Method for trajectory simulation and path optimization of compact ring core feeding system

Abstract

The present invention discloses a method for trajectory simulation and path optimization of a compact ring core feeding system. The method comprises the following steps: S1: setting device parameters, environmental parameters, CT parameters, initial conditions, and vacuum region; S2: establishing a six-degree-of-freedom motion trajectory model in cylindrical coordinates with the tokamak center as the origin; S3: scanning position parameters and recording the corresponding optimization parameters, the minimum distance from the magnetic axis during motion, and the optimization function value; S4: drawing the corresponding contour map and determining the optimal injection point; and S5: simulating the trajectory of the CT after it is injected into the tokamak from the optimal injection point to achieve path optimization. The present invention predicts the optimal injection point of the CT into the tokamak under different conditions, designs and optimizes the CT injection path based on this prediction, and then simulates the optimized motion trajectory using the motion trajectory model.

Description

Technical Field

[0001] The present 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] Nuclear fusion energy is becoming an important component of a cleaner and more sustainable global energy system due to its abundant primary fuel resources, safety, energy efficiency, and minimal environmental impact. In nuclear fusion research, efficient operation of fusion reactors relies on fuel replenishment in the plasma core. However, due to turbulence and instability-driven diffusion, magnetically confined plasmas experience energy and particle losses, requiring a fueling system to replenish these losses. Compact torus injection (CTI) is considered one of the most promising technologies for core fueling in future large-scale fusion reactors. It can effectively improve fusion efficiency, maintain plasma stability, and optimize fuel utilization.

[0003] Under the influence of complex magnetic and electric fields, the trajectory behavior of the compact torus (CT) becomes extremely complex. Its trajectory and stability directly determine the injection efficiency. To ensure the accuracy and efficiency of particle injection, trajectory simulation and design are particularly important. Existing research has focused on simulating particle motion in a uniform magnetic field, while ignoring the nonlinear characteristics of the magnetic field in the tokamak. This leads to significant deviations between simulation results and actual results. Plasma instabilities also complicate particle motion prediction. Therefore, more accurate simulation methods are needed to analyze the particle trajectories during compact torus injection. Furthermore, fuel injection and momentum transport also require efficient trajectory design to improve particle injection efficiency, which will ultimately enhance the operational performance of the tokamak. 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 the compact ring core feeding system, which can realize the prediction of the optimal injection point of CT injection into the tokamak device under different conditions, design and optimize the CT injection path accordingly, and then simulate the optimized motion trajectory through the 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:

[0006] S1: Set device parameters, environmental parameters, CT parameters, initial conditions and vacuum area;

[0007] S2: Use cylindrical coordinates with the tokamak center as the origin Establish a six-degree-of-freedom motion trajectory model;

[0008] S3: Scan position parameters and record corresponding optimization parameters , Minimum distance from the magnetic axis during movement and optimization functions value;

[0009] S4: draw the corresponding contour map and determine the optimal injection point;

[0010] S5: Simulate the trajectory of CT after it is injected into the tokamak device from the optimal injection point to achieve path optimization.

[0011] Preferably, the trajectory model established in S2 is:

[0012]

[0013]

[0014]

[0015] 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 viscous force; For electrical conductivity.

[0016] Preferably, the optimization parameters in S3 and optimization functions They are:

[0017]

[0018]

[0019] in, is the CT velocity; is the tokamak magnetic field; is the duration of the CT movement process.

[0020] Preferably, before drawing the contour map in S4, the cylindrical coordinates Convert to Cartesian coordinates .

[0021] The system for trajectory simulation and path optimization of a compact ring core feeding system proposed in the present invention includes:

[0022] Setting module, setting device parameters, environmental parameters, CT parameters, initial conditions and vacuum area;

[0023] The calculation module uses cylindrical coordinates with the tokamak center as the origin Establish a six-degree-of-freedom motion trajectory model;

[0024] Recording module, scan position parameters and record corresponding optimization parameters , Minimum distance from the magnetic axis during movement and optimization functions value;

[0025] The update 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 map and determine the optimal injection point;

[0026] 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.

[0027] The present invention proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for trajectory simulation and path optimization of a compact ring core feeding system.

[0028] Beneficial technical effects of the present invention:

[0029] The present invention can simulate the motion trajectories of three different forms of CT injected from any position and at any angle under any experimental conditions, and find the optimal injection point of CT in the current situation to optimize the path; by scanning position parameters, the optimal injection point of CT in different situations is predicted, and based on the obtained optimal injection point and parameter conditions, the motion trajectory of CT after injection into the tokamak in the current situation is designed and simulated, 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 future compact ring core feeding systems to achieve deeper feeding depths and higher efficiency in tokamak devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flowchart of the method for trajectory simulation and path optimization of a compact ring core feeding system proposed in the present invention;

[0031] Figure 2 This is a schematic diagram of the optimal injection point outline proposed by the present invention;

[0032] Figure 3This is a three-dimensional schematic diagram of the CT motion trajectory proposed by the present invention;

[0033] Figure 4 This is a schematic diagram of energy changes during CT motion proposed by the present invention. DETAILED DESCRIPTION

[0034] The present invention will be further explained below with reference to specific embodiments.

[0035] Example 1

[0036] 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:

[0037] 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 there is a vacuum area.

[0038] S2: Use cylindrical coordinates with the tokamak center as the origin A six-degree-of-freedom trajectory model was established. After the CT is injected into the tokamak, its trajectory is affected by a variety of forces, including the tokamak's magnetic field (including the interaction between the CT's own magnetic field and the tokamak's magnetic field, magnetic repulsion, and magnetic reconnection), the CT's own rotation, the Lorentz force, magnetohydrodynamic (MHD) drag, thermal diffusion, radiation pressure, inertia, viscosity, conductivity, and gravitational potential energy. This model primarily considers the CT's kinetic energy, its own rotation, the interaction between the dipole and the tokamak, magnetic potential energy, and MHD drag, while also taking into account the other influencing factors mentioned above.

[0039] The specific model is:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] 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 viscous 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); represents the moment of inertia of CT; represents angular velocity; represents the magnetic moment of the 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 diffusivity; 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 velocity between CT and plasma; Indicates the current of CT; Represents the characteristic length of CT.

[0054] Furthermore, the CT morphology can be determined based on the CT parameters set in S1, and the corresponding calculation formula can be selected. For example, existing models typically consider the CT as a sphere, but the present invention expands the CT to include cylinders and rings to accommodate simulations in different experimental objectives and situations. The magnitude of the forces acting on the CT after injection into the tokamak differs depending on the CT morphology. Based on the set CT parameters, the CT morphology is determined, and the corresponding solution formula is selected and applied to the model described in S2 for solution.

[0055] The advantages of a cylindrical CT are: a) it is more realistic; b) it is more suitable for achieving more stable injection during long-pulse operation, making it particularly suitable for EAST simulations. EAST aims to verify advanced tokamak operation modes, focusing on long-pulse and steady-state operation; and c) the cylindrical shape makes it easier to adjust its posture when controlling the injection direction.

[0056] The advantages of the toroidal CT are: a) the toroidal CT has a larger surface area, which increases its contact surface with the plasma, 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 over a larger range, enhancing the heating effect on the tokamak plasma.

[0057] 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 .

[0058] S3: Scan position parameters and record corresponding optimization parameters , Minimum distance from the magnetic axis during movement and optimization functions value.

[0059] 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.

[0060] Optimization function , 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.

[0061] By scanning the position parameters (i.e. all injection positions of CT), the results of CT injection from different positions are obtained under the current definition. and , calculated according to the definition of the optimization function value and record it in a custom file.

[0062] S4: Draw the corresponding contour map and determine the best injection point. The range of choices considered as the best injection point.

[0063] According to the records 、 and value, draw the corresponding contour map to help design the optimization trajectory, where The range of choices considered as the best injection point.

[0064] When drawing the contour map, convert the cylindrical coordinates into Cartesian coordinates: .

[0065] 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 CT radial, annular and axial velocities, three-dimensional motion trajectory diagram and energy change timing diagram at each moment under the optimal injection point.

[0066] Based on the optimal injection point and the equation solutions obtained from the model in S2, a schematic diagram of the tokamak device and the trajectory of the CT injection into the tokamak is drawn in three dimensions. In addition, the trajectory is also extracted separately to provide a clearer understanding of the movement of the CT.

[0067] Example 2

[0068] The system for trajectory simulation and path optimization of a compact ring core feeding system proposed in the present invention includes:

[0069] Setting module, setting device parameters, environmental parameters, CT parameters, initial conditions and vacuum area;

[0070] The calculation module uses cylindrical coordinates with the tokamak center as the origin Establish a six-degree-of-freedom motion trajectory model;

[0071] Recording module, scan position parameters and record corresponding optimization parameters , Minimum distance from the magnetic axis during movement and optimization functions value;

[0072] The update 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 map and determine the optimal injection point;

[0073] 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.

[0074] Example 3

[0075] The present invention proposes a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the method for trajectory simulation and path optimization of a compact ring core feeding system in Example 1 is implemented.

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: Set 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 the position parameters and record the corresponding optimization parameters S para , the minimum distance from the magnetic axis during movement ρ min and optimization function f value; S4: draw the corresponding contour map and determine the optimal 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; The trajectory model established in S2 is: L=T linear +T rotational -U magnetic -U dipole -U gravity F=F MHD +F thermal +F radiation +F viscous +F elec Where L is the Lagrangian; F is the Rayleigh dissipation term; T linear is the linear kinetic energy; T rotational is the rotational kinetic energy; U magnetic is the potential energy of magnetic field repulsion; U dipole is the interaction potential energy between the dipole and the tokamak magnetic field; U gravity is the gravitational potential energy; F MHD is the MHD resistance; F thrmal is the thermal diffusion force; F radiation is the radiation pressure; F viscous is the viscous force; F elec is the electrical conductivity; Optimize parameter S in S3 para And the optimization function f are: f≡100*(1-ρ min )+50*S para Where v is the velocity of the compact ring; B is the tokamak magnetic field; [t1, t2] is the duration of the compact ring's motion; Before drawing the contour map in S4, the cylindrical coordinates Convert to Cartesian coordinates 2. 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 tokamak center as the origin Establish a six-degree-of-freedom motion trajectory model; Recording module, scans the position parameters and records the corresponding optimization parameters S para , the minimum distance from the magnetic axis during movement ρ min and optimization function f value; The 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 map and determine the optimal injection point; A 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; The trajectory model established in the calculation module is: L=T linear +T rotational -U magnetic -U dipole -U gravity F=F MHD +F thermal +F radiation +F viscous +F elec Where L is the Lagrangian; F is the Rayleigh dissipation term; T linear is the linear kinetic energy; T rotational is the rotational kinetic energy; U magnetic is the potential energy of magnetic field repulsion; U dipole is the interaction potential energy between the dipole and the tokamak magnetic field; U gravity is the gravitational potential energy; F MHD is the MHD resistance; F thrmal is the thermal diffusion force; F radiation is the radiation pressure; F viscous is the viscous force; F elec is the electrical conductivity; Optimization parameter S in the recording module para And the optimization function f are: f≡100*(1-ρ min )+50*S para Where v is the velocity of the compact ring; B is the tokamak magnetic field; [t1, t2] is the duration of the compact ring's motion; Before drawing the contour in the update module, the cylindrical coordinates Convert to Cartesian coordinates 3. 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 claimed in claim 1 is implemented.

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