p for:

[0088]

[0089] Therefore, the cavity radius and cavity length of the cavity probe can be obtained by solving the following formulas:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] R = j 01 ·c / ω,

[0097] Among them, V p Let L be the peak value of the output signal of the cavity probe, L be the cavity length of the cavity probe, R be the cavity radius of the cavity probe, and j be the peak value of the output signal of the cavity probe. 01 R is the first root of the zeroth-order Bessel equation, i.e., 2.405. s Let α be the surface resistance, ∈0 be the vacuum permittivity, and α be the t-resistivity. t This is the transit time factor, J1 is the first-order Bessel equation, Z is the characteristic impedance of the signal transmission line, typically 50Ω, q is the charge of the beam, ω is the angular frequency of the output signal, ω=2πf, f is the center frequency of the output signal, τ is the decay time of the output signal, which is related to the bandwidth of the output signal, Q0 is the intrinsic quality factor, Q... ext It is the external quality factor, Q load R / Q is the load quality factor, and R / Q is the normalized shunt impedance. The superscript 010 indicates the TM010 mode. For free-electron lasers, the beam length is very short, and its impact on the signal amplitude is negligible. The bandwidth of the output signal is related to its decay time τ; the smaller the bandwidth, the longer the decay time.

[0098] Step S2: Fabricate a cavity probe based on the cavity radius and cavity length of the cavity probe, and use it as an electrical signal pickup probe to build a beam arrival time measurement device based on the electro-optic method.

[0099] The beam arrival time measurement device based on the electro-optic method includes:

[0100] An electrical signal pickup probe is configured to receive the beam current under test and output the output signal of a cavity probe.

[0101] An electro-optic modulator is configured to receive a reference optical pulse and the output signal of a cavity probe, and to modulate the reference optical pulse using the output signal of the cavity probe to output an electro-optic signal.

[0102] A photodetector, configured to receive and measure electro-optic signals; and

[0103] The data acquisition and processing system is configured to simultaneously acquire the output signal from the cavity probe of the electrical signal pickup probe and the electro-optic signal from the photodetector.

[0104] Step S3: Simultaneously acquire the output signal from the cavity probe of the electrical signal pickup probe and the electro-optic signal from the photodetector using the data acquisition and processing system of the beam arrival time measurement device. Determine the beam arrival time using the output signal of the cavity probe and the electro-optic signal.

[0105] The beam arrival time is determined using the output signal of the cavity probe and the electro-optic interaction signal. Specifically, when determining the beam arrival time, the electro-optic interaction signal is normalized using the output signal of the cavity probe to remove the influence of beam charge jitter on the measurement result of the beam arrival time. The normalized result is obtained by dividing the electro-optic interaction signal by the beam charge.

[0106] Experimental results:

[0107] In step S11, the time resolution is set to 20 fs. Therefore, in order to achieve a time resolution of 20 fs with a charge of 100 pC, the required zero-crossing slope is 400 mV / ps.

[0108] In step S12, for the convenience of signal processing, the basic parameter requirements of the beam under test and the TM010 mode signal of the cavity probe are shown in Table 1.

[0109] The center frequency is set to 8 GHz in the C-band to facilitate signal processing.

[0110] Table 1. Basic parameter requirements for the TM010 mode signal of the beam under test and the cavity probe.

[0111]

[0112] In step S12, according to formula (4), the zero-crossing slope k is required to be greater than 400mV / ps, therefore the peak voltage V of the output signal of the corresponding cavity probe is... p It should meet the following requirements:

[0113] 0.995·V p ·ω>400mV / ps,

[0114] Right now:

[0115] In step S13, based on the above frequency and bandwidth, the radius of the cylindrical cavity based on the TM010 mode is calculated to be 14.3 mm using theoretical formulas.

[0116] The calculated peak value V of the output signal of the cavity probe under different cavity probe lengths p As shown in Table 2.

[0117] Table 2 shows the peak output signal of different cavity probes with varying cavity lengths.

[0118] cavity length / mm 8 9 10 Peak amplitude / V 7.8 8.2 8.5

[0119] Therefore, theoretical calculations show that a cavity length of 9 mm or more can meet the zero-crossing slope requirement. Figure 4 This is a waveform diagram of the output signal of a cavity probe with a cavity length of 10mm.

[0120] In steps S2 and S3, the data acquisition and processing system simultaneously acquires the electro-optic signal and the cavity probe signal, and normalizes to remove the influence of beam charge jitter on the measurement results.

[0121] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. Various variations can be made to the above embodiments of the present invention. All simple and equivalent changes and modifications made in accordance with the claims and description of this application fall within the protection scope of the claims of this patent. All aspects not described in detail in this invention are conventional technical content.

Claims

1. A method of measuring the time of arrival of a particle accelerator beam by electro-optical means, characterized in that, The application relates to a method for measuring the arrival time of a beam, and belongs to the technical field of beam measurement. The method comprises the following steps: Step S1: determining the cavity radius and cavity length of a cavity probe which meet the requirement of the arrival time measurement resolution; Step S2: manufacturing the cavity probe according to the cavity radius and cavity length of the cavity probe, and using the cavity probe as an electric signal pickup probe to build a beam arrival time measurement device based on the electro-optical method; Step S3: simultaneously collecting the output signal of the cavity probe from the electric signal pickup probe and the electro-optical interaction signal from the photodetector by using the data acquisition processing system of the beam arrival time measurement device, and determining the arrival time of the beam by using the output signal of the cavity probe and the electro-optical interaction signal. The step S1 specifically comprises the following steps: Step S11: determining the requirement of the zero-crossing point slope of the output signal of the cavity probe according to the requirement of the arrival time measurement resolution; Step S12: setting the charge amount of the beam, the center frequency and the bandwidth of the output signal of the cavity probe; taking the TM010 mode signal of the cavity probe as the output signal of the cavity probe, and determining the requirement of the voltage peak value of the output signal of the cavity probe when the requirement of the zero-crossing point slope is met according to the center frequency of the output signal; Step S13: determining the cavity radius and cavity length of the cavity probe when the requirement of the voltage peak value is met according to the charge amount of the beam, the center frequency and the bandwidth of the output signal set in the step S12. a required value S of a slope of a zero-crossing point of an output signal of the probe slope is: where t resolution is a required value of the time-of-arrival measurement resolution, σ A'norm is the reference light pulse amplitude detection accuracy; V π.RF is the half-wave voltage of the electro-optical modulator.

2. The method of claim 1, wherein, In the step S11, the requirement of the zero-crossing point slope refers to that the zero-crossing point slope of the output signal of the cavity probe is greater than the requirement value of the zero-crossing point slope. In the step S12, the requirement of the voltage peak value of the output signal of the cavity probe refers to that the voltage peak value of the output signal of the cavity probe is greater than the requirement value of the voltage peak value of the output signal of the cavity probe. The requirement of the voltage peak value of the output signal of the cavity probe when the requirement of the zero-crossing point slope is met specifically comprises the following steps: Step S121: determining the relationship between the zero-crossing point slope and the peak value of the output signal of the cavity probe when the TM010 mode signal of the cavity probe is taken as the output signal of the cavity probe; 3. The method of claim 2, wherein, Step S122: determining the requirement value of the peak value of the output signal of the cavity probe according to the requirement value of the zero-crossing point slope and the relationship between the zero-crossing point slope and the peak value of the output signal of the cavity probe in the step S121. k = 0.995 · V p · ω, where k is the zero-crossing slope, ω is the angular frequency of the output signal, ω = 2πf, f is the center frequency of the output signal, V p is the peak value of the output signal.

4. The method of claim 1, wherein, The relationship between the zero-crossing point slope and the peak value of the output signal of the cavity probe is as follows: R = j 01 • c / ω, where V p is the peak value of the output signal of the cavity probe, L is the cavity length of the cavity probe, R is the cavity radius of the cavity probe, j 01 is the first root of the zero-order Bessel equation, R s is the surface resistance, ∈0 is the vacuum permittivity, α t is the transit time factor, J1 is the first-order Bessel equation, Z is the characteristic impedance of the signal transmission line, q is the charge amount of the beam, ω is the angular frequency of the output signal, ω = 2πf, f is the center frequency of the output signal, τ is the decay time of the output signal, which is related to the bandwidth of the output signal, Q0 is the intrinsic quality factor, Q ext is the external quality factor, Q load is the loaded quality factor, R / Q is the normalized shunt impedance, and the superscript 010 represents the TM010 mode.

5. The method of claim 1, wherein, In the step S13, the cavity radius and cavity length of the cavity probe are obtained by the following formula: The beam arrival time measurement device based on the electro-optical method comprises: an electric signal pickup probe which is arranged to receive the beam to be measured and output the output signal of the cavity probe; an electro-optical modulator which is arranged to receive the reference light pulse and the output signal of the cavity probe, modulate the reference light pulse by using the output signal of the cavity probe, and output the electro-optical interaction signal; a photodetector which is arranged to receive and measure the electro-optical interaction signal; and a data acquisition processing system which is arranged to simultaneously collect the output signal of the cavity probe from the electric signal pickup probe and the electro-optical interaction signal from the photodetector.

6. The method of claim 1, wherein, The output signal of the cavity probe and the electro-optic effect signal are used to determine the arrival time of the beam, specifically including: when determining the arrival time of the beam, the output signal of the cavity probe is used to normalize the electro-optic effect signal, so as to remove the influence of the beam charge quantity jitter on the measurement result of the arrival time of the beam.

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