CN111539151B - Particle angle distribution condition acquisition method based on Monte Carlo point flux recording - Google Patents
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Abstract
The invention discloses a particle angular distribution condition acquisition method based on Monte Carlo point flux recording, which solves the problems that the angular distribution calculation efficiency and precision are low and the two-dimensional angular distribution of particles cannot be given in the existing Monte Carlo particle transport technology. The method mainly comprises the following implementation steps: firstly, constructing a three-dimensional particle transport geometric model, then setting radiation source parameters in the three-dimensional geometric model, and setting recording points; then, carrying out numerical simulation on the particle transportation process by adopting a Monte Carlo algorithm; and finally, calculating the particle fluence at each region recording point by using a pointing probability method, thereby obtaining the one-dimensional angle and/or two-dimensional angle distribution condition of the particles in the radiation field.
Description
Technical Field
The invention belongs to the technical field of particle transport numerical simulation, and particularly relates to a particle angle distribution condition acquisition method based on Monte Carlo point flux recording.
Background
The particle angle distribution represents the distribution probability of the particles in different flight directions, is one of important parameters for describing a radiation field, and is concerned about particle physics fields such as ray detection, radiation protection, nuclear radiation field analysis, nuclear data evaluation and the like.
The Monte Carlo method is a random simulation method based on probability theory and carding statistics, and is widely used for particle transport simulation because of its advantages of strong complex geometric processing ability, universal and flexible method, complete nuclear data, etc., and its basic flow is that firstly random numbers are used to sample and carry out random simulation to particle behaviors, and then statistical method is used to give out the estimator of a certain value in random variables.
The method is characterized in that a Monte Carlo method is adopted to simulate and track the transportation behavior of a large number of particles in a medium, the angular distribution information of the particles can be obtained through statistics in a recording mode of surface flow (the number of the particles penetrating through the curved surface) of a specified curved surface, namely, the normal direction of a certain point on the curved surface is taken as a reference direction, a deflection angle between the particle direction and the reference direction is divided into angle boxes with different intervals, and the angular distribution of the particles is given through statistics of the number of the particles penetrating through the curved surface in each angle box. However, the angle distribution calculation method is only suitable for a surface flow recording mode, and in the process of transporting and simulating particles in some complex geometric or large-size spaces, the probability that the particles pass through the designated curved surface is very small, so that the statistical error of the particle number in each angle box is very large, the statistical calculation precision needs to be improved by increasing the simulated particle number, and even when a large number of machines are consumed, the credible angle distribution statistical calculation result cannot be given to the problem of small-probability events passing through the designated curved surface. Meanwhile, the existing calculation method can only give one-dimensional axisymmetric angular distribution, namely deflection angular distribution, and cannot give distribution on an azimuth angle.
The recording of the point flux in monte carlo particle transport is a statistical estimate of the particle flux at a point in space. The point flux counting contribution of the commonly used pointing probability method is derived from the product of the probability of each generation of a particle (source particle and scatter particle), the probability of the particle direction pointing to the detector and the probability of the particle moving from the generation point to the detector without collision. The method is different from the surface flowmeter in counting, contributes to counting results without reaching the specified position by particles, and is small in statistical error and high in precision of the counting results. But the existing spot flux recording method cannot give the angular distribution of the radiation field particles.
The existing modular particle transport program package PHEN (developed and applied of the modular particle transport program package PHEN published by Zhujinhui et al in modern applied physics, volume 9, no. 3 of 2018) develops a particle angular fluence information statistical function, but a general calculation method for particle angular distribution is not provided, and particle two-dimensional angular distribution cannot be provided.
The document (Jure B, on the calculation of regular neutron flux in MCNP at volume 100 of Annals of Nuclear Energy, 2017, 2) post-processes the particle Energy, direction, position and time in the MCNP-simulated particle trace result file to obtain the neutron angle distribution in a certain volume of medium, but the method has a narrow application range as the area-integral-flux calculation method, is difficult to give credible results for small-probability events of certain specified volumes, and is difficult to calculate the particle angle distribution of local positions in a radiation field.
Therefore, those skilled in the art need to develop a calculation method capable of calculating one-dimensional and two-dimensional angular distributions of radiation field particles with high efficiency and high precision, so as to solve the problem of calculating the angular distributions of particles in particle transportation, especially in particle transportation with complex geometry or large size space.
Disclosure of Invention
The invention aims to provide a particle angular distribution condition acquisition method based on Monte Carlo point flux recording, and solves the problems that the angular distribution calculation efficiency and precision are low and the two-dimensional angular distribution of particles cannot be given in the existing Monte Carlo particle transport technology.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the invention provides a method for acquiring the angular distribution condition of radiation field particles based on Monte Carlo simulation, which comprises the following steps:
step 1: constructing a particle transport three-dimensional geometric model according to an actual transport scene;
the three-dimensional geometric model comprises various environment elements forming an actual scene, the shape, the size, the position and the density of each environment element, chemical components of each environment element and the proportion of each chemical component in the environment elements;
and 2, step: setting the position, direction, energy spectrum and time spectrum parameters of a radiation source in the three-dimensional geometric model, and setting recording points;
and step 3: simulating the transportation process of the particles in the three-dimensional geometric model by using a Monte Carlo method to obtain the position, direction, energy and time information of the virtual particles; the virtual particles comprise particles emitted by the radiation source and particles scattered in the model;
specifically, the initial position, energy, flight direction, etc. of the particle can be obtained by probability sampling of the distribution of the source, whether the particle has a collision action with the medium is determined by sampling the interaction cross section of the particle and the substance, and the direction after the collision is determined by probability sampling of the particle exit direction.
And 4, step 4: establishing a three-dimensional coordinate system XYZ of a three-dimensional geometric model, and setting the positive direction of a Z axis as a deflection angle reference direction omega θ (ii) a Taking the virtual particle motion direction and the reference direction omega θ The included angle in the forward direction is a deflection angle theta;
the running direction of the virtual particles is expressed as a one-dimensional vector of omega (theta), the running direction of the virtual particles is expressed as the one-dimensional vector of omega (theta), theta is a deflection angle of the running direction of the virtual particles, the range of the deflection angle is set to be 0-pi, and the one-dimensional distribution of the directions of the particles in the space is represented;
and 5: dividing the deflection angle direction of 0-pi into delta omega θ1 、ΔΩ θ2 、…ΔΩ θn A total of n sub-regions;
step 6: and calculating the particle fluence in each subarea by using a pointing probability method, thereby obtaining the distribution condition of the particle fluence in n subareas, namely obtaining the one-dimensional angular distribution (namely the deflection angle distribution of the virtual particles) of the particles.
Further, the particle fluence in a subarea at the recording point is the sum of the counting contributions of all the virtual particles in the subarea to the recording point, and the specific expression is as follows:
where φ is the gamma fluence in any sub-region at any recording point, i represents the ith gamma particle, F i Is the ith oneThe contribution of gamma particles to the gamma fluence at the recording point, n is all gamma particles of the corresponding deflection angle partition, i.e. the deflection angle satisfies (theta) i-1 ＜θ＜θ i ) All of the particles of (a);
r is the distance between the source or scattering point and the recording point, Ω is the solid angle in which the particle emission direction points to the recording point, p (Ω) d Ω is the probability that the particle emission direction is within d Ω units of solid angle, s is the displacement towards the probe direction, Σ t (s) is the total cross section over s displacement, w is the imaginary particle weight, dA is the maximum area of the detector perpendicular to the Ω direction, and w/dA is its contribution to the particle fluence.
The invention is also suitable for obtaining the two-dimensional angular distribution condition of the particles, and the specific process is as follows:
step 1: constructing a particle transport three-dimensional geometric model according to an actual transport scene;
the three-dimensional geometric model comprises various environment elements forming an actual scene, the shape, the size, the position and the density of each environment element, chemical components of each environment element and the proportion of each chemical component in the environment elements;
step 2: setting the position, direction, energy spectrum and time spectrum parameters of a radiation source in the three-dimensional geometric model, and setting recording points;
and step 3: simulating the transportation process of the particles in the three-dimensional geometric model by using a Monte Carlo method to obtain the position, direction, energy and time information of the virtual particles; the virtual particles comprise particles emitted by the radiation source and particles scattered in the model;
specifically, the initial position, energy, flight direction, etc. of the particle can be obtained by probability sampling of the distribution of the source, whether the particle has a collision action with the medium is determined by sampling the interaction cross section of the particle and the substance, and the direction after the collision is determined by probability sampling of the particle exit direction.
And 4, step 4: establishing a three-dimensional coordinate system XYZ of a three-dimensional geometric model, and setting the positive direction of a Z axis as a deflection angle reference direction omega θ (ii) a Taking the virtual particle motion direction and the reference direction omega θ The included angle of the forward direction is a deflection angle theta;
setting the positive direction of the X axis as the azimuth angle reference direction
Is at and omega θ The vertical plane is a reference plane; from the reference direction omega θ Positively looking self-reference direction->
The angle rotated by the projection of the positive counter-clockwise direction onto the reference plane into the virtual particle movement direction is azimuth angle->
The direction of travel of the imaginary particles is represented as a two-dimensional vector of omega (theta, phi),
deflection angles and azimuth angles of virtual particle running directions are respectively set, the range of the deflection angle is set to be 0-pi, the range of the azimuth angle is set to be 0-2 pi, and the deflection angle and the azimuth angle form a three-dimensional space;
and 5: the deflection angle direction of 0-pi is divided into delta omega θ1 、ΔΩ θ2 、…ΔΩ θn A total of n sub-regions; divide the azimuth direction of 0-2 pi into
The three-dimensional space is divided into n multiplied by m subareas by the two subareas;
step 6: the particle fluence in each subarea is calculated by using a pointing probability method, so that the distribution condition of the particle fluence in n multiplied by m subareas is obtained, and the two-dimensional angular distribution (namely, the deflection angle and the azimuth angle distribution of the virtual particles) of the particles can be obtained.
Further, the particle fluence in a subarea of the recording point is the sum of the counting contributions of all virtual particles in the subarea to the recording point, and the specific expression is as follows:
wherein phi ij For the gamma fluence in a sub-zone at any one recording point, k denotes the gamma particles in the sub-zone, F k For the contribution of gamma particle k to the gamma fluence at the recording point, n is all the gamma particles corresponding to the deflection angle and azimuth subarea, i.e. the deflection angle and the azimuth satisfy
All the particles of (a);
r is the distance between the source or scattering point and the recording point, Ω is the solid angle in which the particle emission direction points to the recording point, p (Ω) d Ω is the probability that the particle emission direction is within the d Ω solid angle, s is the displacement towards the detector direction, Σ t (s) is the total cross section over s displacement, w is the imaginary particle weight, dA is the maximum area of the detector perpendicular to the Ω direction, and w/dA is its contribution to the particle fluence.
The invention has the beneficial effects that:
the method has the advantages that the angular distribution of the radiation field particles is calculated based on Monte Carlo point flux recording, the one-dimensional angular distribution and the two-dimensional angular distribution of the particles at any position in the radiation field can be provided, the limitation that the angular distribution in the prior art is low in calculation efficiency and precision and cannot give the two-dimensional angular distribution of the particles is broken through, and the technical support can be provided for researches such as ray detection, radiation protection, nuclear radiation field analysis and nuclear data evaluation.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a three-dimensional geometric model and the deflection angle and azimuth angle of virtual particle directions.
FIG. 3 is a schematic view of the partition of the deflection angle for the calculation of the one-dimensional angular distribution of radiation field particles in the embodiment.
Fig. 4 is a comparison of the one-dimensional angular distribution of radiation field particles with the surface-integrated flow angular distribution given in the examples.
FIG. 5 is a schematic view of azimuthal zoning for calculation of two-dimensional angular distribution of radiation field particles in the example.
Fig. 6 shows the calculation of the two-dimensional angular distribution of the radiation field particles given in the example.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The flow chart for implementing the invention, as shown in figure 1,
firstly, constructing a particle transport three-dimensional geometric model, then setting radiation source parameters in the three-dimensional geometric model, and setting recording points; then, carrying out numerical simulation on the particle transportation process by adopting a Monte Carlo algorithm; and finally, calculating the particle fluence at each region recording point by using a pointing probability method, thereby obtaining the one-dimensional angle and/or two-dimensional angle distribution condition of the particles in the radiation field.
In order to verify the practical effect of the method of the present invention, the following examples are provided, and the method is compared with the existing surface current angular distribution method to verify the one-dimensional angular distribution of the particles in the radiation field, and the specific process is as follows:
in this embodiment, the setting scenario is to calculate the particle angle distribution at a certain recording point during the transportation process of gamma rays in a uniform solid iron ball. Wherein the gamma ray source is positioned at the center of a sphere and is an isotropic point source. The source energy was 2MeV and the particle weight was 1.
The concrete links are introduced as follows:
(1) A three-dimensional geometric model of gamma ray transport is built from the scene, as shown in FIG. 2. Three-dimensional geometric model main knotThe structure is evenly distributed solid iron balls, and the density is 7.86g/cm 3 The radius of the iron ball is 20cm. The gamma ray source is located at the center of the sphere, i.e., the origin of coordinates O. The particle angle distribution recording points are four points P1, P2, P3, P4 and the like in the Z-axis direction, and the spherical center distances are 2.5cm, 5cm, 7.5cm and 10cm respectively. In order to verify the radiation field particle angle distribution recording algorithm, the surface integral flow angle distribution on the spherical surfaces S1, S2, S3 and S4 on which the four points P1, P2, P3 and P4 are correspondingly positioned is recorded for comparison and verification.
(2) Simulating the transportation process of the particles in the three-dimensional geometric model by using a Monte Carlo method to obtain the position, direction, energy and time information of the virtual particles; the virtual particles comprise particles emitted by the radiation source and particles scattered in the model;
(3) Acquiring deflection angles of the virtual particle running direction and the reference direction, and partitioning;
specifically, the Z-axis positive direction in fig. 2 is set as the reference direction Ω θ0 And the included angle between the motion direction of each virtual particle and the reference direction is a deflection angle theta. In the embodiment, theta is 1/12 pi, 2/12 pi, 8230phi and pi, and the deflection angle direction of 0-pi is divided into delta omega θ1 、ΔΩ θ2 、…ΔΩ θ12 And 12 subareas are equal. Direction partition delta omega corresponding to virtual particle motion direction omega θi As shown in fig. 3.
(4) And calculating the contribution of each source particle or scattering particle to the particle fluence of four recording points such as P1, P2, P3, P4 and the like by using a directional probability method, and calculating the one-dimensional angular distribution of the radiation field particles according to the deflection angles of the virtual particle direction and the reference direction.
The specific process is as follows: the one-dimensional angular distribution of the radiation field particles can be recorded by accumulating the fluence contribution generated by the dummy particles into each partition. The calculated one-dimensional angular distribution of the four recording points P1, P2, P3, P4, etc. is shown in fig. 4. For comparison, the particle angular distribution obtained by the prior art surface fluence angular distribution counting method is also given in the figure. For the spherical symmetry model of the present embodiment, the one-dimensional angular distribution of radiation field particles using pointing probability should theoretically coincide with the surface current angular distribution. As can be seen from fig. 4, the one-dimensional angular distribution calculated by the present embodiment is better in accordance with the calculation result of the surface current angular distribution.
On the basis of the above (1) and (2), the embodiment further performs verification of the two-dimensional angular distribution, and the specific process is as follows:
obtaining deflection angles and azimuth angles of the virtual particle running direction and the reference direction, and partitioning;
specifically, the z-axis positive direction in fig. 2 is set as the reference direction Ω θ0 And the positive direction of the x-axis perpendicular thereto is the reference direction
Is at and omega θ0 The vertical xoy plane is the reference plane. As shown in fig. 2, the virtual particle movement direction Ω and the reference direction Ω θ0 The included angle is a deflection angle theta, and the angle rotated from the positive direction of the Z direction to the projection of the virtual particle motion direction on the xoy plane from the positive direction of the x axis in the anticlockwise direction is an azimuth angle->
In this embodiment, theta is 1/8 pi, 2/8 pi, \ 8230, and pi, and the deflection angle of 0-pi is divided into delta omega θ1 、ΔΩ θ2 、…ΔΩ θ8 Waiting for 8 subareas;
1/4 pi, 2/4 pi, \ 8230, 2 pi, dividing the azimuth direction of 0-2 pi into
And 8 subareas are waited. Direction division delta omega corresponding to virtual particle deflection angle θi As shown in fig. 3. Direction partition corresponding to the imaginary particle azimuth>
As shown in fig. 5. Deflection angle theta and azimuth angle->
The two parts divide the three-dimensional space into 64 subareas of 8 multiplied by 8A domain. Dividing a zone delta omega according to the deflection angle direction corresponding to the virtual particle motion direction omega (theta, phi) θi And azimuth direction zone>
And determining the direction subarea in the three-dimensional space.
And calculating the particle fluence corresponding to the n multiplied by m subareas aiming at the four recording points such as P1, P2, P3, P4 and the like to obtain the distribution situation of the particle fluence of the four recording points in the n multiplied by m subareas, namely the two-dimensional angle distribution of the particles of the four recording points such as P1, P2, P3, P4 and the like. Fig. 5 shows the calculated two-dimensional angular distribution of the particles of the recording point P1, which visually represents the distribution of the particle directions at the recording point P1 in the three-dimensional space. The particle direction characteristics in the distribution are obvious, and the overall distribution rule is consistent with the particle transport theory.
The method for acquiring the particle angular distribution based on the monte carlo point flux recording is not limited to the above specific embodiments. Other embodiments obtained by the technical solutions of the present invention by those skilled in the art also belong to the technical innovation scope of the present invention.
Claims (6)
1. A radiation field particle angular distribution situation acquisition method based on Monte Carlo simulation is characterized by comprising the following steps:
step 1: constructing a particle transport three-dimensional geometric model according to an actual transport scene;
the three-dimensional geometric model comprises various environment elements forming an actual scene, the shape, the size, the position and the density of each environment element, chemical components of each environment element and the proportion of each chemical component in the environment elements;
step 2: setting the position, direction, energy spectrum and time spectrum parameters of a radiation source in the three-dimensional geometric model, and setting recording points;
and step 3: simulating the transportation process of the particles in a three-dimensional geometric model by using a Monte Carlo method to obtain the position, direction, energy and time information of the virtual particles; the virtual particles comprise particles emitted by the radiation source and particles scattered in the model;
and 4, step 4: establishing a three-dimensional coordinate system XYZ of a three-dimensional geometric model, and setting the positive direction of a Z axis as a deflection angle reference direction omega θ (ii) a Taking the virtual particle motion direction and the reference direction omega θ The included angle in the forward direction is a deflection angle theta;
the running direction of the virtual particles is expressed as a one-dimensional vector of omega (theta), theta is a deflection angle of the running direction of the virtual particles, the range of the deflection angle is set to be 0-pi, and the one-dimensional distribution of the particle directions in the space is represented;
and 5: dividing the deflection angle of 0-pi into
A total of n sub-regions;
step 6: and calculating the particle fluence in each subarea at the recording point by using a pointing probability method, thereby obtaining the distribution condition of the particle fluence in n subareas, namely obtaining the one-dimensional angular distribution of the particles.
2. The radiation field particle angle distribution situation acquisition method based on the Monte Carlo simulation as claimed in claim 1, wherein: the particle fluence in a subarea of a recording point is the sum of the counting contributions of all virtual particles in the subarea to the recording point, and the specific expression is as follows:
where φ is the gamma fluence in any sub-region at any recording point, i represents the ith gamma particle, F i For the contribution of the ith gamma particle to the gamma fluence at the recording point, n is all gamma particles in the corresponding deflection angle partition, i.e. the deflection angle satisfies (theta) i-1 ＜θ＜θ i ) All the particles of (a);
r is the distance between the source point, the scattering point and the recording point, Ω is the solid angle in which the particle emission direction points to the recording point, p (Ω) d Ω is the probability that the particle emission direction is within d Ω unit solid angle, s is the displacement towards the probe direction, Σ t (s) is the total cross section over s displacement, w is the imaginary particle weight, dA is the maximum area of the detector perpendicular to the Ω direction, and w/dA is its contribution to the particle fluence.
3. The radiation field particle angle distribution situation acquisition method based on the Monte Carlo simulation as claimed in claim 1, wherein: the specific content of the Monte Carlo method used for simulating the transportation process of the particles in the three-dimensional geometric model in the step 3 is as follows: the initial position, energy and flight direction of the particles are obtained by sampling the distribution probability of the radiation source, whether the particles collide with the medium or not is determined by sampling the interaction cross section of the particles and the substance, and the collision rear direction is determined by sampling the probability of the particle emergence direction.
4. A radiation field particle angular distribution situation acquisition method based on Monte Carlo simulation is characterized by comprising the following steps:
step 1: constructing a particle transport three-dimensional geometric model according to an actual transport scene;
the three-dimensional geometric model comprises various environment elements forming an actual scene, the shape, the size, the position and the density of each environment element, chemical components of each environment element and the proportion of each chemical component in the environment elements;
step 2: setting the position, direction, energy spectrum and time spectrum parameters of a radiation source in the three-dimensional geometric model, and setting recording points;
and step 3: simulating the transportation process of the particles in a three-dimensional geometric model by using a Monte Carlo method to obtain the position, direction, energy and time information of the virtual particles; the virtual particles comprise particles emitted by the radiation source and particles scattered in the model;
and 4, step 4: establishing a three-dimensional coordinate system XYZ of a three-dimensional geometric model, and setting Z-axis correctionTo a reference direction omega for deflection angles θ (ii) a Taking the virtual particle motion direction and the reference direction omega θ The included angle of the forward direction is a deflection angle theta;
setting the positive direction of the X axis as the azimuth angle reference direction
Is at and omega θ The vertical plane is a reference plane; from the reference direction omega θ Positively looking self-reference direction->
The angle rotated by the projection of the positive counter-clockwise direction onto the reference plane into the virtual particle movement direction is azimuth angle->
The direction of travel of the imaginary particles is represented as a two-dimensional vector of omega (theta, phi),
deflection angles and azimuth angles of virtual particle running directions are respectively set, the range of the deflection angle is set to be 0-pi, the range of the azimuth angle is set to be 0-2 pi, and the deflection angle and the azimuth angle form a three-dimensional space;
and 5: dividing the deflection angle of 0-pi into
A total of n sub-regions; divide the azimuth direction of 0-2 pi into->
The three-dimensional space is divided into n multiplied by m subareas by the two subareas;
step 6: and calculating the particle fluence in each subarea at the recording point by using a pointing probability method, thereby obtaining the distribution condition of the particle fluence in n multiplied by m subareas, namely obtaining the two-dimensional angular distribution of the particles.
5. The method for obtaining the angular distribution of the particles in the radiation field based on the Monte Carlo simulation, according to claim 4, wherein: the particle fluence in a subarea of a recording point is the sum of the counting contributions of all virtual particles in the subarea to the recording point, and the specific expression is as follows:
wherein phi is ij For gamma fluence in a zone at any one recording point, k denotes the gamma particles in the zone, F k For the contribution of gamma particle k to the gamma fluence at the recording point, n is all the gamma particles corresponding to the deflection angle and the azimuthal bin, i.e. the deflection angle and the azimuthal bin satisfy
All the particles of (a);
r is the distance between the source or scattering point and the recording point, Ω is the solid angle in which the particle emission direction points to the recording point, p (Ω) d Ω is the probability that the particle emission direction is within d Ω units of solid angle, s is the displacement towards the probe direction, Σ t (s) is the total cross section over s displacement, w is the imaginary particle weight, dA is the maximum area of the detector perpendicular to the Ω direction, and w/dA is its contribution to the particle fluence.
6. The method for obtaining the angular distribution of the particles in the radiation field based on the Monte Carlo simulation, according to claim 4, wherein: the specific content of the Monte Carlo method used for simulating the transportation process of the particles in the three-dimensional geometric model in the step 3 is as follows: the initial position, energy and flight direction of the particles are obtained by sampling the distribution probability of the radiation source, whether the particles collide with the medium or not is determined by sampling the interaction cross section of the particles and the substance, and the collision rear direction is determined by sampling the probability of the particle emergence direction.
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