Simulation method for synergistic effect of Tokamak neutral beam heating and ion cyclotron resonance heating

Abstract

The invention belongs to the field of plasma heating, and discloses a simulation method for a synergistic effect of Tokamak neutral beam heating and ion cyclotron resonance heating. In the process of numerical simulation of the synergistic effect of neutral beam heating and ion cyclotron resonance heating in the Tokamak device, firstly, according to specific neutral beam injection parameters, a distribution function of deposition of high-energy ions generated by ionization in the Tokamak device is calculated; calculating a wave electric field generated by ion cyclotron resonance heating according to the thermionic ion distribution function, the high-energy ion distribution function and radio frequency wave antenna parameters, and simulating the evolution process of corresponding high-energy ions along with time and a quasi-steady-state distribution function through Monte Carlo test particles; and repeating radio-frequency wave electric field calculation by using the updated quasi-steady-state distribution function until the deposition power of ion cyclotron resonance heating reaches convergence, thereby obtaining a quasi-steady-state ion distribution function and power deposition under the synergistic effect of neutral beam heating and ion cyclotron resonance heating.

Description

Technical Field

[0001] The present invention belongs to the field of plasma heating, and relates to the numerical simulation of plasma heating in a Tokamak device in the field of magnetically confined controlled nuclear fusion. In particular, it relates to a simulation method for the synergistic effect of neutral beam heating and ion cyclotron resonance heating in a Tokamak. Background Art

[0002] Magnetically confined controlled nuclear fusion has the potential to solve the future energy problems faced by humanity, and the Tokamak device is the most promising device to achieve magnetically confined controlled nuclear fusion. For fusion plasmas, they first need to achieve an increase in plasma temperature and density through external auxiliary heating and fuel injection to reach the parameter region where fusion reactions can occur to generate high-energy ions for self-heating. Currently, most of the experimental discharge parameters temporarily cannot reach this parameter region with net energy output. Therefore, in order to improve the effect of auxiliary heating and effectively increase the plasma parameters, it is important to perform a self-consistent and accurate simulation of the existing auxiliary heating. Currently, the main ion auxiliary heating methods in experiments are neutral beam injection heating and ion cyclotron resonance heating. Neutral beam injection heating is achieved by injecting high-energy neutral particles generated by an accelerator into the device. These high-energy particles are ionized in the plasma and heat the bulk plasma through collision effects. Ion cyclotron resonance heating is achieved by using electromagnetic waves generated by a radio frequency wave antenna to heat ions, which can effectively heat the ions in the core of the device. Neutral beam heating and ion cyclotron resonance heating are not relatively independent heating means, and they have a further synergistic heating effect, that is, the effect of ion cyclotron resonance heating depends on the distribution function of the neutral beam injected ions, and the further heating of the neutral beam ions depends on the wave electric field of ion cyclotron resonance heating. Therefore, in order to optimize the parameters of auxiliary heating and improve the effect of auxiliary heating, it is crucial to perform a self-consistent and convergent simulation prediction and experimental comparison for neutral beam heating and ion cyclotron resonance heating.

[0003] At present, the simulation of neutral beam injection mainly uses the Monte Carlo particle method to simulate the distribution function of injected high-energy ions, so as to study the characteristics such as the slowing down and loss of neutral beam injection particles. Usually, the influence of other heating methods on high-energy ions of the neutral beam is not considered. For ion cyclotron resonance heating, a wave equation solver and a quasilinear Fokker-Planck equation solver are often coupled to solve the bounce-averaged distribution function and the corresponding heating power under the condition of low-dimensional approximation. The distribution function of high-energy particles generated by neutral beam heating can only be coupled into this calculation process by giving the toroidally averaged approximate distribution through an external program. The co-heating simulation of neutral beam heating and ion cyclotron resonance heating has been carried out less. Even in the existing methods, there are problems such as magnetic field spatial geometry approximation, heating parameter approximation, and no self-consistent iterative calculation. Therefore, there is an urgent need for a simulation method that can self-consistently simulate the co-heating of neutral beam heating and ion cyclotron resonance heating under a real three-dimensional magnetic field configuration. The method proposed by the present invention can well achieve the self-consistent simulation of co-heating, improve the calculation accuracy of the existing simulation method, has high calculation efficiency and strong stability, and is an accurate and reliable numerical simulation method. Summary of the Invention

[0004] The present invention solves the problem that the co-heating simulation of neutral beam heating and ion cyclotron resonance heating cannot be realized under the real three-dimensional magnetic field geometry and real heating parameters in the existing methods. It realizes the self-consistent evolution of information such as the distribution function of the plasma under the co-heating of neutral beam heating and ion cyclotron resonance heating in the real tokamak configuration.

[0005] The technical solution of the present invention:

[0006] A simulation method for the combined action of neutral beam heating and ion cyclotron resonance heating in a tokamak realizes the self-consistent calculation of the plasma distribution function and absorption power under neutral beam heating and ion cyclotron resonance heating, and can more accurately describe the properties of high-energy ions generated by co-heating under the real three-dimensional tokamak configuration. The specific steps are as follows:

[0007] Step 1: Confirm the device parameters and discharge parameters;

[0008] Confirm the tokamak device parameters and discharge parameters, including the configuration geometry of the device, the equilibrium magnetic field of the discharge, and the density and temperature profiles of the main plasma components. Take the device parameters as the simulated equilibrium quantity parameters and do not evolve them during the simulation process; the equilibrium magnetic field is mainly obtained from the data given by the equilibrium inversion program, and the density and temperature profiles of each plasma component are obtained from experimental measurement data;

[0009] Step 2: Calculate the initial distribution of high-energy beam ions injected by the neutral beam;

[0010] Confirm the neutral beam heating parameters used in the verification experiment, including the neutral beam injection position, injection angle, and the energy of the injected ionized ions; calculate and give the initial deposition distribution of the high-energy beam ions injected by using the beam current model;

[0011] Step 3: Calculate the slowing-down distribution of the neutral beam ion distribution function;

[0012] Use the guiding center orbit constructed in the Monte Carlo particle program to evolve the high-energy ion distribution function until a quasi-steady high-energy ion distribution function is obtained, that is, the slowing-down distribution of the neutral beam ion distribution function;

[0013] Step 4: Calculate the radio frequency wave electric field under the slowing-down distribution of the beam ions;

[0014] Confirm the radio frequency antenna parameters of the tokamak device, that is, the shape parameters, position parameters, frequency parameters of the radio frequency wave, and the corresponding toroidal wave number distribution of the radio frequency antenna; use the radio frequency antenna parameters and the simulated equilibrium quantity parameters obtained in Step 1, and use the wave equation solver to solve the ion cyclotron resonance heating wave field information under the high-energy beam ion distribution, that is, solve the wave equation to obtain the wave electric field E;

[0015]

[0016] where ω RF is the circular frequency of the radio frequency wave; c is the speed of light; K is the dielectric tensor; J ant is the radio frequency antenna current, which is given by the radio frequency antenna model using the antenna geometric parameters; is the spatial derivative operator; where the wave electric field E has three components of left-handed, right-handed, and parallel, which are E + 、E - 、E ∥ respectively; the wave vector k ∥ in the direction of the parallel magnetic field of the radio frequency wave is given by the radio frequency antenna, and the wave vector k ⊥ in the direction perpendicular to the magnetic field of the radio frequency wave is given by the dispersion relation;

[0017] Step 5: Calculate the beam ion distribution under ion cyclotron resonance heating;

[0018] Construct a quasilinear operator for the action of the radio frequency wave under the guiding center orbit in the Monte Carlo particle program, apply the action of ion cyclotron resonance heating to the motion of the ions under the guiding center orbit, and evolve the beam ion distribution function until a new quasi-steady state of the system under the new neutral beam heating and ion cyclotron resonance heating is obtained; the specific steps are as follows:

[0019] Step 5.1: According to the particle guiding center orbit information, judge whether the particle is a resonant particle, that is, whether it satisfies the resonance condition:

[0020] ω RF -k ∥ v∥ -nω c = 0

[0021] where v ∥ is the particle velocity parallel to the magnetic field, ω c is the particle cyclotron frequency, and n is the harmonic number of positive integers;

[0022] Step 5.2: If the particle is a resonant particle, then according to the quasilinear diffusion coefficient, use Ito's lemma to give the change of the particle in phase space:

[0023]

[0024] where and Δv ∥ are the changes in the particle's perpendicular and parallel magnetic field velocities v ⊥ and v ∥ under the action of the radio frequency wave, respectively; Δt is the time step used in the simulation, R is a random number uniformly distributed in the interval [0,1]; Γ ⊥ and Γ ∥ are obtained through the diffusion coefficients D ⊥⊥ , D ∥∥ , D ∥⊥ and D ⊥∥ , and the expressions of the diffusion coefficients are:

[0025]

[0026] where q is the particle charge, m is the particle mass, and J n is the nth-order Bessel function; superimpose the change on the unperturbed orbit to obtain the corrected particle orbit under the action of the radio frequency wave;

[0027] Step 5.3: Evolve all beam ions until the distribution function reaches a quasi-steady state, that is, the distribution function of the beam ions no longer has obvious changes, that is, the quasi-steady state of the system under collaborative heating is obtained;

[0028] Step 6: Repeat Step 4 and Step 5 until a convergent beam ion distribution function is obtained, that is, the system reaches a quasi-steady state under self-consistent calculation, and statistically analyze the phase space properties, transport properties of high-energy ions, and the corresponding power deposition of ion cyclotron resonance heating at this quasi-steady state to give an analysis of the effect of collaborative heating.

[0029] Advantages of the present invention: The present invention realizes a simulation method for the synergistic effect of neutral beam heating and ion cyclotron resonance heating in a tokamak device, solves the problems of ineffective coupling of different heating methods and simplification of models and coordinate systems in existing methods, can more accurately and self-consistently describe the plasma distribution function and power deposition information under the synergistic effect of neutral beam heating and ion cyclotron resonance heating, has high calculation accuracy and strong numerical stability, and is an efficient and stable numerical simulation method. Description of the Drawings

[0030] Figure 1 It is an example diagram of the tokamak configuration and equilibrium magnetic field applicable in the present invention.

[0031] Figure 2 It is an example diagram of the neutral beam line applicable in the present invention.

[0032] Figure 3 It is an example diagram of the wave electric field generated by ion cyclotron resonance heating in the present invention.

[0033] Figure 4 It is an example diagram of the change in the total energy storage of the plasma under the synergistic heating in the present invention.

[0034] Figure 5 It is the main flow chart for the present invention to simulate and calculate ion cyclotron resonance heating. Detailed Embodiment

[0035] The following further illustrates the detailed embodiment of the present invention in combination with the drawings and technical solutions.

[0036] The magnetic field of the tokamak device is composed of nested magnetic surfaces. The configuration geometry and the corresponding example diagram of the magnetic surfaces are as Figure 1 shown. The neutral beam heating mainly injects high-energy neutral beam particles from the outer boundary window of the device to the inside. The distribution schematic diagram of the neutral beam line is as Figure 2 shown. The ion cyclotron resonance heating mainly directly heats the core plasma by generating electromagnetic waves with a radio frequency antenna. The example diagram of the wave electric field mainly used is as Figure 3 shown. Under the synergistic heating, the high-energy ions injected by the neutral beam will be further accelerated by the ion cyclotron resonance heating after reaching the slowing-down distribution, so as to achieve an increase in the overall plasma pressure and energy storage. The increase in the plasma energy storage is as Figure 4 shown. Due to the dependence relationship between the wave electric field and the particle distribution function, the synergistic heating effect of the neutral beam heating and the ion cyclotron resonance heating needs to be solved by self-consistent coupling, that is, after the wave electric field corrects the distribution function, a new quasi-steady state distribution function needs to be used to further correct the wave electric field. Therefore, the above steps need to be repeated multiple times, and finally the physical properties of the plasma under the self-consistent and convergent synergistic heating are obtained.

[0037] The specific implementation steps are as follows:

[0038] Step 1: Confirm the device parameters of the tokamak discharge experiment, mainly the tokamak device configuration parameters, including device size, limiter position, and vacuum equilibrium magnetic field strength. These factors constitute the basic simulation region and background equilibrium quantities, as shown in the appendix Figure 1 The figure shows the poloidal cross-section of the configuration and the equilibrium magnetic surface of the Experimental Advanced Superconducting Tokamak (EAST). This data can be obtained through the output of the equilibrium inversion program. Additionally, for plasma numerical simulation, due to its complex time scale, fast and slow processes need to be distinguished during the simulation. For the high-energy particles injected by neutral beams, the properties of the main plasma can be regarded as slowly varying and thus remain unchanged throughout the simulation. This part mainly involves the confirmation of the main plasma density profile and temperature profile, which can be obtained through experimental measurements. This step is the experimental parameter acquisition step before simulation;

[0039] Step 2: Calculate the initial deposition distribution of neutral beams. This step first requires confirming the neutral beam heating parameters used in the experiment according to the experimental device, namely the neutral beam injection position, injection angle, and the energy of the ionized ions injected. Then, convert them into the coordinates required by the beam model to obtain the initial distribution of high-energy ionized particles deposited in the tokamak plasma region that the beam model can give. Due to the randomness of sampling, this initial distribution actually represents the overall properties of the neutral beam source, that is, set the deposition distribution function of the injected particles per unit time. This step is the initial sampling step of the Monte Carlo particle simulation;

[0040] Step 3: After confirming the equilibrium parameters and calculating the initial deposition distribution of the high-energy beam ions injected by neutral beams, they can be used as input parameters into the Monte Carlo particle program. Taking the initial deposition distribution of beam ions as the source term, continuously supplement particles into the system during the calculation to achieve the neutral beam injection process. With the collision and energy transfer between high-energy beam ions and the background plasma, the average energy of the particles will drop to a specific slowing-down level, and the total particle energy will also reach a quasi-steady state where injection and loss are equivalent. At this time, the slowing-down distribution function of beam ions can be obtained, and the overall properties of beam ions will no longer change significantly. This step is fully implemented in the Monte Carlo particle program;

[0041] Step 4: After obtaining the distribution function of the beam ions, the beam ions can be regarded as a component of the plasma and participate in the solution of the wave equation. In this process, it is necessary to solve the wave equation solver. The basic parameters include the radio frequency antenna parameters, that is, the shape parameters, position parameters of the radio frequency antenna, the frequency parameter of the radio frequency wave, and the corresponding toroidal wave number distribution. In addition, there are also the equilibrium magnetic field parameters and the main plasma parameters confirmed in Step 1, as well as the beam ion distribution function. The purpose of this step is to obtain the wave electric field of the radio frequency wave in the plasma, so that the heating information of the radio frequency wave on the plasma can be calculated using the wave electric field. The specific wave equation and the required output parameters are as follows:

[0042]

[0043] where ω RF is the circular frequency of the radio frequency wave, c is the speed of light, K is the dielectric tensor, and J ant is the radio frequency antenna current, which is given by the radio frequency antenna model using the antenna geometric parameters. Among them, the wave electric field E needs to give three components E + / E - / E ∥ . The wave vector k of the radio frequency wave parallel to the magnetic field direction is given by the radio frequency antenna ∥ , and the wave vector k of the radio frequency wave perpendicular to the magnetic field direction is given by the dispersion relation ⊥ . This step is all implemented in the wave equation solver. The example diagram of the obtained wave electric field is as shown in Figure 3 ;

[0044] Step 5: After obtaining the wave electric field of the ion cyclotron resonance heating under the initial beam ion distribution, it can be used as an input quantity into the Monte Carlo particle program to calculate the acceleration effect of the wave electric field on the beam ions, and further obtain the updated quasi-steady state beam ion distribution. In this step, it is necessary to construct a quasilinear operator for the action of the radio frequency wave under the guiding center orbit in the Monte Carlo particle program, and apply the phase space random variation given by the quasilinear operator to the resonant particles that satisfy the resonance condition ω RF -k ∥ v ∥ -nω c =0:

[0045]

[0046]

[0047] Thus, the corrected particle orbit under the action of the radio frequency wave is obtained. Evolve all beam ions until the distribution function reaches a quasi-steady state, that is, the distribution function of the beam ions no longer has obvious changes, and the quasi-steady state of the system under collaborative heating is obtained. This step is completely implemented in the Monte Carlo particle program;

[0048] ​​​Step 6: Since the effect of the combined neutral beam heating and ion cyclotron resonance heating needs to be solved self-consistently due to the dependence of the wave electric field and the particle distribution function, that is, after the wave electric field corrects the distribution function, the new quasi-steady state distribution function needs to be used to further correct the wave electric field. Therefore, steps 4 and 5 need to be repeated until a converged beam ion distribution function is obtained, that is, the system reaches the quasi-steady state under self-consistent calculation. The phase space properties, transport properties of high-energy ions, and the corresponding power deposition of ion cyclotron resonance heating are statistically analyzed under this quasi-steady state, and the effect analysis of the combined heating is given.

[0049] The above content is a further detailed description of the present invention in combination with the preferred technical solutions, and it cannot be determined that the specific implementation of the invention is limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, simple deductions and substitutions can also be made, which should all be regarded as the protection scope of the present invention.

Claims

1. A method for simulating the synergistic effect of neutral beam heating and ion cyclotron resonance heating in a tokamak, characterized in that: Here are the steps: Step 1: Confirm the device parameters and discharge parameters; Confirm the tokamak device parameters and discharge parameters, including the device's configuration geometry, the discharge equilibrium magnetic field, and the density and temperature profiles of the main plasma components. The device parameters are used as simulated equilibrium parameters and are not evolved during the simulation process. The equilibrium magnetic field is mainly obtained from the data given by the equilibrium inversion program, and the density and temperature profiles of each plasma component are obtained through experimental measurement data. Step 2: Calculate the initial distribution of high energy beam ions injected by neutral beam; Confirm the neutral beam heating parameters used in the experiment, including the neutral beam injection position, injection angle, and injected ion energy; The initial deposition distribution of high energy beam ions injected by neutral beam is calculated by using beam model. Step 3: Calculate the slowing-down distribution of the neutral beam ion distribution function; The high energy ion distribution function is evolved by using the guiding track constructed in the Monte Carlo particle program until a quasi-steady state high energy ion distribution function, i.e. a neutral beam ion distribution function of a slowed-down distribution, is obtained; Step 4: Calculate the radio frequency wave electric field under the beam ion slowing distribution; Confirm the radio frequency antenna parameters of the tokamak device, i.e., the shape parameters, position parameters, frequency parameters of the radio frequency wave, and the corresponding circumferential wave number distribution of the radio frequency antenna; use the radio frequency antenna parameters and the simulated balance quantity parameters obtained in step 1 to use a wave equation solver to solve the ion cyclotron resonance heating wave field information under the high energy beam ion distribution, i.e., solve the wave equation to obtain the wave electric field E; Among them, ω RF is the circular frequency of the radio frequency wave; c is the speed of light; K is the dielectric tensor; J ant is the RF antenna current, which is given by the RF antenna model using the antenna geometric parameters; is the spatial derivative operator; the wave electric field E has three components: left-handed, right-handed, and parallel, which are E + 、E - 、E ∥ ; The RF wave vector k is given by the RF antenna in the direction parallel to the magnetic field ∥ , the wave vector k of the RF wave perpendicular to the magnetic field is given by the dispersion relation ⊥ ; Step 5: Calculate the beam ion distribution under ion cyclotron resonance heating; A quasi-linear operator of the radio frequency wave action under the guiding orbit is constructed in the Monte Carlo particle program, and the ion cyclotron resonance heating effect is applied to the motion of ions under the guiding orbit. The beam ion distribution function is evolved until a new quasi-steady state of the system under new neutral beam heating and ion cyclotron resonance heating is obtained; the specific steps are as follows: Step 5.1: According to the particle's center-guided orbit information, determine whether the particle is a resonant particle, that is, whether it meets the resonance condition: ω RF -k ∥ v ∥ -nω c =0 Among them, v ∥ is the particle parallel to the magnetic field velocity, ω c is the particle cyclotron frequency, n is the harmonic number of a positive integer; Step 5.2: If the particle is a resonant particle, the change of the particle in the phase space is given by using the Ito lemma based on the quasi-linear diffusion coefficient: in, and Δv ∥ are the particle velocities v perpendicular to and parallel to the magnetic field, respectively ⊥ and v ∥ The change under the action of radio frequency waves; Δt is the time step used in the simulation, R is a random number uniformly distributed in the interval [0,1]; Γ ⊥ and Γ ∥ The diffusion coefficient D ⊥⊥ , D ∥∥ , D ∥⊥ and D ⊥∥ It turns out that the expression of the diffusion coefficient is: Where q is the particle charge, m is the particle mass, and J n is an n-order Bessel function; the variation is superimposed on the undisturbed orbit to obtain the modified particle orbit under the action of the radio frequency wave; Step 5.3: Evolve all beam ions until the distribution function achieves a quasi-steady state, that is, the distribution function of the beam ions no longer has obvious changes, that is, the quasi-steady state of the system under cooperative heating is obtained; Step 6: Repeat steps 4 and 5 until a converged beam ion distribution function is obtained, that is, the system reaches a quasi-steady state under self-consistent calculation. Statistically analyze the phase space properties, transport properties and corresponding power deposition of ion cyclotron resonance heating of high-energy ions in this quasi-steady state, and give an analysis of the effect of synergistic heating.

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