阅读说明：本技术 一种自给能中子探测器静电效应的评估方法 (Method for evaluating electrostatic effect of self-powered neutron detector ) 是由 张清民 桑耀东 邓邦杰 曹良志 李云召 于 2019-10-16 设计创作，主要内容包括：一种自给能中子探测器静电效应的评估方法,步骤如下：(1)由蒙特卡罗程序模拟得到零时刻绝缘层电荷沉积速率V<Sub>q,dep,0</Sub>(r,t),并且此时电荷流失速率V<Sub>q,out,0</Sub>(r,t)为零；(3)由V<Sub>q,dep,0</Sub>(r,t)和V<Sub>q,out,0</Sub>(r,t)得到零时刻电荷净沉积速率V<Sub>q,0</Sub>(r,t)；(4)设定时间步长为Δt,将前一个时间点的电荷沉积速率、电荷流失速率作为当前时间点的初值,得到当前时间绝缘层电荷分布Q(r,t)；(5)根据Q(r,t)以及绝缘层体积获得绝缘层电荷密度ρ<Sub>0</Sub>(r,t),并拟合得到其解析式ρ(r,t)；(6)将ρ(r,t)代入泊松方程并求解,得到绝缘层电势与电场；(7)将电场加入蒙特卡罗模拟过程中得到当前时间点新的电荷净沉积速率,并重复步骤(4)-(7),直到得到稳定的电荷净沉积速率V<Sub>q</Sub>(r,t)；(8)若V<Sub>q</Sub>(r,t)满足收敛要求则输出电场与电势,否则重复上述步骤。(A method for evaluating electrostatic effect of a self-powered neutron detector comprises the following steps: (1) obtaining the charge deposition rate V of the insulating layer at the zero moment by Monte Carlo program simulation q,dep,0 (r, t), and at this time the charge loss rate V q,out,0 (r, t) is zero; (3) from V q,dep,0 (r, t) and V q,out,0 (r, t) obtaining a net deposition rate V of the charge at time zero q,0 (r, t); (4) setting the time step as delta t, and taking the charge deposition rate and the charge loss rate of the previous time point as initial values of the current time point to obtain the charge distribution Q (r, t) of the insulating layer at the current time; (5) obtaining the charge density rho of the insulating layer according to Q (r, t) and the volume of the insulating layer 0 (r, t) and fitting to obtain an analytic expression rho (r, t) thereof; (6) substituting rho (r, t) into a Poisson equation and solving to obtain the potential and the electric field of the insulating layer; (7) adding the electric field into the Monte Carlo simulation process to obtain new net deposition rate of electric charge at the current time point, and repeating the steps (4) - (7) until stable net deposition rate of electric charge V is obtained q (r, t); (8) if V q (r, t) if the convergence requirement is satisfied, then outputAnd (4) generating an electric field and electric potential, otherwise, repeating the steps.)

1. A self-powered neutron detector electrostatic effect assessment method is characterized by comprising the following steps: the method comprises the following steps:

step 1: providing the neutron-photon source distribution near a self-powered neutron detector in an actual reactor as the input of a Monte Carlo program; simulating a particle transport process in the self-powered neutron detector by a Monte Carlo program to obtain charge deposition rate distribution v at different radius positions of an insulating layer of the self-powered neutron detector under the unit average neutron and photon flux density of an emitter of the self-powered neutron detector in unit time_q，dep(r，t)；

step 2: average neutron flux density phi of emitter of neutron detector with actual self-power in reactor_n，emiAverage photon flux density phi_γ，emiAnd step 1, obtaining charge deposition rate distribution v at different radius positions of an insulating layer of the self-powered neutron detector under the unit average neutron and photon flux density of the emitter of the self-powered neutron detector in unit time_q，dep(r, t) is substituted into the formula (1) to obtain the charge deposition rate distribution V corresponding to different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，dep，0(r，t)；

V_q，dep，0(r，t)＝(φ_n，emi+φ_γ，emi)·v_q，dep(r，t) (1)

And step 3: the electric charge quantity accumulated in the insulating layer of the self-powered neutron detector at the zero moment is zero, and no electric field exists, so that the charge loss rate distribution V caused by the existence of the electric field at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，out，0(r, t) is zero;

And 4, step 4: v obtained in step 2 and step 3_q，dep，0(r, t) and V_q，out，0(r, t) is substituted into the formula (2) to obtain the net deposition rate distribution V of charges at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，0(r，t)；

V_q，0(r，t)＝V_q，dep，0(r，t)-V_q，out，0(r，t) (2)

V_q，cur(r，t)＝V_{q，dep，pre}(r，t)-V_{q，out，pre}(r，t) (2-1)

V_q(r，t)＝V_q，dep(r，t)-V_q，out(r，t) (2-2)

And 5: setting the time step as delta t, and setting the charge deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the time point before the single time step_{q，dep，pre}(r, t) and a charge loss rate distribution V_{q，out，pre}(r, t) is taken as an initial value of the current time point, linear change of the total charge deposition rate and the total charge loss rate in a single time step is assumed, charge self-balancing iterative calculation in the single time step is carried out, and stable charge deposition rate distribution V at different radius positions in an insulating layer of the self-powered neutron detector at the current time point is obtained_q，dep(r, t) and a charge loss rate distribution V_q，out(r, t) by the following steps: (a) will V_{q，dep，pre}(r, t) and V_{q，out，pre}(r, t) is substituted into the formula (2-1) to obtain the charge net deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point_q，cur(r, t) and detecting the self-powered neutrons at a point in time prior to the current time stepNet deposition rate distribution of charge V at different radial positions in the insulator layer_q(r, t- Δ t), charge distribution Q (r, t- Δ t), and V_q，cur(r, t) and the time step delta t are substituted into a formula (3) to obtain the charge distribution Q (r, t) at different radius positions in the insulating layer of the self-powered neutron detector at the current time point; (b) obtaining the charge density distribution rho at different radius positions in the insulating layer of the self-powered neutron detector at the current time point according to the Q (r, t) obtained in the step (a) and the volume of the insulating layer of the self-powered neutron detector₀(r, t) and fitting to obtain an analytic expression rho (r, t) thereof; (c) substituting rho (r, t) obtained in the step (b) into a Poisson equation (4) and solving to obtain the potential distribution at different radius positions in the insulating layer of the self-powered neutron detector at the current time pointAnd obtaining the electric field distribution at different radius positions in the insulating layer of the self-powered neutron detector at the current time point by the formula (5)(d) Subjecting the product obtained in step (c)Adding the new charge deposition rate distribution at different radius positions in the insulating layer of the self-powered neutron detector at the current time point by adopting the methods of the step 1 and the step 2 in the Monte Carlo simulation process; (e) due to the existence of the electric field, current can be formed in the insulating layer of the self-powered neutron detector, and the current density distribution at different radius positionsObtained by the formula (6); (f) charge loss rate distribution V caused by electric field at different radius positions in insulating layer of self-powered neutron detector at current time point_{q，out，cur}(r, t) is obtained from formula (7); (g) if the charge loss rate distribution V obtained by two times of iterative calculation_q，out(r，t，i-1)、V_q，out(r, t, i) satisfiesIf the condition is (8), the self-balancing iterative computation is converged, otherwise, the steps (a) to (f) are repeated;

Q(r，t)＝Q(r，t-Δt)+0.5·Δt·[V_q(r，t)+V_q(r，t-Δt)] (3)

Wherein epsilon is the relative dielectric constant of the insulating layer material of the self-powered neutron detector;

Wherein sigma is the conductivity of the insulating layer material of the self-powered neutron detector at the corresponding temperature;

In the formula (I), the compound is shown in the specification,The current density distribution at a radius position behind different radius intervals in an insulating layer of the self-powered neutron detector is realized; s (r) -2 pi rL is the axial sectional area of the insulating layer of the self-powered neutron detector at different radius positions, and L is the length of the self-powered neutron detector;

|V_q，out(t，i)-V_q，out(t，i-1)|＜ε₀ (8)

In the formula, V_q，out(t，i)＝∑V_q，out(r, t, i) is the total charge loss rate in the insulating layer of the self-powered neutron detector at the current time point obtained by the ith iterative calculation of charge self-balancing calculation in a single time step; v_q，out(t, i-1 ═ Σ Vq, out (r, t, i-1) is obtained by the i-1 st iterative calculation of charge self-balancing calculation in a single time stepThe total loss rate of charge in the insulating layer of the self-powered neutron detector at the current time point; epsilon₀Calculating a convergence residual for self-balancing iteration;

Step 6: the stable charge deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point obtained in the step 5_q，dep(r, t) and a charge loss rate distribution V_q，out(r, t) is substituted into the formula (2-2) to obtain stable charge net deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point_q(r，t)；

If V is obtained from step 6_q(r, t) satisfies the condition (9), which indicates that the charge distribution Q (r, t) in the insulating layer of the self-powered neutron detector is stable, the global balance iterative computation is converged, and the potential distribution at different radius positions of the insulating layer of the self-powered neutron detector is outputAnd electric field distributionOtherwise, repeating the step 5 and the step 6 to continue the global balance iterative computation;

|V_q(t)|＜ε₁ (9)

In the formula, V_q(t)＝∑V_q(r, t) is the stable net deposition rate of total charge in the insulating layer of the self-powered neutron detector at the current point in time; epsilon₁A convergence residual is calculated for the global balanced iteration.

2. The method for evaluating electrostatic effects of a self-powered neutron detector of claim 1, wherein: and 4, the net deposition rate distribution of the charges at different radius positions in the insulating layer of the self-powered neutron detector at the current time point is obtained by subtracting the charge loss rate distribution caused by the existence of the electric field from the charge deposition rate distribution caused by the rays at the different radius positions of the insulating layer of the self-powered neutron detector at the current time point.

Technical Field

The invention belongs to the technical field of neutron detection, and particularly relates to an evaluation method for electrostatic effect of a self-powered neutron detector.

Background

A self-powered neutron detector generally consists of an emitter, an insulating layer, and a collector. The emitter is generally made of a material with a large neutron capture cross section, and secondary electrons generated in the emitter or an insulating layer by rays generated by reaction of neutrons and the emitter material reach the collector to generate current, so that neutron flux is measured. The material of the insulating layer generally has good electrical insulating properties, and is resistant to high temperature and high pressure and strong irradiation. The collector is used for receiving electrons emitted from the emitter or the insulating layer, and the material has the characteristics of high temperature and high pressure resistance and corrosion resistance, and has small deformation at high temperature so as to ensure that the self-powered neutron detector has a stable mechanical structure.

electrons moving to the insulating layer may stay in the insulating layer due to insufficient energy or the electrons in the insulating layer are ionized to leave the original position and leave positive charges, and the charges cannot flow away in time due to poor conductivity of the insulating layer and are accumulated, so that the generated electric field influences the transportation of subsequent electrons in the insulating layer, and further influences the detection signal, namely the electrostatic effect of the self-powered neutron detector. Therefore, the electrostatic effect should be taken into account when building a calculation model for the response of the self-powered neutron detector.

at present, scholars at home and abroad make a lot of theoretical researches and experimental researches on the response of a self-powered neutron detector, so that a lot of achievements are obtained, and meanwhile, the scholars have some defects: 1) the electrostatic effect is considered in most theoretical model researches, but the distribution of the electrostatic charge in the insulating layer comes from the assumption, the resistivity of the material of the insulating layer and the real ray flux density near the detector in the pile are not considered, and therefore, the electrostatic effect is not considered in the assumed form to have any practical significance; 2) the response of a self-powered neutron detector can be well simulated by establishing a numerical calculation model, but the relevant literature does not consider the electrostatic effect in the detector numerical model, so that the calculation model is incomplete.

Disclosure of Invention

In order to solve the problems in the prior art, an object of the present invention is to provide a method for evaluating an electrostatic effect of a self-powered neutron detector, which quantitatively describes an electrostatic field and an electrostatic potential existing in an insulating layer due to electrostatic charge deposition, and can quantitatively study the influence of the electrostatic effect on the performance of the self-powered neutron detector, so as to better guide the application of the self-powered neutron detector in practice.

In order to achieve the above purpose, the invention adopts the following technical scheme:

A method for evaluating electrostatic effect of a self-powered detector comprises the following steps:

Step 1: providing the neutron-photon source distribution near a self-powered neutron detector in an actual reactor as the input of a Monte Carlo program; simulating a particle transport process in the self-powered neutron detector by a Monte Carlo program to obtain charge deposition rate distribution v at different radius positions of an insulating layer of the self-powered neutron detector under the unit average neutron and photon flux density of an emitter of the self-powered neutron detector in unit time_q，dep(r，t)；

step 2: average neutron flux density phi of emitter of neutron detector with actual self-power in reactor_n，emiAverage photon flux density phi_γ，emiand step 1, obtaining charge deposition rate distribution v at different radius positions of an insulating layer of the self-powered neutron detector under the unit average neutron and photon flux density of the emitter of the self-powered neutron detector in unit time_q，dep(r, t) is substituted into the formula (1) to obtain the charge deposition rate distribution V corresponding to different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，dep，0(r，t)；

V_q，dep，0(r，t)＝(φ_n，emi+φ_γ，emi)·v_q，dep(r，t) (1)

And step 3: the electric charge quantity accumulated in the insulating layer of the self-powered neutron detector at the zero moment is zero, and no electric field exists, so that the charge loss rate distribution V caused by the existence of the electric field at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，out，0(r, t) is zero;

And 4, step 4: v obtained in step 2 and step 3_q，dep，0(r, t) and V_q，out，0(r, t) is substituted into the formula (2) to obtain the net deposition rate distribution V of charges at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，0(r，t)；

V_q，0(r，t)＝V_q，dep，0(r，t)-V_q，out，0(r，t) (2)

V_q，cur(r，t)＝V_{q，dep，pre}(r，t)-V_{q，out，pre}(r，t) (2-1)

V_q(r，t)＝V_q，dep(r，t)-V_q，out(r，t) (2-2)

And 5: setting the time step as delta t, and setting the charge deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the time point before the single time step_{q，dep，pre}(r, t) and a charge loss rate distribution V_{q，out，pre}(r, t) is taken as an initial value of the current time point, linear change of the total charge deposition rate and the total charge loss rate in a single time step is assumed, charge self-balancing iterative calculation in the single time step is carried out, and stable charge deposition rate distribution V at different radius positions in an insulating layer of the self-powered neutron detector at the current time point is obtained_q，dep(r, t) and a charge loss rate distribution V_q，out(r, t) by the following steps: (a) will V_{q，dep，pre}(r, t) and V_{q，out，pre}(r, t) is substituted into the formula (2-1) to obtain the charge net deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point_q，our(r, t) and distributing the net deposition rate V of the electric charges at different radius positions in the insulating layer of the energy-saving neutron detector at a time point before the current time step_q(r, t- Δ t), charge distribution Q (r, t- Δ t), and V_q，cur(r, t) and the time step delta t are substituted into a formula (3) to obtain the charge distribution Q (r, t) at different radius positions in the insulating layer of the self-powered neutron detector at the current time point; (b) obtaining proper volume according to Q (r, t) obtained in step (a) and an insulating layer of the self-powered neutron detectorCharge density distribution rho at different radius positions in an insulating layer of a self-powered neutron detector at a previous time point₀(r, t) and fitting to obtain an analytic expression rho (r, t) thereof; (c) substituting rho (r, t) obtained in the step (b) into a Poisson equation (4) and solving to obtain the potential distribution at different radius positions in the insulating layer of the self-powered neutron detector at the current time pointAnd obtaining the electric field distribution at different radius positions in the insulating layer of the self-powered neutron detector at the current time point by the formula (5)(d) Subjecting the product obtained in step (c)Adding the new charge deposition rate distribution at different radius positions in the insulating layer of the self-powered neutron detector at the current time point by adopting the methods of the step 1 and the step 2 in the Monte Carlo simulation process; (e) due to the existence of the electric field, current can be formed in the insulating layer of the self-powered neutron detector, and the current density distribution at different radius positionsObtained by the formula (6); (f) charge loss rate distribution V caused by electric field at different radius positions in insulating layer of self-powered neutron detector at current time point_{q，out，cur}(r, t) is obtained from formula (7); (g) if the charge loss rate distribution V obtained by two times of iterative calculation_q，out(r，t，i-1)、V_q，out(r, t, i) satisfying the condition (8), converging the self-balancing iterative computation, otherwise, repeating the steps (a) - (f);

Q(r，t)＝Q(r，t-Δt)+0.5·Δt·[V_q(r，t)+V_q(r，t-Δt)] (3)

Wherein epsilon is the relative dielectric constant of the insulating layer material of the self-powered neutron detector;

Wherein sigma is the conductivity of the insulating layer material of the self-powered neutron detector at the corresponding temperature;

In the formula (I), the compound is shown in the specification,The current density distribution at a radius position behind different radius intervals in an insulating layer of the self-powered neutron detector is realized; s (r) -2 pi rL is the axial sectional area of the insulating layer of the self-powered neutron detector at different radius positions, and L is the length of the self-powered neutron detector;

|V_q，out(t，i)-V_q，out(t，i-1)|＜ε₀ (8)

In the formula, V_q，out(t，i)＝∑V_q，out(r, t, i) is the total charge loss rate in the insulating layer of the self-powered neutron detector at the current time point obtained by the ith iterative calculation of charge self-balancing calculation in a single time step; v_q，out(t，i-1)＝∑V_q，out(r, t, i-1) is the total charge loss rate in the insulating layer of the self-powered neutron detector at the current time point obtained by the i-1 th iteration calculation of charge self-balancing calculation in a single time step; epsilon₀Calculating a convergence residual for self-balancing iteration;

Step 6: the stable charge deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point obtained in the step 5_q，dep(r, t) and a charge loss rate distribution V_q，out(r, t) is substituted into the formula (2-2) to obtain the self-powered neutron detector insulating layer at the current time pointStable net charge deposition rate profile V at different radial locations_q(r，t)。

if V is obtained from step 6_q(r, t) satisfies the condition (9), which indicates that the charge distribution Q (r, t) in the insulating layer of the self-powered neutron detector is stable, the global balance iterative computation is converged, and the potential distribution at different radius positions of the insulating layer of the self-powered neutron detector is outputAnd electric field distributionOtherwise, repeating the step 5 and the step 6 to continue the global balance iterative computation;

|V_q(t)|＜ε₁ (9)

In the formula, V_q(t)＝∑V_q(r, t) is the stable net deposition rate of total charge in the insulating layer of the self-powered neutron detector at the current point in time; epsilon₁a convergence residual is calculated for the global balanced iteration.

Compared with the traditional method, the method has the following advantages: (1) the charge accumulation process in the insulating layer of the self-powered neutron detector can be simulated, and stable charge distribution in the insulating layer is obtained finally without approximating the charge distribution in an assumed mode; (2) the real ray flux density in the pile and the resistivity of the insulating layer material at a specific temperature can be considered, so that the calculation result is more accurate.

Drawings

FIG. 1 is a flow chart of the present invention.

FIG. 2 is a self-balancing charge calculation flow diagram for an insulating layer of a self-powered neutron detector in a single time step.

FIG. 3 is a graphical representation of net deposition rate of charge in an insulating layer of a self-powered neutron detector as a function of time.

FIG. 4 is a schematic diagram of a self-powered neutron detector.

FIG. 5 is a graph of charge deposition rate distribution at different radii of an insulating layer per average neutron flux density of an emitter of a self-powered neutron detector at time zero per unit time.

FIG. 6 is a graph of charge deposition rate distribution at different radial locations in an insulating layer of an energy-self neutron detector at time zero.

FIG. 7 is a graph of net deposition rate distribution of charge at different radial locations in an insulating layer of an energy-self neutron detector at time zero.

FIG. 8 is a graph of net deposition rate distribution of charge at different radial locations in an insulating layer of an energy-efficient neutron detector at a first point in time.

FIG. 9 is a charge distribution within an insulating layer of a self-powered neutron detector at a first point in time.

FIG. 10 is a graph of electric field distribution at different radial locations in an insulating layer of an energy-efficient neutron detector at a first point in time.

FIG. 11 is a graph of potential distribution at different radial locations in an insulating layer of an energy-efficient neutron detector at a first point in time.

FIG. 12 is a graph of net deposition rate of charge in an insulating layer of an energy-self-powered neutron detector over time.

FIG. 13 is a steady state charge distribution at different radial locations in an insulating layer of an energy-efficient neutron detector.

FIG. 14 is a steady state electric field distribution at different radial locations in an insulating layer of an energy-efficient neutron detector.

FIG. 15 is a steady state potential distribution at different radial positions in an insulating layer of an energy-efficient neutron detector.

Detailed Description

The invention is described in further detail below with reference to the following figures and specific embodiments.

The invention discloses an evaluation method of electrostatic effect of a self-powered detector, which comprises the following steps: the specific process is shown in figure 1.

step 1: the neutron-photon source distribution in the actual reactor near the self-powered neutron detector is given as input to the monte carlo procedure. Simulating a particle transport process in the self-powered neutron detector by a Monte Carlo program to obtain the electric charges at different radius positions of an insulating layer of the self-powered neutron detector under the unit average neutron and photon flux density of an emitter of the self-powered neutron detector in unit timeDeposition rate profile v_q，dep(r，t)；

step 2: average neutron flux density phi of emitter of neutron detector with actual self-power in reactor_n，emiAverage photon flux density phi_γ，emiAnd step 1, obtaining charge deposition rate distribution v at different radius positions of an insulating layer of the self-powered neutron detector under the unit average neutron and photon flux density of the emitter of the self-powered neutron detector in unit time_q，dep(r, t) is substituted into the formula (1) to obtain the charge deposition rate distribution V corresponding to different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，dep，0(r，t)；

V_q，dep，0(r，t)＝(φ_n，emi+φ_γ，emi)·v_q，dep(r，t) (1)

And step 3: the electric charge quantity accumulated in the insulating layer of the self-powered neutron detector at the zero moment is zero, and no electric field exists, so that the charge loss rate distribution V caused by the existence of the electric field at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，out，0(r, t) is zero;

And 4, step 4: v obtained in step 2 and step 3_q，dep，0(r, t) and V_q，out，0(r, t) is substituted into the formula (2) to obtain the net deposition rate distribution V of charges at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，0(r，t)；

V_q，0(r，t)＝V_q，dep，0(r，t)-V_q，out，0(r，t) (2)

V_q，cur(r，t)＝V_{q，dep，pre}(r，t)-V_{q，out，pre}(r，t) (2-1)

V_q(r，t)＝V_q，dep(r，t)-V_q，out(r，t) (2-2)

And 5: as shown in FIG. 2, the time step is set to be delta t, and the charge deposition rate distribution V at different radius positions in the insulating layer of the energy-saving neutron detector at the time point before the single time step_{q，dep，pre}(r, t) and a charge loss rate distribution V_{q，out，pre}(r, t) is taken as an initial value of the current time point, linear change of the total charge deposition rate and the total charge loss rate in a single time step is assumed, charge self-balancing iterative calculation in the single time step is carried out, and stable charge deposition rate distribution V at different radius positions in an insulating layer of the self-powered neutron detector at the current time point is obtained_q，dep(r, t) and a charge loss rate distribution V_q，out(r, t) by the following steps: (a) will V_{q，dep，pre}(r, t) and V_{q，out，pre}(r, t) is substituted into the formula (2-1) to obtain the charge net deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point_q，cur(r, t) and distributing the net deposition rate V of the electric charges at different radius positions in the insulating layer of the energy-saving neutron detector at a time point before the current time step_q(r, t- Δ t), charge distribution Q (r, t- Δ t), and V_q，cur(r, t) and the time step delta t are substituted into a formula (3) to obtain the charge distribution Q (r, t) at different radius positions in the insulating layer of the self-powered neutron detector at the current time point; (b) obtaining the charge density distribution rho at different radius positions in the insulating layer of the self-powered neutron detector at the current time point according to the Q (r, t) obtained in the step (a) and the volume of the insulating layer of the self-powered neutron detector₀(r, t) and fitting the equation by adopting a polynomial (3-1) to obtain an analytic expression rho (r, t); (c) substituting rho (r, t) obtained in the step (b) into a Poisson equation (4) and solving to obtain the potential distribution at different radius positions in the insulating layer of the self-powered neutron detector at the current timeAnd obtaining the electric field distribution at different radius positions in the insulating layer of the self-powered neutron detector at the current time according to the formula (5)(d) Subjecting the product obtained in step (c)Adding the self-powered neutron detector insulating layer obtained in the step 1 and the step 2 in the Monte Carlo simulation processnew charge deposition rate distribution V at different radial positions_q，dep(r, t); (e) due to the existence of the electric field, current can be formed in the insulating layer of the self-powered neutron detector, and the current density distribution at different radius positionsObtained by the formula (6); (f) charge loss rate distribution V caused by electric field at different radius positions in insulating layer of self-powered neutron detector at current time point_q，out(r, t) is obtained from formula (7); (g) if V is obtained by two times of iterative calculation_q，out(r, t) satisfies the condition (8), the self-balancing iterative computation converges, otherwise steps (a) - (f) are repeated.

Q(r，t)＝Q(r，t-Δt)+0.5·Δt·[V_q(r，t)+V_q(r，t-Δt)] (3)

In the formula, a_iAnd b_iIs a polynomial coefficient; n and m are the maximum order of the polynomial.

Wherein epsilon is the relative dielectric constant of the insulating layer material of the self-powered neutron detector.

In the formula (I), the compound is shown in the specification,The current density distribution at different radius positions in an insulating layer of the self-powered neutron detector is realized; sigma is the conductance of insulating layer material of the self-powered neutron detector at corresponding temperatureRate;The distribution of electric fields at different radius positions in an insulating layer of the neutron detector is self-powered.

In the formula (I), the compound is shown in the specification,The current density distribution at a radius position behind different radius intervals in an insulating layer of the self-powered neutron detector is realized; and S (r) -2 pi rL is the axial sectional area of the insulating layer of the self-powered neutron detector at different radius positions, and L is the length of the self-powered neutron detector.

|V_q，out(t，i)-V_q，out(t，i-1)|＜ε₀ (8)

In the formula, V_q，out(t，i)＝∑V_q，out(r, t, i) is the total charge loss rate in the insulating layer of the self-powered neutron detector at the current time point obtained by the ith iterative calculation of charge self-balancing calculation in a single time step; v_q，out(t，i-1)＝∑V_q，out(r, t, i-1) is the total charge loss rate in the insulating layer of the self-powered neutron detector at the current time point obtained by the i-1 th iteration calculation of charge self-balancing calculation in a single time step; epsilon₀The convergence residual is calculated for self-balancing iterations.

the specific process for solving the poisson equation is as follows: since the neutron detector is in a cylindrical geometry, the potential in the insulating layerRelated only to the radius r, and thus Poisson's equation (4) can be written as equation (8-1)

Substituting formula (3-1) for formula (8-1) to obtain formula (8-2)

in the formula, A and B are constant coefficients.

To obtain finallyGeneral solution of (1):

from the boundary conditions:

In the formula: r is_minIs the inner radius of the insulating layer, r_maxThe outer radius of the insulating layer.

Obtaining:

Wherein:

Solving to obtain the coefficient:

So the solution is determined as:

The electric field strength is therefore:

Step 6: the stable charge deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point obtained in the step 5_q，dep(r, t) and a charge loss rate distribution V_q，out(r, t) is substituted into the formula (2-2) to obtain stable charge net deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point_q(r，t)。

as indicated by t in FIG. 3₅Shown if V is obtained from step 6_q(r, t) satisfies the condition (9), which indicates that the charge distribution Q (r, t) in the insulating layer of the self-powered neutron detector is stable, the global balance iterative computation is converged, and the potential distribution at different radius positions of the insulating layer of the self-powered neutron detector is outputAnd electric field distributionOtherwise, repeating the step 5 and the step 6 to continue the global balance iterative computation.

|V_q(t)|＜ε₁ (9)

In the formula, V_q(t)＝∑V_q(r, t) is the stable net deposition rate of total charge in the insulating layer of the self-powered neutron detector at the current point in time; epsilon₁A convergence residual is calculated for the global balanced iteration.

Examples of the applications

Taking a vanadium self-powered neutron detector as an example, the structure and the size of the detector are shown in fig. 4. The emitter material is natural vanadium and has a density of 6.11g/cm³. The insulating layer is made of alumina and has a density of 1.9g/cm³. The collector material is Inconel-600, and the density is 8.51g/cm³. Resistivity of the insulation layer the resistivity of the insulation layer was determined according to the literature [ Zareen Khan Abdul Jalil Khan, Mohd Idris Taib, Izhar Abu Husin,&Nurfarhana Ayuni(2010).Comparison study on in-core neutron detector for online neutron flux mapping of research and powerreactor.RnD Seminar 2010：Research and Development Seminar2010，Malaysia.http：//inis.iaea.org/search/search.aspx？orig_q＝RN：43056490]Is set to 6 x 10¹⁰Ω·m。

The neutron-photon source distribution near the self-powered neutron detector in the actual reactor adopts a single-energy isotropic neutron surface source with the energy of 0.0253eV on the outer surface of the collector as the input of a Monte Carlo program. Simulating the particle transport process in the self-powered neutron detector by a Monte Carlo program to obtain the charge deposition rate distribution v at different radiuses of the insulating layer under the unit average neutron flux density of the emitter of the self-powered neutron detector in unit time_q，dep(r, t) as shown in FIG. 5.

Neutron flux density phi of emitter of actual self-powered neutron detector in reactor_n，emiGet 10¹³n·cm^-2·s^-1. By phi_n，emiAnd v_q，dep(r, t) obtaining the charge deposition rate distribution V corresponding to different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，dep，0(r, t) as shown in FIG. 6.

The electric charge quantity accumulated in the insulating layer of the self-powered neutron detector at the zero moment is zero, and no electric field exists, so that the charge loss rate distribution V caused by the existence of the electric field at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，out，0(r, t) is zero.

From V_q，dep，0(r, t) and V_q，out，0(r, t) obtaining the net deposition rate distribution V of electric charges at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，0(r, t) as shown in FIG. 7.

Setting the time step length to be 0.02s, and distributing the charge deposition rate V at different radius positions in the insulating layer of the self-powered neutron detector at the zero moment_q，dep，0(r, t) and a charge loss rate distribution V_q，out，0(r, t) as initial values of current time point, and performing charge self-balancing in a single time step assuming that the total deposition rate and total loss rate of charge change linearly in the single time stepIterative calculation is carried out to obtain stable charge deposition rate distribution V at different radius positions in the insulating layer of the self-powered neutron detector at the current time point_q，dep(r, t) and a charge loss rate distribution V_q，out(r, t). In the charge self-balancing iterative calculation within a single time step, the parameters n and m in the polynomial (3-1) in this example take 5 and 1, respectively, for the fitting of the charge density distribution ρ (r, t) at different radial positions in the insulating layer of the self-powered neutron detector.

Stable charge deposition rate distribution V at different radius positions in insulating layer of neutron detector powered by current time point_q，dep(r, t) and a charge loss rate distribution V_q，out(r, t) obtaining a stable net deposition rate profile V of charge_q(r, t) as shown in FIG. 8. At this time, the charge distribution Q (r, t) in the insulating layer of the self-powered neutron detector is shown in fig. 9, and the corresponding electric field distribution and electric potential distribution are shown in fig. 10 and 11, respectively. It can be seen that the charge density in the insulating layer of the self-powered neutron detector gradually decreases with the increase of the radius, and the electric field and the electric potential are smaller. The potential has a maximum of about 1.086kV, so electrons from the emitter or collector must have an energy greater than 1.086keV to be able to pass through the insulating layer.

Stable net deposition rate distribution V of electric charge at different radius positions in the insulating layer of the neutron detector from power if the current time point_q(r, t) satisfies the condition (9), which indicates that the charge distribution Q (r, t) in the insulating layer of the self-powered neutron detector is stable, the global balance iterative computation is converged, otherwise, the steps are repeated, and the global balance iterative computation is continued.

As shown in fig. 12, through the global balance iterative calculation, the net deposition rate of charge in the insulating layer of the self-powered neutron detector finally approaches zero, which indicates that the charge distribution tends to be stable. The steady-state charge distribution Q (r, t) in the insulating layer of the self-powered neutron detector is finally obtained as shown in fig. 13, and the corresponding electric field distribution and electric potential distribution are respectively shown in fig. 14 and fig. 15. At the moment, the charge density in the insulating layer of the self-powered neutron detector is increased, the insulating layer presents a distribution with a high middle and two low sides, and the electric field and the electric potential are increased accordingly. The potential has a maximum of about 486.816kV and therefore electrons from the emitter or collector must have an energy of more than 486.816keV to be able to penetrate the insulating layer. It follows that electrostatic effects do affect the transport of electrons in insulators, and that accurate potential and electric field distributions must be obtained by iterative calculations.

While the invention has been described with reference to embodiments, it is understood that the terminology used is intended to be in the nature of words of description and illustration, rather than of limitation. As the present invention may be embodied in several forms without departing from the spirit or essential characteristics thereof, it should also be understood that the above-described embodiments are not limited by any of the details of the foregoing description, but rather should be construed broadly within its spirit and scope as defined in the appended claims, and therefore all changes and modifications that fall within the meets and bounds of the claims, or equivalences of such meets and bounds are therefore intended to be embraced by the appended claims.