A quantitative analysis method and system for self-powered detector space charge effect

Abstract

The application discloses a kind of quantitative analysis method and system of self-powered detector space charge effect, comprising the following steps: obtaining parameter, the size of total current at different radius of detector is obtained;Based on the size of total current at different radius of detector, the free charge density variation rate in the different radius interval of insulator is calculated according to the law of charge conservation;According to the free charge density variation rate of current moment, the average free charge density variation rate in next time step is solved iteratively, whether the total free charge density variation of adjacent two steps iteration meets the total charge density variation amount iterative convergence limit in single time step is judged;Whether the total free charge density variation meets the total free charge density variation stable convergence limit is judged, whether electric field reaches stable is confirmed.The application simplifies the calculation process, realizes the efficient, high-precision calculation of self-powered neutron detector insulating layer electrostatic field.

Description

Technical Field

[0001] This invention belongs to the field of neutron detection technology and relates to a quantitative analysis method and system for the space charge effect of a self-powered detector. Background Technology

[0002] Self-powered neutron detectors are widely used in reactor neutron measurement due to their simple structure, resistance to high temperatures and pressures, and resistance to strong radiation. The detector mainly consists of an emitter, an insulating layer, and a collector. Placed inside the reactor, the detector reacts with neutrons and releases electrons through several different pathways. When these electrons reach the collector and are collected, a current is generated in the circuit. The intensity of this current is related to the neutron flux density within the reactor; by measuring this current, the neutron flux can be measured.

[0003] However, during the operation of a self-powered neutron detector, electrons may remain trapped in the insulating layer due to insufficient kinetic energy. These electrons may be ionized, creating holes in their original locations. Since the resistivity and conductivity of the insulating layer are generally high, the accumulated charge cannot be discharged in time, thus forming a space electric field within the insulating layer. This space electric field affects the transport behavior of subsequent electrons in the insulating layer, thereby affecting the detector's sensitivity. Therefore, to improve the accuracy of detector sensitivity calculations, a quantitative analysis of the space charge effect (also known as the electrostatic effect) of the insulating layer is necessary.

[0004] There has been much research on the electrostatic effects of self-powered neutron detectors, but these studies still have some shortcomings: 1) In most studies, the charge distribution of the insulating layer is assumed and the dynamic equilibrium process of the electric field is not taken into account, which is quite different from the actual situation; 2) Some studies simulate charge deposition using the Monte Carlo method and fit the charge distribution with a polynomial and solve the Poisson equation, which can reflect the distribution and dynamic changes of the electric field to a certain extent. However, the computational efficiency of simulating charge deposition is low, the statistical process is complex, and the real charge distribution cannot be completely described by a polynomial, so there is a certain fitting error. Summary of the Invention

[0005] The purpose of this invention is to solve the problems in the prior art and provide a quantitative analysis method and system for the space charge effect of a self-powered detector, thereby solving the problem of low calculation efficiency and accuracy of the electrostatic field of the insulating layer of a self-powered neutron detector.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] A quantitative analysis method for the space charge effect of a self-powered detector includes the following steps:

[0008] Obtain the parameters to determine the magnitude of the total current at different radii of the detector;

[0009] Based on the magnitude of the total current at different radii of the detector, the rate of change of free charge density in different radius intervals of the insulator is calculated according to the law of conservation of charge.

[0010] Based on the rate of change of free charge density at the current moment, iteratively solve the average rate of change of free charge density in the next time step, and determine whether the total change of free charge density in two adjacent iterations meets the convergence limit of the total change of charge density in a single time step.

[0011] Determine whether the change in total free charge density satisfies the stable convergence limit of the change in total free charge density, and confirm whether the electric field has reached stability.

[0012] Furthermore, the total current at different radii of the detector includes irradiation current and conduction current, as shown in the following formula:

[0013] J = J rad +J cond

[0014] Among them, J rad Represents irradiation current, J cond This represents conduction current.

[0015] Furthermore, the irradiation current J rad Calculated by Monte Carlo simulation software:

[0016] Given the radiation field information at the location of the self-powered neutron detector and the parameters required for calculation, use them as input to the Monte Carlo program;

[0017] The interaction between the ray and the detector was simulated using a Monte Carlo program, and the irradiation current density J at different radii of the detector was statistically analyzed. rad ;

[0018] The conduction current J cond The electric field of the insulating layer was calculated as follows:

[0019] At time t, the conduction current J at radius r cond The relationship between (r, t) and the electric field intensity E(r, t) at point r is shown by the following equation:

[0020] J cond (r, t) = σE(r, t)

[0021] Where σ is the conductivity of the insulating layer and the electric field strength E(r, 0) = 0.

[0022] Furthermore, the radiation field information includes particle type, particle energy and momentum distribution, and radiation field flux density; the parameters required for the calculation include detector geometry, materials, and initial electric field.

[0023] Furthermore, the calculation process for the rate of change of free charge density is as follows:

[0024] According to the law of conservation of charge, we have

[0025]

[0026] Integrating it by volume and applying Gauss's theorem, we have...

[0027]

[0028] Where S is the boundary surface of volume V, ρ(r, 0) = 0, and J(r, t) represents the total current density at radius r at time t;

[0029] The detector's insulating layer is uniformly divided into N cylindrical shell layers along the radius. The inner radius of the k-th cylindrical layer is denoted as rk, and the outer radius is denoted as r. k+1 Then the inner radius of the detector's insulating layer is r1, and the outer radius is r. N+1 Where k = 1, 2, 3, ..., N; then for the k-th cylindrical shell layer, we have

[0030]

[0031] The rate of change of free charge density in the k-th cylindrical shell at time t is shown in the following equation:

[0032]

[0033] Among them, J k (t) represents a radius of r k Total current density at the location, J k+1 (t) represents a radius of r k+1 The total current density at that location.

[0034] Furthermore, the calculation process for the total change in free charge density is as follows:

[0035] The rate of change of free charge density at time t is used as the initial estimate of the average rate of change of free charge density of the k-th cylindrical shell layer from t to t+Δt. That is, as shown in the following formula:

[0036]

[0037] The initial value of the change in free charge density of the kth cylindrical shell layer within the period from t to t+Δt is given by the following formula:

[0038]

[0039] Let s be the algebra solved by the following sub-loop iteration, with an initial value of 0;

[0040] The charge density ρ of the k-th cylindrical shell at time t+Δt k，s (t+Δt) can be calculated using the following formula:

[0041]

[0042] The electric field distribution E(r, t+Δt) at time t+Δt in the s-th iteration is solved using the mirror method.

[0043] Calculate the total current at different radii of the detector insulator under the electric field setting E(r, t+Δt);

[0044] Calculate the rate of change ρ′ of the free charge density in the k-th cylindrical shell under the electric field setting E(r, t+Δt). k (t+Δt), then calculate the rate of change of the average free charge density of the k-th cylindrical shell layer within the range of t to t+Δt according to the following formula. With the change in free charge density

[0045]

[0046]

[0047] Furthermore, the process of using the mirror method to solve for the electric field distribution E(r, t+Δt) at time t+Δt in the s-th iteration is as follows:

[0048] For ρ k By fitting (t+Δt), the free charge density distribution function ρ(r, t+Δt) at time t+Δt is obtained, and then the electric field is calculated by the following formula:

[0049]

[0050] Alternatively, the electric field intensity E(r, t+Δt) at different radii of the insulator at time t+Δt can be obtained numerically according to the following formula:

[0051]

[0052]

[0053]

[0054] (When k = 2, 3, ..., N)

[0055]

[0056] (when r) k ≤r<r k+1 hour).

[0057] Furthermore, the iterative convergence limit for the change in total charge density within a single time step is ε. step If the following requirement is met, then output the current E(r, t+Δt) and ρ. k (t+Δt) represents the electric field distribution and charge density at time t+Δt:

[0058]

[0059] Where, ε step This is the threshold requirement for the relative difference in the change of free charge before and after two adjacent iterations; if the electric field distribution is obtained by fitting an analytical expression of the charge distribution, then integration is performed directly; if the electric field distribution is obtained by numerical integration, then the corresponding potential is calculated by the following formula:

[0060]

[0061]

[0062] in,

[0063]

[0064] Otherwise, exit this step and begin the next iteration.

[0065] Furthermore, the stable convergence limit of the total free charge density change is ε. stable If the change in total free charge density satisfies the following equation, the electric field is considered to have reached a stable state:

[0066]

[0067] Otherwise, repeat the calculation for the next time step until the rate of change of the average total free charge density reaches a stable level.

[0068] A quantitative analysis system for the space charge effect of a self-powered detector, comprising:

[0069] The acquisition module, whose calculation module is used to acquire parameters, obtains the magnitude of the total current at different radii of the detector;

[0070] The calculation module is used to calculate the rate of change of free charge density within different radius ranges of the insulator based on the magnitude of the total current at different radii of the detector and the law of conservation of charge.

[0071] The iterative module is used to iteratively solve the average free charge density change rate in the next time step based on the free charge density change rate at the current time, and to determine whether the total free charge density change in two adjacent iterations meets the convergence limit of the total charge density change in a single time step.

[0072] The judgment module is used to determine whether the change in total free charge density meets the stable convergence limit of the change in total free charge density, and to confirm whether the electric field has reached stability.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] This invention provides a quantitative analysis method for the space charge effect of a self-powered neutron detector. Based on the law of charge conservation, it proposes an efficient statistical method for the charge distribution of the insulating layer, requiring only the statistical analysis of the current at different radii of the insulating layer, without needing to trace the movement paths of individual electrons. Furthermore, based on the method of images and Gauss's law, it replaces the previous process of solving differential equations with an integral method, eliminating the need to fit the charge distribution function. This analytical method effectively improves computational accuracy and efficiency, and directly derives the electric field distribution from the charge distribution, simplifying the calculation process and thus enabling efficient and high-precision calculation of the electrostatic field of the insulating layer of a self-powered neutron detector. Attached Figure Description

[0075] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0076] Figure 1 This is a schematic diagram of the quantitative analysis method for the space charge effect of the self-powered detector of the present invention.

[0077] Figure 2 This is a schematic diagram of the cross-sectional layering of the detector of the present invention.

[0078] Figure 3 This is a flowchart of the iterative calculation of total charge change at a single time step according to the present invention.

[0079] Figure 4 This is a schematic diagram of the integration path for solving the potential according to the present invention.

[0080] Figure 5 This is a graph showing the change in charge deposition rate of the insulating layer of the rhodium self-powered detector of the present invention.

[0081] Figure 6 This is a diagram showing the charge density distribution of the insulating layer of the rhodium self-powered detector under steady-state conditions according to the present invention.

[0082] Figure 7 This is a diagram showing the electric field intensity distribution of the insulating layer of the rhodium self-powered detector under steady-state conditions according to the present invention.

[0083] Figure 8 This is a potential distribution diagram of the insulating layer of the rhodium self-powered detector under steady-state conditions according to the present invention.

[0084] Figure 9 This is a schematic diagram of the structure of a quantitative analysis system for the space charge effect of a self-powered detector according to a preferred embodiment of the present invention.

[0085] Figure 10 This is a schematic diagram of the electronic device structure according to a preferred embodiment of the present invention. Detailed Implementation

[0086] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of this application, including various details to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0087] Obviously, the described embodiments are only some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0088] It should be noted that the terminals involved in the embodiments of this application may include, but are not limited to, mobile phones, personal digital assistants (PDAs), wireless handheld devices, tablet computers, personal computers (PCs), MP3 players, MP4 players, wearable devices (e.g., smart glasses, smartwatches, smart bracelets), smart home devices, and other smart devices.

[0089] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0090] The present invention will now be described in further detail with reference to the accompanying drawings:

[0091] See Figure 1This invention provides a quantitative analysis method for the space charge effect of a self-powered detector, comprising the following steps:

[0092] Step 1: Calculate the total current at different radii of the detector. The total current J includes the irradiation current J. rad With conduction current J cond As shown in the following formula:

[0093] J = J rad +J cond

[0094] Among them, the irradiation current J rad The data is obtained by Monte Carlo simulation software. Specifically, given the radiation field information at the location of the self-energized neutron detector (including particle type, particle energy and momentum distribution, radiation flux density, etc.) and the parameters required for calculation (detector geometry, materials, and initial electric field, etc.), these are used as inputs to the Monte Carlo program. The Monte Carlo program simulates the interaction between the radiation and the detector, and statistically analyzes the irradiation current density J at different radii of the detector. rad .

[0095] Since irradiation may produce unstable nuclides, which cannot completely decay within the current time step due to their long half-lives, we can statistically analyze the current generated by the decay of the current radiation field within the current time step and the current generated by the decay of unstable nuclides accumulated in previous time steps within the current time step, which is the true free charge deposition model. Alternatively, we can assume that the unstable nuclides generated by the current radiation field completely decay within the current time step, and statistically analyze the current generated by the decay of the current radiation field within the current time step under this simplified condition, which is the simplified free charge deposition model.

[0096] The two free charge deposition models can be selected based on the needs of the research problem: (1) If the focus is on the actual evolution of the spatial electric field, the actual free charge deposition model should be used. (2) If only the steady-state electric field is considered, the simplified free charge deposition model can be selected to save computation time, provided that the steady-state electric fields established by the two models are consistent. The two models differ only in the statistical irradiation current; the subsequent steps are completely identical, so they will not be elaborated further.

[0097] And the conduction current J cond The electric field of the insulating layer is calculated. Since the self-powered detector structure is a coaxial cylinder and the detector length is much larger than its radius, its current distribution can be considered to be only related to r. At time t, the conduction current J at radius r is... cond The relationship between (r, t) and the electric field intensity E(r, t) at point r is shown by the following formula:

[0098] J cond (r, t) = σE(r, t)

[0099] Where σ is the conductivity of the insulating layer, E(r, 0) = 0.

[0100] Step 2: Obtain the rate of change of free charge density within different radius ranges of the insulator based on the law of conservation of charge.

[0101] Since the self-powered detector is a coaxial cylinder and its length L is much larger than its radius R, its charge and current distribution can be considered to depend only on r. According to the law of conservation of charge, we have...

[0102]

[0103] Taking a volume integral of the above equation and applying Gauss's theorem, we have...

[0104]

[0105] Where S is the boundary surface of volume V, and ρ(r, 0) = 0.

[0106] like Figure 2 As shown, the detector's insulating layer is uniformly divided into N cylindrical shell layers along the radius, and the inner radius of the k-th cylindrical layer is denoted as r. k The outer radius is denoted as r. k+1 (Then the inner radius of the detector's insulating layer is r1, and the outer radius is r) N+1 ), where k = 1, 2, 3, ..., N. When N is sufficiently large, it can be assumed that the charge distribution within each cylindrical shell layer is uniform, i.e., the charge density ρ within that layer is... k (t) is independent of r. Therefore, for the k-th cylindrical shell layer, we have:

[0107]

[0108] In the formula, J(r,t) represents the total current density at a radius of r at time t.

[0109] Therefore, the rate of change of the free charge density of the k-th cylindrical shell at time t is as shown in the following equation:

[0110]

[0111] Among them, J k (t) represents the radius r k Total current density at the location, J k+1 (t) represents the radius r k+1 The total current density at that location.

[0112] Step 3: Using the rate of change of free charge density at the current moment, iteratively solve for the average rate of change of free charge density in the next time step. Determine whether the total change of free charge in the two iterations meets the convergence limit of the total change of charge in a single time step. If it does not meet the limit, repeat the iteration. If it does meet the limit, output the accurate change of free charge in different radius intervals of the insulator at that time step, as well as the corresponding free charge distribution, electric field intensity distribution, and electric potential distribution.

[0113] Step 2 yields the rate of change of free charge density ρ′ of the k-th cylindrical shell at time t. k (t), but the rate of change of free charge density from t to t+Δt is not constant. To obtain the free charge density of the k-th cylindrical shell at time t+Δt, it is necessary to solve for the average rate of change of free charge density of the k-th cylindrical shell over the time interval from t to t+Δt. Since the average rate of change of free charge density from t to t+Δt cannot be directly obtained at time t, iterative solution is required. ρ k (t) represents the free charge density of the k-th cylindrical shell at time t, which is given by the previous iteration or by the initial value (for a detector that is not yet operational, there is no free charge in the insulator at time 0 when it starts operating).

[0114] like Figure 3 As shown, the rate of change of free charge density at time t is used as the initial estimate of the average rate of change of free charge density of the k-th cylindrical shell layer from t to t+Δt. That is, as shown in the following formula:

[0115]

[0116] The initial value of the change in free charge density of the kth cylindrical shell layer within the period from t to t+Δt is given by the following formula:

[0117]

[0118] Let s be the algebra solved by the following sub-loop iteration, with an initial value of 0.

[0119] S1: s = s + 1.

[0120] The charge density ρ of the k-th cylindrical shell at time t+Δt k，s (t+Δt) can be calculated using the following formula:

[0121]

[0122] Considering the structural symmetry of the self-powered neutron detector, the mirror image method can be used to directly solve the electric field in the insulating layer from the charge distribution. For a self-powered neutron detector with an inner radius \(R_1\) and an outer radius \(R_2\) in the insulating layer, since its length \(L\) is much larger than the radius \(R\), it can be considered as an infinitely long cylinder. For the case where the volume charge density distribution in the insulating layer is \(\rho(r)\), the linear charge density \(\tau(r) = 2\pi r\rho(r)dr\) in a cylindrical shell with a radius \(r\) and a thickness \(dr\) in the insulating layer. In this problem, both the emitter and the collector are conductors, and the boundary conditions are that the electric potentials of the inner and outer conductors are both 0, that is

[0123]

[0124] Then, outside the solution region, the boundary conditions are replaced by image charges (without changing the charge distribution in the solution region). According to the uniqueness theorem, the electric field distribution generated by the image charges and the original charges together is the original electric field distribution in the solution region. The amount and position of the image charges are determined by the boundary conditions. Therefore, the image charges should be located at \(r < R_1\) and \(r > R_2\), and according to symmetry, the image charges are also distributed in cylindrical shells coaxial with the insulating layer.

[0125] The charge density at the radius \(r\) of the insulator is \(\rho(r)\), and its corresponding linear density is \(2\pi r\rho(r)\). Let the linear charge density of its image charge at \(R\) 内 (R 内 \(< R_1)\) be \(\tau_1\), and the linear charge density of its image charge at \(R\) 外 (R 外 \(> R_2)\) be \(\tau_2\). For an infinitely long thin cylindrical shell with a linear charge density \(\tau\) and a radius \(R\), the electric field inside the shell is 0, and the electric field outside the shell is \(\tau / 2\pi r\). Selecting the electric potential at \(R_0\) outside the shell to be 0, then the electric potential distribution in space is

[0126]

[0127] The mirror image method requires removing the conductor and filling it with the insulating layer medium, and at the same time replacing the boundary conditions with image charges So, the following equations hold for the electric potentials generated by the free charge at \(r\) and the corresponding image charges at the boundary:

[0128]

[0129]

[0130] Subtracting the above two equations gives

[0131]

[0132] Since the image charge τ2 is distributed outside the insulating layer, it will not affect the electric field inside the insulating layer due to axisymmetry, so it does not need to be included in the calculation. On the other hand, the image charge τ1 is symmetrically distributed within the range of the emitter location. Due to symmetry, the electric field it generates in the insulating layer is equivalent to the electric field generated by the image charge concentrated on the central axis. Therefore, the specific location of the image charge τ1 does not need to be calculated.

[0133] The total image charge linear density τ within the insulating layer (R1~R2) in the range of the emitter location t for

[0134]

[0135] According to Gauss's law for electrostatics, the electric field strength E(r) in an insulator with radius r (R1≤r≤R2) can be expressed as follows:

[0136]

[0137] Where ε is the dielectric constant of the insulator.

[0138] Organizing can yield

[0139]

[0140] The calculated space charge distribution can be fitted to obtain an analytical expression for the charge distribution function (various function forms can be selected depending on the situation). Substituting this expression into the above formula and solving by integration yields the electric field distribution. Alternatively, discretization can be performed directly for numerical integration. The smaller the mesh size, the closer the integration result will be to the true value, avoiding the time-consuming fitting calculation and errors from the fitting process. For discrete numerical integration, the insulating layer needs to be uniformly divided into N cylindrical shells along its radius. When N is sufficiently large, the charge density within each shell can be considered approximately the same. Therefore, the inner radius of the k-th cylinder can be denoted as r. k The outer radius is denoted as r. k+1 (Then the inner radius of the detector's insulating layer is r1, and the outer radius is r) N+1 The charge density can be denoted as ρ. k Then E(r) is expressed as

[0141]

[0142] Organizing can yield

[0143]

[0144] make

[0145]

[0146] Obviously there is

[0147]

[0148] (When k = 2, 3, ..., N)

[0149] (when r) k ≤r <r k+1 hour)

[0150] This iterative calculation of the electric field at different radii can avoid a lot of redundant calculations and save computation time.

[0151] Based on this, the potential distribution can also be calculated (optional; not calculating the potential distribution does not affect the solution of the electric field). Considering the structural symmetry of the self-powered neutron detector and its axial length being much larger than its radial radius, both the potential and electric field distributions depend only on r, and the direction of the electric field is also along the radial direction, i.e.

[0152]

[0153] Since the inner radius R1 of the insulation layer is the interface between the conductor and the insulator, R1 is chosen as the zero potential point. That is, 0; the potential distribution within the insulating layer (R1≤r≤R2) can be expressed as a line integral of the second kind.

[0154]

[0155] In the formula, Γ represents the path from radius R1 to radius r. Since the curl of the electrostatic field is 0, the integral result expressed in the above formula depends only on the start and end points of the integration and is independent of the integration path; furthermore, considering the axisymmetry of the detector, according to... Figure 4 Choosing the integration path Γ, where the direction of Γ is on the same straight line as the electric field direction, the integral of Γ is the portion along the radius r within the range [R1, r]. The line integral can be simplified to a single definite integral along the radius.

[0156]

[0157] Similarly, the calculated space charge distribution can be fitted to obtain the analytical expression of the charge distribution function (various function forms can be selected according to the situation), thereby solving the analytical expression of the electric field, and then substituting it into the above equation to obtain the potential distribution through integration; alternatively, it can be directly discretized for numerical integration. As long as the mesh is sufficiently small, the integration result will be closer to the true value, avoiding the time consumption of fitting calculations and the errors from fitting. For discrete numerical integration, the insulating layer needs to be uniformly divided into N cylindrical shells in radius. When N is sufficiently large, the charge density in each shell can be considered to be approximately the same, then the inner radius of the kth cylinder can be denoted as r. k The outer radius is denoted as r. k+1(Then the inner radius of the detector's insulating layer is r1, and the outer radius is rN) +1 The charge density can be denoted as ρ. k .

[0158] Since the electric potential is independent of the integration path and only depends on the start and end points, it can be simplified. The solution for r k <r≤r k+1 The electric potential can be expressed as

[0159]

[0160] make

[0161]

[0162]

[0163] Obviously there is

[0164]

[0165] C k Substitution The expression for r k <r≤r k+1 ,have

[0166]

[0167] You can get points after accumulating points.

[0168]

[0169] in,

[0170]

[0171] Alternatively, based on the obtained E(r), numerical integration (trapezoidal rule, Newton-Cotes quadrature formula, composite quadrature formula, etc.) can be used to directly obtain the value.

[0172] In summary, the method of images can be used to solve for the electric field distribution based on a fitted formula of the charge density distribution, or by directly performing numerical integration based on the actual charge distribution in the insulating layer. The fitted method can directly produce a theoretical solution with good smoothness, but it may introduce fitting errors, and performing fitting at every step reduces computational efficiency. Numerical solutions can avoid fitting errors and are more computationally efficient.

[0173] The method of images is used to solve for the electric field distribution E(r, t+Δt) at time t+Δt in the s-th iteration. Specifically, ρ can be used for calculation. kThe free charge density distribution function ρ(r, t+Δt) at time t+Δt is obtained by fitting (the fitting form can be polynomial, exponential, or other function forms). Then, the electric field is calculated using the following formula:

[0174]

[0175] Alternatively, the electric field intensity E(r, t+Δt) at different radii of the insulator at time t+Δt can be obtained numerically according to the following formula:

[0176]

[0177]

[0178]

[0179] (When k = 2, 3, ..., N)

[0180]

[0181] (when r) k ≤r<r k+1 hour)

[0182] S2: Obtain the total current at different radii of the detector insulator under the electric field E(r, t+Δt) setting, following the method in step 1.

[0183] S3: Obtain the rate of change ρ′ of the free charge density of the k-th cylindrical shell under the electric field E(r, t+Δt) setting, following the method in step 2. k (t+Δt), then calculate the rate of change of the average free charge density of the k-th cylindrical shell layer within the range of t to t+Δt according to the following formula. With the change in free charge density

[0184]

[0185]

[0186] S4: If

[0187]

[0188] Where ε step This is a threshold requirement for the relative difference in the change of free charge before and after two adjacent iterations. If the above requirement is met, then: 1) Output the current E(r, t+Δt) and ρ k(t+Δt) represents the electric field distribution and charge density at time t+Δt; 2) If the electric field distribution is obtained by fitting the charge distribution analytically, then integration can be performed directly; if the electric field distribution is obtained by numerical integration, then the corresponding potential can be calculated using the following formula; 3) Exit the loop.

[0189]

[0190]

[0191] in

[0192]

[0193]

[0194] In the formula, C is a parameter introduced when numerically solving the electric field.

[0195] Otherwise, exit the sub-step and start the next iteration from sub-step 1.

[0196] Step 4: Determine whether the change in total free charge meets the stable convergence limit of the change in total free charge. If not, advance the time step and repeat the above steps to calculate the change in total free charge for the next time step until the convergence condition is met. At this point, the electric field is considered to have reached stability, and the calculation terminates.

[0197] The steady-state convergence limit of the rate of change of the average total free charge density is set to ε. stable If the change in total charge density satisfies the following formula, the electric field is considered to have reached stability and the calculation ends; otherwise, repeat steps 1 to 3 to calculate the next time step until the average rate of change of total free charge density reaches stability.

[0198]

[0199] Example 1:

[0200] This embodiment uses a typical cobalt self-powered neutron detector, which is 1 cm in length. The detector dimensions and materials are shown in the table below.

[0201] Table 1 Detector Dimensions and Materials

[0202] Geometric shape Outer radius (cm) Material <![CDATA[Density (g / cm 3 )]]> emitter 0.025 <![CDATA[ 103 Rh]]> 12.4 Insulation layer 0.05 <![CDATA[Al2O3]]> 2.9 Collection pole 0.075 Inconel 8.4 Detector channel air gap 0.1 He 2.14E-4

[0203] The radioactive source is a cylindrical isotropic source located at the emitter surface, employing a 0.0253 eV monoenergetic thermal neutron source with a flux density of 3.23 E14 n·cm⁻¹. -2 s· -1The resistivity of the insulating layer is set to 1E¹² Ω·m. Since the rhodium detector is a delayed SPND, the electric field changes calculated using the real charge deposition model and the simplified charge deposition model are different, but the steady-state results are the same. Here, the simplified model is used as an example. Figure 5 The calculated curves showing the changes in charge deposition rate and charge loss rate reveal that after 190 seconds, the charge loss rate and charge deposition rate become essentially the same, the net charge deposition rate approaches zero and remains largely unchanged, indicating that the electric field has reached a steady state. After reaching steady state, the charge density distribution of the insulating layer is as follows: Figure 6 As shown; the electric field intensity distribution of the insulating layer is as follows Figure 7 As shown; the potential distribution of the insulating layer is as follows Figure 8 As shown, since the charge mainly originates from the emitter and collector, the charge is primarily deposited at the inner and outer boundaries of the insulating layer, resulting in a relatively large electric field strength at the boundaries. In this embodiment, the maximum potential is 55.874 kV. Therefore, the signal electrons at the emitter need to overcome an additional potential barrier of 55.874 keV, in addition to overcoming the resistance of the insulating layer material, to reach the collector.

[0204] Since the electric field strength is affected by various parameters such as detector size, material, and radiation source parameters, the electric field of the insulating layer must be calculated when the detector is actually used in order to evaluate the impact of electrostatic effects on the detector output signal.

[0205] Example 2:

[0206] Embodiment 2 provided by this invention is an embodiment of the quantitative analysis system for the space charge effect of the self-powered detector provided by this invention, such as... Figure 9 As shown, an embodiment of the system includes: an acquisition module, a calculation module, an iteration module, and a judgment module.

[0207] The acquisition module, whose calculation module is used to acquire parameters, obtains the magnitude of the total current at different radii of the detector;

[0208] The calculation module is used to calculate the rate of change of free charge density within different radius ranges of the insulator based on the magnitude of the total current at different radii of the detector and the law of conservation of charge.

[0209] The iterative module is used to iteratively solve the average free charge density change rate in the next time step based on the free charge density change rate at the current time, and to determine whether the total free charge density change in two adjacent iterations meets the convergence limit of the total charge density change in a single time step.

[0210] The judgment module is used to determine whether the change in total free charge density meets the stable convergence limit of the change in total free charge density, and to confirm whether the electric field has reached stability.

[0211] It is understood that the quantitative analysis system for the space charge effect of the self-powered detector provided by the present invention corresponds to the quantitative analysis method for the space charge effect of the self-powered detector provided in the foregoing embodiments. The relevant technical features of the quantitative analysis system for the space charge effect of the self-powered detector can be referred to the relevant technical features of the quantitative analysis method for the space charge effect of the self-powered detector, and will not be repeated here.

[0212] like Figure 10 As shown, another object of the present invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor performing the steps of the method for quantitative analysis of the space charge effect of the self-powered detector.

[0213] The quantitative analysis method for the space charge effect of the self-powered detector includes the following steps:

[0214] Obtain the parameters to determine the magnitude of the total current at different radii of the detector;

[0215] Based on the magnitude of the total current at different radii of the detector, the rate of change of free charge density in different radius intervals of the insulator is calculated according to the law of conservation of charge.

[0216] Based on the rate of change of free charge density at the current moment, iteratively solve the average rate of change of free charge density in the next time step, and determine whether the total change of free charge density in two adjacent iterations meets the convergence limit of the total change of charge density in a single time step.

[0217] Determine whether the change in total free charge density satisfies the stable convergence limit of the change in total free charge density, and confirm whether the electric field has reached stability.

[0218] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method for quantitative analysis of the space charge effect of the self-powered detector.

[0219] The quantitative analysis method for the space charge effect of the self-powered detector includes the following steps:

[0220] Obtain the parameters to determine the magnitude of the total current at different radii of the detector;

[0221] Based on the magnitude of the total current at different radii of the detector, the rate of change of free charge density in different radius intervals of the insulator is calculated according to the law of conservation of charge.

[0222] Based on the rate of change of free charge density at the current moment, iteratively solve the average rate of change of free charge density in the next time step, and determine whether the total change of free charge density in two adjacent iterations meets the convergence limit of the total change of charge density in a single time step.

[0223] Determine whether the change in total free charge density satisfies the stable convergence limit of the change in total free charge density, and confirm whether the electric field has reached stability.

[0224] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0225] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0226] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0227] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0228] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A quantitative analysis method for the space charge effect of a self-powered detector, characterized in that, Includes the following steps: Obtain the parameters to determine the magnitude of the total current at different radii of the detector; Based on the magnitude of the total current at different radii of the detector, the rate of change of free charge density in different radius intervals of the insulator is calculated according to the law of conservation of charge. Based on the rate of change of free charge density at the current moment, iteratively solve the average rate of change of free charge density in the next time step, and determine whether the total change of free charge density in two adjacent iterations meets the convergence limit of the total change of charge density in a single time step. Determine whether the change in total free charge density satisfies the stable convergence limit of the change in total free charge density, and confirm whether the electric field has reached stability. The calculation process for the rate of change of free charge density is as follows: According to the law of conservation of charge, we have Integrating it by volume and applying Gauss's theorem, we have... Where S is the boundary surface of volume V. , This represents the total current density at a radius of r at time t; The detector's insulating layer is uniformly divided into N cylindrical shell layers along the radius, and the inner radius of the k-th cylindrical layer is denoted as . The outer radius is denoted as Then the inner radius of the detector's insulating layer is The outer radius is Where k = 1, 2, 3, ..., N; then for the k-th cylindrical shell layer, we have The length of the detector; The rate of change of free charge density in the k-th cylindrical shell at time t is shown in the following equation: in, Indicates radius as Total current density at the location, Indicates radius as Total current density at the location; The calculation process for the total change in free charge density is as follows: Let the rate of change of free charge density at time t be the first... k A cylindrical shell layer in Initial estimate of the rate of change of the average free charge density within That is, as shown in the following formula: No. k A cylindrical shell layer in The initial value of the change in free charge density within is given by the following formula: Let s be the algebra solved by the following sub-loop iteration, with an initial value of 0; No. k A cylindrical shell layer in Charge density at time The following formula can be used to calculate: Solving using the mirror method Electric field distribution at time s-th iteration ; Calculation in electric field The magnitude of the total current at different radii of the detector insulator under the given conditions; Calculation in electric field The rate of change of free charge density in the k-th cylindrical shell layer is set as follows. Then, calculate the k-th cylindrical shell layer according to the following formula. Rate of change of average free charge density within With the change in free charge density : 。 2. The quantitative analysis method for the space charge effect of a self-powered detector according to claim 1, characterized in that, The total current at different radii of the detector includes irradiation current and conduction current, as shown in the following formula: in, Indicates irradiation current. This represents conduction current.

3. The quantitative analysis method for the space charge effect of a self-powered detector according to claim 2, characterized in that, The irradiation current Calculated by Monte Carlo simulation software: Given the radiation field information at the location of the self-powered neutron detector and the parameters required for calculation, use them as input to the Monte Carlo program; The interaction between the ray and the detector was simulated using a Monte Carlo program, and the irradiation current density at different radii of the detector was statistically analyzed. ; The conduction current The electric field of the insulating layer was calculated as follows: At time t, the conduction current at radius r electric field strength at point r The relationship is shown in the following formula: in, The conductivity of the insulating layer and the electric field strength are given. .

4. The quantitative analysis method for the space charge effect of a self-powered detector according to claim 3, characterized in that, The radiation field information includes particle type, particle energy and momentum distribution, and radiation field flux density; the parameters required for the calculation include detector geometry, materials, and initial electric field.

5. The quantitative analysis method for the space charge effect of a self-powered detector according to claim 1, characterized in that, The solution is obtained using the mirror method. Electric field distribution at time s-th iteration The process is as follows: right By fitting, we can obtain Free charge density distribution function at time t Then the electric field is calculated using the following formula: The dielectric constant of the insulator is _____. The inner radius of the insulation layer, The outer radius of the insulation layer; Alternatively, the insulator at different radii can be obtained numerically using the following formula. electric field intensity at time : When k=2,3,...N hour.

6. The quantitative analysis method for the space charge effect of a self-powered detector according to claim 5, characterized in that, The convergence limit of the iterative change in total charge density within a single time step is: If the following requirement is met, then output the current value. and As t+ Electric field distribution and charge density at time: in, This is the threshold requirement for the relative difference in the change of free charge before and after two adjacent iterations; if the electric field distribution is obtained by fitting an analytical expression of the charge distribution, then integration is performed directly; if the electric field distribution is obtained by numerical integration, then the corresponding potential is calculated by the following formula: in, Otherwise, exit this step and begin the next iteration.

7. The quantitative analysis method for the space charge effect of a self-powered detector according to claim 6, characterized in that, The stability convergence limit of the total free charge density change is: If the change in total free charge density satisfies the following equation, the electric field is considered to have reached a stable state: Otherwise, repeat the calculation for the next time step until the rate of change of the average total free charge density reaches a stable level.

8. A quantitative analysis system for the space charge effect of a self-powered detector, characterized in that, The steps for implementing the method of claim 1 include: The acquisition module, whose calculation module is used to acquire parameters, obtains the magnitude of the total current at different radii of the detector; The calculation module is used to calculate the rate of change of free charge density in different radius intervals of the insulator based on the magnitude of the total current at different radii of the detector and the law of conservation of charge. The iterative module is used to iteratively solve the average free charge density change rate in the next time step based on the free charge density change rate at the current time, and to determine whether the total free charge density change in two adjacent iterations meets the convergence limit of the total charge density change in a single time step. The judgment module is used to determine whether the change in total free charge density meets the stable convergence limit of the change in total free charge density, and to confirm whether the electric field has reached stability.

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