CN113435096B - High-precision numerical model calculation method and system for steady-state response of self-powered detector - Google Patents
High-precision numerical model calculation method and system for steady-state response of self-powered detector Download PDFInfo
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Abstract
The application discloses a high-precision numerical model calculation method and system for self-powered detector steady-state response, which comprises the following steps: acquiring the energy-range data corresponding relation of electrons in different materials based on data interpolation or probability density distribution function of a Monte Carlo simulation result; analyzing the minimum kinetic energy of electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation; and calculating to obtain a track length probability function by utilizing the minimum kinetic energy and through the energy-range data corresponding relation of the electrons in different materials. According to the invention, different types of self-powered neutron detectors are selected according to the neutron energy spectrum condition during the operation of the reactor, so that the differential measurement is realized, and the measurement result is more accurate. Meanwhile, when the self-powered neutron detector is used for measurement, the emitter material of the detector can be continuously burnt along with the prolonging of the measurement time, so that the detection efficiency is greatly optimized.
Description
Technical Field
The invention relates to a high-precision numerical model calculation method and system for steady-state response of a self-powered detector.
Background
The self-powered detector is a detector specially used for measuring the reactor core high-rice dumpling fluence rate, which is developed in the last 60 th century, and has the most prominent characteristic that an output electric signal of the detector is originated from a component called an emitter in the detector, and the component emits beta electrons to generate ionization when being irradiated by neutrons, so that an external working power supply is not needed. Due to the particular operating environment, different detector designs are often required for different reactor environments.
Currently, the design work of self-powered detectors is mainly to evaluate their working performance by the monte carlo algorithm. The steps are generally simulation calculation of large statistics by a Monte Carlo algorithm aiming at specified detector design parameters (emitter, insulator material type and geometric dimension) and specified radiation environment (neutron spectrum and flux), and further statistical analysis is carried out to obtain the expected working performance of the detector design scheme. Due to the particularity of the working principle of the self-powered detector, a large number of simulation events (the number of incident neutrons is more than or equal to 1E7) are generally required for obtaining a reliable simulation result, so that the simulation calculation is long in time, and a dozen of hours is generally required for a set of design parameter calculation process.
Disclosure of Invention
The invention aims to overcome the defects and provide a high-precision numerical model calculation method and a high-precision numerical model calculation system for steady-state response of a self-powered detector, so as to solve the problem of how to improve the calculation speed of performance evaluation of the self-powered detector.
In order to achieve the purpose, the invention adopts the technical scheme that: a method for calculating a high accuracy numerical model of a steady state response of a self powered probe, comprising:
acquiring the energy-range data corresponding relation of electrons in different materials based on data interpolation or probability density distribution function of a Monte Carlo simulation result;
analyzing the minimum kinetic energy of electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation;
and calculating to obtain a track length probability function by utilizing the minimum kinetic energy and through the energy-range data corresponding relation of the electrons in different materials.
Further, calculating a track length probability function according to the energy-range data corresponding relation of the electrons in different materials, wherein the track length probability function comprises the following steps:
firstly, describing the randomness of the transport process of electrons in an emitter by adopting a kinetic energy-displacement probability density distribution function of the electrons;
and then, convolving the kinetic energy-displacement probability density distribution function with the track length probability function to obtain a data table of integration results in different integration ranges.
Further, the obtaining energy-range data corresponding relations of electrons in different materials comprises: and compiling a data table of the energy-range of the electrons in different materials.
Another object of the present invention is to provide a high-precision numerical model calculation system for steady-state response of a self-powered probe, comprising:
the acquisition module is used for acquiring the energy-range data corresponding relation of electrons in different materials based on data interpolation or probability density distribution function of a Monte Carlo simulation result;
the analysis module is used for analyzing the minimum kinetic energy of the electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation;
and the output module is used for calculating to obtain a track length probability function through the energy-range data corresponding relation of the electrons in different materials by utilizing the minimum kinetic energy.
Further, the output module includes:
the determining submodule is used for describing the randomness of the transport process of the electrons in the emitter by adopting a kinetic energy-displacement probability density distribution function of the electrons;
and the convolution submodule is used for convolving the kinetic energy-displacement probability density distribution function with the track length probability function to obtain a data table of integration results in different integration ranges.
Further, the acquisition module comprises a compiling sub-module for compiling an energy-range data table of the electrons in different materials.
The invention has the beneficial effects that:
the realization is simple, include: acquiring the energy-range data corresponding relation of electrons in different materials based on data interpolation or probability density distribution function of a Monte Carlo simulation result; analyzing the minimum kinetic energy of electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation; and calculating to obtain a track length probability function by utilizing the minimum kinetic energy and through the energy-range data corresponding relation of the electrons in different materials. According to the simulation result of the calculation program, the staff of the nuclear power station can select self-powered neutron detectors of different models according to the neutron energy spectrum condition when the reactor runs, so that differential measurement is realized, and the measurement result is more accurate. Meanwhile, when the self-powered neutron detector is used for measurement, the emitter material of the detector can be continuously burnt along with the prolonging of the measurement time, so that the detection efficiency of the detector is greatly optimized.
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The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
FIG. 1 is a flow chart of a high accuracy numerical model calculation method of the self powered probe steady state response of the present invention.
Detailed Description
As used in the specification and in the claims, certain terms are used to refer to particular components. As one skilled in the art will appreciate, manufacturers may refer to a component by different names. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. "substantially" means within an acceptable error range, and a person skilled in the art can solve the technical problem within a certain error range to substantially achieve the technical effect. The description which follows is a preferred embodiment of the present application, but is made for the purpose of illustrating the general principles of the application and not for the purpose of limiting the scope of the application. The protection scope of the present application shall be subject to the definitions of the appended claims.
Referring to fig. 1, a method for calculating a high-precision numerical model of a steady-state response of a self-powered probe according to the present invention includes:
s101, acquiring energy-range data corresponding relations of electrons in different materials based on data interpolation or probability density distribution functions of Monte Carlo simulation results;
step S102, analyzing the minimum kinetic energy of electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation;
and S103, calculating to obtain a track length probability function through the energy-range data corresponding relation of the electrons in different materials by using the minimum kinetic energy.
In an embodiment of the present application, specifically, the calculating the track length probability function according to the energy-range data correspondence of the electrons in different materials includes:
firstly, describing the randomness of the transport process of electrons in an emitter by adopting a kinetic energy-displacement probability density distribution function of the electrons;
and then, convolving the kinetic energy-displacement probability density distribution function with the track length probability function to obtain a data table of integration results in different integration ranges.
In an embodiment of the present application, specifically, the obtaining energy-range data corresponding relations of electrons in different materials includes: and compiling a data table of the energy-range of the electrons in different materials.
It is another object of the present invention to provide a high accuracy numerical model calculation system for steady state response of a self powered probe, comprising:
the acquisition module is used for acquiring the energy-range data corresponding relation of electrons in different materials based on data interpolation or probability density distribution function of a Monte Carlo simulation result;
the analysis module is used for analyzing the minimum kinetic energy of the electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation;
and the output module is used for calculating to obtain a track length probability function through the energy-range data corresponding relation of the electrons in different materials by utilizing the minimum kinetic energy.
In an embodiment of the present application, specifically, the output module includes:
the determining submodule is used for describing the randomness of the transport process of the electrons in the emitter by adopting a kinetic energy-displacement probability density distribution function of the electrons;
and the convolution submodule is used for convolving the kinetic energy-displacement probability density distribution function with the track length probability function to obtain a data table of integration results in different integration ranges.
In an embodiment of the present application, the obtaining module includes a compiling sub-module for compiling an energy-range data table of the electrons in different materials.
The calculation method cited in the present invention is summarized by the following triple integral expression:
wherein
Is the energy loss of beta electrons in the insulating layer of the self-powered detector,
the energy loss data table, which includes the energy loss of electrons in both the insulating materials magnesium oxide and aluminum oxide, is calculated by numerical interpolation from the energy loss data table accompanying the program, and the energy range of the electrons is [1keV,5MeV ].
B (E) is the energy distribution function of the electrons released after the decay of the atomic nucleus beta, and the independent variable E is the initial energy of the electrons. Can be set in the program according to the requirement103Rh、51V or9Beta decay electron spectra of the three Be isotopes.
Sigma (En) is the nuclear reaction cross-section for neutron absorption from the energy detector emitter material, the independent variable En is the neutron incident energy, numerically interpolated through the cross-section data table attached to the programThe values are calculated in a manner that the section data table comprises103Rh、51V or9Be three isotope materials with neutron incident energy range of [1E-5eV,20MeV]。
Phi (En) is a neutron energy distribution function after the normalization of a neutron field in the reactor and needs to be input as an input quantity.
f (En) is the self-shielding factor of the detector emitter material, achieved in the program by reference to the data listed in the original literature.
N (R (E') -R (E)) is an integrand of the probability of penetration of electrons in the insulating layer. Specific mathematical expressions are listed in the original literature, but it has been verified that the functional form diverges in the integral domain. The integral function is thus obtained by consulting other documents in combination with self-derivation. The function argument R is the range of electrons in the insulating layer material. Since the energy loss of electrons in the insulating layer is obtained in the program by numerical interpolation of the numerical table, on the basis of the energy loss of electrons, the energy loss of electrons is integrated in advance to obtain a range data table of the electrons in the insulating material, and then the calculated range table is interpolated to realize the function R so as to improve the calculation speed in the subsequent numerical integration.
The present invention still follows a classical analytical model in framework. However, in the calculation process, elements (such as Emin and N functions) related to the randomness of the particle transportation process are expressed by data interpolation or probability density distribution functions based on Monte Carlo simulation results, so that the influence of the random process is considered in a classical analysis model, and the calculation result of the classical model is obviously improved. On the other hand, because the Monte Carlo simulation result used in the calculation scheme is a pre-programmed data file or a numerical interpolation function, the Monte Carlo simulation calculation of large statistics is not involved in specific calculation, so that the calculation amount is far less than that of direct Monte Carlo simulation calculation adopted by most of similar works.
For example, for a self-powered detector with Rh as emitter material and MgO as insulating layer material, a pre-programmed data table (based on Monte card) of range and path length of electrons with different energies in the above-mentioned materials is first obtainedRoche simulation result compilation), calculating the minimum kinetic energy E of the insulating layer flying out under the condition of the specified outer diameter re of the insulating layer and the radius ri of the emittermin. According to an analytical model, EminIs present because electrons flying off the emitter due to space charge effect are repelled by the insulating layer and thus need to have a certain kinetic energy EminCan be collected. The minimum value of the thickness of the insulating layer through which electrons need to pass can be calculated by a theoretical model of the space charge effect
And then converted into the minimum kinetic energy Emin. Energy loss table in material using electrons in classical model
Converted to EminThis requires that the trajectory of the electron in the material is assumed to be a straight line, but the trajectory of the actual electron in the material is obviously deflected, and the distance actually required to fly is far greater than the displacement
Thus leading to the classical model for EminThe estimate of (c) is significantly smaller. In the technical scheme, a pre-programmed data table interpolation value E of the electron energy based on the Monte Carlo simulation result and the range of the electron energy in the material is used for calculatingminAnd the model calculation precision is improved. On the other hand, the calculation process of the step has no significant efficiency difference compared with the classical model because the numerical interpolation value is based on the existing data table.
In the calculation of the probability function N of the track length, the lost energy condition after beta electrons with certain initial energy generate the designated displacement r is calculated based on the pre-programmed Monte Carlo simulation result data table instead of the energy loss relation of the electrons in the material (namely, the R (E) function does not pass the energy loss relation any more
Calculation, but based on a previously compiled monte carlo simulation results data sheet, thereby improving the modelThe accuracy of the pattern calculation. Furthermore, because the calculation of the N function needs to relate to the probability that electrons with different initial energies keep certain kinetic energy when flying out of the outer surface of the emitter, in order to better describe the random process, the invention defines the probability density distribution function of the initial kinetic energy and the displacement of the electrons through a pre-programmed electron energy-range data table, and further defines the N function as the convolution of the N function of the original model and the probability density distribution function, thereby improving the description precision of the invention on the transportation process of beta electrons in the emitter. Finally, in order to improve the calculation efficiency, the invention calculates the convolution process in detail in different integral ranges in advance and then compiles a data table. In addition, the calculation steps of the technical scheme are consistent with those of the classical model.
It should be noted that the monte carlo simulation result data table compiled in the above technical solution is for the specified limited number (emitter material: metal rhodium Rh, metal vanadium V; insulation layer material: magnesium oxide MgO, aluminum oxide Al) in advance2O3) The relation between the energy and the electron range of electrons of different energies in the material is obtained by high-precision large-statistic Monte Carlo simulation under the condition that the medium is uniform and infinite. Since no geometrical information of the medium is involved in the simulation process, the data table compiled based on the simulation process can be applied to the calculation of the detector model under any geometrical condition. This also means that the estimation process of the present solution is the same for detector designs of different geometrical parameters.
Examples
And (3) program language: python3, interprets the run by an ipython interpreter.
The base library depends on: drawing calls matplotlib, numerical integration and interpolation calls numpy, and numerical calculation calls scipy.
Recommending a computing environment: linux + jupyter lab
Calculating a reference data source: neutron cross-section data was extracted from ENDF VI, and electron energy loss data was referenced from NIST's ESTAR.
The specific calculation process is described below using rhodium emitters as an example. The calculation formula comprises three integral calculations, and the described physical processes are the emission of electrons, the beta decay energy distribution of the electrons and the capture of neutrons.
The emitter material half-life for a self-powered neutron detector is long (rhodium half-life is 42 seconds, vanadium half-life is 3.75 minutes), and the current output signal from a self-powered neutron detector can reach a steady state after a few half-life lengths of material since neutron flux changes. In the calculations of this procedure, it is assumed that the current is in equilibrium with the incident neutron flux and that the calculated emitter is not burning up.
In calculating the integral of neutron capture, the absorption cross section of rhodium on neutrons of different energies is different in consideration of the neutron flux distribution of the reactor and the complexity of energy spectrum.
The function initxs (fn) is used to introduce the neutron absorption cross section of rhodium (from a self-powered neutron detector emitter material, vanadium being interchangeable) and is passed to the list rh _ lib.
Function xsN (En, xs _ lib) is used for one-dimensional linear interpolation of rhodium neutron capture rate (neutron energy units eV).
The function xsNv (v, xs _ lib) is used to calculate a one-dimensional linear interpolation of the rhodium neutron capture rate (neutron energy in m/s).
Rhodium neutron absorption cross sections in the list rh _ lib are drawn with pyplot in matplotlib.
Function B (E) formula according to Fermi
A normalized beta decay spectrum of rhodium is calculated.
Calculating the energy loss of electrons according to the formula of Beth
Wherein N is the number of target material atoms in a unit volume, Z is the target material atomic number, and I is the average excitation and ionization energy of the target atoms. This formula is the ionization loss of electrons at low energies, without taking into account relativistic effects. Since the maximum energy of the electrons produced by rhodium decay is around 2MeV, this formula is applicable.
For calculating the average energy loss at rhodium for an electron of a given energy Ee.
The function dExRh1(Ee) is used for one-dimensional linear interpolation to return energy loss corresponding to electrons with kinetic energy Ee.
The function R _ rh (E) is used for one-dimensional linear interpolation of electron energy at rhodium range
Plotting the energy-range diagram of electrons in rhodium
The electron range between magnesium oxide and aluminum oxide is calculated in the same way
There are upper and lower limits to the integral of the energy that an electron has to reach the emitter surface. EMIN is the minimum average energy of emitter surface electrons that contributes to the current sensitivity of the self-powered neutron detector. Due to the inevitable presence of internal defects inside the insulator, electrons may be trapped to form space charges, creating a built-in electric field inside the insulator. In the insulator, the low-energy electrons of the emitter return to the emitter due to repulsion by the space charge electric field, and thus do not contribute to the current sensitivity of the self-powered neutron detector. After some electrons are trapped to form space charge, a dynamic equilibrium is formed. I.e. some electrons leave the insulator under the influence of the space charge electric field, while some electrons enter the insulator from the emitter (and the shell). At a radial point r of the insulator0The potential has a peak at this point, and the direction of the electric field changes at this point. Under the equilibrium condition, solving r according to the Poisson equation0，
Wherein r isiIs the insulator outer diameter, and k is the ratio of the emitter radius to the insulator outer diameter
EMin _ Mg (k, t) and EMin _ Al (k, t) were used to calculate EMin in magnesium and aluminum oxide from the ratio k of a given emitter radius to the insulator outer diameter and the insulator wall thickness t.
The function N _ quad (l) is used to calculate the track length probability function. The track length probability function is a segmented function, and the function is segmented by using conditional statements. The track length probability function of the cylinder has been accurately calculated and its correctness verified. However, this trajectory length probability function has certain application limitations, which require that the electrons generated by the decay of the emitter material be uniform throughout the volume and that the trajectory of the electrons be a straight line. In practical physical processes, due to the complex neutron flux distribution within the reactor, the probability of an emitter material absorbing neutrons in a sensitive volume to generate electrons is not the same, that is, the electrons are not uniform throughout the volume. Meanwhile, due to the interaction of elastic collision, inelastic collision and the like of electrons in a substance, the moving direction of the electrons is constantly changed, and the moving tracks are not in a straight line. However, the error thus generated is compared with the experimental value, and the calculated error is within an acceptable range.
When P is less than or equal to 1,
when P is greater than or equal to 1
In this formula:
reis the radius of the emitter
P is the ratio of the track length to the emitter diameter
Alpha is the ratio of emitter length to emitter diameter
K (P) is a complete elliptic integral of the first kind
E (P) is the second type of elliptic integral
The limit value of the probability function of the track length N (l) is
When the alpha is greater than 1, the alpha is,
wherein S is the emitter surface area
V is the emitter volume
The function C _ quad (E) is used to calculate the beta particle escape probability, which is the product of the specific energy loss of electrons and the integral of the function N _ quad (l).
The function epsilon _ Mg (re, t, L) is used to calculate the beta particle escape probability. It is the integral of the function C _ quad (e). The three parameters of the function input are the radius of a self-powered neutron detector emitter, the thickness of an insulator and the length of a detector.
The function N _ plot (l) is used to plot the track length probability function.
The function sense (par) calculates the current sensitivity of neutrons at an energy of 2200 m/s. par is a list containing the radius of the emitter of the self-powered neutron detector, the thickness of the insulator, and the length of the detector.
The calculation model is used for designing a self-powered neutron detector of a nuclear reactor core, and can be used for calculating the unit sensitivity of the self-powered neutron detector of the beta decay type. It includes the electron generation rate of the emitter, the probability of electrons escaping from the emitter, the energy loss of electrons in the emitter, and the effect of the insulator on the detector sensitivity.
Tests show that the deviation of the calculated result and the experimental measurement result is about 10%, and the error is completely acceptable. The reliability and the practicability of the calculation model are fully explained by the calculation result. The calculation model is written by python3 on the basis of the original calculation model, and is explained and operated by an ipython interpreter, so that the time required by calculation is greatly shortened, and quick, accurate and reliable calculation is realized. Without extensive experimental planning, it is beneficial to use a computational model to study the effects of emitter geometry and type and dielectric thickness. In the calculation program, neutrons with the energy of 2200m/s can be calculated, and complex neutron energy spectrums of the reactor can be adapted by modifying parameters, so that the calculation program not only has theoretical feasibility, but also has practical feasibility. Meanwhile, for different emitter materials, the influence of the different emitter materials on the output signal of the self-powered neutron detector can be calculated by modifying data such as neutron cross sections and electron energy loss of the introduced emitter materials. Similarly, for different insulator materials, the influence of the different insulator materials on the output signal of the self-powered neutron detector can be calculated by modifying the data such as the electronic energy loss of the introduced insulator materials. And the diameter of an emitter, the length of the emitter and the wall thickness of an insulator of the self-powered neutron detector are different from each other for different models of the self-powered neutron detector. For the emitter diameter, the emitter length and the insulator wall thickness of self-powered neutron detectors of different models, the influence of parameters such as the emitter diameter, the emitter length and the insulator wall thickness on the output signal of the detector can be researched.
In practical application, for manufacturers of self-powered neutron detectors, the calculation of the calculation program has instructive significance for designing the detectors. The influences of emitter materials, insulator materials, emitter diameters, emitter lengths and insulator wall thicknesses on the performance of the detector can be obtained according to calculation results obtained by a calculation program without experiments and making a detector real object, and the parameters are the most important elements in the design of the self-powered neutron detector. Meanwhile, the calculation program is also significant for upgrading and updating the self-powered neutron detector. The emitter materials used for self-powered neutron detectors are currently mostly rhodium and vanadium, but these materials have a long half-life for absorbing neutron decay, and some materials have a shorter half-life than the materials, so that the signal response of the detector can be improved. Using this procedure, it was simulated to investigate whether these materials would be suitable as emitter materials for self-powered neutron detectors. For insulator materials, finding a smaller cross-sectional material that interacts with electrons is also a viable direction of improvement from a powered neutron detector. The absorption consumption of electrons in the insulator is reduced, and the output signal amplitude of the detector can be improved. For nuclear power plants using self-powered neutron detectors, self-powered neutron detectors are widely used in nuclear power plants. Due to the complexity of neutron spectra in reactors, the application of self-powered neutron detectors of various types to reactors is not the same. According to the simulation result of the calculation program, the staff of the nuclear power station can select self-powered neutron detectors of different models according to the neutron energy spectrum condition when the reactor runs, so that differential measurement is realized, and the measurement result is more accurate. Meanwhile, when the self-powered neutron detector is used for measurement, the emitter material of the detector can be continuously burnt along with the prolonging of the measurement time, so that the detection efficiency of the detector is greatly optimized. This calculation procedure may also assist the staff of the nuclear power plant in correcting the measurement results. Burnup of emitter materials from self-powered neutron detectors has also prompted researchers to find emitter materials that are more burnup resistant. The calculation program can also be used for searching for the emitter material guide direction with higher fuel consumption resistance, blind experimental tests are avoided, unnecessary labor and material cost is reduced, the research and development efficiency can be greatly improved, and the research and development period is shortened.
The invention has the beneficial effects that:
the realization is simple, include: acquiring the energy-range data corresponding relation of electrons in different materials based on data interpolation or probability density distribution function of a Monte Carlo simulation result; analyzing the minimum kinetic energy of electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation; and calculating to obtain a track length probability function by utilizing the minimum kinetic energy and through the energy-range data corresponding relation of the electrons in different materials. According to the simulation result of the calculation program, the staff of the nuclear power station can select self-powered neutron detectors of different models according to the neutron energy spectrum condition when the reactor runs, so that differential measurement is realized, and the measurement result is more accurate. Meanwhile, when the self-powered neutron detector is used for measurement, the emitter material of the detector can be continuously burnt along with the prolonging of the measurement time, so that the detection efficiency of the detector is greatly optimized.
The foregoing description shows and describes several preferred embodiments of the present application, but as aforementioned, it is to be understood that the application is not limited to the forms disclosed herein, but is not to be construed as excluding other embodiments and is capable of use in various other combinations, modifications, and environments and is capable of changes within the scope of the application as described herein, commensurate with the above teachings, or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the application, which is to be protected by the claims appended hereto.
Claims (6)
1. A method for calculating a high accuracy numerical model of a steady state response of a self powered probe, comprising:
acquiring the energy-range data corresponding relation of electrons in different materials based on data interpolation or probability density distribution function of a Monte Carlo simulation result;
analyzing the minimum kinetic energy of electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation;
calculating to obtain a track length probability function through the energy-range data corresponding relation of the electrons in different materials by utilizing the minimum kinetic energy;
the following triple integral expression was used for the calculation:
wherein
For the energy loss of beta electrons in the insulating layer of the self-powered detector, it is calculated by numerical interpolation from a program-accompanied energy loss data table comprising the energy losses of electrons in both insulating materials magnesium oxide and aluminium oxide, the energy range of the electrons being [1keV,5MeV ]]；
B (E) is an electron energy distribution function released after the decay of the atomic nucleus beta, and an independent variable E is the initial energy of the electron; can be set in the program according to the requirement103Rh、51V or9Beta decay electron spectra of the three Be isotopes;
Σ(En) Nuclear reaction cross section for neutron absorption from a self-powered detector emitter material, independent variable EnIs the incident energy of neutrons, and is calculated by numerical interpolation using a section data table attached to the program, the section data table including103Rh、51V or9Be three isotope materials with neutron incident energy range of [1E-5eV,20MeV]；
Φ(En) The neutron energy distribution function after the normalization of the neutron field in the reactor needs to be input as an input quantity;
f(En) Is the self-shielding factor of the detector emitter material;
n (R (E') -R (E)) is an integrand of the penetration probability of electrons in the insulating layer;
EMIN represents the minimum kinetic energy that an electron has to fly out of an insulating layer.
2. The method for calculating a high-precision numerical model of the steady-state response of a self-powered probe according to claim 1, wherein the track length probability function is calculated through the energy-range data corresponding relation of the electrons in different materials, and comprises the following steps:
firstly, describing the randomness of the transport process of electrons in an emitter by adopting a kinetic energy-displacement probability density distribution function of the electrons;
and then, convolving the kinetic energy-displacement probability density distribution function with the track length probability function to obtain a data table of integration results in different integration ranges.
3. The method for calculating a high-precision numerical model of the steady-state response of a self-powered probe according to claim 2, wherein the obtaining the energy-range data corresponding relation of electrons in different materials comprises: and compiling a data table of the energy-range of the electrons in different materials.
4. A high accuracy numerical model calculation system for steady state response from a powered probe, comprising:
the acquisition module is used for acquiring the energy-range data corresponding relation of electrons in different materials based on data interpolation or probability density distribution function of a Monte Carlo simulation result;
the analysis module is used for analyzing the minimum kinetic energy of the electrons flying out of the insulating layer under the conditions of the specified outer diameter of the insulating layer and the radius of the emitter according to the energy-range data corresponding relation;
the output module is used for calculating to obtain a track length probability function through the energy-range data corresponding relation of the electrons in different materials by utilizing the minimum kinetic energy;
the following triple integral expression was used for the calculation:
wherein
For the energy loss of beta electrons in the insulating layer of the self-powered detector, it is calculated by numerical interpolation from a program-accompanied energy loss data table comprising the energy losses of electrons in both insulating materials magnesium oxide and aluminium oxide, the energy range of the electrons being [1keV,5MeV ]]；
B (E) is an electron energy distribution function released after the decay of the atomic nucleus beta, and an independent variable E is the initial energy of the electron; can be set in the program according to the requirement103Rh、51V or9Beta decay electron spectra of the three Be isotopes;
Σ(En) Nuclear reaction cross section for neutron absorption from a self-powered detector emitter material, independent variable EnIs the incident energy of neutrons, and is calculated by numerical interpolation using a section data table attached to the program, the section data table including103Rh、51V or9Be three isotope materials with neutron incident energy range of [1E-5eV,20MeV]；
Φ(En) The neutron energy distribution function after the normalization of the neutron field in the reactor needs to be input as an input quantity;
f(En) Is the self-shielding factor of the detector emitter material;
n (R (E') -R (E)) is an integrand of the penetration probability of electrons in the insulating layer;
EMIN represents the minimum kinetic energy that an electron has to fly out of an insulating layer.
5. The self-powered probe steady-state response high accuracy numerical model calculation system of claim 4, wherein the output module comprises:
the determining submodule is used for describing the randomness of the transport process of the electrons in the emitter by adopting a kinetic energy-displacement probability density distribution function of the electrons;
and the convolution submodule is used for convolving the kinetic energy-displacement probability density distribution function with the track length probability function to obtain a data table of integration results in different integration ranges.
6. A high accuracy numerical model calculation system for the steady state response of a self-powered probe as recited in claim 5, wherein said acquisition module includes a compiling sub-module for compiling tables of energy-range data of electrons in different materials.
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