An integrated analysis method, apparatus, and medium for fast ion loss and redistribution

Abstract

The application discloses an integrated analysis method, device and medium for fast ion loss and redistribution, which comprises the following steps: initializing a fast ion phase space classification topology; generating sample particles of full-coverage co-directional and reverse fast ions in the fast ion phase space at one time; performing fast ion initial orbit loss analysis in the fast ion phase space; constructing a magnetic field ripple loss area mark in the fast ion phase space based on a theoretical model GWB criterion, and automatically determining that a sample particle is a ripple loss particle when the phase space position of the sample particle falls into the marked magnetic field ripple loss area; on the basis of the marked magnetic field ripple loss area, considering a wave-particle resonance loss area and a redistribution area after MHD disturbance according to whether the MHD frequency is a limited frequency or a zero frequency, and marking a phase space random area by using a probe particle pair vector rotation method; and evaluating the phase space random area distribution caused by different MHD disturbance amplitudes in the evolution of wave-particle nonlinear interaction.

Description

Technical Field

[0001] This application belongs to the technical field of loss and transport mechanism assessment in nuclear fusion devices, specifically relating to an integrated analytical method, device, and medium for fast ion loss and redistribution. Background Technology

[0002] The key to improving tokamak plasma parameters and fusion ignition is that fast ion confinement is good enough. The channels that cause loss and redistribution include initial orbital loss, magnetic field ripple perturbation, MHD perturbation, the synergistic effect of MHD and magnetic field ripple perturbation, and wave-particle nonlinear system evolution.

[0003] Existing fast ion loss and redistribution assessment techniques mainly fall into two categories: One is based on a large number of experimental particle tracking calculations, which is time-consuming but accurate. Specifically, given an equilibrium configuration, a specific perturbation distribution function, such as the MHD and magnetic field ripple perturbation, is superimposed. A large number of fast ions are tracked within the total magnetic field configuration, while considering collision slowing and scattering fast ion orbital corrections. After tracking for a certain period, information on lost and unlost particles is statistically analyzed. This method generally can only consider a certain type of instability, and the loss caused by magnetic field ripple perturbation has a collision cumulative effect, requiring the tracking of a large number of particles within the slowing timescale, which is computationally very resource-intensive. The other category marks the fast ion density distribution and loss region in the fast ion phase space. However, magnetic field ripple loss can only characterize the ripple loss region for fast ions with specific energies, thus limiting its application to specific energy levels. Planar; studies of specific MHD modes and fast ion interactions can only be conducted in... Because it is planar, this technique cannot handle complex mode analyses such as the synergistic loss of MHD and magnetic field ripples, the interaction of multiple MHD modes, and the nonlinear evolution of wave-particle systems. Summary of the Invention

[0004] To address the problems existing in the prior art, the aim is to provide an integrated analytical method, apparatus, and medium for fast ion loss and redistribution.

[0005] This application is achieved through the following technical solution:

[0006] An integrated analytical method for fast ion loss and redistribution, comprising:

[0007] Initialize the fast ion phase space classification topology: Based on the equilibrium configuration obtained from the tokamak design stage or experimental inversion, and the fast ion distribution characteristics, characterize the maximum and minimum magnetic field values ​​and magnetic axis positions of the plasma region in the phase space, the loss boundaries of co-current and anti-current particles, the two solutions of particle parameters at the magnetic axis, and the capture-passing particle conversion critical line, to obtain a series of fast ion motion trajectory type region classifications in the two phase space planes;

[0008] Sample particles that fully cover both unidirectional and antidirectional fast ions are generated in a single step in the fast ion phase space;

[0009] Fast ion initial orbital loss analysis was performed in the fast ion phase space.

[0010] Based on the theoretical model GWB criterion, a magnetic field ripple loss region marker is constructed in the fast ion phase space. When the phase space position of the sample particle falls into the marked magnetic field ripple loss region, the sample particle is automatically determined to be a ripple loss particle.

[0011] Based on the marked magnetic field ripple loss region, depending on whether the MHD frequency is a finite frequency or a zero frequency, the wave-particle resonance loss region and redistribution region after MHD perturbation are considered, and the random region of phase space is marked by the probe particle pair vector rotation method.

[0012] Based on magnetic field ripple loss, wave-particle resonance calculation and redistribution caused by MHD, the random distribution of phase space caused by different MHD perturbation amplitudes in the evolution of wave-particle nonlinear interaction is evaluated.

[0013] In some embodiments, the method of generating sample particles that fully cover both unidirectional and antidirectional fast ions in a single step in the fast ion phase space includes:

[0014] The sample particles were generated using a Monte Carlo numerical procedure based on a physical model;

[0015] Alternatively, the sample particles can be generated by constructing an analytical function based on the theoretical model.

[0016] In some implementations, the generation of the sample particles based on analytical functions in the theoretical model includes:

[0017] Phase space network partitioning: Sampling intervals are set on two types of phase space planes, including the normalized canonical circumferential angular momentum range and its resolution setting, the fast ion energy range and its resolution setting, and the magnetic moment range and its resolution setting.

[0018] Distribution function construction and amplitude weighting: Based on the fast ion generation mechanism, the specific forms of the distribution functions corresponding to the two types of phase space planes are constructed respectively;

[0019] Sample particles are generated at each node in the two types of phase space plane grids, and the weight is equal to the distribution function value in the corresponding grid multiplied by the grid area.

[0020] In some embodiments, the fast ion initial orbital loss analysis performed in the fast ion phase space includes:

[0021] In the fast ion phase space, analyze which orbital type the fast ion is in, whether it is constrained or lost.

[0022] In some implementations, the construction of magnetic field ripple loss region markers in the fast ion phase space based on the theoretical model GWB criterion includes:

[0023] Obtain the design parameters of the magnetic field system of the tokamak device, and ensure that the resolution covering the plasma region meets the requirements for longitudinal waviness distribution and longitudinal coil number; wherein the resolution satisfies that the spatial grid spacing is 1-2 orders of magnitude smaller than the waviness perturbation characteristic length;

[0024] The region marked in the phase space plane with a ripple degree greater than the GWB criterion of the theoretical model is the magnetic field ripple loss region.

[0025] In some embodiments, the consideration of the wave-particle resonance loss region and redistribution region after MHD perturbation, based on the marked magnetic field ripple loss region and depending on whether the MHD frequency is a finite frequency or zero frequency, includes:

[0026] When considering MHD perturbations at finite frequencies, the wave-particle resonance loss region and redistribution region are marked using the high-frequency TAE perturbation distribution function, long-term wave-particle energy exchange statistics, or the real fast ion distribution function and MHD perturbation distribution function.

[0027] In some embodiments, the method of marking random regions in phase space using a probe particle pair vector rotation method includes:

[0028] A finite-frequency or zero-frequency MHD perturbation field is superimposed on a balanced magnetic field. The mode information and amplitude are taken from experimental diagnosis or simulation conclusions. The interaction between the two will result in a series of intact KAM surfaces, discrete resonance islands and chaotic regions.

[0029] Then, multiple pairs of probe particles are scattered in each phase space plane interval region. Among them, the phase space distribution parameters of the two probe particles in each pair are consistent except for the polar magnetic flux distribution.

[0030] Tracking the probe particle pair within the transport scale, when the trajectory of the probe particle pair lies on the intact KAM surface, the relative velocity change of the probe particle pair ensures that the change in the azimuth angle of the connection vector does not exceed [a certain value]. When the probe particle pair is located in the resonance island or the chaotic region, the change in the azimuth angle of the connecting vector of the probe particle pair exceeds... And it continuously rotates around the center point of the resonance island or the center point of the chaotic region, i.e., local transport or direct loss, changing the azimuth angle of the connecting vector by more than The region is marked as a random region.

[0031] In some implementations, the evaluation of the phase space random region distribution caused by different MHD perturbation amplitudes in the wave-particle nonlinear interaction evolution includes:

[0032] For the analysis of MHD perturbation amplitude that evolves self-consistently over time, the phase space random region labeling of the previous step is repeated based on the current evaluation analysis results.

[0033] Secondly, this application proposes an electronic device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the integrated analysis method described in any of the above embodiments.

[0034] Thirdly, this application proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the integrated analysis method described in any of the above embodiments.

[0035] This application proposes an integrated analytical method for fast ion loss and redistribution. This method enables comprehensive and quantitative evaluation of fast ion loss and redistribution during the rapid iteration phase of engineering and physics design required for tokamak devices, improving design efficiency and reducing design time. In the experimental analysis phase, it accurately identifies fast ion loss pathways and fractions, and assesses the synergistic effects of various loss mechanisms. This application has validated and reduced the evaluation time from several days to minutes, significantly accelerating device design iteration. It achieves high integration of fast ion physics analysis, clear and accurate understanding of physical mechanisms, and efficient numerical computation. This application has already been used in multiple tokamak designs and experimental analyses, validating the effectiveness, convenience, and accuracy of this technology.

[0036] Accordingly, the electronic device and computer-readable storage medium proposed in this application also possess the same technical effects as described above. Attached Figure Description

[0037] The accompanying drawings, which are included to provide a further understanding of the embodiments of this application and form part of this application, do not constitute a limitation on the embodiments of this application. In the drawings:

[0038] Figure 1 This is a flowchart of the integrated analysis method proposed in the embodiments of this application;

[0039] Figure 2a Classification of the fast ion phase spatial plane in typical small and medium-sized tokamaks;

[0040] Figure 2b Classification of fast ion phase spatial planes for large and medium-sized tokamak;

[0041] Figure 2c Classification of fast ion phase spatial planes with fixed magnetic moment distribution;

[0042] Figure 3a The density distribution of the initial fusion alpha particles in the tokamak in phase space;

[0043] Figure 3b The density distribution of the initial distribution of unidirectional NBI fast ions in phase space in a tokamak;

[0044] Figure 4 Marking the magnetic field ripple loss region constructed in phase space;

[0045] Figure 5a The perturbation function distribution of the typical MHD instability TAE mode in a tokamak;

[0046] Figure 5b The density distribution of the positions in phase space marked by the wave-particle energy exchange labeling method for the MHD perturbation and fast ion interaction regions;

[0047] Figure 5c The initial distribution of inverse alpha particles is used to probe random regions;

[0048] Figure 6 Schematic diagram of particle pair vector rotation marking for fast ion phase space detection;

[0049] Figure 7 To detect wave-particle resonance islands, i.e., random region distributions, using the particle pair vector rotation method;

[0050] Figure 8a The positive throwing angle used in the vector rotation method is used to detect the distribution of particle pairs;

[0051] Figure 8b The negative throwing angle used in the vector rotation method is used to detect the distribution of particle pairs;

[0052] Figure 8c To detect the random region distribution detected by the vector rotation method of particle pairs in the fast ion phase space;

[0053] Figure 8d Distribution of wave-particle resonance regions marked using the wave-particle energy exchange method;

[0054] Figure 9a The distribution of the wave-particle resonance region in phase space for a smaller TAE perturbation saturation amplitude;

[0055] Figure 9b The distribution of the saturation amplitude of a large TAE perturbation in the wave-particle resonance region in phase space;

[0056] Figure 10 This is a schematic diagram of the electronic device proposed in the embodiments of this application;

[0057] Figure 11 This is a schematic diagram of a computer-readable storage medium proposed in an embodiment of this application.

[0058] Figure reference numerals and corresponding component names:

[0059] 100 - Electronic device; 110 - Memory; 120 - Processor; 111 - Computer program A; 200 - Computer-readable storage medium; 211 - Computer program B. Detailed Implementation

[0060] In the following, the terms “comprising” or “may include” as used in the various embodiments of this application indicate the presence of a function, operation, or element of the invention and do not limit the addition of one or more functions, operations, or elements. Furthermore, as used in the various embodiments of this application, the terms “comprising,” “having,” and their cognates are intended only to indicate a specific feature, number, step, operation, element, component, or combination of the foregoing and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing, or adding one or more combinations of the foregoing.

[0061] In various embodiments of this application, the expression "or" or "at least one of A and / or B" includes any combination or all combinations of the words listed simultaneously. For example, the expression "A or B" or "at least one of A and / or B" may include A, may include B, or may include both A and B.

[0062] The terms used in the various embodiments of this application (such as "first," "second," etc.) may modify various constituent elements in the various embodiments, but do not limit the corresponding constituent elements. For example, the above terms do not limit the order and / or importance of the elements. The above terms are only used for the purpose of distinguishing one element from other elements. For example, a first user device and a second user device refer to different user devices, although both are user devices. For example, without departing from the scope of the various embodiments of this application, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element.

[0063] It should be noted that if a description is made of "connecting" one component to another, then the first component can be directly connected to the second component, and a third component can be "connected" between the first and second components. Conversely, when a component is "directly connected" to another component, it can be understood that there is no third component between the first and second components.

[0064] The terminology used in the various embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the various embodiments of this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of this application pertain. The terms (such as those defined in a generally used dictionary) are to be interpreted as having the same meaning as in the context of the relevant technical field and are not to be interpreted as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of this application.

[0065] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this application are only for explaining this application and are not intended to limit this application.

[0066] Existing fast ion loss and redistribution assessment techniques based on large-scale particle tracking calculations require long-term tracking of a large number of fast ions. While accurate, these techniques are extremely time-consuming and detrimental to scanning key influencing parameters. Furthermore, methods that label fast ion density distributions and loss regions in the fast ion phase space can only handle single perturbation modes and cannot address the synergistic effects of MHD perturbations and magnetic field ripple perturbations, nor can they handle fast ion loss and redistribution during wave-particle nonlinear interactions. To address these issues, this application proposes an integrated analysis method for fast ion loss and redistribution. This integrated analysis method describes the ion deposition region, initial orbital loss region, ripple loss region, fast ion random region caused by MHD, and wave-particle interaction region after MHD evolution saturation in three-dimensional phase space. It synergistically and self-consistently combines two phase space planes with different loss and transport mechanisms and achieves rapid, accurate assessment and visualization through numerical analysis techniques.

[0067] Specifically, such as Figure 1 As shown, this ensemble analysis method includes the following steps:

[0068] Step 1, Initialize the fast ion phase space classification topology: Based on the equilibrium configuration obtained during the tokamak design phase or experimental inversion, and the fast ion distribution characteristics, characterize the maximum and minimum magnetic field values ​​and magnetic axis positions of the plasma region in the phase space, the loss boundaries of co-current and anti-current particles, multiple phase space boundary conditions for particle parameters passing through the magnetic axis, and the capture-passing particle conversion critical line, to obtain a series of fast ion motion trajectory type region classifications in two types of phase space planes. Figure 2a , Figure 2b , Figure 2c It shows and Two types of phase space planes (based on the motion behavior of fast ions in the equilibrium magnetic field of a tokamak and the Hamiltonian theory of the guide center, there are three conserved quantities in the periodic motion of fast ions, namely the canonical circumferential angular momentum) ,energy and magnetic moment Without considering disturbances and collisions, the conserved quantities remain constant during the movement of fast ions. When the energy or magnetic moment of the fast ion distribution is kept constant, two types of phase space planes can be obtained: one with fixed fast ion energy. get Planar, fixed fast ion magnetic moment get Various markings in the plane, where the plus or minus sign of the subscript indicates fast ions thrown in the same or opposite directions. Indicates the region of confinement for passing particles. Indicates the region of loss of passing particles. Indicates the region where particles are trapped. This indicates the region of loss due to captured particles. Figure 2a This demonstrates the fast ion phase space of a typical small to medium-sized tokamak. Plane classification, Figure 2b Demonstrates the fast ion phase space of large and medium-sized tokamak Plane classification, Figure 2c Demonstrates a fast ion phase space with a fixed magnetic moment distribution. Planar classification. The loss region in the figure is the initial orbital loss region for fast ions. The loss mechanism stems from the finite width and distribution position of the fast ion orbitals. In practical applications, pinging fast ion losses often requires tracking from the initial distribution. In this case, the fast ion energies are unified to the initial energies, thus fixing the particle energy distribution is possible. Planar analysis. The magnetic moment of the fast ion slowing distribution exhibits a typical value distribution. Simultaneously, during wave-particle interaction, the magnetic moment of the fast ions remains conserved. Therefore, under the condition of magnetic moment conservation... Phase space planes are a product of natural selection. Two phase space planes can complement each other, describing fast ion confinement behavior.

[0069] Step 2: Generate sample particles covering both co-directional and anti-directional fast ions in the fast ion phase space in a single step. This step aims to achieve full coverage of the phase space constraint region for both co-directional and anti-directional fast ions in a single step. The sample particles can be generated by a Monte Carlo numerical program from the physical model or constructed based on analytical functions in the theoretical model. The phase space labeling logic is consistent after generating the sample particles using both methods. Further, taking the construction of analytical functions as an example, the sample particle generation process includes:

[0070] Phase space mesh generation: in the canonical ring phase angular momentum and normalized magnetic moment The two-dimensional plane formed superior( (This refers to the magnetic field strength at the magnetic axis), and a sampling interval is defined, where the normalized... The value range is [-1.5, 0.5], resolution Divide into 200 equal parts; The value range is [0, 1.5], resolution Divide into 200 equal parts.

[0071] Distribution function construction and weight assignment: Based on the fast ion generation mechanism, the distribution function is constructed. Specific format: If it is NBI fast ion, use fast ion density The magnetic moment distribution function can be assumed to be a Gaussian distribution. It is the characteristic width parameter of the Gaussian distribution. (This is the center value of the fast ion magnetic moment distribution). If it is an alpha particle distribution, we can assume that the velocity space is isotropic, the size is slowed down, and the density is Gaussian.

[0072] In phase space grid Sample particles are generated at each node in the grid, and the weight is equal to the distribution function value in that grid multiplied by the grid area. This allows for simultaneous coverage of unidirectional, anti-directional, and capture / passage particles in a single calculation, eliminating the need for multiple repeated sampling.

[0073] In a two-dimensional plane of phase space with a fixed magnetic moment distribution The method of generating sample particles and in a two-dimensional plane The method for generating sample particles is the same, which is to sample the above operations: first, perform phase space grid division, then construct the distribution function and assign weights, and finally generate sample particles on each node in the phase space grid.

[0074] Step 3 involves analyzing the orbital type of the fast ion in the fast ion phase space, determining whether it is constrained or lost, i.e., fast ion initial orbital loss analysis. Different devices exhibit consistent phase space region classification topologies, such as... Figure 3a and Figure 3b It is obtained by fixing fast ion energy in different devices. Although the size of the region varies for specific orbit types, the Hamiltonian theory of the guide center maintains a consistent topological structure in the plane. Figure 3a and Figure 3b The initial distributions of fusion alpha particles and co-directional NBI fast ions in the phase space of the tokamak are shown respectively. The density distributions in the images show the distributions of fast ions under fusion alpha particles and NBI injection, respectively. The quality of these fast ions confinement is crucial to achieving the fusion ignition conditions.

[0075] Step 4: Based on the loss region marking caused by tokamak magnetic field ripple perturbation, and using the theoretical model Goldston-White-Boozer (GWB) criterion, a magnetic field ripple loss region marker is constructed in the fast ion phase space. If the phase space position of a sample particle is located within the marked magnetic field ripple loss region, the particle is automatically identified as a ripple loss particle, which is accurate and efficient. Further, the magnetic field ripple loss region marking method specifically includes:

[0076] To obtain the design parameters of the magnetic field system of the tokamak device, the longitudinal waviness distribution and the number of longitudinal coils with sufficiently high resolution covering the plasma region are obtained. The waviness of the poloidal section is defined as... ;in, It refers to the degree of waviness. These are the major radius and vertical position coordinates of the polar section, respectively. and These represent the maximum and minimum magnetic field values ​​at the circumferential angles of the layout, respectively, with the polar position fixed. The resolution generally requires the spatial grid spacing to be 1-2 orders of magnitude smaller than the ripple disturbance feature length, and the specific values ​​are related to the device size.

[0077] exist In-plane marking waviness greater than The area, in which It is the number of longitudinal coils. It is the reciprocal of the local aspect ratio. It is the Larmor cyclotron radius of fast ions. It is a safety factor radial micro-business, This is the GWB criterion. When the turning point of the captured particle's banana trajectory is located in the marked region (i.e., as shown in the image)... Figure 4 When the fast ion falls within the red area marked by GWB, it means that the fast ion will experience collision-free rippled random diffusion loss. The distribution of this loss region overlaps with the rippled magnetic trapping loss region and is much larger than the latter. Therefore, the phase space distribution of the rippled loss region can be completely described by the GWB criterion alone. When the phase space position of a fast ion sample particle falls into the red area marked by GWB, the sample particle is automatically identified as a rippled loss particle, and its energy and position are recorded without the need for long-term orbit tracking.

[0078] Step 5: Based on the marked magnetic field ripple loss region, further consider the wave-particle resonance loss region and redistribution region after MHD perturbation. The specific operation method varies depending on whether the MHD (magnetohydrodynamic instability) frequency is finite or zero. When considering finite-frequency MHD perturbations, it can be based on... Figure 5a , Figure 5b , Figure 5c The analysis is performed using the numerical methods described below, where... Figure 5aThis demonstrates a typical high-frequency MHD perturbation function distribution; Figure 5b The density distribution of the MHD perturbation and fast ion interaction region in phase space marked by the energy exchange labeling method is shown. If this region is adjacent to the above-mentioned enhanced orbital loss boundary, it indicates that there is fast ion loss directly caused by MHD perturbation. Figure 5c This demonstrates the use of reverse alpha particle initial distributions to detect random regions. Specifically, the embodiments of this application propose using real fast ion distribution functions and MHD perturbation distribution functions to determine whether there is a significant net energy exchange through time-averaged statistical wave-particle energy exchange.

[0079] When considering the interaction between zero-frequency or finite-frequency MHD and fast ions, step 5 of this section utilizes a numerical method in the fast ion phase space to mark random regions using the vector rotation method of probe particle pairs within a precise mesh. One of the resonance conditions for fast ions and MHD perturbation modes is that the resonance helicity must be a low-order rational number. The resonance helicity can only determine the position of wave-particle resonance, not the resonance amplitude. The kinetic Poincaré diagram of the high-energy particle phase space is used as a standard tool to evaluate the transport intensity and transport timescale of particles. Because the interaction between high-energy particle orbits and the perturbation field results in a series of perfect KAM surfaces (Kolmogorov–Arnold–Moser, the KAM theorem guarantees that fast ions can still be analyzed using Hamiltonian mechanics after being perturbed by MHD), the KAM surfaces cut the fast ion phase space into a layered nested structure. Chaotic orbits cannot cross the KAM surfaces, thus prohibiting radial diffusion of fast ions. Under typical MHD perturbation, discrete resonance islands and chaotic regions formed by the KAM surfaces can be seen in the fast ion phase space. The numerical method for marking random regions in the fast ion phase space using the vector rotation method of probe particle pairs is as follows: Figure 6 As shown, the specific implementation process includes:

[0080] First, a finite-frequency or zero-frequency MHD perturbation field is superimposed on the equilibrium magnetic field, with the mode information and amplitude obtained from experimental diagnosis or simulation conclusions.

[0081] Then A pair of closely spaced probe particles are scattered across a flat surface. It is the poloidal angle during the fast ion motion process, and it is used to detect the phase space distribution parameters of the particles, excluding the poloidal magnetic flux distribution. Small distance Apart from the other parameters, the distribution of other parameters is consistent, and multiple pairs of probe particles are scattered in small intervals within each phase space to ensure the statistical effect of phase influence.

[0082] Tracking a large number of probe pairs within the transport scale, typically within a timescale of several thousand fast ion circumduction cycles, allows for the detection of all low-order resonances and the vast majority of high-order resonances. When the probe pair's trajectory lies on a well-preserved KAM plane, the relative velocity change of the probe pair ensures that the change in the azimuth angle of the connection vector does not exceed [a certain value]. This means undisturbed. It is a constant. When the probe particle pair is located in the resonance island region, the change in the azimuth angle of the probe particle pair connection vector exceeds... The continuous rotation around the center point of the resonance island implies that wave-particle resonance leads to Landau mixing, i.e., localized transport or direct loss. The rotation vector of the chaotic region after resonance island overlap is similar, meaning the change in the azimuth angle of the connecting vector by the particle exceeds... And it keeps rotating; for ease of description, this is collectively referred to as the phase vector rotation method, where the azimuth rotation exceeds... The region is a random region and is numerically marked. Figure 7 This demonstrates the wave-particle resonance random region (i.e., obtained using the probe particle pair vector rotation method) obtained by means of the probe particle pair vector rotation method. Figure 7 The figure (highlighted in blue) illustrates three methods: the kinetic Poincaré diagram of wave-particle resonance islands (black lines representing the KAM surface and random regions), the radial position marked by the fast ion orbital resonance helicity (red box), and the probe particle pair vector rotation method (blue markers). As can be seen from the figure, the probe particle pair vector rotation method demonstrates superior accuracy and efficiency in both the resonance island position marked by resonance helicity and the resonance island region in the kinetic Poincaré diagram. The embodiments of this application developed a numerical module based on this method and have confirmed in numerous practical scenarios that the vector rotation method is the most comprehensive, accurate, and efficient in detecting MHD-induced fast ion phase space transport.

[0083] Figure 8a and Figure 8b The positive and negative pitch angles used in the vector rotation method are used to detect the phase space distribution of particle pairs. The core idea is to cover all fast ions with both positive and negative pitch angles, preferring to cover more of the loss region rather than less of the constraint region, and to avoid repeated statistics. Figure 8c The distribution of wave-particle resonance random regions obtained by using the phase space probe particle pair vector rotation method is shown. These random regions are located in the plasma core, which means redistribution. If they are adjacent to the loss region, it means direct fast ion loss. Figure 8d The wave-particle resonance region labeled using the wave-particle energy exchange method (i.e., energy exchange between co-directional alpha particles and TAE) is demonstrated. The two methods corroborate each other, and the energy exchange labeling method can... and It is applicable to both flat surfaces.

[0084] Step 6: Based on the magnetic field ripple loss, the loss caused by MHD, and the redistribution, evaluate the phase space random region distribution caused by different MHD perturbation amplitudes in the wave-particle nonlinear interaction evolution. That is, for the analysis of the MHD perturbation amplitude that evolves self-consistently over time, repeat step 5 based on the evaluation results of step 6. Figure 9a and Figure 9b The saturation amplitudes of smaller and larger TAE (Toroidal Alfven Eigenmode) perturbations are shown in phase space, respectively. Distribution of wave-particle resonance regions in a plane.

[0085] Compared to traditional analysis methods that require tracking a large number of discrete sample particles on a slowed-down timescale, typically taking tens to hundreds of hours, and weeks for tracking alpha particles, the integrated analysis method proposed in this application, through the motion conservation theory model in the phase space integrated analysis model, phase space labeling modeling of multiple loss mechanisms, and numerical analysis methods, can integrate and process all loss and redistribution mechanisms (fast ion initial orbital loss, magnetic field ripple loss, and MHD-induced loss and redistribution) in phase space. It also achieves wave-particle resonance analysis under different perturbation amplitudes in the wave-particle nonlinear evolution process, with computation time on the order of minutes, greatly improving analysis efficiency. This integrated analysis method has been applied to the design of several new tokamak devices and the HL-3 experimental analysis. Test results show that the integrated analysis method proposed in this application achieves rapid and accurate calculation of all fast ion losses and redistribution assessments, demonstrating broad application prospects.

[0086] Based on the same technical concept described above, this application also proposes an electronic device, such as... Figure 10 As shown, the electronic device 100 includes: a memory 110, a processor 120, and a computer program A111 stored in the memory 110 and executable on the processor 120. When the processor 120 executes the computer program A111, it performs the following steps:

[0087] Initialize the fast ion phase space classification topology;

[0088] Sample particles that fully cover both unidirectional and antidirectional fast ions are generated in a single step in the fast ion phase space;

[0089] Initial orbital loss analysis of fast ions is performed in the fast ion phase space;

[0090] Based on the theoretical model GWB criterion, a magnetic field ripple loss region marker is constructed in the fast ion phase space. When the phase space position of a sample particle falls into the marked magnetic field ripple loss region, the sample particle is automatically determined to be a ripple loss particle.

[0091] Based on the marked magnetic field ripple loss region, depending on whether the MHD frequency is a finite frequency or a zero frequency, the wave-particle resonance loss region and redistribution region after MHD perturbation are considered, and the random region of phase space is marked by the probe particle pair vector rotation method.

[0092] Based on magnetic field ripple loss, loss and redistribution caused by MHD, the random distribution of phase space caused by different MHD perturbation amplitudes in the evolution of wave-particle nonlinear interaction is evaluated.

[0093] Optionally, when the processor 120 executes the computer program A111, it can implement any of the embodiments in the corresponding examples of the above-described integrated analysis method.

[0094] It should be noted that the electronic device proposed in this application embodiment is a device used to implement the above-described integration analysis method. Therefore, based on the above-described integration analysis method proposed in this application embodiment, those skilled in the art can understand the specific implementation method and various variations of the electronic device in this application embodiment. Therefore, the specific implementation method of the above-described integration analysis method will not be described in detail here. Any electronic device used by those skilled in the art to implement the above-described integration analysis method is within the scope of protection of this application.

[0095] Based on the same technical concept described above, embodiments of this application also propose a computer-readable storage medium, such as... Figure 11 As shown, the computer-readable storage medium 200 stores a computer program B211, which, when executed by a processor, performs the following steps:

[0096] Initialize the fast ion phase space classification topology;

[0097] Sample particles that fully cover both unidirectional and antidirectional fast ions are generated in a single step in the fast ion phase space;

[0098] Initial orbital loss analysis of fast ions is performed in the fast ion phase space;

[0099] Based on the theoretical model GWB criterion, a magnetic field ripple loss region marker is constructed in the fast ion phase space. When the phase space position of a sample particle falls into the marked magnetic field ripple loss region, the sample particle is automatically determined to be a ripple loss particle.

[0100] Based on the marked magnetic field ripple loss region, depending on whether the MHD frequency is a finite frequency or a zero frequency, the wave-particle resonance loss region and redistribution region after MHD perturbation are considered, and the random region of phase space is marked by the probe particle pair vector rotation method.

[0101] Based on magnetic field ripple loss, loss and redistribution caused by MHD, the random distribution of phase space caused by different MHD perturbation amplitudes in the evolution of wave-particle nonlinear interaction is evaluated.

[0102] Optionally, when the computer program B211 is executed by the processor, it can implement any of the embodiments corresponding to the above-described integrated analysis method.

[0103] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0104] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0105] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0106] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0107] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0108] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above description is only a specific embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. An integrated analytical method for fast ion loss and redistribution, characterized in that, include: Initialize the fast ion phase space classification topology: Based on the equilibrium configuration obtained from the tokamak design stage or experimental inversion, and the fast ion distribution characteristics, characterize the maximum and minimum magnetic field values ​​and magnetic axis positions of the plasma region in the phase space, the loss boundaries of co-current and anti-current particles, the two solutions of particle parameters at the magnetic axis, and the capture-passing particle conversion critical line, to obtain a series of fast ion motion trajectory type region classifications in the two phase space planes; Sample particles that fully cover both unidirectional and antidirectional fast ions are generated in a single step in the fast ion phase space; Fast ion initial orbital loss analysis was performed in the fast ion phase space. Based on the theoretical model GWB criterion, a magnetic field ripple loss region marker is constructed in the fast ion phase space. When the phase space position of the sample particle falls into the marked magnetic field ripple loss region, the sample particle is automatically determined to be a ripple loss particle. Based on the marked magnetic field ripple loss region, depending on whether the MHD frequency is a finite frequency or a zero frequency, the wave-particle resonance loss region and redistribution region after MHD perturbation are considered, and the random region of phase space is marked by the probe particle pair vector rotation method. Based on magnetic field ripple loss, wave-particle resonance calculation and redistribution caused by MHD, the random distribution of phase space caused by different MHD perturbation amplitudes in the evolution of wave-particle nonlinear interaction is evaluated.

2. The integrated analytical method for fast ion loss and redistribution according to claim 1, characterized in that, The method of generating sample particles that fully cover both unidirectional and antidirectional fast ions in a single operation in the fast ion phase space includes: The sample particles were generated using a Monte Carlo numerical procedure based on a physical model; Alternatively, the sample particles can be generated by constructing an analytical function based on the theoretical model.

3. The integrated analytical method for fast ion loss and redistribution according to claim 2, characterized in that, The method for generating the sample particles based on the analytical function in the theoretical model includes: Phase space network partitioning: Sampling intervals are set on two types of phase space planes, including the normalized canonical circumferential angular momentum range and its resolution setting, the fast ion energy range and its resolution setting, and the magnetic moment range and its resolution setting. Distribution function construction and amplitude weighting: Based on the fast ion generation mechanism, the specific forms of the distribution functions corresponding to the two types of phase space planes are constructed respectively; Sample particles are generated at each node in the two types of phase space plane grids, and the weight is equal to the distribution function value in the corresponding grid multiplied by the grid area.

4. The integrated analytical method for fast ion loss and redistribution according to claim 1, characterized in that, The fast ion initial orbital loss analysis performed in the fast ion phase space includes: In the fast ion phase space, analyze which orbital type the fast ion is in, whether it is constrained or lost.

5. The integrated analytical method for fast ion loss and redistribution according to claim 1, characterized in that, The aforementioned GWB criterion based on the theoretical model, which constructs a magnetic field ripple loss region marker in the fast ion phase space, includes: Obtain the design parameters of the magnetic field system of the tokamak device, and ensure that the resolution covering the plasma region meets the requirements for longitudinal waviness distribution and longitudinal coil number; wherein the resolution satisfies that the spatial grid spacing is 1-2 orders of magnitude smaller than the waviness perturbation characteristic length; The region marked in the phase space plane with a ripple degree greater than the GWB criterion of the theoretical model is the magnetic field ripple loss region.

6. An integrated analytical method for fast ion loss and redistribution according to any one of claims 1-5, characterized in that, Based on the marked magnetic field ripple loss region, and depending on whether the MHD frequency is a finite frequency or zero frequency, the wave-particle resonance loss region and redistribution region after MHD perturbation are considered, including: When considering MHD perturbations at finite frequencies, the wave-particle resonance loss region and redistribution region are marked using the high-frequency TAE perturbation distribution function, long-term wave-particle energy exchange statistics, or the real fast ion distribution function and MHD perturbation distribution function.

7. The integrated analytical method for fast ion loss and redistribution according to claim 6, characterized in that, The method of marking random regions in phase space using the probe particle pair vector rotation method includes: A finite-frequency or zero-frequency MHD perturbation field is superimposed on a balanced magnetic field. The mode information and amplitude are taken from experimental diagnosis or simulation conclusions. The interaction between the two will result in a series of intact KAM surfaces, discrete resonance islands and chaotic regions. Then, multiple pairs of probe particles are scattered in each phase space plane interval region. Among them, the phase space distribution parameters of the two probe particles in each pair are consistent except for the polar magnetic flux distribution. Tracking the probe particle pair within the transport scale, when the trajectory of the probe particle pair lies on the intact KAM surface, the relative velocity change of the probe particle pair ensures that the change in the azimuth angle of the connection vector does not exceed [a certain value]. When the probe particle pair is located in the resonance island or the chaotic region, the change in the azimuth angle of the connecting vector of the probe particle pair exceeds... And it continuously rotates around the center point of the resonance island or the center point of the chaotic region, i.e., local transport or direct loss, changing the azimuth angle of the connecting vector by more than The region is marked as a random region.

8. The integrated analytical method for fast ion loss and redistribution according to claim 1, characterized in that, The evaluation of the phase space random region distribution caused by different MHD perturbation amplitudes in the wave-particle nonlinear interaction evolution includes: For the analysis of MHD perturbation amplitude that evolves self-consistently over time, the phase space random region labeling of the previous step is repeated based on the current evaluation analysis results.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the integrated analysis method according to any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the integrated analysis method according to any one of claims 1-8.

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