Simulation method for tokamak neutral beam injection and fast ion deposition

Abstract

The application discloses a simulation method for tokamak neutral beam injection and fast ion deposition. In the numerical simulation of the neutral beam particle injection and ionization process in a tokamak device, the physical parameters of the neutral beam injection device are determined first, then the injection source is simplified by using a narrow particle beam model, the neutral beam particle density of a reference point given under geometric conditions is calculated, the average free path of the neutral beam particle ionization is calculated after the parameters of the position of the reference point in the plasma interior are obtained, the ions in different regions are divided by using a non-uniform grid and are given different weights, and finally the simulation process of the neutral beam injection is realized. The application realizes the simulation of the injection process of the neutral beam particles by using the narrow particle beam model, can obtain the neutral particle and fast ion distribution at any position in the plasma, has high calculation efficiency and strong numerical stability, and is a stable and efficient numerical simulation method.

Description

Technical Field

[0001] This invention belongs to the field of magnetically confined controlled nuclear fusion and relates to numerical simulation of tokamak device feeding, specifically a simulation method for neutral beam injection and fast ion deposition in tokamak. Background Technology

[0002] With the continuous progress and development of society, human demand for energy is constantly increasing. For a long time, human life and production have relied mainly on fossil fuels, but fossil fuel reserves are limited, and burning fossil fuels also causes environmental pollution. Nuclear fusion energy has the advantages of abundant resources and not producing carbon dioxide, thus avoiding the greenhouse effect, making it an ideal new energy source. Among many controlled nuclear fusion schemes, magnetic confinement is considered the most feasible method. Therefore, to solve this problem, seven countries, including my country, jointly launched the International Thermonuclear Experimental Reactor (ITER) project. To achieve magnetically confined controlled nuclear fusion, the stability of plasma under quasi-steady-state operation in the tokamak reactor must first be addressed. Currently, the development and research of nuclear fusion energy has entered the second stage, namely solving the steady-state combustion problem. This requires in-depth research into fusion combustion physics and experimental processes, including steady-state combustion, fueling efficiency, combustion efficiency, steady-state heating and energy transfer, high-energy particle physics, and fracture physics and control. Tokamaks commonly use ohmic heating to initiate plasma discharge, but because ohmic heating transformers can only operate in pulses, they are not suitable for the steady-state operation of fusion reactors. Therefore, to achieve the plasma temperature required for fusion and ensure the steady-state operation of the fusion reactor, auxiliary heating and non-inductive current driving of the plasma are necessary. Currently, external high-energy neutral beam injection (NBI) is mainly used to heat the fusion reactor. Since neutral beam particles are uncharged, they can pass through the magnetic field and be injected into the plasma. The injected high-energy neutral particle beam is confined through ionization or charge exchange with charged particles, and then gradually slowed down through collisions, thus heating the plasma.

[0003] Currently, the Monte Carlo method is mainly used to simulate neutral beam injection. Although this method can obtain accurate simulation results, it requires huge computational resources. Summary of the Invention

[0004] To address the high computational resource requirements of existing Monte Carlo algorithms for neutral beam injection modules, and to achieve high-precision simulation results with limited computational resources under the condition of a neutral beam injection source with finite width, this invention provides a simulation method for neutral beam injection and fast ion deposition in tokamak devices. The narrow particle beam model proposed in this invention considers the focusing and angular scattering geometry of the neutral beam injection. Since the size of the injection source in modern tokamak devices is very small compared to the distance from the injection source to the tokamak, the actual ion source can be described using a reference point within the narrow particle beam. Simultaneously, the geometric length of the beam center is approximated as the distance the particles travel in the plasma to calculate the ionization process of the neutral beam, and the discreteness introduced by the injection aperture on the injection source is ignored. The spatial distribution of neutral beam particles is obtained analytically, which is the construction principle of the narrow particle beam model. This simplification using the narrow particle beam model achieves the simulation of the neutral beam injection process in tokamak plasma. Compared to the Monte Carlo model, which has a relatively high computational cost but is more physically accurate, the beam model balances the accuracy of the physical process with computational efficiency.

[0005] The technical solution adopted in this invention is as follows:

[0006] A simulation method for neutral beam injection and fast ion deposition in a tokamak includes the following steps:

[0007] Step 1: Describe the actual ion source using a reference point within a narrow particle beam. Simultaneously, approximate the geometric length of the beam center as the distance the particles travel in the plasma to calculate the ionization process of the neutral beam, neglecting the discreteness introduced by the injection orifice on the injection source, thus constructing a narrow particle beam model. Without considering ionization, the formula for calculating the spatial distribution of neutral beam particle density using the narrow particle beam model is:

[0008]

[0009] Where Δθ is the beam diffusion angle, x b ,y b Let (z, θ, φ) be the space between the two directions of the beam plane, and let (z, θ, φ) be the coordinate system established based on the neutral beam emission source plane. z The direction is the axial direction of the neutral beam towards the plasma, e θ With e φ The direction describes the focusing and divergence of the neutral beam; such a coordinate system can construct a non-uniform grid and obtain a certain number of reference points within the plasma; θ b For the reference point and the point on the bundle plane (x) b ,y b The straight line formed by (x) and (x) b ,y b Based on the angle formed by the directions of the projectiles emitted by the focusing parameters, we can obtain:

[0010]

[0011] Step 2: Obtain key physical parameters of the neutral beam injection device, such as the position of the beam plane, focal length, divergence angle, etc., and simplify them using a narrow particle beam model to obtain the reference point position information.

[0012] Step 3: The neutral beam density at the reference points divided in the z-coordinate system can be obtained based on the geometric configuration of the narrow particle beam model. And a continuous density distribution is obtained through interpolation;

[0013] Step 4: Transform the reference point position on the z-coordinate to the cylindrical coordinate system used to describe the tokamak. After obtaining parameters such as electron density and temperature at the reference point position, the mean free path of the neutral beam particles undergoing ionization, charge exchange, and other processes can be calculated.

[0014] Step 5: Calculate the number of fast ions and the velocity of fast ions at the reference point using the neutral beam density and mean free path. The specific steps are as follows:

[0015] Step 5.1: Calculate the density of fast ions at the reference point using the neutral beam density and mean free path.

[0016] Step 5.2: Integrate the density spatially to obtain the number of fast ions in the given space;

[0017] Step 5.3: Re-divide the weights of the reference point ions using a non-uniform mesh to reduce errors in subsequent propulsion processes.

[0018] Step 6: Store the information of fast ions for subsequent propulsion.

[0019] The beneficial effects of this invention are as follows: This invention achieves accurate simulation of neutral beam injection under different tokamak devices, solves the problem of excessive computational load and large consumption of computational resources in the existing Monte Carlo method for simulating neutral beam injection, and adopts a narrow particle beam injection method, which can efficiently and accurately calculate the ionization rate of neutral beam particles inside the plasma. It has high computational efficiency and strong numerical stability, and is an efficient and stable numerical simulation method. Attached Figure Description

[0020] Figure 1 This is a three-dimensional diagram of a neutral beam-injected tokamak to which the method of this invention is applicable.

[0021] Figure 2 This is a diagram of the narrow beam model constructed in this invention.

[0022] Figures 3(a) and 3(b) are the temperature and density profiles of the ITER device 130504 gun at 260s in the embodiment.

[0023] Figure 4 This is the main flowchart of the method of the present invention. Detailed Implementation

[0024] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0025] The magnetic field of a tokamak device consists of nested magnetic surfaces. During neutral beam injection, given the physical parameters of the injection device, as shown in Table 1, the density distribution of neutral beam particles can be determined by… Figure 2 The results were calculated using the narrow particle model shown. This embodiment first uses a narrow particle beam model to simulate the injection of the neutral beam. Experimentally, neutral beam particles pass through a series of devices from generation to injection into the tokamak plasma, resulting in a relatively long path. Under these conditions, the narrow particle beam model can accurately simulate the distribution of the neutral beam particles. Then, based on parameters such as electron density and temperature at the location of the neutral beam particles, and combined with a scattering cross-section database, the mean free path of the ionization and charge exchange processes of the neutral beam particles can be calculated. Figures 3(a) and 3(b) show the temperature and density profiles of the ITER device. Finally, the distribution of high-energy ions generated by the neutral beam injection is obtained, as shown in the three-dimensional schematic diagram. Figure 1 As shown.

[0026] Table 1 Neutral beam injection parameters of the ITER device

[0027]

[0028] The basic process of this invention is as follows: Figure 4 As shown, the specific implementation steps are as follows:

[0029] Step 1: Obtain key physical parameters of the neutral beam injection device. Taking the ITER device as an example, obtain information such as the injection radius, horizontal and vertical focal lengths, and diffusion angle of the neutral beam injection system of the ITER device, as shown in Table 1. Then, a narrow particle beam model is used to process the physical process of neutral beam injection. This model allows the definition of a z-coordinate system to construct a non-uniform mesh and obtain a certain number of reference points within the plasma.

[0030] Step 2: The neutral beam density at the reference points divided in the z-coordinate system can be obtained based on the geometric configuration of the narrow particle beam model. And a continuous density distribution is obtained through interpolation;

[0031] Step 3: Transform the reference point position on the z-coordinate to the cylindrical coordinate system commonly used to describe ITER. After obtaining information such as the electron density and temperature profile of a certain shot of the ITER device, interpolation is used to obtain parameters such as electron density and temperature at the reference point position. Figures 3(a) and 3(b) show the temperature and density profile of shot 130504 of the ITER device at 298.5s. Then, the mean free path of the neutral beam particles undergoing ionization and charge exchange processes at this location is calculated using Janev's collision database.

[0032] Step 4: Using the neutral beam density and mean free path at the reference point, the number of fast ions and the velocity of fast ions at the reference point can be calculated. The specific steps are as follows:

[0033] Step 4.1: Calculate the density of fast ions at the reference point using the neutral beam density and mean free path.

[0034] Step 4.2: Integrate the density spatially to obtain the number of fast ions in the given space;

[0035] Step 4.3: Re-divide the weights of the reference point ions using a non-uniform mesh to reduce errors in the subsequent propulsion process.

[0036] Step 5: Store the information of fast ions for subsequent propulsion.

Claims

1. A simulation method for neutral beam injection and fast ion deposition in a tokamak, characterized in that, Includes the following steps: Step 1: Describe the actual ion source using a reference point within a narrow particle beam. Simultaneously, approximate the geometric length of the beam center as the distance the particles travel in the plasma to calculate the ionization process of the neutral beam, neglecting the discreteness introduced by the injection aperture on the injection source, thus constructing a narrow particle beam model. Without considering ionization, the formula for calculating the spatial distribution of the neutral beam particle density using the narrow particle beam model is: Where Δθ is the beam diffusion angle, x b ,y b Let (z, θ, φ) be the space between the two directions of the beam plane, and let (z, θ, φ) be the coordinate system established based on the neutral beam emission source plane. z The direction is the axial direction of the neutral beam towards the plasma, e θ With e φ The direction describes the focusing and divergence of the neutral beam; such a coordinate system can construct a non-uniform grid and obtain a certain number of reference points within the plasma; θ b For the reference point and the point on the bundle plane (x) b ,y b The straight line formed by (x) and (x) b ,y b Based on the angle formed by the directions of the projectiles emitted by the focusing parameters, we can obtain: Step 2: Obtain the key physical parameters of the neutral beam injection device, including the position of the beam plane, focal length and divergence angle. Simplify the model using a narrow particle beam to obtain the reference point position information. Step 3: Determine the neutral beam density at the reference points in the z-coordinate system based on the geometric configuration of the narrow particle beam model. And a continuous density distribution is obtained through interpolation; Step 4: Transform the reference point position on the z-coordinate to the cylindrical coordinate system used to describe the tokamak, obtain the parameters of the reference point position including electron density and temperature, and then calculate the mean free path of the neutral beam particles, including the processes of ionization and charge exchange. Step 5: Calculate the number of fast ions and the velocity of fast ions at the reference point using the neutral beam density and mean free path. The specific steps are as follows: Step 5.1: Calculate the density of fast ions at the reference point using the neutral beam density and mean free path. Step 5.2: Integrate the density spatially to obtain the number of fast ions in the given space; Step 5.3: Re-divide the weights of the reference point ions using a non-uniform mesh to reduce errors in subsequent propulsion processes; Step 6: Store the information of fast ions for subsequent propulsion.

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