A method for quantifying mixed radiation field of accelerator neutron source

Abstract

The present invention discloses a method for quantifying the mixed radiation field of an accelerator neutron source, which comprises three steps: establishing an accelerator neutron source calculation model, meshing the accelerator neutron source model, obtaining the density of nuclear materials in all meshes, and establishing an accelerator neutron source meshing model; calculating the transport equation of the mixed photon radiation field of the accelerator neutron source; completing the photon transport calculation in the accelerator neutron source based on the established accelerator neutron source meshing model and the photon transport equation in the accelerator neutron source, thereby obtaining the mixed photon radiation field in the accelerator neutron source and the epithermal neutron fluence rate at the exit position of the accelerator neutron source. Compared with the prior art, the present invention can quickly obtain the overall radiation field and the epithermal neutron fluence rate at a characteristic position, so as to quickly check whether the epithermal neutron fluence rate at the exit position of the accelerator neutron source head meets the standard of the epithermal neutron fluence rate of medical neutrons of the International Atomic Energy Agency.

Description

Technical Field

[0001] The invention relates to the technical field of boron neutron capture therapy, and in particular to a method for quantifying a mixed radiation field of an accelerator neutron source. Background Art

[0002] Boron Neutron Capture Therapy (BNCT) is a tumor treatment method that achieves the purpose of tumor treatment through the high capture probability of neutrons by the boron-10 isotope. The basic principle of this therapy is that the patient is first injected with a compound containing the boron-10 isotope. Then, the patient is irradiated with a neutron beam, which will react with the boron-10 to release an alpha particle and a helium ion, which has a high / local killing effect on tumor tissue. Due to the high capture cross-section (capture probability) of the boron-10 isotope for neutrons and the high energy release of the reaction products, BNCT has potential advantages in tumor treatment. Because the neutron beam only reacts with tumor cells carrying boron-10, more precise tumor treatment can be achieved compared to surrounding normal tissues, thereby reducing damage to healthy tissues.

[0003] Due to the complex geometric design and numerous material components, the accelerator neutron source is a typical large-scale neutron transport problem. In particular, the calculation of the epithermal neutron flux rate at the nose outlet of the accelerator neutron source must meet the relevant standards of the International Atomic Energy Agency before neutron therapy for cancer patients can be carried out. In order to determine the mixed radiation field value and the epithermal neutron flux rate at the nose outlet of the accelerator neutron source, the mixed radiation field of the accelerator neutron source needs to be quantified. In the prior art, the most important thing for quantifying the mixed radiation field of the accelerator neutron source is to determine the transport equation of the mixed radiation field of the accelerator neutron source. In the process of deterministically calculating the transport equation of the mixed radiation field of the accelerator neutron source, it is necessary to use the intra-group transport equation iteration algorithm of the subspace method, but the intra-group transport equation iteration algorithm often takes a long time to iterate and cannot meet the needs of actual treatment. Summary of the invention

[0004] In order to overcome the deficiencies of the prior art, the present invention proposes a method for quantifying the mixed radiation field of an accelerator neutron source.

[0005] The technical solution of the present invention is implemented as follows: a method for quantifying a mixed radiation field of an accelerator neutron source, comprising the steps of:

[0006] S1, establish the accelerator neutron source model, mesh the accelerator neutron source model, obtain the density of nuclear materials in the mesh, use the Monte Carlo method to homogenize, and obtain the local uniform multi-group constants, which will be used for the subsequent transport calculation solution;

[0007] S2, calculating the transport equation of the mixed radiation field of the accelerator neutron source, including the following steps:

[0008] S21, an iterative algorithm for intra-group transport equations based on the subspace method; combining the parallel scanning algorithm with the subspace method to ensure parallel calculation of the iterative format, including the steps:

[0009] S211, the linear system of the gth group of the multi-group mixed radiation field transport equation after multi-group approximation, discrete ordinate approximation and differential discretization is written in the following operator form:

[0010] (12)

[0011] (13)

[0012] in, For the Group angular flux vector; For the Group flux moment vector; For the The group source vector, which contains Group The outscattering and fission sources of the group; is the mixed radiation field input operator; E is the mapping operator from angular flux to moment flux; is the mapping operator from moment flux to angular flux;

[0013] Operator The storage capacity is too large. In order to avoid storing ,Will Applying the inverse of (3) yields: (14);

[0014] S212, write equation (5) in standard form as follows:

[0015] (15)

[0016] (16)

[0017] (17)

[0018] The subspace method is applied to calculate equation (6), including the following steps:

[0019] S2121, exogenous from h group After a parallel transport scan, the right-hand side of the equation is obtained ;

[0020] S2122, by initial flux Calculate the initial residual , and the initial basis vectors ,in ;

[0021] S2123, iterative basis vector for the previous step Execution Matrix The operation is then used to further calculate the basis vector of the current iteration step. , and calculate the matrix ;

[0022] S2124, according to the matrix Calculate the minimum residual for the current step , and the approximate solution of the current step ;

[0023] S2125, if If the convergence criterion is met, the calculation is exited. That is the approximate solution obtained, otherwise, execute step S2123;

[0024] S22, for the iteration matrix Preprocessing is performed to change the properties of the iteration matrix and accelerate the convergence of the subspace method, including the steps of: determining a physical preconditioner as the subspace method, and the specific preconditioner expression is:

[0025] (18);

[0026] S23, expanding the intra-group mixed radiation field transport equation to a multi-group form, applying the subspace method to the multi-group mixed radiation field transport equation to decouple the dependencies between energy groups, and realizing parallel calculation between energy groups, including the steps of:

[0027] Expand the source term on the right side of equation (6) by energy group:

[0028] (19)

[0029] Where H is the maximum energy group number, is the fission source of the hth group, Indicates To The scattering matrix of the group, writing the above H equations into matrix form, is:

[0030] (20)

[0031] (twenty one)

[0032] (twenty two)

[0033] in, , , apply the subspace iteration method to equation (16) to achieve parallel computation in the energy group space;

[0034] S3, based on the established accelerator neutron source grid partitioning model and the accelerator neutron source transport equation described in S2, complete the accelerator neutron source mixed radiation field transport calculation, so as to obtain the mixed radiation field value and epithermal neutron injection rate at the accelerator neutron source exit position.

[0035] Furthermore, S3 also includes the step of: if the value of the epithermal neutron fluence rate is less than the value specified by the International Atomic Energy Agency, prompting the operator of the accelerator control hall to conduct troubleshooting until the value of the epithermal neutron fluence rate is greater than or equal to the value specified by the International Atomic Energy Agency again.

[0036] Further or even further, S3 also includes the step of: displaying the mixed radiation field value of the neutron source of the accelerator in real time on a display screen in the control hall.

[0037] The beneficial effect of the present invention is that, compared with the prior art, the present invention can quickly obtain mixed radiation field values ​​so as to quickly check whether the epithermal neutron fluence rate of the accelerator neutron source meets the standards of the International Atomic Energy Agency on the epithermal neutron fluence rate for medical neutrons. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 The present invention is a flow chart of a method for numerically quantifying a mixed radiation field of an accelerator neutron source. DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] See also Figure 1 , a flow chart of a method for quantifying epithermal neutron fluence rate of an accelerator neutron source according to the present invention. The present invention comprises three steps:

[0041] S1, establish the accelerator neutron source model, mesh the accelerator neutron source model, obtain the nuclear material density in all grids, establish the accelerator neutron source mesh model, use the Monte Carlo method for homogenization, and obtain the local uniform multi-group constants, which will be used for the subsequent transport calculation solution;

[0042] S2, calculate the numerical transport equation of the mixed radiation field of the accelerator neutron source;

[0043] S3, based on the established accelerator neutron source grid division model and the accelerator neutron source neutron source mixed radiation field numerical transport equation described in S2, complete the accelerator neutron source mixed radiation field numerical transport calculation, so as to obtain the overall mixed radiation field data of the accelerator neutron source and the epithermal neutron injection rate at the accelerator neutron source exit position.

[0044] Among them, step S2 is the most important to calculate the numerical transport equation of the mixed radiation field of the accelerator neutron source. Step S2 includes the following steps:

[0045] S21, combine the parallel scanning algorithm with the subspace method. When calculating problems with strong inhomogeneity or large scattering, the traditional source iteration method will have the problem of easy divergence and unstable iteration. Therefore, the intra-group transport equation iteration algorithm based on the subspace method; combine the parallel scanning algorithm with the subspace method to ensure the parallel calculation of the iterative format.

[0046] S22, establish a high-efficiency iterative calculation strategy for preconditioners and matrix preprocessing. When solving linear systems with large matrix condition numbers, the subspace method has a large number of iterations and a slow calculation speed. In order to reduce the number of iterations of the subspace method and improve the calculation efficiency, the acceleration algorithm used by the traditional discrete ordinate method is used as a preconditioner to preprocess the iterative matrix of the discrete ordinate equation, reduce the condition number of the iterative matrix, and thus reduce the number of iterations of the subspace method.

[0047] S23, establish a high-efficiency group parallel algorithm based on the combination of GS iteration and multi-group subspace iteration. In the accelerator neutron source transport problem, the upscattering of thermal group neutrons causes strong inter-group coupling. The traditional transport method uses GS iteration to deal with this coupling, but GS iteration cannot easily achieve efficient parallel computing. In order to tap the parallel potential between energy groups, it is necessary to carry out the multi-group subspace method to decouple the calculations between energy groups.

[0048] The subspace method is an advanced non-fixed-point iterative algorithm mainly used for dimensional linear system The solution is to find the matrix B in the subspace. The approximate solution of ,in For an iteration vector The subspace spanned:

[0049] .(twenty three)

[0050] Approximate solution It can also be seen as Projection in the above subspace. It can be shown that the dimension of the subspace is generally less than , which means that the method will be The solution of the linear system with solution is obtained within the step. In addition, it can be seen that the subspace The construction process involves only the matrix and vector This brings the following two advantages to numerical computing and program development: (1) In numerical programs, as long as the matrix-vector multiplication operation is implemented, there is no need to explicitly store the matrix , thus realizing a matrix-free algorithm, greatly saving memory space; (2) the matrix-vector multiplication operation does not impose any dependency information between the rows of the matrix, so it is very suitable for parallel computing. This means that the subspace iteration method can be applied not only to the solution of intra-group equations, but also to the solution of multi-group equations, tapping the parallel potential between energy groups and greatly improving the efficiency of three-dimensional transport calculations of neutron sources in accelerators.

[0051] The above two characteristics make the subspace method very suitable for parallel solving of large-scale sparse matrices in a matrix-free manner. However, the subspace method cannot always find the solution to the problem within a small number of iterations. For ill-conditioned matrices or matrices with large condition numbers, the subspace convergence speed is slow, and the matrix needs to be corrected. Use preconditioners to preprocess and improve the convergence speed of the subspace. Preprocessing means using a The matrix The inverse left-multiplied linear system is as follows:

[0052] (twenty four)

[0053] The preprocessed matrix It will have good properties and be easy to solve. The diffusion equation itself is a good approximation of the transport equation. The comprehensive diffusion acceleration method based on diffusion theory uses the addition operator to correct the transport results, which can be easily extended to the preconditioner of the subspace method to improve the computational efficiency. In summary, the subspace method based on preconditioning will have great application potential in solving the three-dimensional neutron transport equation of accelerator neutron sources.

[0054] In step S21, the steps are included:

[0055] S211, the multi-group neutron transport equation after multi-group approximation, discrete ordinate approximation and differential discretization The linear system of the group can be written in the following operator form:

[0056] (25)

[0057] (26)

[0058] in, For the Group angular flux vector; For the Group flux moment vector; For the The group source vector, which contains Group The outscattering and fission sources of the group; is the neutron input operator; E is the mapping operator from angular flux to moment flux; is the mapping operator from moment flux to angular flux;

[0059] Operator The storage capacity is too large. In order to avoid storing ,Will Applying the inverse of (3) yields: (27);

[0060] S212, write equation (5) in standard form as follows:

[0061] (28)

[0062] (29)

[0063] (30)

[0064] The subspace method is applied to calculate equation (6), including the following steps:

[0065] S2121, exogenous from h group After a parallel transport scan, the right-hand side of the equation is obtained ;

[0066] S2122, by initial flux Calculate the initial residual , and the initial basis vectors ,in ;

[0067] S2123, iterative basis vector for the previous step Execution Matrix The operation is then used to further calculate the basis vector of the current iteration step. , and calculate the matrix ;

[0068] S2124, according to the matrix Calculate the minimum residual for the current step , and the approximate solution of the current step ;

[0069] S2125, if If the convergence criterion is met, the calculation is exited. That is the approximate solution obtained, otherwise, execute step S2123;

[0070] S22, for the iteration matrix Preprocessing is performed to change the properties of the iteration matrix and accelerate the convergence of the subspace method, including the steps of: determining a physical preconditioner as the subspace method, and the specific preconditioner expression is:

[0071] (31);

[0072] S23, expanding the intra-group transport equation to a multi-group form, applying the subspace method to the multi-group transport equation to decouple the dependencies between energy groups, and realizing parallel calculation between energy groups, including the steps of:

[0073] Expand the source term on the right side of equation (6) by energy group:

[0074] (32)

[0075] Where H is the maximum energy group number, is the fission source of the hth group, Indicates To The scattering matrix of the group, writing the above H equations into matrix form, is:

[0076] (33)

[0077] (34)

[0078] (35)

[0079] in, , , apply the subspace iteration method to equation (16) to achieve parallel computation in the energy group space;

[0080] By applying the subspace iteration method to equation (16), parallel computation can be performed in the energy group space.

[0081] In step S3, based on the established accelerator neutron source grid partitioning model and the energy group space parallel calculation method in step S2, a high-precision and high-efficiency deterministic neutron transport calculation of the accelerator neutron source is completed, thereby obtaining the epithermal neutron fluence rate at the accelerator neutron source outlet position. The epithermal neutron fluence rate value is displayed in real time on a display screen in the accelerator control hall. If the epithermal neutron fluence rate value is less than the value specified by the International Atomic Energy Agency, the operator in the accelerator control hall will be prompted to conduct troubleshooting work so as to make the epithermal neutron fluence rate value greater than or equal to the value specified by the International Atomic Energy Agency again.

[0082] The above is a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for quantifying mixed radiation field of accelerator neutron source, characterized in that: Includes steps: S1, establish the accelerator neutron source model, mesh the accelerator neutron source model, obtain the nuclear material density in all grids, establish the accelerator neutron source mesh model, use the Monte Carlo method for homogenization, and obtain the local uniform multi-group constants, which will be used for the subsequent transport calculation solution; S2, calculating the transport equation of the mixed radiation field of the accelerator neutron source, including the following steps: S21, an iterative algorithm for intra-group transport equations based on the subspace method; combining the parallel scanning algorithm with the subspace method to ensure parallel calculation of the iterative format, including the steps: S211, the transport equation of multi-group mixed radiation field after multi-group approximation, discrete ordinate approximation and differential discretization The linear system of the group is written in the following operator form: (1) (2) in, For the Group angular flux vector; For the Group flux moment vector; For the The group source vector, which contains Group The outscattering and fission sources of the group; is the mixed radiation field input operator; E is the mapping operator from angular flux to moment flux; is the mapping operator from moment flux to angular flux; Operator The storage capacity is too large. In order to avoid storing ,Will Applying the inverse of (3) yields: (3); S212, write equation (5) in standard form as follows: (4) (5) (6) The subspace method is applied to calculate equation (6), including the following steps: S2121, exogenous from h group After a parallel transport scan, the right-hand side of the equation is obtained ; S2122, by initial flux Calculate the initial residual , and the initial basis vectors ,in ; S2123, iterative basis vector for the previous step Execution Matrix The operation is then used to further calculate the basis vector of the current iteration step. , and calculate the matrix ; S2124, according to the matrix Calculate the minimum residual for the current step , and the approximate solution of the current step ; S2125, if If the convergence criterion is met, the calculation is exited. That is the approximate solution obtained, otherwise, execute step S2123; S22, for the iteration matrix Preprocessing is performed to change the properties of the iteration matrix and accelerate the convergence of the subspace method, including the steps of: determining a physical preconditioner as the subspace method, and the specific preconditioner expression is: (7)； S23, expanding the intra-group mixed radiation field equation to a multi-group form, applying the subspace method to the multi-group mixed radiation field equation to decouple the dependencies between energy groups, and realizing parallel calculation between energy groups, including the steps of: Expand the source term on the right side of equation (6) by energy group: (8) Where H is the maximum energy group number, is the fission source of the hth group, Indicates To The scattering matrix of the group, writing the above H equations into matrix form, is: (9) (10) (11) in, , , apply the subspace iteration method to equation (16) to achieve parallel computation in the energy group space; S3, based on the established accelerator neutron source grid partitioning model and the accelerator neutron source mixed radiation field equation described in S2, the accelerator neutron source neutron transport calculation is completed to obtain the epithermal neutron injection rate at the accelerator neutron source exit position.

2. The accelerator neutron source mixed radiation field quantification method according to claim 1, characterized in that: The S3 further includes the step of: if the value of the epithermal neutron fluence rate is less than the value specified by the International Atomic Energy Agency, prompting the operator of the accelerator control hall to conduct troubleshooting until the value of the epithermal neutron fluence rate is greater than or equal to the value specified by the International Atomic Energy Agency again.

3. The accelerator neutron source mixed radiation field quantification method according to claim 1 or 2, characterized in that: S3 also includes the step of: displaying the mixed radiation field value of the neutron source of the accelerator in real time on the display screen in the control hall.

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