Method for track simulation and path optimization of compact ring core charging system

Abstract

The invention discloses a track simulation and path optimization method for a compact ring core charging system. The method comprises the following steps: S1, setting device parameters, environment parameters, CT parameters, initial conditions and a vacuum area; s2, establishing a six-degree-of-freedom motion trail model by using a cylindrical coordinate # imgabs0 # with the tokamak center as an original point; s3, scanning position parameters, and recording a corresponding optimization parameter # imgabs 1 #, a minimum distance # imgabs 2 # to a magnetic axis in a movement process and an optimization function # imgabs 3 # value; s4, drawing a corresponding contour map, and determining an optimal injection point; and S5, simulating a track after the CT is injected into the Tokamak device from the optimal injection point to realize path optimization. According to the method, prediction of the optimal injection point of the CT injection Tokamak device under different conditions is achieved, the injection path of the CT is designed and optimized accordingly, and then the optimized movement track is simulated through the movement track model.

Description

Technical Field

[0001] The invention relates to the technical field of magnetic confinement fusion, and in particular to a method for trajectory simulation and path optimization of a compact ring core feeding system. Background Art

[0002] Since the main fuel resources for nuclear fusion are very abundant, and it has the advantages of high safety, high energy efficiency, and less impact on the environment, nuclear fusion energy has gradually become an important member of a cleaner and more sustainable global energy system. In nuclear fusion research, the efficient operation of fusion reactors is inseparable from the fuel replenishment of the plasma core. However, due to the diffusion driven by turbulence and instability, magnetically confined plasmas will experience energy and particle losses, and the fueling system is required to replenish the particle losses in a timely manner. Compact torus injection (CTI) is considered to be the most promising technology for core fueling of future large fusion reactors. It can effectively improve fusion efficiency, maintain plasma stability, and optimize fuel utilization.

[0003] Under the action of complex magnetic and electric fields, the motion trajectory of the compact torus (CT) becomes extremely complex. Its motion trajectory and stability directly determine the injection efficiency. In order to ensure the accuracy and efficiency of particle injection, trajectory simulation and design are particularly important. Existing research focuses on the simulation of particle motion in a uniform magnetic field, while ignoring the nonlinear change characteristics of the magnetic field in the tokamak device, resulting in a large deviation between the simulation results and the actual results. The instability of plasma also increases the difficulty of predicting particle motion. Therefore, a more accurate simulation method is needed to analyze the motion trajectory of particles during compact torus injection. In addition, fuel injection and momentum transport also require efficient trajectory design to improve particle injection efficiency, which will help improve the operating performance of the tokamak device. Summary of the invention

[0004] Based on the technical problems existing in the background technology, the present invention proposes a method for trajectory simulation and path optimization of a compact ring core feeding system, which can realize the prediction of the optimal injection point of CT injection into a tokamak device under different conditions, and accordingly design and optimize the injection path of CT, and then simulate the optimized motion trajectory through a motion trajectory model.

[0005] The method for trajectory simulation and path optimization of a compact ring core feeding system proposed in the present invention comprises the following steps: S1: Set device parameters, environmental parameters, CT parameters, initial conditions and vacuum area; S2: Use cylindrical coordinates with the tokamak center as the origin Establish a six-degree-of-freedom motion trajectory model; S3: Scan position parameters and record corresponding optimization parameters , the minimum distance from the magnetic axis during movement and optimization function value; S4: draw the corresponding contour map and determine the best injection point; S5: Simulate the trajectory of CT after it is injected into the tokamak device from the optimal injection point to achieve path optimization.

[0006] Preferably, the trajectory model established in S2 is: in, is the Lagrangian; is the Rayleigh dissipation term; ; is the linear kinetic energy; is the rotational kinetic energy; is the potential energy of magnetic field repulsion; is the interaction potential energy between the dipole and the tokamak magnetic field; is the gravitational potential energy; is the MHD resistance; is the thermal diffusion force; is the radiation pressure; is the viscosity force; For electrical conductivity.

[0007] Preferably, the optimization parameters in S3 are and optimization function They are: in, is the CT speed; is the tokamak magnetic field; is the duration of the CT movement process.

[0008] Preferably, before drawing the contour map in S4, the cylindrical coordinates Convert to Cartesian coordinates .

[0009] The system for trajectory simulation and path optimization of a compact ring core feeding system proposed by the present invention comprises: Setting module, setting device parameters, environmental parameters, CT parameters, initial conditions and vacuum area; The calculation module uses cylindrical coordinates with the center of the tokamak as the origin. Establish a six-degree-of-freedom motion trajectory model; Recording module, scans position parameters and records corresponding optimization parameters , the minimum distance from the magnetic axis during movement and optimization function value; The updating module continuously updates the position coordinates of the CT according to the motion trajectory model, which is used to draw the corresponding motion trajectory schematic diagram and contour diagram, and determine the best injection point; The post-processing module is used to simulate the trajectory of CT after it is injected into the tokamak device from the optimal injection point to achieve path optimization.

[0010] The present invention proposes a computer-readable storage medium storing a computer program, which implements the above-mentioned method for trajectory simulation and path optimization of a compact ring core feeding system when executed by a processor.

[0011] Beneficial technical effects of the present invention: The present invention can simulate the motion trajectory of three different forms of CT injected from any position and at any angle under any experimental conditions, and find the best injection point of CT in the current situation to optimize the path; predict the best injection point of CT in different situations by scanning position parameters, and design and simulate the motion trajectory of CT after being injected into the tokamak in the current situation according to the obtained best injection point and parameter conditions, so that CT can reach the magnetic axis position and deposit as much as possible, thereby improving the particle injection efficiency; through simulation and optimization, the trial and error cost of actual experiments is reduced, and the feasibility of the experiment is greatly improved; at the same time, parameter optimization targets are provided for the future compact ring core feeding system to achieve deeper feeding depth and higher efficiency in the tokamak device. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A flowchart of a method for trajectory simulation and path optimization of a compact ring core feeding system proposed by the present invention; Figure 2 This is a schematic diagram of the optimal injection point outline proposed by the present invention; Figure 3 A three-dimensional schematic diagram of the CT motion trajectory proposed by the present invention; Figure 4 This is a schematic diagram of energy changes during CT motion proposed by the present invention. DETAILED DESCRIPTION

[0013] The present invention will be further explained below in conjunction with specific embodiments.

[0014] Example 1 Reference Figure 1 The method for trajectory simulation and path optimization of a compact ring core feeding system proposed in the present invention comprises the following steps: S1: Set device parameters, environmental parameters, CT parameters, initial conditions and vacuum region; specifically, select parameters of existing devices (EAST, HL-2A and ITER) or customize device parameters (device maximum radius and small radius a), custom environmental parameters (plasma density , magnetic field strength at the magnetic axis , electron temperature , average particle mass , magnetic torque coefficient k), CT parameters (density , magnetic field strength ,quality , Outer radius , inner radius ,high ), initial conditions (initial injection velocity , rotation angle , solution time length) and determine whether it contains vacuum areas.

[0015] S2: Use cylindrical coordinates with the tokamak center as the origin A six-degree-of-freedom motion trajectory model is established; after the CT is injected into the tokamak, its motion trajectory will be affected by a variety of forces, such as the magnetic field force of the tokamak (including the interaction between the CT's own magnetic field and the tokamak's magnetic field, magnetic field repulsion, magnetic reconnection, etc.), the rotation of the CT itself, the Lorentz force, magnetohydrodynamics (MHD) resistance, thermal diffusion force, radiation pressure, inertial force, viscosity force, conductivity force, gravitational potential energy, etc. In this model, the five main aspects involved are the kinetic energy of the CT, the rotation of the CT itself, the interaction between the dipole and the tokamak, the magnetic potential energy, and the MHD resistance, and the above-mentioned other influencing factors are also considered.

[0016] The specific model is: in, is the Lagrangian; is the Rayleigh dissipation term; ; is the linear kinetic energy; is the rotational kinetic energy; is the potential energy of magnetic field repulsion; is the interaction potential energy between the dipole and the tokamak magnetic field; is the gravitational potential energy; is the MHD resistance; is the thermal diffusion force; is the radiation pressure; is the viscosity force; is the electrical conductivity; Indicates the quality of CT; Indicates the average radius of the CT (when the CT is cylindrical, its height must be considered when calculating the MHD resistance, so it is necessary to multiply it by the height additionally); represents the moment of inertia of CT; represents angular velocity; represents the magnetic moment of CT itself; represents the tokamak background magnetic field; Indicates the magnetic field strength at the magnetic axis; represents the volume of CT; represents the tokamak plasma density; represents the Alfvén speed; represents the acceleration due to gravity; represents the thermal diffusion coefficient; represents the surface area of ​​CT; represents the temperature gradient, i.e. the rate of change of the temperature of the tokamak plasma; represents the radiated power density; represents the speed of light; represents the plasma viscosity coefficient; represents the relative speed between CT and plasma; Indicates the current of CT; Represents the characteristic length of CT.

[0017] In addition, the CT shape can be judged according to the CT parameters set in S1, and the corresponding calculation formula can be selected; for example, the existing model usually regards the CT as a sphere, and the CT can be expanded to a cylinder and a ring in the present invention to adapt to simulations under different experimental purposes and situations. After CTs of different shapes are injected into the tokamak device, the solution method for the magnitude of the force they are subjected to is different. According to the set CT parameters, the shape of the CT is judged, the corresponding solution formula is selected and brought into the model described in S2 for solution.

[0018] The advantages of cylindrical CT are: a) it is more realistic; b) it is more suitable for more stable injection in long pulse operation, and is therefore particularly suitable for EAST simulation. EAST aims to verify the operation mode of advanced tokamaks, focusing on long pulse operation and steady-state operation; c) when controlling the injection direction, the cylindrical shape is easier to adjust its posture.

[0019] The advantages of the toroidal CT are: a) the toroidal CT has a larger surface area, which makes its contact surface with the plasma larger, thereby improving the energy exchange efficiency; b) it is suitable for higher frequency injection; c) it has better thermal diffusion performance, and its larger surface area enables the CT to conduct and dissipate heat in a larger range, enhancing the heating effect on the tokamak plasma.

[0020] The model is solved using the fourth-order-fifth-order Runge-Kutta method, which provides candidate solutions through the fourth-order method and controls the error through the fifth-order method. It is a numerical solution method for ordinary differential equations with adaptive step size, and its overall truncation error is .

[0021] S3: Scan position parameters and record corresponding optimization parameters , the minimum distance from the magnetic axis during movement and optimization function value.

[0022] Optimization parameters It is used to measure the integral of the particle momentum in the direction of the magnetic field, specifically: ;in for speed; is the magnetic field; is the duration of the CT movement process.

[0023] Optimizing functions , to find the best injection point, where is the minimum distance from the magnetic axis during the movement, which is further calculated from the results of the S2 model.

[0024] By scanning the position parameters (i.e. all injection positions of CT), we can obtain the results of CT injection from different positions under the current definition. and , calculated according to the definition of the optimization function value and record it in a custom file.

[0025] S4: Draw the corresponding contour map and determine the best injection point. The selection range considered as the best injection point.

[0026] According to the records , and value, draw the corresponding contour map to help design the optimization trajectory, where The selection range considered as the best injection point.

[0027] When drawing the contour map, convert the cylindrical coordinates to Cartesian coordinates: .

[0028] S5: Simulate the trajectory of CT after it is injected into the tokamak device from the optimal injection point to achieve path optimization, and output the radial, annular and axial velocities of CT at each moment under the optimal injection point, the three-dimensional motion trajectory diagram and the energy change timing diagram.

[0029] According to the optimal injection point and the equation solution obtained by the model in S2, a schematic diagram of the tokamak device and the motion trajectory of CT injected into the tokamak is drawn in three-dimensional space. In addition, the motion trajectory is also extracted separately to facilitate a clearer understanding of the movement direction of CT.

[0030] Example 2 The system for trajectory simulation and path optimization of a compact ring core feeding system proposed by the present invention comprises: Setting module, setting device parameters, environmental parameters, CT parameters, initial conditions and vacuum area; The calculation module uses cylindrical coordinates with the center of the tokamak as the origin. Establish a six-degree-of-freedom motion trajectory model; Recording module, scans position parameters and records corresponding optimization parameters , the minimum distance from the magnetic axis during movement and optimization function value; The updating module continuously updates the position coordinates of the CT according to the motion trajectory model, which is used to draw the corresponding motion trajectory schematic diagram and contour diagram, and determine the best injection point; The post-processing module is used to simulate the trajectory of CT after it is injected into the tokamak device from the optimal injection point to achieve path optimization.

[0031] Example 3 The present invention proposes a computer-readable storage medium storing a computer program, which implements the method for trajectory simulation and path optimization of a compact ring core feeding system in Example 1 when executed by a processor.

Claims

1. A method for trajectory simulation and path optimization of a compact ring core feeding system, characterized in that: The steps are as follows: S1: Setting device parameters, environmental parameters, compact ring parameters, initial conditions and vacuum region; S2: Use cylindrical coordinates with the tokamak center as the origin Establish a six-degree-of-freedom motion trajectory model; S3: Scan position parameters and record corresponding optimization parameters , the minimum distance from the magnetic axis during movement and optimization function value; S4: draw the corresponding contour map and determine the best injection point; S5: Simulate the trajectory of the compact ring after it is injected into the tokamak device from the optimal injection point to achieve path optimization.

2. The method for trajectory simulation and path optimization of a compact ring core feeding system according to claim 1, characterized in that: The trajectory model established in S2 is: in, is the Lagrangian; is the Rayleigh dissipation term; ; is the linear kinetic energy; is the rotational kinetic energy; is the potential energy of magnetic field repulsion; is the interaction potential energy between the dipole and the tokamak magnetic field; is the gravitational potential energy; is the MHD resistance; is the thermal diffusion force; is the radiation pressure; is the viscosity force; For electrical conductivity.

3. The method for trajectory simulation and path optimization of a compact ring core feeding system according to claim 1, characterized in that: Optimizing parameters in S3 and optimization function They are: in, is the compact ring speed; is the tokamak magnetic field; is the duration of the movement of the compact ring.

4. The method for trajectory simulation and path optimization of a compact ring core feeding system according to claim 1, characterized in that: Before drawing the contour map in S4, the cylindrical coordinates Convert to Cartesian coordinates .

5. A system for trajectory simulation and path optimization of a compact ring core feeding system, characterized in that: include: Setting module, setting device parameters, environmental parameters, compact ring parameters, initial conditions and vacuum area; The calculation module uses cylindrical coordinates with the center of the tokamak as the origin. Establish a six-degree-of-freedom motion trajectory model; Recording module, scans position parameters and records corresponding optimization parameters , the minimum distance from the magnetic axis during movement and optimization function value; An updating module continuously updates the position coordinates of the compact ring according to the motion trajectory model, which is used to draw the corresponding motion trajectory schematic diagram and contour diagram and determine the optimal injection point; The post-processing module is used to simulate the trajectory of the compact ring after it is injected into the tokamak device from the optimal injection point to achieve path optimization.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for trajectory simulation and path optimization of a compact ring core feeding system as described in any one of claims 1 to 4 is implemented.

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