Plasma diagnosis method and system thereof

Abstract

The invention discloses a plasma diagnosis method and system, and the method comprises the steps: determining a proton source image based on a proton source; generating a first proton beam through the proton source; enabling the first proton beam to pass through the to-be-diagnosed area to form a second proton beam; receiving the second proton beam, and determining a target image; based on the proton source image and the target image, constructing an optimal transport problem from the proton source image to the target image; solving an optimal transport problem, and obtaining an optimal transport probability from the proton source image to the target image; and on the basis of the optimal transport probability, diagnosing the plasma in the to-be-diagnosed area. The plasma diagnosis method has higher calculation progress, and can overcome the defect of difficult convergence caused by singularity of a calculation equation in a strong magnetic field.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of plasma, in particular to a plasma diagnosis method and system thereof. BACKGROUND

[0002] Proton radiography is a diagnostic technique that uses a high-energy proton beam as a "probe" to image the internal structure or electromagnetic field distribution of matter, and is widely used in high-energy density physics, inertial confinement fusion (ICF) and other fields. Among them, proton radiography has the characteristics of strong penetration ability, high sensitivity, beam separation and high spatial resolution, and can well perform perspective radiography on the self-generated electromagnetic field of plasma and obtain its electromagnetic field information.

[0003] The process of proton radiography is to generate a high-energy proton beam and pass the high-energy proton beam through a region to be diagnosed, wherein the region to be diagnosed has plasma. The proton beam passing through the region to be diagnosed is deflected due to the Lorentz force in the self-generated electromagnetic field of the plasma in the region to be diagnosed. The deflected proton beam is received, and by analyzing the flux distribution of the deflected proton beam, the information of the self-generated electromagnetic field of the plasma in the region to be diagnosed can be inferred, thereby realizing the diagnosis of the self-generated electromagnetic field of the plasma in the region to be diagnosed.

[0004] However, the existing plasma diagnosis method has the problems of difficulty in solving and large error. SUMMARY

[0005] The problem solved by the present application is how to improve the diagnosis accuracy of the electromagnetic field of the plasma itself and reduce the diagnosis difficulty.

[0006] To solve the above problems, the present application provides a plasma diagnosis method, comprising:

[0007] Based on a proton source, a proton source image is determined; a first proton beam is generated by the proton source; the first proton beam passes through a region to be diagnosed to form a second proton beam; the second proton beam is received to determine a target image; based on the proton source image and the target image, an optimal transport problem from the proton source image to the target image is constructed; the optimal transport problem is solved to obtain an optimal transport probability from the proton source image to the target image; and the plasma in the region to be diagnosed is diagnosed based on the optimal transport probability.

[0008] Optionally, the step of constructing the optimal transport problem from the proton source image to the target image based on the proton source image and the target image comprises: determining a Wasserstein distance based on the proton source image and the target image; the step of solving the optimal transport problem to obtain the optimal transport probability from the proton source image to the target image comprises: obtaining the optimal transport probability from the proton source image to the target image based on the Wasserstein distance.

[0009] Optionally, the step of determining the Wasserstein distance comprises: determining a proton source flux probability density distribution based on the proton source image; determining a target flux probability density distribution based on the target image; determining a cost matrix based on the proton source flux probability density distribution and the target flux probability density distribution; determining the Wasserstein distance based on the cost matrix.

[0010] Optionally, at least one of the step of determining the proton source flux probability density distribution and the step of determining the target flux probability density distribution comprises: performing gridding and normalization on an image to determine a flux probability density distribution corresponding to the image, wherein the image is one of the proton source image and the target image.

[0011] Optionally, the step of obtaining the optimal transport probability from the proton source image to the target image comprises: determining a transport entropy based on the transport probability; determining a transport functional based on the Wasserstein distance and the transport entropy; obtaining the optimal transport probability from the proton source image to the target image based on the transport functional.

[0012] Optionally, the step of obtaining the optimal transport probability from the proton source image to the target image comprises: using a Sinkhorn iterative algorithm to solve the transport functional to obtain the optimal transport probability from the proton source image to the target image.

[0013] Optionally, the step of diagnosing the plasma in the to-be-diagnosed region comprises: determining a position mapping relationship from the proton source image to the target image based on the optimal transport probability; determining a proton deflection angle based on the position mapping relationship; determining a magnetic field of the plasma in the to-be-diagnosed region based on the proton deflection angle.

[0014] Optionally, the step of determining the position mapping relationship from the proton source image to the target image based on the optimal transport probability comprises: determining a centroid mapping form; determining the position mapping relationship based on the optimal transport probability and the centroid mapping form, wherein the position mapping relationship is a one-to-one mapping relationship.

[0015] Optionally, the step of determining the position mapping relationship from the proton source image to the target image based on the optimal transport probability further comprises: determining the position mapping relationship on the grid points based on the position mapping relationship after determining the position mapping relationship; and the step of determining the proton deflection angle comprises: determining the proton deflection angle based on the position mapping relationship on the grid points.

[0016] Optionally, the step of determining the position mapping relationship on the grid points comprises: determining the position mapping relationship on the grid points by means of third-order interpolation.

[0017] Correspondingly, the application also provides a plasma diagnosis system, comprising:

[0018] a proton source configured to generate a first proton beam; the first proton beam passes through a region to be diagnosed to form a second proton beam; a receiving surface configured to receive the second proton beam to obtain a target image; a processor configured to construct an optimal transport problem from the proton source image to the target image based on the proton source image and the target image, and solve the optimal transport problem to obtain an optimal transport probability from the proton source image to the target image; and a diagnostic device configured to diagnose the plasma in the region to be diagnosed based on the optimal transport probability.

[0019] Optionally, the processor comprises a construction module configured to determine a Wasserstein distance based on the proton source image and the target image, and obtain the optimal transport probability from the proton source image to the target image based on the Wasserstein distance.

[0020] Optionally, the processor further comprises a solution module configured to determine a transport entropy based on the transport probability, and determine a transport functional in combination with the Wasserstein distance; and the solution module is further configured to obtain the optimal transport probability from the proton source image to the target image based on the transport functional.

[0021] Optionally, the solution module utilizes a Sinkhorn iterative algorithm to solve the transport functional to obtain the optimal transport probability from the proton source image to the target image.

[0022] Optionally, the solution module comprises a GPU.

[0023] Compared with the prior art, the technical scheme of the application has the following advantages:

[0024] In the technical scheme of the present application, the optimal transport problem from the proton source image to the target image is constructed through the proton source image and the target image; and the optimal transport probability from the proton source image to the target image is obtained by solving the optimal transport problem. Through the construction of the optimal transport problem, the deflection information of the protons in the proton photography is converted into the optimal transport problem in the sense of probability distribution, and the one-to-one mapping relationship between the proton source image and the target image in the process of the proton beam transmission is changed into the many-to-many mapping relationship of the optimal transport, thereby avoiding the singular area of the unit image caused by the proton aggregation, eliminating the error in the solution of the Monge-Ampere equation, overcoming the problem of difficult convergence caused by the singular area, and effectively ensuring the accuracy and reliability of the results, especially in the case of strong electromagnetic field.

[0025] In the optional scheme of the present application, the step of obtaining the optimal transport probability from the proton source image to the target image comprises: determining the transport functional based on the Wasserstein distance and in combination with the transport entropy. By introducing the transport entropy, the solution of the optimal transport problem is constructed as a convex optimization problem, thereby avoiding the oscillation and difficult problem caused by the solution of the non-convex problem.

[0026] In the optional scheme of the present application, the step of obtaining the optimal transport probability from the proton source image to the target image comprises: using the Sinkhorn iterative algorithm to solve the transport functional and obtain the optimal transport probability from the proton source image to the target image. The time complexity of the Sinkhorn iterative algorithm is nearly linear, and the GPU acceleration is supported, thereby realizing the applicability to the real-time diagnosis scene. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 FIG. 1 is a flowchart of the plasma diagnosis method in some embodiments of the present application.

[0028] Figure 2 FIG. 2 is a structural schematic diagram of the system used in the plasma diagnosis method in some embodiments of the present application.

[0029] Figure 3 FIG. 3 is a schematic diagram of the many-to-many mapping transport relationship from the proton source image 101 to the target image 102 in some embodiments of the present application.

[0030] Figure 4 FIG. 4 is a flowchart of the step of determining the Wasserstein distance in the plasma diagnosis method in some embodiments of the present application.

[0031] Figure 5 FIG. 5 is a flowchart of the step of obtaining the optimal transport probability from the proton source image to the target image in the plasma diagnosis method in some embodiments of the present application.

[0032] Figure 6is a flowchart of a diagnosis step of plasma in a region to be diagnosed in a plasma diagnosis method in some embodiments of the present application.

[0033] Figure 7 is a flowchart of a step of determining a position mapping relationship from a proton source image to a target image based on an optimal transport probability in a plasma diagnosis method in some embodiments of the present application.

[0034] Figure 8 is a schematic diagram of a result obtained by a plasma diagnosis method in some embodiments of the present application.

[0035] Figure 9 is a schematic diagram of a result obtained by a plasma diagnosis method in some embodiments of the present application.

[0036] Figure 10 is a schematic diagram of a result obtained by a plasma diagnosis method in some embodiments of the present application.

[0037] Figure 11 is a schematic diagram of a result obtained by a plasma diagnosis method in some embodiments of the present application.

[0038] Figure 12 is a functional block diagram of a processor in a plasma diagnosis system in some embodiments of the present application. DETAILED DESCRIPTION

[0039] As known from the background, the existing plasma diagnosis method is prone to problems of difficulty in solving and large error.

[0040] The existing method of deducing information of a self-generated electromagnetic field of plasma by proton back projection mainly includes a forward calculation method and a direct inversion method.

[0041] The forward calculation method mainly uses a Monte Carlo or particle tracking method to simulate the distribution of a proton beam deflected in a self-generated electromagnetic field of plasma in a region to be diagnosed by using an assumed electromagnetic field, and the assumed electromagnetic field is repeatedly adjusted after comparing the calculation result with the experimental image, so as to finally obtain the information of the self-generated electromagnetic field of the plasma in the region to be diagnosed. The forward calculation method seriously depends on the assumption of the initial electromagnetic field, has high calculation cost, and is difficult to handle a strong magnetic field that may cause nonlinear deflection.

[0042] The other method of deducing information of a self-generated electromagnetic field of plasma is the direct inversion method. The direct inversion method directly inverts the information of the self-generated electromagnetic field of plasma in a region to be diagnosed by a proton beam from an imaging image by establishing a mathematical relationship between the proton beam and the electromagnetic field.

[0043] In the direct inversion method, based on the one-to-one correspondence between the regions in the proton source image and the regions in the target image, the proton beam deflection angle Monge-Ampere equation is established by using the proton beam particle number conservation to obtain the deflection angle, and then the integral average magnetic field strength in the proton passing path is obtained.

[0044] The Monge-Ampere equation is established based on the weak field approximation, and can only be adapted to the linear region with small magnetic field strength. With the increase of the electromagnetic field strength, the protons will gradually appear the gathering phenomenon. The gathering of protons will make the Monge-Ampere equation approach a singular point, so that the solving difficulty appears, and the error will also increase. Specifically, in the strong magnetic field case, if multiple regions in the proton source image correspond to the same region or the adjacent region in the target image, the proton beam deflection angle Monge-Ampere equation approaches a singularity (the Jacobian determinant of the conservation transformation approaches zero), and cannot be solved or the error of the solution is large.

[0045] It can be seen that in the case of strong electromagnetic field, the direct inversion method of solving the Monge-Ampere equation has problems such as large error, low calculation efficiency, even difficult to converge, and the result is seriously distorted.

[0046] To solve the technical problem, the present application provides a kind of plasma diagnostic method, by the construction of optimal transport problem, the deflection information of protons in proton photography is converted into the optimal transport problem in the sense of probability distribution, the one-to-one mapping relationship between the proton source image and the target image in the process of proton beam transmission is changed into the mapping relationship of multiple-to-multiple of optimal transport, thereby avoiding the singular area of unit image caused by the gathering of protons, eliminating the error in the solution of Monge-Ampere equation, overcoming the problem of difficult to converge caused by equation singularity, especially for in the case of strong electromagnetic field, the accuracy and reliability of the result can be effectively guaranteed.

[0047] In order to make the above-mentioned purpose, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the drawings.

[0048] Reference Figure 1 , shows the flowchart of the plasma diagnostic method in some embodiments of the present application.

[0049] The plasma diagnostic method comprises:

[0050] Step S110, determining a proton source image based on the proton source; step S120, generating a first proton beam by the proton source; step S130, passing the first proton beam through the region to be diagnosed to form a second proton beam; step S140, receiving the second proton beam to determine a target image; step S150, constructing an optimal transport problem from the proton source image to the target image based on the proton source image and the target image; step S160, solving the optimal transport problem to obtain an optimal transport probability from the proton source image to the target image; and step S170, diagnosing the plasma in the region to be diagnosed based on the optimal transport probability.

[0051] The technical solutions of the embodiments of the plasma diagnosis method will be described in detail below with reference to the drawings.

[0052] With reference to Figure 2 , a structural schematic diagram of a system used in the plasma diagnosis method in some embodiments of the present application is shown.

[0053] The plasma diagnosis method comprises: first performing step S110, determining a proton source image based on the proton source.

[0054] The proton source image is a two-dimensional distribution of the proton beam emitted by the proton source. Specifically, step S110 of determining the proton source image based on the proton source comprises: determining the proton source image based on the energy distribution and emission of the proton beam.

[0055] As shown in some embodiments of Figure 2 , step S110 of determining the proton source image based on the proton source 111 comprises: determining the energy distribution, divergence angle of the proton beam generated by the proton source 111, and the distance r i between the proton source 111 and the region to be diagnosed 113 based on the proton source 111; and calculating and drawing the proton source image based on the energy distribution, divergence angle of the proton beam generated by the proton source 111, and the distance r i between the proton source 111 and the region to be diagnosed 113.

[0056] It should be noted that the images of different types of proton sources are not the same. In some embodiments of the present application, the proton source can include one of a planar target proton source and a gas target proton source. The planar target proton source refers to a proton source in which a short-pulse laser bombards a planar target to generate a proton beam; and the gas target proton source refers to a proton source in which multiple lasers are focused to a gas target filled with D3He to generate a proton beam.

[0057] Specifically, the plasma diagnosis method further comprises: after determining the proton source, performing step S120 of generating a first proton beam by the proton source.

[0058] In some embodiments of the present application, the proton source is a single-energy proton source, and the protons in the first proton beam have the same energy. Using a single-energy proton source to generate the first proton beam can effectively improve the definition of the obtained target image, thereby effectively improving the reliability and accuracy of the plasma diagnosis result.

[0059] As shown in some embodiments, Figure 2 The proton source 111 generates protons to form the first proton beam 112, and the proton source 111 has a proton source image.

[0060] The plasma diagnosis method further includes, after the first proton beam is generated, the step S130 of passing the first proton beam through the region to be diagnosed to form a second proton beam.

[0061] Specifically, the region to be diagnosed has a plasma. During the passing of the first proton beam through the region to be diagnosed, the first proton beam is deflected by the self-generated electromagnetic field of the plasma in the region to be diagnosed, and the proton beam obtains a deflection speed when leaving the region to be diagnosed, so as to modulate the flux density of the proton beam, thereby changing the flux density of the proton beam emitted from the region to be diagnosed.

[0062] As shown in some embodiments, Figure 2 The region to be diagnosed 113 has a first size d and a second size l, where the first size d is the size of the region to be diagnosed 113 along the direction of incidence of the first proton beam 112, and the second size l is the size of the region to be diagnosed 113 in the plane of the direction of incidence of the first proton beam 112. The region to be diagnosed 113 has a plasma, and the plasma in the region to be diagnosed 113 forms a self-generated electromagnetic field. The self-generated electromagnetic field interacts with the protons passing through the region to be diagnosed 113, so that the protons are deflected to form a second proton beam 114 emitted from the region to be diagnosed 113.

[0063] The plasma diagnosis method further includes, after the second proton beam is formed, the step S140 of receiving the second proton beam to determine a target image.

[0064] The target image is the distribution of the proton flux on the receiving surface, which is the distribution of protons per unit time and per unit area on the receiving surface. Specifically, the step of receiving the second proton beam to determine the target image includes receiving the second proton beam emitted from the region to be diagnosed to determine the target image. For example, the step of receiving the second proton beam emitted from the region to be diagnosed to determine the target image includes receiving the second proton beam emitted from the region to be diagnosed by a detector to determine the target image. The detector can be a RCF stack or a CR-39 detector.

[0065] AsFigure 2 In some embodiments as shown, the second proton beam 114 emitted from the region to be diagnosed 113 is incident to the receiving surface 115 of the detector to obtain the target image.

[0066] With reference back to Figure 1 , after determining the proton source image and the target image, the plasma diagnosis method further comprises: performing step S150, constructing an optimal transport problem from the proton source image to the target image based on the proton source image and the target image.

[0067] By constructing the optimal transport problem from the proton source image to the target image through the proton source image and the target image, the proton beam deflection information is converted into an optimal transport problem in the sense of probability distribution, and the one-to-one mapping relationship between the proton source image and the target image in the ion beam transmission process is converted into a many-to-many mapping relationship of optimal transport, thereby avoiding the singular area of the unit image caused by the proton aggregation, eliminating the error in the solution of the Monge-Ampere equation, and overcoming the problem of difficult convergence caused by the singular area. In particular, in the case of a strong electromagnetic field, the accuracy and reliability of the results can be effectively guaranteed.

[0068] In some embodiments of the application, the step of performing step S150, constructing an optimal transport problem from the proton source image to the target image based on the proton source image and the target image, comprises: constructing a Kantorovich optimal transport problem from the proton source image to the target image based on the proton source image and the target image.

[0069] The Kantorovich optimal transport problem is a problem of solving how to transport one probability distribution to another probability distribution with minimum cost. The Kantorovich optimal transport problem constructs a solvable linear programming problem by introducing a relaxed way of "transport plan". Based on the proton source image and the target image, the Kantorovich optimal transport problem from the proton source image to the target image is constructed, which converts the solution of the one-to-one mapping problem from the proton source image to the target image into the solution of the many-to-many mapping problem from the proton source image to the target image, thereby avoiding the singular area of the unit image caused by the particle aggregation, and overcoming the defects of large error and difficult convergence of the Monge-Ampere equation in a strong electromagnetic field.

[0070] As Figure 3 shown in some embodiments, the Kantorovich optimal transport problem from the proton source image 101 to the target image 102 represents a many-to-many mapping transport problem from the proton source image 101 to the target image 102, that is, a proton from one place of the proton source image 101 can be transported to different positions of the target image 102 based on different probabilities; the proton at one place in the target image 102 can be caused by the proton source image 101 in multiple places with different probabilities.

[0071] In some embodiments of the present invention, the steps of constructing the optimal transport problem from the proton source image to the target image based on the proton source image and the target image include: determining the Wasserstein distance based on the proton source image and the target image.

[0072] In the Kontrowevich optimal transport problem, the Wasserstein distance is used to measure the difference in probability distributions. Specifically, the Wasserstein distance is obtained based on the cost function and is related to minimizing cost.

[0073] like Figure 4 As shown, in some embodiments, the steps for determining the Wasserstein distance include: step S151, determining the proton source flux probability density distribution based on the proton source image; step S152, determining the target flux probability density distribution based on the target image; step S153, determining the cost matrix based on the proton source flux probability density distribution and the target flux probability density distribution; and step S154, determining the Wasserstein distance based on the cost matrix.

[0074] In the Kontrowevich optimal transport problem, the concept of a "transport plan" is introduced. This plan describes the transport quantity from a location in the proton source image to a location in the target image using a joint probability distribution. The problem is a transport problem from one probability distribution to another. Therefore, step S151, determining the proton source flux probability density distribution based on the proton source image, and step S152, determining the target flux probability density distribution based on the target image, are configured to convert the images into probability distributions.

[0075] In some specific embodiments, at least one of the steps of determining the proton source flux probability density distribution and determining the target flux probability density distribution includes: meshing and normalizing the image to determine the flux probability density distribution corresponding to the image, wherein the image is one of the proton source image and the target image.

[0076] Specifically, the image is gridded and normalized to prepare for constructing a discretized or matrix-based optimal transport problem. The steps of gridding and normalizing the image include: determining the number of grid points based on the fine structure appearing in the image.

[0077] In some examples, the number of grid points differs between the step of meshing the proton source image and the step of meshing the target image. For example... Figure 3In some of the embodiments shown, in the step of meshing and normalizing the proton source image 101, the proton source image 101 is meshed and normalized based on a regular two-dimensional mesh; in the step of meshing and normalizing the target image 102, the target image 102 is meshed and normalized based on an irregular two-dimensional mesh.

[0078] For example, in step S151, based on the proton source image, determine the proton source flux probability density distribution P. i :P i ={p i}, where i is a positive integer, i≤N, and N is the number of grid points in the proton source image; Step S152, based on the target image, determine the target flux probability density distribution Q. j Q j ={q j}, where j is a positive integer, j≤M, and M is the number of grid points in the proton source image.

[0079] After determining the proton source flux probability density distribution and the target flux probability density distribution, step S153 is executed to determine the cost matrix based on the proton source flux probability density distribution and the target flux probability density distribution.

[0080] The cost matrix describes the cost required to transport one unit mass from each location in the proton source image to each location in the target image.

[0081] Specifically, based on the proton source flux probability density distribution P i and the target flux probability density distribution Q j Determine the cost matrix C ij :C ij =||p i -q j || 2 Each element C in the cost matrix ij The cost from grid point i in the proton source image to grid point j in the target image is: if element C ij The smaller the value, the lower the cost from grid point i in the proton source image to grid point j in the target image, and the higher the transport probability from grid point i in the proton source image to grid point j in the target image.

[0082] After determining the cost matrix, step S154 is executed to determine the Wasserstein distance based on the cost matrix. The Wasserstein distance represents the geometric transport cost from the proton source image to the target image.

[0083] Specifically, based on the cost matrix C ij Determine the square of the Wasserstein distance W2. 2 :

[0084]

[0085] wherein U(P i , Q j ) is a set of mappings from the proton source flux probability density distribution P i to the target flux probability density distribution Q j , satisfying the flow flux probability distribution. P ij is a transport probability, representing the transport probability between the grid point i in the proton source image to the grid point j in the target image in the sense of probability distribution, and the greater P ij , the greater the transport probability. P ij represents all transport probabilities for completely transporting the proton source flux probability density distribution P i to the target flux probability density distribution Q j . The transport probability P ij is a transport matrix P composed of elements P ij : P = [P ij ] N×M , 1≤i≤N, 1≤j≤M. R represents a real number, that is, P is a dxd-dimensional matrix.

[0086] With reference to Figure 1 , the plasma diagnosis method further comprises: after constructing the optimal transport problem, performing step S160 of solving the optimal transport problem to obtain the optimal transport probability of the proton source image to the target image.

[0087] In some embodiments of the present application, the optimal transport problem is the Kantorovich optimal transport problem, so solving the optimal transport problem is to calculate the transport probability P ij that minimizes the square of the Wasserstein distance.

[0088] Specifically, the step of constructing the optimal transport problem comprises: determining the Wasserstein distance; and the step of solving the optimal transport problem to obtain the optimal transport probability of the proton source image to the target image comprises: based on the Wasserstein distance, obtaining the optimal transport probability of the proton source image to the target image.

[0089] The step of obtaining the optimal transport probability of the proton source image to the target image based on the Wasserstein distance is to obtain the optimal transport probability by calculating the optimization problem with the minimum Wasserstein distance.

[0090] As Figure 5In some embodiments as shown, the step of obtaining the optimal transport probability from the proton source image to the target image comprises: a step S161 of determining a transport entropy based on the transport probability; a step S162 of determining a transport functional based on the Wasserstein distance in combination with the transport entropy; and a step S163 of obtaining the optimal transport probability from the proton source image to the target image based on the transport functional. By introducing the transport entropy, the solution of the optimal transport problem is constructed as a convex optimization problem, thereby avoiding oscillation and difficult problems caused by the solution of non-convex problems.

[0091] The transport entropy characterizes the uncertainty of the transport probability distribution of the proton source flux probability density distribution P x The complete transport to the target flux probability density distribution Q v The transport entropy is determined based on the transport probability P ij In the step S161 of determining the transport entropy based on the transport probability P .

[0092] The transport functional is determined based on the Wasserstein distance and the transport entropy. On the basis of the Wasserstein distance, the constraint of the uncertainty of the probability distribution is added, thereby being able to convert the non-convex optimization problem into a convex optimization problem, thereby avoiding oscillation and difficult problems caused by the solution of non-convex problems.

[0093] In the step S162 of determining the transport functional based on the Wasserstein distance in combination with the transport entropy, the transport functional F is:

[0094]

[0095] Wherein, λ is a regularization factor used to control the smoothness of the solution to maintain numerical stability under strong magnetic fields and noisy data.

[0096] With reference back to Figure 5 , after the transport functional is determined, the step S163 of determining the optimal transport probability P is executed based on the transport functional. Specifically, the optimal transport probability P is the transport probability from the proton source image to the target image with the lowest total cost and the highest uncertainty, i.e., the transport probability with the minimum Wasserstein distance and the maximum transport entropy.

[0097] In some embodiments, the step of obtaining the optimal transport probability from the proton source image to the target image comprises: using a Sinkhorn iterative algorithm to solve the transport functional and obtain the optimal transport probability P The core of the Sinkhorn iterative algorithm is a large number of vectorized matrix operations and element-wise operations (such as exp, division, log-sum-exp, and the like), which are suitable for conversion into GPU parallel kernel functions (kernel) and are suitable for conversion into a form suitable for GPU parallel processing, that is, the code can be rewritten or optimized so that it can be executed simultaneously on multiple threads of the GPU, and the kernel function on the GPU can be designed and implemented to achieve efficient parallel computing.

[0098] The number of iterations of the Sinkhorn iterative algorithm is about , and each iteration requires a matrix-vector multiplication, and the computational complexity of each iteration is , and the complexity of all iterations is , and it is not a completely linear method.

[0099] In some embodiments of the present application, the Sinkhorn iterative algorithm is used to solve the transport functional to obtain the optimal transport probability from the proton source image to the target image in the step of obtaining the optimal transport probability from the proton source image to the target image by using the Sinkhorn iterative algorithm to solve the transport functional based on the approximate kernel method. The approximate kernel method can include fast Gaussian transform. In the approximate kernel method, the Sinkhorn algorithm can achieve a complexity of O(nlogn) or O(n) in an approximate sense, and such a computational complexity is referred to as "near-linear", thereby enabling the application in real-time diagnosis scenarios.

[0100] With reference to Figure 1 , the optimal transport probability is obtained, and the plasma diagnosis method further includes: a step S170 of diagnosing the plasma in the region to be diagnosed based on the optimal transport probability .

[0101] The optimal transport probability represents the transport probability with the lowest total cost and the highest uncertainty from the proton source image to the target image, and represents the mapping relationship from the proton source image to the target image. The target image is obtained after the proton beam generated by the proton source is deflected by the self-electromagnetic field of the plasma in the region to be diagnosed, and therefore the mapping relationship from the proton source image to the target image can reflect the deflection information of the proton beam in the region to be diagnosed, can reflect the properties of the self-electromagnetic field of the plasma in the region to be diagnosed, and can further diagnose the plasma in the region to be diagnosed.

[0102] Specifically, the steps for diagnosing the plasma in the region to be diagnosed are configured to determine the proton deflection angle, and thus determine the magnetic field of the plasma in the region to be diagnosed.

[0103] like Figure 6 As shown, in some embodiments, the steps for diagnosing the plasma in the region to be diagnosed include: step S171, based on the optimal transport probability Step S172: Determine the positional mapping relationship between the proton source image and the target image; Step S173: Determine the proton deflection angle based on the positional mapping relationship; Step S174: Determine the magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle.

[0104] The Kontarovich optimal transport problem solves the transport problem from one probability distribution to another, obtaining the optimal transport probability. This reflects a many-to-many mapping from the proton source image to the target image. Step S171, based on the optimal transport probability... The step of determining the positional mapping relationship between the proton source image and the target image is used to determine the one-to-one positional mapping relationship between the proton source image and the target image.

[0105] like Figure 7 As shown, in some embodiments, step S171, which determines the positional mapping relationship from the proton source image to the target image based on the optimal transport probability, includes: step S171a, determining the centroid mapping form; step S171b, determining the positional mapping relationship based on the optimal transport probability and the centroid mapping form, wherein the positional mapping relationship is a one-to-one mapping relationship.

[0106] Determining the centroid mapping form provides a basis for determining the positional mapping relationship between the proton source image and the target image. Determining the centroid mapping form means obtaining the specific deflection position of the proton, i.e., the probabilistic centroid position, through probability averaging. Specifically, in step S171a, the determined centroid mapping form... for .

[0107] Specifically, in step S171b, based on the optimal transport probability... Combining the centroid mapping form, the position mapping relationship is determined. The determined position mapping relationship is as follows: .

[0108] It should be noted that the mapped position obtained under the position mapping relationship is not guaranteed to be located at a grid point in the target image. Therefore, as... Figure 7As shown, in some embodiments, step S171, which determines the positional mapping relationship from the proton source image to the target image based on the optimal transport probability, further includes: step S171b, after determining the positional mapping relationship, performing step S171c, which determines the positional mapping relationship on the grid points based on the positional mapping relationship. In some example embodiments, the step of determining the positional mapping relationship on the grid points includes: determining the positional mapping relationship on the grid points using third-order interpolation.

[0109] Continue to refer to Figure 6 After determining the position mapping relationship, the steps for diagnosing the plasma in the region to be diagnosed also include: executing step S172 to determine the proton deflection angle based on the position mapping relationship; and then executing step S173 to determine the magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle.

[0110] In some embodiments, the position mapping relationship is a position mapping relationship on grid points; therefore, step S172, the step of determining the proton deflection angle, includes: determining the proton deflection angle based on the position mapping relationship on grid points.

[0111] Specifically, in the step of determining the proton deflection angle based on the position mapping relationship on the grid points, the proton deflection angle... for: , where r s Indicates the distance between the area to be diagnosed 113 and the receiving surface 115 (e.g. Figure 2 (As shown).

[0112] Step S173, the step of determining the magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle, includes: based on the proton deflection angle... Determine the deflection potential Based on deflection potential Determine the magnetic field of the plasma in the region to be diagnosed. .

[0113] Specifically, based on the proton deflection angle Determine the deflection potential In the steps, based on the proton deflection angle With deflection potential Relationship: proton deflection angle The deflection potential is obtained by performing a transverse integration along the direction perpendicular to the proton beam. Integral along the direction of the proton beam .

[0114] Specifically, based on deflection potential Determine the magnetic field of the plasma in the region to be diagnosed. In the steps, based on the deflection potential With magnetic field Relationship: Determine the magnetic field , where m p W is the mass of the proton, c is the speed of light, and q is the charge of the proton, i.e., q = +e, where e is the elementary charge unit.

[0115] Reference Figure 8 The diagram illustrates the results obtained by the plasma diagnostic method in some embodiments of the present invention.

[0116] like Figure 8 As shown, the horizontal axis represents position in micrometers (μm), and the vertical axis represents the integrated spliced ​​magnetic field strength in megagauss-micrometers (MG-μm). The red data line represents the magnetic field results obtained by the plasma diagnostic method of this invention; the blue data line represents the magnetic field results obtained by solving the Monge-Ampère equation; and the black dashed line represents the results obtained by the analytical equation of the magnetic field.

[0117] like Figure 8 In some of the embodiments shown, the proton source is a single-energy proton source of 4.3 MeV. The distance r between the proton source and the region to be diagnosed is... i The distance r between the area to be diagnosed and the receiving surface is 1.2 millimeters (mm). s The distance is 2 centimeters (cm). The probability density distribution of the proton source flux P i To ensure uniform distribution, a 256×256 grid was used for meshing; the target flux probability density distribution Q j The resolution is 256×256 grid.

[0118] like Figure 8 In some of the embodiments shown, the magnetic field in the region to be diagnosed is a toroidal magnetic field, the analytical form of which is: Where B0 is the characteristic intensity or amplitude of the magnetic field; r xy Z is the radial coordinate, i.e., the distance from the axis in the cylindrical coordinate system; σ is the radial characteristic scale parameter; z0 is the axial coordinate; and b is the axial characteristic size parameter. The magnetic field in the region to be diagnosed is a nonlinear magnetic field with a radial characteristic scale parameter σ of 30 micrometers (μm) and a magnetic field strength of 200 megagauss (MG).

[0119] The magnetic field in the region to be diagnosed is solved using the plasma diagnostic method of this invention. In the transport functional, the regularization factor λ is 0.01; and the convergence error is 0.001 during the solution of the transport functional using the Sinkhorn iterative algorithm.

[0120] like Figure 8As shown in the figure, the horizontal axis represents the transverse position in units of micrometers (μm), and the vertical axis represents the integrated average magnetic field strength in units of mega-gauss-micrometers (MG·μm). The results show that the magnetic field results obtained by the plasma diagnostic method of the present application represented by the red data line are closer to the results obtained by the magnetic field analytical equation represented by the black dashed line, and are more consistent.

[0121] The error between the magnetic field results obtained by the plasma diagnostic method of the present application and the results obtained by the magnetic field analytical equation is less than 5%. The inversion error of the magnetic field results obtained by the plasma diagnostic method of the present application is 0.028758, which is significantly lower than the inversion error of 0.069202 of the magnetic field results obtained by solving the Monge-Ampere equation.

[0122] In combination with reference Figure 9 , a schematic diagram of the results obtained by the plasma diagnostic method in some embodiments of the present application is shown.

[0123] Figure 9 As shown in the figure, the horizontal axis represents the transverse position in units of micrometers (μm), and the vertical axis represents the integrated average magnetic field strength in units of mega-gauss-micrometers (MG·μm). The red data line represents the magnetic field results obtained by the plasma diagnostic method of the present application; the blue data line represents the magnetic field results obtained by solving the Monge-Ampere equation; and the black dashed line represents the results obtained by the magnetic field analytical equation.

[0124] As shown in some embodiments Figure 9 , the proton source is a single-energy proton source of 4.3 mega-electron-volts (MeV). The distance r i between the proton source and the region to be diagnosed is 1.2 millimeters (mm). The distance r s between the region to be diagnosed and the receiving surface is 2 centimeters (cm). The proton source flux probability density distribution P i is uniformly distributed and is gridded using a 256x256 grid; the resolution of the target flux probability density distribution Q j is a 256x256 grid.

[0125] As shown in some embodiments Figure 9 , the magnetic field in the region to be diagnosed is a toroidal magnetic field, and its analytical form is: , wherein B0 is the characteristic strength or amplitude of the magnetic field; r xy is the radial coordinate, i.e., the distance to the axis in the cylindrical coordinate system, σ is the radial characteristic scale parameter, z0 is the axial coordinate, and b is the axial characteristic dimension parameter. The magnetic field in the region to be diagnosed is a strong nonlinear magnetic field, the radial characteristic scale parameter σ is 30 micrometers (μm), and the magnetic field strength is 310 mega-gauss (MG).

[0126] The magnetic field in the region to be diagnosed is solved by the plasma diagnosis method of the application. In the transport functional, the regularization factor λ is 0.01; in the process of solving the transport functional by the Sinkhorn iteration algorithm, the convergence error is 0.001.

[0127] As shown in Figure 9 , compared with the magnetic field result obtained by solving the M-A equation represented by the blue data line, the magnetic field result obtained by the plasma diagnosis method of the application represented by the red data line is still closer to the result obtained by the magnetic field analytical equation represented by the black dashed line, and is more consistent.

[0128] In addition, as shown in Figure 9 , the magnetic field result obtained by solving the M-A equation represented by the blue data line deviates greatly from the result obtained by the magnetic field analytical equation represented by the black dashed line at the transverse position between 0 microns (μm) and 200 microns (μm) (as shown in the blue data line in the middle green solid line) Figure 9 , which indicates that the magnetic field result obtained by solving the M-A equation has a false bulge between 0 microns (μm) and 200 microns (μm), that is, when the magnetic field in the region to be diagnosed is a strong nonlinear magnetic field as high as 310 megagauss (MG), the proton beam will converge, resulting in singularity and non-convergence in solving the M-A equation.

[0129] In combination with reference Figure 10 , a schematic diagram of the result obtained by the plasma diagnosis method in some embodiments of the application is shown.

[0130] As shown in Figure 10 , in some embodiments, the proton source is a single-energy proton source of 4.3 megaelectron volts (MeV). The distance r i between the proton source and the region to be diagnosed is 1.2 millimeters (mm). The distance r s between the region to be diagnosed and the receiving surface is 2 centimeters (cm). The proton source flux probability density distribution P i is uniformly distributed, and is gridded using a 256x256 grid; the resolution of the target flux probability density distribution Q j is a 256x256 grid.

[0131] The magnetic field in the region to be diagnosed is composed of a magnetic field in the form of spherical harmonics: , wherein B0 is the magnetic field reference strength, (l, m) is the spherical harmonic parameter, A lm is the expansion coefficient, P l m (sinθ) is the pair of spherical harmonics, θ is the polar angle, is the azimuth angle, The circular function term is an item. Specifically, the magnetic field reference strength B0 value is in a range of 13 mega Gauss (MG) to 342 mega Gauss (MG), and the proton imaging result on the receiving screen is in a range of 100 microns (μm) to 1 millimeter (mm).

[0132] The magnetic field in the region to be diagnosed is solved by the plasma diagnosis method of the application. In the transport functional, the regularization factor λ is 0.005; in the process of solving the transport functional by the Sinkhorn iterative algorithm, the convergence error is 0.01, and the maximum iteration number is 150 times.

[0133] Figure 10 The plasma diagnosis results of the magnetic field with the spherical harmonic parameters (l=1, m=-1), (l=2, m=-1), and (l=3, m=-1) are shown. Figure 10 The plasma diagnosis results of the magnetic field with the three spherical harmonic functions mixed according to the weights of 0.1, 0.2, and 0.7 are also shown.

[0134] Specifically, Figure 10 The first row in the figure shows the actual target image formed by the second proton beam formed after the first proton beam passes through the region to be diagnosed with the above-mentioned self-generated electromagnetic field; Figure 10 The second row in the figure shows the theoretical deflection potential determined based on the analytical expression of the different self-generated electromagnetic fields; Figure 10 The third row in the figure shows the deflection potential of the self-generated electromagnetic field obtained by the plasma diagnosis method of the application based on the target image and the proton source image; Figure 10 The fourth row in the figure shows the inversion target image obtained by calculating the trajectory of the second proton beam according to the particle simulation based on the deflection potential of the third row; Figure 10 The fifth row in the figure shows the one-dimensional distribution of the preset position in the target image, wherein the red dashed line shows the one-dimensional distribution of the blue dashed line position in the actual target image corresponding to the first row, and the blue dashed line shows the one-dimensional distribution of the blue dashed line position in the inversion target image corresponding to the fourth row.

[0135] As Figure 10 shown in the third row, the deflection potential of the self-generated electromagnetic field obtained by the plasma diagnosis method of the application matches the distribution of the corresponding theoretical deflection potential shown in the second row. The inversion target image shown in the fourth row matches the distribution of the corresponding actual target image shown in the first row. In the one-dimensional distribution shown in the fifth row, the one-dimensional distribution of the same position of the actual target image and the inversion target image matches.

[0136] It should be noted that Figure 10The fourth row in the figure shows that based on the deflection potential of the third row, the inversion target image of the second proton beam obtained by calculating the trajectory of the second proton beam according to the particle simulation is based on the proton source image, in combination with the deflection potential, the trajectory of the second proton beam is determined according to the proton motion equation, and then the inversion target image of the receiving surface is determined, wherein the proton motion equation is:

[0137]

[0138] wherein m is the mass of the proton, q is the charge of the proton, is the velocity of the proton, and B is the magnetic field strength.

[0139] In combination with reference Figure 11 , a schematic diagram of the results obtained by the plasma diagnosis method in some embodiments of the present application is shown.

[0140] As shown in Figure 11 , the horizontal axis represents the position, and the unit is micrometers (μm), and the vertical axis represents the transverse integral average magnetic field strength, and the unit is megagauss-micrometers (MG·μm). The data line represents the one-dimensional distribution of the target image formed by the second proton beam on the x-axis based on different magnetic fields.

[0141] As shown in some embodiments of Figure 11 , the proton source is a single-energy proton source of 4.3 megaelectron volts (MeV). The distance r i between the proton source and the region to be diagnosed is 1.2 millimeters (mm). The distance r s between the region to be diagnosed and the receiving surface is 2 centimeters (cm). The proton source flux probability density distribution P i is uniformly distributed, and is gridded using a 256x256 grid; the resolution of the target flux probability density distribution Q j is a 256x256 grid.

[0142] As shown in some embodiments of Figure 11 , the magnetic field in the region to be diagnosed is a Gaussian magnetic field, and the analytical expression of the magnetic field B(z) is: wherein B0 is the characteristic strength or amplitude of the magnetic field, B0=80 MG, σ is the radial characteristic scale parameter, and z is the radial coordinate, i.e., the position coordinate from the center.

[0143] Figure 11The red solid line in the figure shows the one-dimensional distribution of the target image formed by the second proton beam projected on the x-axis based on the magnetic field analytical expression; the green dashed line, the blue dot-dashed line and the pink dot-dashed line all show the one-dimensional distribution of the target image formed by the second proton beam projected on the x-axis based on the magnetic field result obtained by solving the plasma diagnostic method of the application, wherein the green dashed line shows the one-dimensional distribution of the magnetic field result based on the regularization factor λ of 0.001, the blue dot-dashed line shows the one-dimensional distribution of the magnetic field result based on the regularization factor λ of 0.005, and the pink dot-dashed line shows the one-dimensional distribution of the magnetic field result based on the regularization factor λ of 0.01.

[0144] As shown in Figure 11 , the setting of the regularization factor λ can control the smoothness of the result to maintain numerical stability under strong magnetic fields and noisy data: the smaller the regularization factor λ, the smoother the result; the larger the regularization factor λ, the rougher the result. Moreover, the statistical error between the one-dimensional distribution of the magnetic field result based on the regularization factor λ of 0.01 and the one-dimensional distribution obtained based on the magnetic field analytical expression is 0.069202; the statistical error between the one-dimensional distribution of the magnetic field result based on the regularization factor λ of 0.001 and the one-dimensional distribution obtained based on the magnetic field analytical expression is 0.028758; it can be seen that the smaller the regularization factor λ, the closer the magnetic field result obtained by solving the plasma diagnostic method of the application is to the magnetic field analytical expression.

[0145] Correspondingly, the application also provides a plasma diagnostic system.

[0146] Reference Figure 2 is shown, which shows the structural schematic diagram of the plasma diagnostic system in some embodiments of the application.

[0147] The plasma diagnostic system comprises:

[0148] a proton source 111 configured to generate a first proton beam 112; the first proton beam 112 passes through a region to be diagnosed 113 to form a second proton beam 114; a receiving surface 115 configured to receive the second proton beam 114 to obtain a target image; a processor 130 configured to construct an optimal transport problem from the proton source image to the target image based on the proton source image and the target image, and solve the optimal transport problem to obtain an optimal transport matrix from the proton source image to the target image; and a diagnostic device 140 configured to diagnose the plasma in the region to be diagnosed 113 based on the optimal transport matrix.

[0149] In some embodiments of the present application, the plasma diagnostic system is configured to perform the steps of the plasma diagnostic method of the present application. The specific technical solutions of the plasma diagnostic system can refer to the embodiments of the plasma diagnostic method described above.

[0150] The proton source 111 is configured to generate a first proton beam 112.

[0151] In some embodiments, the proton source 111 can include one of a planar target proton source and a gas target proton source. The planar target proton source refers to a proton source in which a short-pulse laser bombards a planar target to generate a proton beam; the gas target proton source refers to a proton source in which multiple beams of laser are focused to a gas target filled with D3He to generate a proton beam.

[0152] In some embodiments, the proton source 111 is a single-energy proton source, and the protons in the first proton beam 112 have the same energy. Using a single-energy proton source to generate the first proton beam 112 can effectively improve the clarity of the obtained target image, thereby effectively improving the reliability and accuracy of the plasma diagnostic result.

[0153] As shown in some embodiments, Figure 2 As shown in some embodiments, the proton source 111 generates protons to form the first proton beam 112, and the proton source 111 has a proton source image.

[0154] The region to be diagnosed has a plasma. In the process of passing through the region to be diagnosed, the first proton beam is deflected by the self-generated electromagnetic field of the plasma in the region to be diagnosed, and the proton beam obtains a deflection speed when it leaves the region to be diagnosed, so as to modulate the flux density of the proton beam, thereby changing the flux density of the proton beam emitted from the region to be diagnosed.

[0155] As shown in some embodiments, Figure 2 As shown in some embodiments, the region to be diagnosed 113 has a first distance r1 from the proton source 111. The region to be diagnosed 113 has a first size d and a second size l, where the first size d is the size of the region to be diagnosed 113 along the direction of incidence of the first proton beam 112; the second size l is the size of the region to be diagnosed 113 in the plane of the direction of incidence of the first proton beam 112. The region to be diagnosed 113 has a plasma, and the plasma in the region to be diagnosed 113 forms a self-generated electromagnetic field. The self-generated electromagnetic field interacts with the protons passing through the region to be diagnosed 113, causing the protons to be deflected and forming a second proton beam 114 emitted from the region to be diagnosed 113.

[0156] The receiving surface 115 is configured to receive the second proton beam 114 to obtain a target image.

[0157] Specifically, the plasma diagnostic system includes a detector having the receiving surface. In some example embodiments, the detector may be an RCF (Radiochromic Film Stack) or a CR-39 detector.

[0158] like Figure 2 In some of the embodiments shown, a second proton beam 114 emitted from the region to be diagnosed 113 is incident on the receiving surface 115 of the detector 120 to obtain a target image.

[0159] The processor 130 constructs an optimal transport problem, transforming the proton deflection information in proton photography into an optimal transport problem in the sense of probability distribution. It transforms the one-to-one mapping relationship between the proton source image and the target image during proton beam transmission into a many-to-many mapping relationship for optimal transport. This avoids singularity in the unit image area caused by proton aggregation, eliminates errors in solving the Monge-Abe equation, and overcomes the convergence problem caused by equation singularity. In particular, it can effectively ensure the accuracy and reliability of the results under strong electromagnetic field conditions.

[0160] like Figure 12 As shown, in some embodiments of the present invention, the processor 130 constructs a Kantorovich optimal transport problem from the proton source image to the target image based on the proton source image and the target image. The Kantorovich optimal transport problem is about how to transport one probability distribution to another with minimum cost. By introducing a relaxation method of "transport plan," the Kantorovich optimal transport problem is constructed into a solvable linear programming problem. The processor 130 constructs the Kantorovich optimal transport problem from the proton source image to the target image based on the proton source image and the target image, transforming the solution of the one-to-one mapping problem from the proton source image to the target image into the solution of a many-to-many mapping problem. This avoids the singularity of the unit image area caused by particle aggregation and overcomes the defects of large error and difficulty in convergence of the Monge-Abe equation under strong electromagnetic fields.

[0161] In some embodiments of the present invention, the processor 130 includes a construction module 130a, which is configured to determine the Wasserstein distance based on the proton source image and the target image, and to obtain the optimal transport matrix from the proton source image to the target image based on the Wasserstein distance. In the Kontrowevich optimal transport problem, the Wasserstein distance is used to measure the difference in probability distributions. Specifically, the processor 130 obtains the Wasserstein distance based on a cost function, which is related to minimizing cost.

[0162] In some embodiments, the constructing module 130a comprises: a discrete element 131a configured to determine a proton source flux probability density distribution based on the proton source image, and configured to determine a target flux probability density distribution based on the target image; a cost element 132a configured to determine a cost matrix based on the proton source flux probability density distribution and the target flux probability density distribution; and a distance element 133a configured to determine the Wasserstein distance based on the cost matrix.

[0163] In Kantorovich's optimal transport problem, the concept of "transport plan" is introduced, which describes the transport amount from a position in the proton source image to a position in the target image through a joint probability distribution. The problem to be solved is a transport problem from one probability distribution to another probability distribution. Therefore, the discrete element 131a is configured to convert the image into a probability distribution.

[0164] In some embodiments, the discrete element 131a grids and normalizes the image to determine the flux probability density distribution corresponding to the image, wherein the image is one of the proton source image and the target image.

[0165] Specifically, the discrete element 131a grids and normalizes the image, thereby preparing for constructing the discretized or matrix optimal transport problem. The discrete element 131a determines the number of grid points based on the fine structure appearing in the image.

[0166] In some embodiments, the discrete element 131a grids different images according to different grids. The different grids can be different in grid shape or different in the number of grid points. Figure 3 In some embodiments, the discrete element 131a grids and normalizes the proton source image 101 based on a regular two-dimensional grid; and the discrete element 131a grids and normalizes the target image 102 based on an irregular two-dimensional grid.

[0167] In the step of gridding the proton source image and the step of gridding the target image, the number of grid points is different.

[0168] In some embodiments, the discrete element 131a determines the proton source flux probability density distribution P based on the proton source image, wherein P = {p i : P i = {p i}, wherein i is a positive integer, i ≤ N, and N is the number of grid points of the proton source image; and the discrete element 131a determines the target flux probability density distribution Q based on the target image, wherein Q = {q j : Q j= {q j}, where j is a positive integer, j≤M, and M is the number of grid points of the proton source image.

[0169] The cost element 132a determines a cost matrix C i based on the proton source flux probability density distribution P j and the target flux probability density distribution Q ij . The cost matrix C ij is used to describe the cost of transporting a unit mass from each position in the proton source image to each position in the target image.

[0170] Specifically, the cost element 132a determines the cost matrix C ij : C i =||p j -q 2 ||. ij Each element C ij in the cost matrix represents the cost of transporting a proton from the i-th grid point in the proton source image to the j-th grid point in the target image: the smaller the element C ij , the smaller the cost of transporting a proton from the i-th grid point in the proton source image to the j-th grid point in the target image, and the higher the probability of transporting a proton from the i-th grid point in the proton source image to the j-th grid point in the target image.

[0171] The distance element 133a determines the Wasserstein distance based on the cost matrix determined by the cost element 132a. The Wasserstein distance represents the geometric transport cost of the proton source image to the target image.

[0172] Specifically, the distance element 133a determines the square of the Wasserstein distance W2 2 based on the cost matrix C ij :

[0173]

[0174] where U(P i , Q j ) is a set of mappings from the proton source flux probability density distribution P i to the target flux probability density distribution Q j that satisfy the flow flux probability distribution: . P ij is the transport probability, representing the transport probability between the i-th grid point in the proton source image and the j-th grid point in the target image in the sense of probability distribution, and the larger P ij , the higher the transport probability. represents the transport probability P ij is the transport probability between the i-th grid point in the proton source image and the j-th grid point in the target image. iThe probability density distribution of the complete transport flux to the target Q j All transport probabilities. Transport probability P ij As element P ij The transport matrix P is constructed as follows: P = [P ij ] N×M , 1≤i≤N, 1≤j≤M. R represents a real number, that is, P is a matrix of dimension d×d.

[0175] like Figure 12 As shown, in some embodiments, the processor 130 further includes a solution module 130b, which is configured to solve the optimal transport problem constructed by the construction module to obtain the optimal transport matrix from the proton source image to the target image.

[0176] In some embodiments, the optimal transport problem is the Kontorovich optimal transport problem, and the solution module 130b calculates the transport probability P that minimizes the squared Wasserstein distance. ij Specifically, the solution module 130b obtains the optimal transport probability from the proton source image to the target image based on the Wasserstein distance. The solution module 130b obtains the optimal transport probability by calculating an optimization problem that minimizes the Wasserstein distance.

[0177] In some embodiments, the solution module 130b is configured to determine the transport entropy based on the transport probability and, in conjunction with the Wasserstein distance, determine the transport functional; the solution module 130b obtains the optimal transport matrix from the proton source image to the target image based on the transport functional.

[0178] Specifically, the solution module 130b includes: an entropy construction element 131b, which determines the transport entropy based on the transport probability; a functional element 132b, which determines the transport functional based on the Wasserstein distance and the transport entropy; and an optimal element 133b, which obtains the optimal transport probability from the proton source image to the target image based on the transport functional. In the solution module 130b, the functional element 132b introduces the transport entropy through the entropy construction element 131b, constructing the solution of the optimal transport problem as a convex optimization problem, thereby avoiding the oscillations and solution difficulties caused by the optimal element 133b solving non-convex problems.

[0179] Transport entropy characterizes the probability density distribution of proton source flux P. x The probability density distribution of the complete transport flux to the target Q v The uncertainty of the transport probability distribution. Specifically, in step S161, based on the transport probability P... ijIn the step of determining the transport entropy, the determined transport entropy is .

[0180] The functional element 132b determines the transport functional based on the Wasserstein distance and the transport entropy, and adds a constraint of probability distribution uncertainty on the basis of the Wasserstein distance, so as to convert a non-convex optimization problem into a convex optimization problem, thereby avoiding oscillation and difficulty in solving the non-convex problem.

[0181] Specifically, the transport functional determined by the functional element 132b is .

[0182]

[0183] wherein λ is a regularization factor, used to control the smoothness of the solution, so as to maintain numerical stability under a strong magnetic field and noisy data.

[0184] The optimal element 133b of the solving module 130b determines the optimal transport probability based on the transport functional . Specifically, the optimal transport probability is the transport probability of the proton source image to the target image with the lowest total cost and the highest uncertainty, that is, the transport probability with the minimum Wasserstein distance and the maximum transport entropy.

[0185] In some specific embodiments, the optimal element 133b in the solving module 130b uses a Sinkhorn iterative algorithm to solve the transport functional and obtain the optimal transport probability of the proton source image to the target image . The core of the Sinkhorn iterative algorithm is a large number of vectorized matrix operations and element-by-element operations (such as exp, division, log-sum-exp, etc.), and both the vectorized matrix operations and the element-by-element operations are suitable for being converted into a parallel kernel function (kernel) of GPU and are suitable for being converted into a form suitable for GPU parallel processing, that is, the code can be rewritten or optimized so that it can be executed simultaneously on multiple threads of GPU, and the kernel function on GPU can be designed and implemented to realize efficient parallel computing. For example, the optimal element 133b in the solving module 130b includes a GPU.

[0186] The number of iterations of the Sinkhorn iterative algorithm is about , and a matrix-vector multiplication is required once per iteration, and the computational complexity of each iteration is , and the complexity of all iterations is , which is not a completely linear method.

[0187] In some embodiments of the present application, the optimal element 133b solves the transport functional to obtain the optimal transport probability from the proton source image to the target image based on an approximate kernel method using a Sinkhorn iterative algorithm . The approximate kernel method can include a fast Gaussian transform. In the approximate kernel method, the Sinkhorn algorithm can achieve a complexity of O(nlogn) or O(n) in an approximate sense, which is referred to as "near-linear", so as to realize the application in a real-time diagnosis scenario.

[0188] With reference to Figure 2 , the plasma diagnosis system further comprises a diagnostic device 140. The diagnostic device 140 diagnoses the plasma in the region to be diagnosed based on the optimal transport probability obtained by the processor 130 .

[0189] The optimal transport probability obtained by the processor 130 represents the transport probability with the lowest total cost and the highest uncertainty from the proton source image to the target image, and represents the mapping relationship from the proton source image to the target image. The target image is obtained after the proton beam generated by the proton source is deflected by the self electromagnetic field of the plasma in the region to be diagnosed, so that the mapping relationship from the proton source image to the target image obtained by the processor 130 can reflect the deflection information of the proton beam in the region to be diagnosed, and the diagnostic device 140 can determine the properties of the self electromagnetic field of the plasma in the region to be diagnosed, thereby realizing the diagnosis of the plasma in the region to be diagnosed.

[0190] Specifically, the diagnostic device 140 is configured to determine the proton deflection angle, and further determine the magnetic field of the plasma in the region to be diagnosed.

[0191] In some embodiments, the diagnostic device 140 determines the position mapping relationship from the proton source image to the target image based on the optimal transport probability . The diagnostic device 140 further determines the proton deflection angle based on the position mapping relationship, and determines the magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle.

[0192] The Kantorovich optimal transport problem solves a transport problem from one probability distribution to another probability distribution. The optimal transport probability obtained by the processor 130 reflects a many-to-many mapping from the proton source image to the target image. The diagnostic device 140 can determine a one-to-one position mapping relationship from the proton source image to the target image.

[0193] As Figure 7As shown, in some embodiments, the diagnostic tool 140 is provided with a centroid mapping form; the diagnostic tool 140 determines the position mapping relationship based on the optimal transport probability and the centroid mapping form, and the position mapping relationship is a one-to-one mapping relationship.

[0194] The centroid mapping method refers to obtaining the specific deflection position of the proton, i.e., the probabilistic centroid position, through probability averaging. Specifically, the centroid mapping method set within the diagnostic device 140... for Specifically, the position mapping relationship determined by the diagnostic tool 140 is as follows: .

[0195] It should be noted that the mapped position obtained under the position mapping relationship is not guaranteed to be located at a grid point in the target image. Therefore, after determining the position mapping relationship, the diagnostic tool 140 also determines the position mapping relationship at the grid point based on the position mapping relationship. In some exemplary embodiments, the diagnostic tool 140 determines the position mapping relationship at the grid point using third-order interpolation.

[0196] The diagnostic tool 140 also determines the proton deflection angle based on the position mapping relationship, and determines the magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle.

[0197] In some embodiments, the position mapping relationship is a position mapping relationship on grid points; the diagnostic tool 140 determines the proton deflection angle based on the position mapping relationship on grid points.

[0198] Specifically, the proton deflection angle determined by the diagnostic device 140 for: , where r s Indicates the distance between the area to be diagnosed 113 and the receiving surface 115 (e.g. Figure 2 (As shown).

[0199] The diagnostic device 140 is also based on the proton deflection angle. Determine the deflection potential Based on deflection potential Determine the magnetic field of the plasma in the region to be diagnosed. .

[0200] Specifically, the diagnostic device 140 is based on the proton deflection angle. With deflection potential Relationship: proton deflection angle The deflection potential is obtained by performing a transverse integration along the direction perpendicular to the proton beam. Integral along the direction of the proton beam .

[0201] Specifically, the diagnostic device 140 determines the magnetic field in relation to the deflection potential : , where m p is the mass of the proton, W is the energy of the proton, c is the value of the speed of light, and q is the charge of the proton, i.e. q = +e, where e is the elementary charge unit.

[0202] In summary, by using the proton source image and the target image, an optimal transport problem from the proton source image to the target image is constructed, and by solving the optimal transport problem, an optimal transport probability from the proton source image to the target image is obtained. By constructing the optimal transport problem, the deflection information of the proton in the proton photography is converted into an optimal transport problem in the sense of probability distribution, and the one-to-one mapping relationship between the proton source image and the target image in the process of the proton beam transmission is changed into a many-to-many mapping relationship of the optimal transport, thereby avoiding the singular area of the unit image caused by the proton aggregation, eliminating the error in the solution of the Monge-Ampere equation, overcoming the problem of difficult convergence caused by the singular area, and effectively ensuring the accuracy and reliability of the results, especially in the case of strong electromagnetic field.

[0203] Moreover, the step of obtaining the optimal transport probability from the proton source image to the target image includes determining a transport functional based on the Wasserstein distance and in combination with a transport entropy. By introducing the transport entropy, the solution of the optimal transport problem is constructed as a convex optimization problem, thereby avoiding the oscillation and difficult problem caused by the solution of the non-convex problem.

[0204] In addition, the step of obtaining the optimal transport probability from the proton source image to the target image includes using a Sinkhorn iterative algorithm to solve the transport functional and obtain the optimal transport probability from the proton source image to the target image. The Sinkhorn iterative algorithm has a nearly linear time complexity and supports GPU acceleration, thereby realizing the applicability to real-time diagnosis scenarios.

[0205] Although the present application is disclosed as above, the present application is not limited thereto. Any person skilled in the art, without departing from the spirit and scope of the present application, can make various changes and modifications, and therefore the protection scope of the present application should be subject to the scope defined by the claims.

Claims

1. A plasma diagnostic method, characterized in that, include: Based on the proton source, determine the proton source image; A first proton beam is generated through the proton source; The first proton beam is passed through the region to be diagnosed to form a second proton beam; Receive the second proton beam to determine the target image; Based on the proton source image and the target image, construct the optimal transport problem from the proton source image to the target image; Solve the optimal transport problem to obtain the optimal transport probability from the proton source image to the target image; Based on the optimal transport probability, the plasma in the region to be diagnosed is diagnosed.

2. The plasma diagnostic method as described in claim 1, characterized in that, The steps for constructing the optimal transport problem from the proton source image to the target image based on the proton source image and the target image include: determining the Wasserstein distance based on the proton source image and the target image; The steps of solving the optimal transport problem to obtain the optimal transport probability from the proton source image to the target image include: obtaining the optimal transport probability from the proton source image to the target image based on the Wasserstein distance.

3. The plasma diagnostic method as described in claim 2, characterized in that, The steps to determine the Wasserstein distance include: Based on the proton source image, determine the proton source flux probability density distribution; Based on the target image, determine the target flux probability density distribution; The cost matrix is ​​determined based on the proton source flux probability density distribution and the target flux probability density distribution; Based on the cost matrix, the Wasserstein distance is determined.

4. The plasma diagnostic method as described in claim 3, characterized in that, At least one of the steps of determining the proton source flux probability density distribution and determining the target flux probability density distribution includes: meshing and normalizing the image to determine the flux probability density distribution corresponding to the image, wherein the image is one of the proton source image and the target image.

5. The plasma diagnostic method as described in claim 2, characterized in that, The steps for obtaining the optimal transport probability from the proton source image to the target image include: Determine the transport entropy based on the transport probability; Based on the Wasserstein distance and the transport entropy, the transport functional is determined. Based on the transport functional, the optimal transport probability from the proton source image to the target image is obtained.

6. The plasma diagnostic method as described in claim 5, characterized in that, The step of obtaining the optimal transport probability from the proton source image to the target image includes: using the Sinkhorn iterative algorithm to solve the transport functional and obtain the optimal transport probability from the proton source image to the target image.

7. The plasma diagnostic method as described in claim 1, characterized in that, The steps for diagnosing the plasma in the region to be diagnosed include: Based on the optimal transport probability, determine the positional mapping relationship between the proton source image and the target image; Based on the aforementioned position mapping relationship, the proton deflection angle is determined; Based on the proton deflection angle, the magnetic field of the plasma in the region to be diagnosed is determined.

8. The plasma diagnostic method as described in claim 7, characterized in that, The steps for determining the positional mapping relationship between the proton source image and the target image based on the optimal transport probability include: Determine the form of the centroid mapping; Based on the optimal transport probability and the centroid mapping form, the position mapping relationship is determined, and the position mapping relationship is a one-to-one mapping relationship.

9. The plasma diagnostic method as described in claim 8, characterized in that, The step of determining the positional mapping relationship from the proton source image to the target image based on the optimal transport probability further includes: After determining the position mapping relationship, the position mapping relationship on the grid points is determined based on the position mapping relationship; The steps to determine the proton deflection angle include: determining the proton deflection angle based on the position mapping relationship on the grid points.

10. The plasma diagnostic method as described in claim 9, characterized in that, The steps to determine the positional mapping relationship on the grid points include: determining the positional mapping relationship on the grid points through third-order interpolation.

11. A plasma diagnostic system, characterized in that, include: A proton source, the proton source being configured to generate a first proton beam; The first proton beam passes through the region to be diagnosed, forming a second proton beam; A receiving surface configured to receive the second proton beam to obtain a target image; A processor configured to construct an optimal transport problem from the proton source image to the target image based on the proton source image and the target image, and solve the optimal transport problem to obtain the optimal transport probability from the proton source image to the target image; A diagnostic tool configured to diagnose the plasma in the region to be diagnosed based on the optimal transport probability.

12. The plasma diagnostic system as described in claim 11, characterized in that, The processor includes a construction module configured to determine the Wasserstein distance based on the proton source image and the target image, and to obtain the optimal transport probability from the proton source image to the target image based on the Wasserstein distance.

13. The plasma diagnostic system as described in claim 12, characterized in that, The processor further includes a solution module configured to determine the transport entropy based on the transport probability and, in conjunction with the Wasserstein distance, determine the transport functional. The solution module is also configured to obtain the optimal transport probability from the proton source image to the target image based on the transport functional.

14. The plasma diagnostic system as described in claim 13, characterized in that, The solution module uses the Sinkhorn iterative algorithm to solve the transport functional and obtain the optimal transport probability from the proton source image to the target image.

15. The plasma diagnostic system as described in claim 14, characterized in that, The solution module includes a GPU.

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