Method for calculating thickness of surface oxide film of nuclear power plant fuel assembly

Abstract

The application discloses a kind of nuclear power plant fuel assembly surface oxide film thickness calculation method, comprising the following steps: respectively establishing the finite element model of coil and fuel assembly, the impedance of coil is calculated;Based on the structure of hexagonal winding model, the parasitic capacitance and direct current resistance of coil are calculated, and the corrected coil impedance is obtained;The corrected coil impedance value under multi-frequency excitation is calculated, the influence of cladding tube conductivity and metal coating thickness on coil impedance is eliminated, and the relationship between it and oxide film thickness is fitted;According to the relationship, the thickness of the oxide film is accurately measured and calculated.The calculation method of the application, by calculating the direct current resistance and parasitic capacitance of coil to correct the coil impedance, reduces the difference between simulation results and experimental data, improves the measurement accuracy of fuel rod cladding tube oxide film thickness;Using multi-frequency signal fitting algorithm can eliminate the measurement error caused by factors such as cladding tube conductivity, metal coating thickness and environmental noise, improve the measurement accuracy of oxide film thickness.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic detection and simulation calculation technology, specifically to a simulation calculation method for measuring the thickness of the oxide film on the surface of fuel assemblies in nuclear power plants. Background Technology

[0002] The fuel rod cladding tubes are the components that directly load nuclear fuel and serve as a direct barrier between the fuel and coolant. They face a harsh environment characterized by high temperature, high pressure, strong corrosion, and intense radiation. Therefore, the performance of the fuel rod cladding tubes is a key factor in ensuring the safe and effective operation of a nuclear reactor. Cladding tubes are typically made of zirconium alloy, a material known for its high temperature resistance, corrosion resistance, and good mechanical properties, with pure chromium used as an anti-oxidation coating. However, after prolonged operation in the harsh environment of the reactor, corrosion inevitably occurs in the cladding tubes, resulting in the accumulation of an oxide film of varying thickness on their surface. This oxide film severely affects the thermal conductivity of the cladding tubes and the heat exchange capacity of the fuel assemblies, causing the fuel rod temperature to rise continuously and accelerating the corrosion and aging process. Therefore, regular measurement of the oxide film thickness is necessary to maintain the safe operation of the fuel rods. The oxide film thickness on the fuel rod cladding tubes is typically only tens of micrometers, making the accuracy of oxide film thickness measurement crucial.

[0003] Eddy current technology is used to detect the oxide film thickness on the surface of nuclear fuel rod cladding tubes because it offers advantages such as fast detection speed, no need for coupling agent, simple operation, and low cost. Eddy current detection utilizes the principle of electromagnetic induction. A coil carrying an alternating current is held at a certain distance from the surface of a conductive sample (i.e., lifted off), inducing eddy currents within the conductive material. These induced eddy currents generate a secondary induced magnetic field in space, which is measured by the coil and manifested as impedance. The magnetic field strength varies depending on the distance of the coil from the conductive material; therefore, the magnitude of the lift-off can be calculated by measuring the impedance change of the coil. In the fuel tube cladding structure, if the coil is in close contact with the outer wall of the sample, the thickness of the non-conductive oxide film represents the magnitude of the lift-off and can be measured using the above principle.

[0004] Induction coils are widely used in magnetic field measurements, capable of measuring magnetic field changes over a wide frequency range. Due to the simple structure and reliable performance of standard windings, this type of winding is widely employed in magnetic field measurements. In eddy current detection, a finite element model is typically constructed based on the magnetic field coupling equation to solve for the impedance change of the induction coil during the measurement process. Mature multiphysics electromagnetic numerical simulation software such as COMSOL (USA) and CIVA (France) are widely used for eddy current simulation modeling. Zhiwei.Z et al. studied a degenerate magnetic vector potential equation based on the traditional magnetic vector potential equation, avoiding repeated calculations of the coil probe when the probe is located in different positions, thus reducing the time and resources required for finite element simulation calculations.

[0005] In actual experiments, the equivalent circuit model of the coil should include inductance (L) and parasitic capacitance (C). s The theoretically calculated coil impedance value neglects the parasitic capacitance and DC resistance R of the coil. dc The parasitic capacitance and DC resistance values ​​need to be calculated to correct the theoretically calculated coil impedance in order to reduce the difference between simulation and experimental data. The parasitic capacitance of the induction coil affects its sensitivity to magnetic field changes and its operating frequency range, thus determining the coil's performance in eddy current detection. To accurately calculate the parasitic capacitance of the induction coil, researchers have proposed various analytical models. Among them, the hexagonal winding model proposed by Bin.W et al. has high prediction accuracy for standard winding induction coils. DC resistance (R...) dc The resistance of the coil when direct current flows through it is denoted as Ω. The DC resistance of the coil can be calculated by numerically evaluating the total length of the inductor's conductors and then considering the resistivity of the conductor material, based on the law of resistance.

[0006] When measuring oxide film thickness using a coil, variations in parameters such as the thickness of the metal coating, the conductivity of the cladding tube, and environmental factors can alter the coil impedance, thus affecting the accuracy of the thickness measurement. The measurement accuracy of existing single-frequency detection coils is highly susceptible to these parameter variations. Based on the skin effect, the skin depth of the eddy current varies at different excitation frequencies. Coil impedance data acquired under multi-frequency excitation contains more information about the oxide film thickness, making it easier to eliminate interference and improve the measurement accuracy.

[0007] The above background information is provided only to assist in understanding the inventive concept and technical solution of this invention. It does not necessarily belong to the prior art of this patent application. In the absence of clear evidence that the above information was disclosed before the filing date of this patent application, the above background information should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0008] In view of this, in order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a method for calculating the thickness of the oxide film on the surface of nuclear power plant fuel assemblies.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A method for calculating the thickness of the oxide film on the surface of a nuclear power plant fuel assembly includes the following steps:

[0011] Finite element models of the coil and fuel assembly were established separately, and the impedance of the coil was calculated.

[0012] Based on the hexagonal winding model structure, the parasitic capacitance and DC resistance of the coil are calculated, and the corrected coil impedance is obtained.

[0013] Calculate the corrected coil impedance value under multi-frequency excitation, eliminate the influence of the cladding tube conductivity and metal coating thickness on the coil impedance, and fit its relationship with the oxide film thickness.

[0014] Based on this relationship, the thickness of the oxide film can be accurately measured and calculated.

[0015] According to some preferred embodiments of the invention, the fuel assembly includes a fuel rod cladding tube and an oxide film thereon.

[0016] According to some preferred embodiments of the invention, the finite element model of the fuel assembly has a mesh size that increases proportionally from the center outwards along the Z-axis.

[0017] According to some preferred embodiments of the present invention, the impedance of the measuring coil is calculated according to the following steps:

[0018] The voltage V output by the measuring coil close to the cladding tube wall was obtained by multi-core parallel calculation using the finite element method. Then, based on the current I flowing through the coil, the coil impedance Z was calculated according to (3):

[0019]

[0020] According to some preferred embodiments of the invention, the parasitic capacitance C s The result is obtained using the following formula:

[0021]

[0022] In the formula, N m =l m / d o N l =(D o -D i ) / 2kd o ,but l m It is the axial length of the induction coil, d o It is the outer diameter of the conductor, d i It is the diameter of the conductor after the insulation coating is removed from the wire, D i and D o These are the inner and outer diameters of the coil, respectively; k is the fill factor; C i and C o These are the total internal capacitance and total external capacitance of the conductor, respectively.

[0023] According to some preferred embodiments of the invention, the total internal capacitance C i The result is obtained using the following formula:

[0024]

[0025] In the formula, ε0 is the vacuum permittivity, ε r It is the relative permittivity of the conductor insulation coating material, l t The average circumference of each turn of wire in the coil.

[0026] According to some preferred embodiments of the invention, the total external capacitance C o The result is obtained using the following formula:

[0027]

[0028] Where ε0 is the vacuum permittivity, ε r It is the relative permittivity of the conductor insulation coating material, l t The average circumference of each turn of wire in the coil.

[0029] According to some preferred embodiments of the present invention, the DC resistance of the coil is calculated according to the following steps:

[0030] Based on the hexagonal winding structure of the measuring coil, the total length l of the coil is:

[0031]

[0032] In the formula, ξ r It is the fill factor, ξ r =d o -d o sin(π / 3);

[0033] Based on the law of resistance for conductors, the DC resistance of the coil is:

[0034]

[0035] In the formula, ρ is the resistivity of the conductor in the coil, and S is the cross-sectional area of ​​the conductor.

[0036] According to some preferred embodiments of the invention, the impedance of the corrected coil equivalent circuit for:

[0037]

[0038] In the formula, R is the resistance value of the coil after impedance correction, and X is the reactance value of the coil after impedance correction.

[0039] According to some preferred embodiments of the present invention, the functional relationship f between the oxide film thickness d of the fuel rod cladding tube and the coil impedance is performed according to the following steps:

[0040] First, corrected coil impedance data were collected under n frequency excitations in different fuel rod cladding tube oxide film models. Then, the functional relationship f between the fuel rod cladding tube oxide film thickness d and the coil impedance was fitted.

[0041] d = f(R, x) (14)

[0042] Where R and X are the resistance and reactance values ​​output by the measuring coil at n excitation frequencies when the oxide film thickness is d, respectively. Therefore, both R and X are column vectors containing n data points.

[0043] Because the coil impedance is also affected by the conductivity σ of the fuel rod cladding material. t and its metal coating thickness d c Therefore, in order to eliminate the influence of σ t and d c The effect on oxide film thickness measurement results should be such that the inversion function f is related to σ. t and d c The partial derivatives of all of them are equal to 0, that is...

[0044]

[0045]

[0046] Therefore, the determination of the inversion function f needs to follow these rules:

[0047]

[0048] Thickness measurements were performed on m groups of samples. Based on the output m×n groups of coil impedance data, a coefficient matrix K was introduced. (6*n，1) To fit the inversion function relationship, equation (14) can be rewritten as equation (18):

[0049] d = [ERXR] 2 X 2 RX]·K=Ek0+Rk1+Xk2+R 2 k3+X 2 k4+RXk5 (18)

[0050] Where E is an m×n dimensional identity matrix, k i These are the n×i+1th to n×(i+1th)th data points of matrix K;

[0051] but

[0052]

[0053]

[0054] Based on the optimization rule shown in formula (17), the coefficient matrix K is solved, and the quadratic term relationship between the oxide film thickness d and the coil impedance (R, X) can be obtained. By applying this inversion relationship to the coil impedance correction data of the multi-frequency excitation measurement output of other samples, the oxide film thickness of the sample can be accurately solved.

[0055] Due to the adoption of the above technical solutions, the advantages of this invention compared to the prior art are as follows: The method for calculating the oxide film thickness on the surface of nuclear power plant fuel assemblies of this invention constructs finite element models of oxide film thickness and coils respectively. Through magnetic field coupling models, the impedance of the coil measuring the oxide film thickness of the fuel rod cladding tube can be simulated and calculated. By calculating the DC resistance and parasitic capacitance of the coil to correct the coil impedance, the difference between simulation results and experimental data can be reduced, and the measurement accuracy of the oxide film thickness of the fuel rod cladding tube can be improved. Based on the corrected coil impedance data, a multi-frequency signal fitting algorithm can be used to eliminate measurement errors caused by factors such as cladding tube conductivity, metal coating thickness, and environmental noise, thereby improving the measurement accuracy of oxide film thickness. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a flowchart illustrating the method for calculating the thickness of the oxide film on the surface of a nuclear power plant fuel assembly in a preferred embodiment of the present invention.

[0058] Figure 2 The diagram shows a finite element simulation model of the coil measuring the oxide film thickness of the fuel rod cladding tube in a preferred embodiment of the present invention, wherein (a) is a finite element model of the oxide film thickness of the fuel rod cladding tube; and (b) is a finite element model of the coil.

[0059] Figure 3 This is the equivalent circuit model of the coil in a preferred embodiment of the present invention. Detailed Implementation

[0060] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0061] like Figure 1 As shown, the method for calculating the oxide film thickness on the surface of nuclear power plant fuel assemblies according to the present invention first establishes finite element models of the coil and the oxide film respectively. The impedance change of the measuring coil is calculated using the magnetic field coupling equation. Then, based on the hexagonal winding model structure and according to the material and structural parameters of the actual coil, the DC resistance and parasitic capacitance of the coil are numerically calculated. The probe impedance is then corrected using the coil equivalent circuit model to reduce the difference between simulation and actual experimental data. Finally, the influence of interference factors is suppressed, and the relationship between the corrected coil impedance data measured under multi-frequency excitation and the oxide film thickness of the fuel rod cladding tube is fitted. Based on this functional relationship, the oxide film thickness can be accurately obtained from the coil impedance value during multi-frequency excitation measurement.

[0062] The specific steps are as follows:

[0063] Step 1: Use finite element numerical simulation to solve the impedance of the coil for measuring the oxide film thickness. First, perform finite element modeling of the oxide film structure of the fuel assembly, and then calculate the coil impedance change based on the magnetic field coupling equation.

[0064] Based on the geometric structure of the oxide film on fuel assemblies in actual nuclear power plant scenarios, three-dimensional finite element geometric simulation models of the samples (fuel rod cladding tubes and their oxide films) and the probe (measuring coils) were established, such as... Figure 2 As shown.

[0065] To ensure the accuracy of thickness measurements and conserve computational resources and time, the mesh size was optimized. The mesh size of the sample model increases proportionally from the center outwards along the Z-axis. In the xoy plane, the oxide film structure is divided into three meshes, with other meshes increasing proportionally with their circumferential distance from the oxide film. The air volume around the sample is set sufficiently large to ensure boundary effects. The coil model is precisely subdivided along the circumferential direction, and the axial (N) m ) and radial (N l The number of grid cells is the same as the actual number of turns. The coil is attached to the outer wall of the pipe and located in the middle of the pipe. The oxide film thickness is the lift-off value of this electromagnetic simulation model.

[0066] The coil impedance calculation is based on the degenerate magnetic vector potential equation:

[0067]

[0068]

[0069] In this equation, the magnetic vector potential A (A = A) is... s +A r It is divided into two parts, where A s A represents the magnetic vector potential caused by the current source. rThis represents the magnetic vector potential induced by eddy currents. Therefore, the fuel rod cladding tube and coil can be modeled separately, reducing the number of times the coil needs to be remodeled and the simulation calculation time.

[0070] Using the finite element method for multi-core parallel calculation, the voltage V output by the coil close to the shell wall can be quickly obtained. Then, based on the current flowing through the coil, the coil impedance can be calculated according to (3).

[0071]

[0072] Step 2, the equivalent circuit model of the coil is as follows: Figure 3 As shown, it generally includes DC resistance, parasitic capacitance, and inductance.

[0073] Since the aforementioned finite element eddy current simulation model does not consider the DC resistance and parasitic capacitance of the actual coil, these two parameters are numerically calculated to correct the coil impedance value, making it closer to the coil impedance in the actual oxide film thickness measurement process. In this embodiment, the coil used is a hollow standard winding coil, i.e., without a magnetic core, and the starting end of the next layer of the coil is connected to the ending end of the previous layer. Therefore, based on the hexagonal winding model, and according to the coil structure and material properties, the parasitic capacitance and DC resistance of the coil probe can be obtained through numerical calculation, as follows:

[0074] The parasitic capacitance of the coil (C) s It can be calculated according to formula (4).

[0075]

[0076] Where N m =l m / d o N l =(D o -D i ) / 2kd o ,but l m It is the axial length of the induction coil (measuring coil), d o It is the outer diameter of the conductor, d i It is the diameter of the conductor after the insulation coating is removed from the wire, D i and D o Here, represents the inner and outer diameters of the coil, respectively, and k is a fill factor, k = 0.87. i and C o The total internal capacitance and total external capacitance of the conductor are respectively calculated using formulas (5) and (6):

[0077]

[0078]

[0079] Where ε0 is the vacuum permittivity, ε r It is the relative permittivity of the conductor insulation coating material, l t The average circumference of each turn of wire in the coil.

[0080] Based on the hexagonal winding structure of the measuring coil, the total length (l) of the coil is:

[0081]

[0082] ξ r It is the fill factor, ξ r =d o -d o sin(π / 3). Based on the law of resistance for conductors, the DC resistance of the coil is...

[0083]

[0084] ρ is the resistivity of the conductor in the coil, and S is the cross-sectional area of ​​the conductor.

[0085] In summary, the impedance of the corrected coil equivalent circuit for:

[0086]

[0087] Where R is the resistance of the coil after impedance correction, and X is the reactance of the coil after impedance correction.

[0088] Step 3: Fitting the oxide film thickness using multi-frequency signals

[0089] Based on the above coil impedance calculation and correction method, the method for measuring oxide film thickness based on coil impedance data under multi-frequency excitation in this embodiment first collects the corrected coil impedance data under n frequency excitations in different fuel rod cladding tube oxide film models, and then fits the functional relationship (f) between the fuel rod cladding tube oxide film thickness (d) and the coil impedance.

[0090] d = f(R, X) (14)

[0091] Where R and X are the resistance and reactance values ​​output by the measuring coil at n excitation frequencies when the oxide film thickness is d, respectively. Therefore, both R and X are column vectors containing n data points.

[0092] The coil impedance is also affected by the conductivity (σ) of the fuel rod cladding material. t ) and its metal coating thickness (d c Therefore, in order to eliminate the influence of σ, t and d cThe effect on oxide film thickness measurement results should be such that the above inversion function f is related to σ. t and d c The partial derivatives of all of them are equal to 0, that is:

[0093]

[0094]

[0095] Therefore, the determination of the inversion function f needs to follow these rules:

[0096]

[0097] This embodiment uses a quadratic polynomial to fit the inversion function f: assuming thickness measurements are performed on m groups of samples, based on the output m×n groups of coil impedance data, a coefficient matrix K is introduced. (6*n，1) To fit the inversion function relationship, formula (14) can be written in the form of formula (18).

[0098] d = [ERXR] 2 X 2 RX]·K=Ek0+Rk1+Xk2+R 2 k3+X 2 k4+RXk5 (18)

[0099] Where E is an m×n dimensional identity matrix, k i It is the n×i+1th to n×(i+1th)th data in matrix K.

[0100] but

[0101]

[0102]

[0103] Based on the optimization principle shown in formula (17), the coefficient matrix K is solved, and the quadratic relationship between the oxide film thickness d and the coil impedance (R, X) can be obtained. By applying this inversion relationship (the relationship between oxide film thickness and coil impedance) to the coil impedance correction data of the multi-frequency excitation measurement output of other samples, the oxide film thickness of the sample can be accurately solved.

[0104] Specific Cases

[0105] The method for calculating the oxide film thickness on the surface of nuclear power plant fuel assemblies in this embodiment is based on a finite element simulation model. The calculation is performed on the coil impedance under multi-frequency excitation when measuring four different cladding tube conductivities (1.68 MS / m, 1.43 MS / m, 1.1 MS / m), seven different metal coating thicknesses (6 μm, 8 μm, 10 μm, 12 μm, 15 μm, 18 μm and 20 μm), and four oxide film thicknesses (3 μm, 5 μm, 7 μm and 9 μm). The starting frequency was 0.4MHz, and the ending frequency was 8MHz. A total of 24 frequencies were selected, namely (0.40, 0.46, 0.52, 0.59, 0.67, 0.77, 0.87, 1.00, 1.13, 1.29, 1.47, 1.68, 1.91, 2.17, 2.48, 2.82, 3.21, 3.66, 4.17, 4.75, 5.41, 6.17, 7.02, 8.00)MHz. Based on the coil material and structure, the parasitic capacitance and DC resistance of the coil were theoretically calculated to be 37.21μF and 21.10Ω, respectively. Based on the above data, the corrected coil impedance (R,X) for different parameter models was obtained according to formula (9).

[0106] The coefficient matrix K was optimized using nonlinear programming. This matrix was then applied to the corrected coil impedance of samples with a cladding tube conductivity of 1.25 MS / m, metal coating thicknesses of 7 μm, 13 μm, 14 μm, 17 μm, and 19 μm, and oxide film thicknesses ranging from 2 μm to 10 μm at 24 excitation frequencies. The calculated oxide film thicknesses are shown in Table 1. The average absolute error in the oxide film thickness calculation was 0.1105 μm, with a maximum error less than 0.3 μm.

[0107] Table 1: Measured oxide film thickness at a conductivity of 1.25 MS / m

[0108]

[0109]

[0110] This invention simulates and calculates the coil impedance during fuel rod cladding thickness measurement, reducing the discrepancy between simulation and experiment through impedance correction, thereby improving the accuracy of fuel rod oxide film thickness measurement. The invention proposes an impedance calculation and correction method. A three-dimensional finite element simulation model of fuel rod cladding oxide film thickness measurement is constructed to calculate coil impedance changes. Based on actual coil properties, DC resistance and parasitic capacitance are numerically calculated to obtain the corrected coil impedance, making it closer to the coil impedance value during actual thickness measurement. The oxide film thickness of the fuel rod cladding is calculated based on the corrected impedance data from thickness measurement under multi-frequency excitation. This invention also proposes a method for inverting oxide film thickness using multi-frequency signals. This method, based on the corrected resistance and reactance data obtained from multi-frequency excitation measurements, can suppress the influence of changes in metal coating thickness and cladding conductivity, accurately inverting and calculating the oxide film thickness of the fuel rod cladding.

[0111] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for calculating the thickness of the oxide film on the surface of a nuclear power plant fuel assembly, characterized in that, Includes the following steps: Finite element models of the coil and fuel assembly were established separately, and the impedance of the coil was calculated. Based on the hexagonal winding model structure, the parasitic capacitance and DC resistance of the coil are calculated, and the corrected coil impedance is obtained. Calculate the corrected coil impedance value under multi-frequency excitation, eliminate the influence of the cladding tube conductivity and metal coating thickness on the coil impedance, and fit its relationship with the oxide film thickness. Based on this relationship, the thickness of the oxide film can be accurately measured and calculated; Fitting the oxide film thickness of fuel rod cladding tubes Functional relationship between coil impedance Follow these steps: First, corrected coil impedance data were collected under n frequency excitations in different fuel rod cladding tube oxide film models. Then, the oxide film thickness of the fuel rod cladding tube was fitted. Functional relationship between coil impedance : (14)； in, and The oxide film thickness is respectively At n excitation frequencies, the resistance and reactance values ​​output by the coil are... and Both are column vectors containing n data points; Because the coil impedance is also affected by the conductivity of the fuel rod cladding material. and its metal coating thickness Therefore, in order to eliminate the impact, and The impact on oxide film thickness measurement results should be such that the inversion function... about and The partial derivatives of all of them are equal to 0, that is... （15）； （16）； Therefore, the inversion function The determination of needs to follow these rules: （17）； Thickness measurements were performed on m groups of samples, based on the output m n sets of coil impedance data, introduced into a coefficient matrix. To fit the inversion function relationship, equation (14) can be rewritten as equation (18): （18）； in, yes An identity matrix of dimension 1 It is a matrix The The first to the second One data point; but (19)； (20)； Based on the optimization principle shown in formula (17), the coefficient matrix is ​​solved. That is, to obtain the oxide film thickness and coil impedance ( , The quadratic relationship between the two terms is obtained; by applying the inversion function to the coil impedance correction data of the multi-frequency excitation measurement output of other samples, the oxide film thickness of the sample can be accurately solved.

2. The calculation method according to claim 1, characterized in that, The fuel assembly includes a fuel rod, a cladding tube, and an oxide film on the cladding tube.

3. The calculation method according to claim 1, characterized in that, The finite element model of the fuel assembly has a mesh size that increases proportionally from the center outwards along the Z-axis.

4. The calculation method according to claim 1, characterized in that, The impedance of the coil is calculated according to the following steps: The voltage V output by the coil close to the cladding tube wall was obtained by multi-core parallel calculation using the finite element method. Then, based on the current I flowing through the coil, the coil impedance Z was calculated according to (3): (3)。 5. The calculation method according to claim 1, characterized in that, The parasitic capacitance The result is obtained using the following formula: (4)； In the formula, , ,but ; This is the total length of the coil; It is the axial length of the coil. It is the outer diameter of the wire. and These are the inner and outer diameters of the coil, respectively. It is the fill factor; and These are the total internal capacitance and total external capacitance of the conductor, respectively.

6. The calculation method according to claim 5, characterized in that, The total internal capacitance The result is obtained using the following formula: (5)； In the formula, The vacuum permittivity, It is the relative permittivity of the conductor insulation coating material. It is the diameter of the conductor after the insulation coating is removed from the wire. The average circumference of each turn of wire in the coil. .

7. The calculation method according to claim 5, characterized in that, The total external capacitance The result is obtained using the following formula: (6)； in, The vacuum permittivity, It is the relative permittivity of the conductor insulation coating material. The average circumference of each turn of wire in the coil. .

8. The calculation method according to claim 1, characterized in that, The DC resistance of the coil is calculated according to the following steps: Based on the hexagonal winding structure of the coil, the total length of the coil is... for: (7)； In the formula, It is the fill factor. ; Based on the law of resistance for conductors, the DC resistance of the coil is: (8)； In the formula, Let be the resistivity of the conductor in the coil. Let be the cross-sectional area of ​​the conductor. It is the diameter of the conductor after the insulation coating is removed from the wire. , , , It is the axial length of the coil. It is the outer diameter of the wire. and These are the inner and outer diameters of the coil, respectively. It is the fill factor.

9. The calculation method according to claim 8, characterized in that, Impedance of the corrected coil equivalent circuit for: (9)； In the formula, This is the resistance value of the coil after impedance correction. This represents the reactance of the coil after impedance correction, where Z is the coil impedance. This is the parasitic capacitance of the coil.

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