Plasma diagnostic methods and systems

Abstract

A plasma diagnostic method and system are disclosed. The plasma diagnostic method includes: determining a proton source image based on a proton source; generating a first proton beam through the proton source; passing the first proton beam through a region to be diagnosed to form a second proton beam; receiving the second proton beam and determining a target image; constructing an optimal transport problem from the proton source image to the target image based on the proton source image and the target image; solving the optimal transport problem to obtain the optimal transport probability from the proton source image to the target image; and diagnosing the plasma in the region to be diagnosed based on the optimal transport probability. This invention's plasma diagnostic method has higher computational efficiency and overcomes the convergence difficulty caused by singularity in the computational equations under strong magnetic fields.

Description

Technical Field

[0001] This invention relates to the field of plasma, and in particular to a plasma diagnostic method and system. Background Technology

[0002] Proton radiographs are a diagnostic technique that uses a high-energy proton beam as a "probe" to image the internal structure or electromagnetic field distribution of matter. They are widely used in high-energy-density physics, inertial confinement fusion (ICF), and other fields. Proton radiographs are characterized by strong penetration, high sensitivity, beam splitting capability, and high spatial resolution, enabling them to effectively visualize the self-generated electromagnetic field of plasma and obtain its information.

[0003] The proton backlighting process involves generating a high-energy proton beam and passing it through a region to be diagnosed, which contains plasma. The proton beam, passing through the region, is placed within the self-generated electromagnetic field of the plasma. Due to the Lorentz force, the proton beam is deflected as it passes through the region. By receiving the deflected proton beam and analyzing its flux distribution, information about the self-generated electromagnetic field of the plasma in the region to be diagnosed can be deduced, thus enabling the diagnosis of the self-generated electromagnetic field of the plasma in the region to be diagnosed.

[0004] However, existing plasma diagnostic methods are prone to problems such as difficulty in solving problems and large errors. Summary of the Invention

[0005] The problem addressed by this invention is how to improve the diagnostic accuracy of the electromagnetic field of plasma itself and reduce the diagnostic difficulty.

[0006] To address the above problems, the present invention provides a plasma diagnostic method, comprising:

[0007] Based on a proton source, a proton source image is determined; 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; 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 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.

[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 includes: determining the 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 includes: 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 includes: determining the proton source flux probability density distribution based on the proton source image; determining the 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; and determining the Wasserstein distance based on the cost matrix.

[0010] Optionally, 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.

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

[0013] Optionally, the step of diagnosing the plasma in the region to be diagnosed includes: determining the positional mapping relationship between the proton source image and the target image based on the optimal transport probability; determining the proton deflection angle based on the positional mapping relationship; and determining the magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle.

[0014] Optionally, the step of determining the positional mapping relationship from the proton source image to the target image based on the optimal transport probability includes: determining the centroid mapping form; and 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 correspondence mapping relationship.

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

[0016] Optionally, the steps for determining the positional mapping relationship on the grid points include: determining the positional mapping relationship on the grid points by third-order interpolation.

[0017] Accordingly, the present invention also provides a plasma diagnostic system, comprising:

[0018] A proton source configured to generate a first proton beam; the first proton beam passes through the 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 the 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 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.

[0020] Optionally, 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 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 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.

[0022] Optionally, the solver module may include a GPU.

[0023] Compared with the prior art, the technical solution of the present invention has the following advantages:

[0024] In this invention, an optimal transport problem from the proton source image to the target image is constructed using the proton source image and the target image. The optimal transport probability from the proton source image to the target image is obtained by solving this optimal transport problem. By constructing the optimal transport problem, the proton deflection information in proton photography is transformed into an optimal transport problem in the sense of probability distribution. The one-to-one mapping relationship between the proton source image and the target image during proton beam transmission is transformed 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 area singularity. Especially under strong electromagnetic field conditions, it effectively ensures the accuracy and reliability of the results.

[0025] In an optional embodiment of the present invention, the step of obtaining the optimal transport probability from the proton source image to the target image includes: determining the transport functional based on the Wasserstein distance and combined with the transport entropy. By introducing the transport entropy, the solution to the optimal transport problem is constructed as a convex optimization problem, thereby avoiding the oscillations and solution difficulties caused by solving non-convex problems.

[0026] In an optional embodiment of the present invention, 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 to obtain the optimal transport probability from the proton source image to the target image. The Sinkhorn iterative algorithm has a near-linear time complexity and supports GPU acceleration, thus enabling its applicability to real-time diagnostic scenarios. Attached Figure Description

[0027] Figure 1 This is a schematic flowchart of a plasma diagnostic method in some embodiments of the present invention.

[0028] Figure 2 This is a schematic diagram of the system used in the plasma diagnostic method in some embodiments of the present invention.

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

[0030] Figure 4 This is a flowchart illustrating the step of determining the Wasserstein distance in the plasma diagnostic method of some embodiments of the present invention.

[0031] Figure 5 This is a flowchart illustrating the steps of obtaining the optimal transport probability from the proton source image to the target image in the plasma diagnostic method of some embodiments of the present invention.

[0032] Figure 6This is a schematic flowchart illustrating the steps of diagnosing plasma in the region to be diagnosed in some embodiments of the plasma diagnostic method of the present invention.

[0033] Figure 7 This is a flowchart illustrating the steps of determining the positional mapping relationship between the proton source image and the target image based on the optimal transport probability in the plasma diagnostic method of some embodiments of the present invention.

[0034] Figure 8 This is a schematic diagram of the results obtained by the plasma diagnostic method in some embodiments of the present invention.

[0035] Figure 9 This is a schematic diagram of the results obtained by the plasma diagnostic method in some embodiments of the present invention.

[0036] Figure 10 This is a schematic diagram of the results obtained by the plasma diagnostic method in some embodiments of the present invention.

[0037] Figure 11 This is a schematic diagram of the results obtained by the plasma diagnostic method in some embodiments of the present invention.

[0038] Figure 12 This is a functional block diagram of the processor in the plasma diagnostic system in some embodiments of the present invention. Detailed Implementation

[0039] As can be seen from the background technology, existing plasma diagnostic methods are prone to problems such as difficulty in solving problems and large errors.

[0040] Existing methods for inferring information about the self-generated electromagnetic field of plasma through proton backlighting are mainly divided into two types: forward calculation and direct inversion.

[0041] The forward calculation method primarily uses a priori assumptions about the electromagnetic field and employs methods such as Monte Carlo or particle tracking to simulate the distribution of a proton beam after deflection in the autogenous electromagnetic field of the plasma in the region to be diagnosed. After comparing the calculation results with experimental images, the assumed electromagnetic field is repeatedly adjusted to ultimately obtain information about the autogenous electromagnetic field of the plasma in the region to be diagnosed. However, the forward calculation method heavily relies on the initial electromagnetic field assumptions, has high computational costs, and struggles to handle strong magnetic fields that can cause nonlinear deflection.

[0042] Another method for retrieving information about the spontaneous electromagnetic field of plasma is the direct inversion method. The direct inversion method establishes a mathematical relationship between the proton beam and the electromagnetic field, and directly retrieves information about the spontaneous electromagnetic field of the plasma in the region to be diagnosed through which the proton beam passes from the imaging image.

[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 Monge-Ampère equation for the proton beam deflection angle is established using the conservation of proton beam particle number. After obtaining the deflection angle, the magnetic field strength in the integral average sense of the proton's path is calculated.

[0044] The Monge-Ampère equation, based on the weak-field approximation, only fits linear regions with low magnetic field strength. As the electromagnetic field strength increases, protons tend to cluster. This clustering causes the Monge-Ampère equation to approach a singularity, making it difficult to solve and increasing errors. Specifically, in strong magnetic fields, if multiple regions in the proton source image correspond to the same or adjacent regions in the target image, the Monge-Ampère equation for the proton beam deflection angle approaches a singularity (the Jacobian determinant of the conservation transformation approaches zero), making it unsolvable or resulting in a very large error.

[0045] It is evident that the direct inversion method for solving the Monge-Abe equations in the case of strong electromagnetic fields can lead to problems such as large errors, low computational efficiency, and even difficulty in convergence, as well as serious distortion of results.

[0046] To address the technical problems, this invention provides a plasma diagnostic method. By constructing an optimal transport problem, the deflection information of protons in proton radiography is transformed into an optimal transport problem in the sense of probability distribution. The one-to-one mapping relationship between the proton source image and the target image during proton beam transmission is transformed into a many-to-many mapping relationship of optimal transport. This avoids the singularity of the unit image area caused by proton aggregation, eliminates the error in solving the Monge-Abe equation, and overcomes the convergence problem caused by equation singularity. In particular, under strong electromagnetic field conditions, it can effectively ensure the accuracy and reliability of the results.

[0047] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0048] refer to Figure 1 The diagram shows a schematic flowchart of a plasma diagnostic method in some embodiments of the present invention.

[0049] Plasma diagnostic methods include:

[0050] Step S110: Determine the proton source image based on the proton source; Step S120: Generate a first proton beam through the proton source; Step S130: Pass the first proton beam through the region to be diagnosed to form a second proton beam; Step S140: Receive the second proton beam and determine the target image; Step S150: Construct the optimal transport problem from the proton source image to the target image based on the proton source image and the target image; Step S160: Solve the optimal transport problem to obtain the optimal transport probability from the proton source image to the target image; Step S170: Diagnose the plasma in the region to be diagnosed based on the optimal transport probability.

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

[0052] Reference Figure 2 The diagram shows a schematic representation of the system used in the plasma diagnostic method in some embodiments of the present invention.

[0053] The plasma diagnostic method includes: firstly, performing step S110 to determine a proton source image based on the proton source.

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

[0055] like Figure 2 In some embodiments shown, step S110, determining the proton source image based on the proton source 111, includes: determining the energy distribution, divergence angle, and distance r between the proton source 111 and the region to be diagnosed 113 based on the proton source 111. i Based on the energy distribution and divergence angle of the proton beam generated by proton source 111, and the distance r between proton source 111 and the region to be diagnosed 113, i Calculate and plot the image of the proton source.

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

[0057] Specifically, the plasma diagnostic method also includes: after determining the proton source, performing step S120 to generate a first proton beam through the proton source.

[0058] In some embodiments of the present invention, the proton source is a single-energy proton source, and all protons in the first proton beam have equal energies. Using a single-energy proton source to generate the first proton beam can effectively improve the clarity of the obtained target image, thereby effectively improving the reliability and accuracy of plasma diagnostic results.

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

[0060] The plasma diagnostic method further includes: after generating the first proton beam, step S130, passing the first proton beam through the region to be diagnosed to form a second proton beam.

[0061] Specifically, the region to be diagnosed contains plasma. As the first proton beam passes through the region to be diagnosed, it is deflected by the self-generated electromagnetic field of the plasma in the region. When the proton beam leaves the region to be diagnosed, it will acquire a deflection velocity 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] like Figure 2 In some embodiments shown, a first distance r1 exists between the region to be diagnosed 113 and the proton source 111. The region to be diagnosed 113 has a first dimension d and a second dimension l, where the first dimension d is the size of the region to be diagnosed 113 along the incident direction of the first proton beam 112; and the second dimension l is the size of the region to be diagnosed 113 in the plane along the incident direction of the first proton beam 112. The region to be diagnosed 113 contains plasma, which generates a self-generated electromagnetic field. This self-generated electromagnetic field interacts with protons passing through the region to be diagnosed 113, causing the proton beam to deflect and forming a second proton beam 114 emitted from the region to be diagnosed 113.

[0063] The plasma diagnostic method further includes: after forming the second proton beam, performing step S140 to receive the second proton beam and determine the target image.

[0064] The target image is the distribution of proton flux on the receiving surface, specifically the proton distribution per unit time and per unit area on that surface. Specifically, the steps for receiving the second proton beam and determining the target image include: receiving the second proton beam emitted from the region to be diagnosed and determining the target image. For example, the steps for receiving the second proton beam emitted from the region to be diagnosed and determining the target image include: receiving the second proton beam emitted from the region to be diagnosed through a detector and determining the target image. The detector can be an RCF (Radiochromic Film Stack) detector or a CR-39 detector.

[0065] 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 to obtain a target image.

[0066] Continue to refer to Figure 1 The plasma diagnostic method also includes: after determining the proton source image and the target image, performing step S150 to construct the 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 using proton source and target images, the proton beam deflection information is transformed into an optimal transport problem in the sense of probability distribution. The one-to-one mapping relationship between the proton source and target images during ion beam transmission is transformed into a many-to-many mapping relationship for optimal transport. This avoids the singularity of unit image area caused by proton aggregation, eliminates errors in solving the Monge-Abe equation, and overcomes the convergence problem caused by area singularity. In particular, under strong electromagnetic field conditions, it can effectively ensure the accuracy and reliability of the results.

[0068] In some embodiments of the present invention, the step S150, which involves constructing an optimal transport problem from the proton source image to the target image based on the proton source image and the target image, includes: 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 transport problem is about transporting one probability distribution to another at the lowest cost. By introducing a relaxation method involving a "transport plan," the Kantorovich transport problem is constructed into a solvable linear programming problem. Based on proton source and target images, a Kantorovich transport problem from the proton source image to the target image is developed. This transforms the solution of the one-to-one mapping problem from the proton source image to the target image into a many-to-many mapping problem, thus avoiding the singularity of unit image area caused by particle aggregation and overcoming the large error and poor convergence of the Monge-Abe equation under strong electromagnetic fields.

[0070] like Figure 3 In some of the embodiments shown, the Kantorovich optimal transport problem from proton source image 101 to target image 102 represents a many-to-many mapping transport problem from proton source image 101 to target image 102. That is, a proton can be transported from one location in proton source image 101 to different locations in target image 102 with different probabilities; a proton in one location in target image 102 can be transported from multiple locations in proton source image 101 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] Among them, U(P) i Q j ) is from the probability density distribution P of the proton source flux. i To the target flux probability density distribution Q j The set consisting of mappings that satisfy the probability distribution of flux: P ij It is the transport probability, representing the transport probability between grid point i in the proton source image and grid point j in the target image under the meaning of probability distribution, P ij The larger the size, the greater the chance of successful transportation. P represents the transport probability. ij To determine the probability density distribution P of the proton source flux i The 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.

[0086] Continue to refer to Figure 1 The plasma diagnostic method also includes: after constructing the optimal transport problem, executing step S160 to solve the optimal transport problem and obtain the optimal transport probability from the proton source image to the target image.

[0087] In some embodiments of the present invention, the optimal transport problem is the Kontorovich optimal transport problem; therefore, solving the optimal transport problem is equivalent to calculating the transport probability P that minimizes the squared Wasserstein distance. ij .

[0088] Specifically, the steps for constructing the optimal transport problem include: determining the Wasserstein distance; and 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.

[0089] The step of obtaining the optimal transport probability from the proton source image to the target image based on the Wasserstein distance is to calculate the optimization problem of minimizing the Wasserstein distance to obtain the optimal transport probability.

[0090] like Figure 5In some embodiments shown, the steps for obtaining the optimal transport probability from the proton source image to the target image include: step S161, determining the transport entropy based on the transport probability; step S162, determining the transport functional based on the Wasserstein distance and the transport entropy; and step S163, 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 to the optimal transport problem is constructed as a convex optimization problem, thereby avoiding the oscillations and solution difficulties caused by solving non-convex problems.

[0091] 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... ij In the step of determining the transport entropy, the determined transport entropy is: .

[0092] The transport functional is determined based on the Wasserstein distance and transport entropy. On the basis of the Wasserstein distance, the constraint of probability distribution uncertainty is added, which can transform non-convex optimization problems into convex optimization problems, thereby avoiding the oscillation and solution difficulties caused by solving non-convex problems.

[0093] Specifically, in step S162, which determines the transport functional based on the Wasserstein distance and transport entropy, the transport functional... for:

[0094]

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

[0096] Continue to refer to Figure 5 After determining the transport functional, step S163 is executed to determine the optimal transport probability based on the transport functional. Specifically, the optimal transport probability This is the transport probability from the proton source image to the target image that has the lowest total cost and the highest uncertainty, i.e., the transport probability when the Wasserstein distance is minimized and the transport entropy is maximized.

[0097] In some specific embodiments, 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. The core of the Sinkhorn iterative algorithm consists of a large number of vectorized matrix operations and element-wise operations (such as exp, division, log-sum-exp, etc.). Both vectorized matrix operations and element-wise operations are suitable for conversion into GPU parallel kernel functions, and can be transformed into a form suitable for GPU parallel processing. That is, the code can be rewritten or optimized to execute simultaneously on multiple threads of the GPU. Kernel functions on the GPU can be designed and implemented to achieve efficient parallel computing.

[0098] The Sinkhorn iterative algorithm requires approximately [number] iterations. Each iteration requires one matrix-vector multiplication, and the computational complexity of each iteration is O(n log n). The complexity of all iterative calculations is O(n log n). It is not a completely linear method.

[0099] In some embodiments of the present invention, 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 this step, based on the approximate kernel method, the Sinkhorn iterative algorithm is used to solve the transport functional and obtain the optimal transport probability from the proton source image to the target image. The approximate kernel method can include the Fast Gaussian Transform. Within the approximate kernel method, the Sinkhorn algorithm can achieve a computational complexity of O(nlogn) or O(n) in an approximate sense; this computational complexity is called "near-linear," thus enabling its applicability to real-time diagnostic scenarios.

[0100] Continue to refer to Figure 1 To obtain the optimal transport probability Subsequently, the plasma diagnostic method further includes: step S170, based on the optimal transport probability To diagnose the plasma in the area to be diagnosed.

[0101] Optimal transport probability The transport probability, representing the lowest total cost and highest uncertainty in the process of mapping the proton source pattern to the target image, embodies the mapping relationship between the proton source pattern and the target image. The target image is obtained by deflecting the proton beam generated by the proton source through the electromagnetic field of the plasma in the region to be diagnosed. Therefore, the mapping relationship between the proton source pattern and the target image reflects the deflection information of the proton beam in the region to be diagnosed and the properties of the plasma's electromagnetic field, thus enabling the diagnosis of 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 horizontal position in micrometers (μm), and the vertical axis represents the integrated average magnetic field strength in megagauss-micrometers (MG·μm). The results show that, compared to the magnetic field results obtained by solving the Monge-Ampère equation (represented by the blue data line), the magnetic field results obtained by the plasma diagnostic method of this invention (represented by the red data line) are closer to and more consistent with the results obtained by the analytical magnetic field equation (represented by the black dashed line).

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

[0122] Reference Figure 9 The diagram illustrates the results obtained by the plasma diagnostic method in some embodiments of the present invention.

[0123] Figure 9 As shown, the horizontal axis represents the horizontal position, with units of micrometers (μm), and the vertical axis represents the integrated average magnetic field strength, with units of 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.

[0124] like Figure 9 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.

[0125] like Figure 9 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 strong nonlinear magnetic field with a radial characteristic scale parameter σ of 30 micrometers (μm) and a magnetic field strength of 310 megagauss (MG).

[0126] 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.

[0127] like Figure 9 As shown, compared with the magnetic field results obtained by solving the Monge-Ampère equation (represented by the blue data line), the magnetic field results obtained by the plasma diagnostic method of this invention (represented by the red data line) are still closer to and more consistent with the results obtained by the analytical equation of the magnetic field (represented by the black dashed line).

[0128] In addition, such as Figure 9 As shown, the magnetic field results obtained by solving the Monge-Ampère equation (represented by the blue data line) deviate significantly from the results obtained by the analytical magnetic field equation (represented by the black dashed line) in the horizontal range between 0 micrometers (μm) and 200 micrometers (μm). Figure 9 The blue data line shown in the solid green circle represents the magnetic field result obtained by solving the Monge-Ampère equation. There are false bumps between 0 micrometers (μm) and 200 micrometers (μm). In other words, when the magnetic field in the region to be diagnosed is a strong nonlinear magnetic field of up to 310 megagauss (MG), the proton beam will converge, which will cause the solution of the Monge-Ampère equation to be singular and non-convergent.

[0129] Reference Figure 10 The diagram illustrates the results obtained by the plasma diagnostic method in some embodiments of the present invention.

[0130] like Figure 10 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.

[0131] The magnetic field in the region to be diagnosed is composed of magnetic fields in the form of spherical harmonic functions: Where B0 is the reference magnetic field strength, (l, m) is the spherical harmonic parameter, and A lm P is the expansion coefficient. l m (sinθ) is the exponential spherical harmonic function, where θ is the polar angle. It is the azimuth angle. This is a circular function term. Specifically, the magnetic field reference strength B0 value ranges from 13 megaguas (MG) to 342 megaguas (MG), and the proton imaging results on the receiving screen range from 100 micrometers (μm) to 1 millimeter (mm).

[0132] 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 0.005; during the solution of the transport functional using the Sinkhorn iterative algorithm, the convergence error is 0.01, and the maximum number of iterations is 150.

[0133] Figure 10 The plasma diagnostic results for magnetic fields with spherical harmonic parameters of (l=1, m=-1), (l=2, m=-1), and (l=3, m=-1) are shown. Figure 10 The plasma diagnostic results of the magnetic field based on the mixing of three spherical harmonic functions with weights of 0.1, 0.2, and 0.7 are also shown.

[0134] Specifically, Figure 10 The first row shows the actual target image formed by the second proton beam, which is formed after the first proton beam passes through the region to be diagnosed having the aforementioned self-generated electromagnetic field; Figure 10 The second line shows the theoretical deflection potential determined by analytical expressions based on different self-generated electromagnetic fields; Figure 10 The third line shows the deflection potential of the self-generated electromagnetic field obtained by the plasma diagnostic method of the present invention based on the target image and the proton source image; Figure 10 The fourth row shows the inverted target image obtained by calculating the trajectory of the second proton beam based on the deflection potential in the third row using particle simulation. Figure 10 The fifth row shows the one-dimensional distribution of preset positions in the target image, where the red dashed line shows the one-dimensional distribution of the blue dashed line positions 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 positions in the inverted target image corresponding to the fourth row.

[0135] like Figure 10 As shown, the deflection potential of the self-generated electromagnetic field obtained by the plasma diagnostic method of the present invention, shown in the third row, matches the distribution of the corresponding theoretical deflection potential shown in the second row. The inverted 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 at the same position in the actual target image and the inverted target image matches.

[0136] It should be noted that, Figure 10The fourth row shows the inversion target image obtained based on the deflection potential in the third row. The trajectory of the second proton beam, calculated using particle simulation, is based on the proton source image. Combined with the deflection potential and the proton motion equations, the trajectory of the second proton beam is determined, thus determining the inversion target image of the receiving surface. The proton motion equations are:

[0137]

[0138] Where m is the mass of the proton and q is the charge of the proton. Let B be the velocity of the proton and B be the magnetic field strength.

[0139] Reference Figure 11 The diagram illustrates the results obtained by the plasma diagnostic method in some embodiments of the present invention.

[0140] like Figure 11 As shown, the horizontal axis represents position in micrometers (μm), and the vertical axis represents the transversely integrated average magnetic field strength in megagauss-micrometers (MG-μm). The data lines represent the one-dimensional distribution of the target image formed by the second proton beam, projected onto the x-axis based on different magnetic fields.

[0141] like Figure 11 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.

[0142] like Figure 11 In some of the embodiments shown, the magnetic field in the region to be diagnosed is a Gaussian magnetic field, and the analytical expression for the magnetic field B(z) is: Where B0 is the characteristic intensity 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 relative to the center.

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

[0144] like Figure 11 As shown, the setting of the regularization factor λ can control the smoothness of the results to maintain numerical stability under strong magnetic fields and noisy data: the smaller the regularization factor λ, the smoother the results; the larger the regularization factor λ, the coarser the results. Moreover, the statistical error between the one-dimensional distribution of the magnetic field results 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 results 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 results obtained by solving the plasma diagnostic method of this invention are to the magnetic field analytical expression.

[0145] Accordingly, the present invention also provides a plasma diagnostic system.

[0146] refer to Figure 2 The diagram shows a schematic representation of the plasma diagnostic system in some embodiments of the present invention.

[0147] The plasma diagnostic system includes:

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

[0149] In some embodiments of the present invention, the plasma diagnostic system is used to perform the steps of the plasma diagnostic method of the present invention. Specific technical solutions for the plasma diagnostic system can be found in the foregoing embodiments of the plasma diagnostic method.

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

[0151] In some embodiments, the proton source 111 may include one of a planar target proton source and a gas target proton source. A planar target proton source refers to a proton source in which a short-pulse laser bombards a planar target to generate a proton beam; a gas target proton source refers to a proton source in which multiple laser beams are focused onto 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 all protons in the first proton beam 112 have equal energies. 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 plasma diagnostic results.

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

[0154] The region to be diagnosed contains plasma. As the first proton beam passes through the region to be diagnosed, it is deflected by the self-generated electromagnetic field of the plasma in the region. When the proton beam leaves the region to be diagnosed, it will acquire a deflection velocity 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] like Figure 2 In some embodiments shown, a first distance r1 exists between the region to be diagnosed 113 and the proton source 111. The region to be diagnosed 113 has a first dimension d and a second dimension l, where the first dimension d is the size of the region to be diagnosed 113 along the incident direction of the first proton beam 112; and the second dimension l is the size of the region to be diagnosed 113 in the plane along the incident direction of the first proton beam 112. The region to be diagnosed 113 contains plasma, which generates a self-generated electromagnetic field. This self-generated electromagnetic field interacts with protons passing through the region to be diagnosed 113, causing the proton beam to deflect 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 specific embodiments, the construction module 130a includes: a discrete element 131a, configured to determine the proton source flux probability density distribution based on the proton source image, and further configured to determine the 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 the Kontorovich 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, the discrete element 131a is configured to convert the image into a probability distribution.

[0164] For example, 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 a proton source image and a target image.

[0165] Specifically, the discrete element 131a performs gridding and normalization on the image, thereby preparing for the construction of a discretized or matrix-based 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 of the example, the discrete element 131a meshes different images according to different grids. These different grids can have different grid shapes or different numbers of grid points. For example... Figure 3 In some embodiments shown, the discrete element 131a performs gridding and normalization on the proton source image 101 based on a regular two-dimensional grid; the discrete element 131a performs gridding and normalization on the target image 102 based on an irregular two-dimensional grid.

[0167] The number of grid points differs between the step of gridding the proton source image and the step of gridding the target image.

[0168] For example, the discrete element 131a determines the proton source flux probability density distribution P based on the proton source image. 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; the discrete element 131a determines the target flux probability density distribution Q based on the target image. 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.

[0169] The cost element 132a is based on the proton source flux probability density distribution P determined by the discrete element 131a. i and the target flux probability density distribution Q j Determine the cost matrix C ij The cost matrix describes the cost required to transport one unit of mass from each location in the proton source image to each location in the target image.

[0170] Specifically, the cost element 132a determines 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.

[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 from the proton source image to the target image.

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

[0173]

[0174] Among them, U(P) i Q j ) is from the probability density distribution P of the proton source flux. i To the target flux probability density distribution Q j The set consisting of mappings that satisfy the probability distribution of flux: P ij It is the transport probability, representing the transport probability between grid point i in the proton source image and grid point j in the target image under the meaning of probability distribution, P ij The larger the size, the greater the chance of successful transportation. P represents the transport probability. ij To determine the probability density distribution P of the proton source flux 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 transport entropy. On the basis of the Wasserstein distance, it adds the constraint of probability distribution uncertainty, thereby transforming the non-convex optimization problem into a convex optimization problem, thus avoiding the oscillation and solution difficulties caused by solving non-convex problems.

[0181] Specifically, the transport functional determined by the functional element 132b for:

[0182]

[0183] Where λ is the regularization factor, used to control the smoothness of the solution in order to maintain numerical stability under strong magnetic fields and noisy data.

[0184] The optimal element 133b of the solution module 130b is based on the transport functional to determine the optimal transport probability. Specifically, the optimal transport probability This is the transport probability from the proton source image to the target image that has the lowest total cost and the highest uncertainty, i.e., the transport probability when the Wasserstein distance is minimized and the transport entropy is maximized.

[0185] In some specific embodiments, the optimal element 133b in the solving module 130b 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. The core of the Sinkhorn iterative algorithm consists of numerous vectorized matrix operations and element-wise operations (such as exp, division, log-sum-exp, etc.). These vectorized matrix operations and element-wise operations are suitable for conversion into GPU parallel kernel functions, making them suitable for GPU parallel processing. This means that the code can be rewritten or optimized to execute simultaneously on multiple threads of the GPU. GPU kernel functions can be designed and implemented to achieve efficient parallel computing. For example, the optimal element 133b in the solution module 130b includes a GPU.

[0186] The Sinkhorn iterative algorithm requires approximately [number] iterations. Each iteration requires one matrix-vector multiplication, and the computational complexity of each iteration is O(n log n). The complexity of all iterative calculations is O(n log n). It is not a completely linear method.

[0187] In some embodiments of the present invention, the optimal element 133b is based on the approximate kernel method and utilizes the Sinkhorn iterative algorithm to solve the transport functional, thereby obtaining the optimal transport probability from the proton source image to the target image. The approximate kernel method can include the Fast Gaussian Transform. Within the approximate kernel method, the Sinkhorn algorithm can achieve a computational complexity of O(nlogn) or O(n) in an approximate sense; this computational complexity is called "near-linear," thus enabling its applicability to real-time diagnostic scenarios.

[0188] Continue to refer to Figure 2 The plasma diagnostic system further includes a diagnostic unit 140. The diagnostic unit 140 is based on the optimal transport probability obtained by the processor 130. To diagnose the plasma in the area to be diagnosed.

[0189] The optimal transport probability obtained by the processor 130 The transport probability, representing the lowest total cost and highest uncertainty in the process of mapping the proton source pattern to the target image, represents the mapping relationship between the proton source pattern and the target image. The target image is obtained by deflecting the proton beam generated by the proton source through the electromagnetic field of the plasma in the region to be diagnosed. Therefore, the mapping relationship between the proton source pattern and the target image obtained by the processor 130 can reflect the deflection information of the proton beam in the region to be diagnosed. The diagnostic device 140 can determine the properties of the 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 tool 140 is configured to determine the proton deflection angle, thereby determining the magnetic field of the plasma in the region to be diagnosed.

[0191] In some embodiments, the diagnostic tool 140 is based on the optimal transport probability. The diagnostic tool 140 determines the positional mapping relationship between the proton source image and the target image; it also determines the proton deflection angle based on the positional mapping relationship; and it further determines the magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle.

[0192] The Kontorovich optimal transport problem solves the transport problem from one probability distribution to another, and the processor 130 obtains the optimal transport probability. This reflects a many-to-many mapping from the proton source image to the target image. The diagnostic tool 140 can determine the one-to-one positional mapping relationship between the proton source image and the target image.

[0193] like 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 is based on 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.

[0202] In summary, an optimal transport problem from the proton source image to the target image is constructed using both the source and target images. Solving this optimal transport problem yields the optimal transport probability from the source image to the target image. By constructing this optimal transport problem, the proton deflection information in proton photography is transformed into an optimal transport problem in the sense of probability distribution. The one-to-one mapping relationship between the proton source image and the target image during proton beam transmission is transformed into a many-to-many mapping relationship for optimal transport. This avoids singularity in unit image area caused by proton aggregation, eliminates errors in solving the Monge-Abe equation, and overcomes the convergence problem caused by area singularity. Especially under strong electromagnetic field conditions, this effectively ensures the accuracy and reliability of the results.

[0203] Furthermore, the steps to obtain the optimal transport probability from the proton source image to the target image include: determining the transport functional based on the Wasserstein distance and the transport entropy. By introducing the transport entropy, the solution to the optimal transport problem is constructed as a convex optimization problem, thereby avoiding the oscillations and solution difficulties caused by solving non-convex problems.

[0204] Furthermore, the steps to obtain the optimal transport probability from the proton source image to the target image include: 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 Sinkhorn iterative algorithm has a near-linear time complexity and supports GPU acceleration, thus enabling its applicability to real-time diagnostic scenarios.

[0205] While the present invention has been disclosed above, it is not limited thereto. Any person skilled in the art can make various modifications and alterations without departing from the spirit and scope of the invention; therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

Claims

1. A method of plasma diagnostics, characterized by, The method comprises the following steps: determining a proton source image based on a proton source; generating a first proton beam by the proton source; passing the first proton beam through a region to be diagnosed to form a second proton beam; receiving the second proton beam and determining a target image; constructing an optimal transport problem from the proton source image to the target image based on the proton source image and the target image, wherein 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 the following steps: determining a Wasserstein distance based on the proton source image and the target image, wherein the step of determining the Wasserstein distance comprises the following steps: 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; and determining the Wasserstein distance based on the cost matrix; solving the optimal transport problem to obtain an optimal transport probability from the proton source image to the target image; diagnosing a plasma in the region to be diagnosed based on the optimal transport probability, wherein the step of diagnosing the plasma in the region to be diagnosed based on the optimal transport probability comprises the following steps: 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; and determining a magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle, wherein the step of determining the position mapping relationship from the proton source image to the target image comprises the following steps: determining a centroid mapping form; and 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.

2. The plasma diagnosis method of claim 1, wherein the step of solving the optimal transport problem to obtain the optimal transport probability from the proton source image to the target image comprises the following step: obtaining the optimal transport probability from the proton source image to the target image based on the Wasserstein distance. At least one of the steps of determining the proton source flux probability density distribution and determining the target flux probability density distribution comprises the following steps: griding and normalizing 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.

3. The method of plasma diagnostics of claim 1, wherein, The step of obtaining the optimal transport probability from the proton source image to the target image comprises the following steps:

4. The method of plasma diagnostics of claim 1, wherein, 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. The step of obtaining the optimal transport probability from the proton source image to the target image comprises the following step: solving the transport functional by using a Sinkhorn iterative algorithm to obtain the optimal transport probability from the proton source image to the target image.

5. The method of plasma diagnostics according to claim 4, characterized in that, ​ 6. The method of plasma diagnostics of claim 1, wherein, The step of determining the position 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, a position mapping relationship on a grid point is determined based on the position mapping relationship. The step of determining the proton deflection angle includes determining the proton deflection angle based on the position mapping relationship on the grid point.

7. The method of plasma diagnostics according to claim 6, wherein, The step of determining the position mapping relationship on the grid point includes determining the position mapping relationship on the grid point by means of third-order interpolation.

8. A plasma diagnostic system characterized by, The step of determining the position mapping relationship on the grid point includes determining the position mapping relationship on the grid point by means of third-order interpolation. The proton source is configured to generate a first proton beam; The first proton beam passes through the region to be diagnosed to form a second proton beam; A receiving surface is configured to receive the second proton beam to obtain a target image; A processor is 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 to solve the optimal transport problem to obtain an optimal transport probability from the proton source image to the target image, the processor including: a construction module configured to determine a Wasserstein distance based on the proton source image and the target image, wherein the construction module includes: a discrete element configured to determine a proton source flux probability density distribution based on the proton source image, and to determine a target flux probability density distribution based on the target image; a cost element 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 configured to determine the Wasserstein distance based on the cost matrix; A diagnostic device is configured to diagnose the plasma in the region to be diagnosed based on the optimal transport probability, the diagnostic device 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, and determining a magnetic field of the plasma in the region to be diagnosed based on the proton deflection angle, wherein the diagnostic device is provided with a center-of-mass mapping form, and the diagnostic device determines the position mapping relationship based on the optimal transport probability and the center-of-mass mapping form, the position mapping relationship being a one-to-one mapping relationship.

9. The plasma diagnostic system of claim 8, wherein, The construction module is further configured to obtain the optimal transport probability from the proton source image to the target image based on the Wasserstein distance.

10. The plasma diagnostic system of claim 9, wherein, The processor further includes a solving module configured to determine a transport entropy based on the transport probability, and to determine a transport functional in combination with the Wasserstein distance. The solving module is further configured to obtain the optimal transport probability from the proton source image to the target image based on the transport functional.

11. The plasma diagnostic system of claim 10, wherein, The solving module uses a Sinkhorn iterative algorithm to solve the transport functional to obtain the optimal transport probability from the proton source image to the target image.

12. The plasma diagnostic system of claim 11, wherein, The solving module includes a GPU.

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