Method, apparatus and medium for evaluating ion cyclotron resonance heating efficiency of a stellarator

Abstract

The application provides a method, device and medium for evaluating ion cyclotron resonance heating efficiency of a stellarator. The method comprises the following steps: obtaining plasma parameters of plasma in the stellarator, wave parameters of incident waves used for heating the plasma, and device parameters of the stellarator, calculating single-pass absorption parameters used for evaluating the heating efficiency according to the plasma parameters, the wave parameters and the device parameters, and determining a heating type of ion cyclotron resonance heating according to ion properties of the plasma in the stellarator; determining a single-pass absorption model corresponding to the heating type, and calculating a single-pass absorption rate corresponding to the heating type by using the single-pass absorption model according to the single-pass absorption parameters, the wave parameters and the device parameters; and evaluating the heating efficiency according to the single-pass absorption rate. The heating efficiency evaluation method provided by the application is suitable for a single machine environment, does not consume too much computing power, and has a small error.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nuclear fusion, in particular to a method for evaluating ion cyclotron resonance heating efficiency of a stellarator. BACKGROUND

[0002] Controllable fusion ignition is the key to the development of nuclear fusion energy. Fusion ignition requires the requirement of plasma triple product, i.e. triple product, i.e. to confine the plasma with extremely high density and extremely high temperature for a long enough time. For a stellarator, auxiliary heating is needed to achieve fusion ignition.

[0003] Existing fusion devices mainly rely on three kinds of auxiliary heating methods:

[0004] First, electron cyclotron resonance heating: heating electrons by high-frequency microwave resonance. This method requires an expensive gyrotron system, and the cost of a high-frequency microwave generator is extremely high.

[0005] Second, neutral beam injection: relying on high-energy neutral atomic beam collision ionization heating. This method requires a pre-existing plasma as a target, and in the three-dimensional magnetic field of the stellarator, it is easy to cause fast ion orbit loss, resulting in a decrease in heating efficiency and possible damage to the device wall.

[0006] Third, ion cyclotron resonance heating: directly heating ions through resonance effect. This method has the advantages of high heating efficiency, diverse modes, and no density limit, especially in fusion reactor level high density plasma, it can still effectively penetrate to the core, and has become the mainstream heating scheme.

[0007] In order to more accurately control fusion ignition, the heating efficiency of the heating method needs to be calculated. Although the advantages of ion cyclotron resonance heating are obvious, there is still a contradiction between calculation efficiency and computing power consumption when calculating the heating efficiency. Specifically, the existing heating efficiency calculation generally adopts full-wave method, finite element method or ray tracing method. Among them, the full-wave method and the finite element method are based on Maxwell's equations for calculation, and in the calculation process, high-dimensional dense matrices need to be processed, the calculation complexity is high, and in the calculation, it depends on supercomputer cluster resources, and cannot be realized in a single machine environment. Fast evaluation. While the ray tracing method can be evaluated in a single machine environment, it uses geometric optics approximation to simplify the wave propagation model, which is suitable for short wavelength heating. For ion cyclotron resonance heating, which has a longer wavelength, the diffraction and tunneling effect of the wave beam in the plasma is significant, and the optical approximation is easy to introduce systematic errors, which will result in larger calculation result errors.

[0008] Therefore, in the prior art, the efficiency calculation method for ion cyclotron resonance heating has the problem that the computing power consumption of high-precision algorithms is large, and the precision of single-machine executable algorithms is insufficient. SUMMARY

[0009] The purpose of this invention is to address the problems in existing technologies for calculating the efficiency of ion cyclotron resonance heating, where high-precision algorithms consume significant computational power, while algorithms that can be run on a single machine lack sufficient accuracy. To solve these technical problems, the embodiments of this invention disclose a method for evaluating the efficiency of ion cyclotron resonance heating in a stellarator, comprising: acquiring plasma parameters of the plasma within the stellarator, wave parameters of the incident wave used to heat the plasma, and device parameters of the stellarator; calculating single-pass absorption parameters for evaluating heating efficiency based on the plasma parameters, wave parameters, and device parameters; determining the heating type of ion cyclotron resonance heating based on the ion properties of the plasma within the stellarator; determining a single-pass absorption model corresponding to the heating type; calculating the single-pass absorption rate corresponding to the heating type using the single-pass absorption parameters, wave parameters, and device parameters and the single-pass absorption model; and evaluating the heating efficiency based on the single-pass absorption rate.

[0010] Another specific embodiment of the present invention discloses a method for evaluating the ion cyclotron resonance heating efficiency of a stellarator. The ion properties include the resonance frequency relationship between minority ions and main ions in the plasma; the heating type includes a first heating type and a second heating type, wherein the first heating type is a synergistic heating mode of minority ion heating and harmonic heating, and the second heating type is a single heating mode of minority ion heating; furthermore, determining the heating type of ion cyclotron resonance heating based on the ion properties of the plasma within the stellarator includes: when the resonance frequencies of minority ions and main ions satisfy harmonic resonance... Under certain conditions, the heating type is determined as the first heating type; when the resonance frequency of the minority ions and the main ions does not meet the harmonic resonance condition, the heating type is determined as the second heating type. The resonance frequency relationship is determined based on the multiple relationship between the charge-to-mass ratio of the minority ions and the charge-to-mass ratio of the main ions. If the charge-to-mass ratio of the minority ions and the main ions is an integer multiple, then the resonance frequency of the minority ions and the main ions is determined to meet the harmonic resonance condition; if the charge-to-mass ratio of the minority ions and the main ions is not an integer multiple, then the resonance frequency of the minority ions and the main ions is determined not to meet the harmonic resonance condition.

[0011] In another specific embodiment of the present invention, the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator disclosed in this embodiment includes plasma parameters such as the mass, charge, density, and temperature of minority and main ions; wave parameters such as the parallel beam of the incident wave and the frequency of the incident wave; device parameters such as the large radius of the stellarator and the magnetic field strength of the plasma core; and single-pass absorption parameters such as wave cyclotron frequency, ion cyclotron frequency, plasma frequency, thermal velocity, and plasma specific pressure. Furthermore, the single-pass absorption parameters for evaluating the heating efficiency are calculated based on the plasma parameters, wave parameters, and device parameters, including: calculating the wave cyclotron frequency based on the frequency of the incident wave; calculating the ion cyclotron frequency based on the charge and mass of minority and main ions, the magnetic field strength, and the charge of electrons; calculating the plasma frequency based on the density, mass, and charge of electrons; calculating the thermal velocity based on the temperature and mass of minority and main ions; and calculating the plasma specific pressure based on the density and temperature of minority and main ions and the magnetic field strength.

[0012] In another specific embodiment of the present invention, the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator disclosed in this embodiment calculates the wave cyclotron frequency according to the following formula:

[0013]

[0014] in, The cyclotron frequency is the frequency of the wave. denoted as , where is the frequency of the incident wave.

[0015] The ion cyclotron frequency can be calculated using the following formula:

[0016]

[0017] in, The ion cyclotron frequency, For charge, The charge of an electron. The magnetic field strength, For quality, Taking 1 to represent the main ion, The value of 2 indicates a minority of ions.

[0018] The plasma frequency is calculated using the following formula:

[0019]

[0020] in, For plasma frequency, For the density of electrons, The charge of an electron. For the mass of electrons, It is the vacuum dielectric constant.

[0021] Calculate the heat rate using the following formula:

[0022]

[0023] in, For thermal velocity, For temperature, For quality, Taking 1 to represent the main ion, The value of 2 indicates a minority of ions.

[0024] The plasma specific pressure is calculated using the following formula:

[0025]

[0026] in, The plasma specific pressure, For pressure, where, , density Boltzmann's constant, For temperature, The magnetic field strength, The permeability of free space, Taking 1 to represent the main ion, The value of 2 indicates a minority of ions.

[0027] In another specific embodiment of the present invention, the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator disclosed in this embodiment of the present invention, wherein the single-pass absorption model corresponding to the first heating type is:

[0028]

[0029] in, The single-pass absorption rate corresponding to the first heating type. For the parallel beam of the incident wave, For the large radius of the stellarator, The intrinsic velocity of electromagnetic wave propagation. .

[0030] The single-pass absorption model corresponding to the second heating type is:

[0031]

[0032] in, This represents the single-pass absorption rate corresponding to the second heating type. For the parallel beam of the incident wave, For the large radius of the stellarator, The intrinsic velocity of electromagnetic wave propagation. .

[0033] In another specific embodiment of the present invention, the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator disclosed in this embodiment further includes a third heating type, wherein the third heating type is a primary and secondary heating mode of minority ion heating and mode switching heating; the plasma parameters also include the concentration of minority ions; the wave parameters also include the incident angle; the device parameters also include magnetic field shear; and, when the resonance frequency of minority ions and primary ions does not meet the harmonic resonance condition, the method further includes: determining whether the start-up condition for mode switching heating is met based on the plasma parameters, wave parameters, and device parameters; if yes, the heating type is determined to be the third heating type; if no, the heating type is determined to be the second heating type.

[0034] The initiation conditions for mode switching heating include: the concentration of a minority of ions is below a preset concentration threshold, the angle between the incident angle and the magnetic field is 80° to 100°, and the magnetic field shear rate is higher than a preset shear rate threshold; the single-pass absorption model corresponding to the third heating type is:

[0035]

[0036] in, The single-pass absorption rate corresponding to the third heating type. For the parallel beam of the incident wave, For the large radius of the stellarator, The single-pass absorbance corresponding to the mode switching heating was obtained through fitting. The intrinsic velocity of electromagnetic wave propagation. .

[0037] Another specific embodiment of the present invention discloses a method for evaluating the ion cyclotron resonance heating efficiency of a stellarator, which evaluates the heating efficiency based on the single-pass absorptivity, including at least one of multi-parameter analysis, target-driven optimization, and feasibility verification. The multi-parameter analysis includes: estimating the heating efficiency corresponding to different plasma parameters and wave parameters under the same device parameters, and identifying the parameters that have the greatest impact on the single-pass absorptivity. The target-driven optimization includes: determining the optimal parameter combination using an optimization algorithm based on a preset single-pass absorptivity target value. The feasibility verification includes: determining the feasible range of the wave parameters and plasma parameters under the constraint of fixed device parameters.

[0038] In another specific embodiment of the present invention, the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator disclosed in this embodiment of the present invention uses deuterium ions as the main ion and hydrogen ions or helium-3 ions as a minority of ions.

[0039] An embodiment of the present invention discloses an electronic device, including: a processor and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in any of the above embodiments.

[0040] The present invention discloses a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in any of the above embodiments.

[0041] The beneficial effects of this invention are:

[0042] This application can calculate single-pass absorption parameters based solely on plasma parameters, wave parameters, and stellarator device parameters to assess heating efficiency. It does not rely on complex computing power and can operate on a standalone machine, thus improving computational efficiency. Furthermore, it matches different single-pass absorption models to calculate the single-pass absorptivity according to the heating type, avoiding model distortion and improving computational accuracy. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator provided in this embodiment of the invention.

[0044] Figure 2 This is a contour plot of the single-pass absorption rate in the DH minority ion mode calculated in the evaluation method of stellarator ion cyclotron resonance heating efficiency provided in the embodiments of the present invention. Detailed Implementation

[0045] As described in the background section, existing methods for calculating the efficiency of ion cyclotron resonance heating suffer from several drawbacks: high-precision algorithms require significant computational power, while stand-alone algorithms lack sufficient accuracy. To address these issues, this application provides a method for evaluating the efficiency of ion cyclotron resonance heating in a stellarator. This method calculates single-pass absorption parameters based solely on plasma parameters, wave parameters, and stellarator device parameters to assess heating efficiency. It eliminates the need for complex computing power, allowing for stand-alone operation and improving computational efficiency. Furthermore, by matching different single-pass absorption models to the heating type for calculating the single-pass absorptivity, model distortion is avoided, further enhancing computational accuracy.

[0046] Before describing the assessment method in detail, the relevant terms will be explained.

[0047] Plasma: Generally refers to matter containing free charged particles with sufficient energy, whose motion is primarily influenced by electromagnetic forces. It typically refers to ionized gas, whose behavior is dominated by the self-consistent interaction between charged particles and electric and magnetic fields.

[0048] Stellarator: One of the most important experimental devices for controlled magnetic confinement fusion research. Its name comes from the English word "stellar," signifying the ability to generate high-temperature thermonuclear fusion plasma similar to that of a star. This device typically consists of a closed toroidal stainless steel vacuum chamber and external helical windings, poloidal and circumferential field coils to generate the magnetic field. First, a neutral fuel gas (such as a deuterium-tritium mixture) is injected into the vacuum chamber, where it is heated and ionized by waves to form plasma. This confines charged particles within the toroidal vacuum chamber under the influence of a three-dimensional helical magnetic field. Next, a high-power radio frequency wave or neutral beam is injected to further heat the plasma, achieving very high temperatures, densities, and energy confinement times to achieve fusion ignition.

[0049] Example 1:

[0050] This embodiment provides a method for evaluating the ion cyclotron resonance heating efficiency of a stellarator, referring to... Figure 1 This includes the following steps:

[0051] First, the plasma parameters of the plasma inside the stellarator, the wave parameters of the incident wave used to heat the plasma, and the device parameters of the stellarator are obtained. Based on the plasma parameters, wave parameters, and device parameters, the single-pass absorption parameters used to evaluate the heating efficiency are calculated. Then, the heating type of ion cyclotron resonance heating is determined based on the ion properties of the plasma inside the stellarator.

[0052] Secondly, determine the single-pass absorption model corresponding to the heating type, and calculate the single-pass absorption rate corresponding to the heating type using the single-pass absorption model based on the single-pass absorption parameters, wave parameters, and device parameters.

[0053] Then, the heating efficiency was evaluated based on the single-pass absorption rate.

[0054] Specifically, plasma parameters refer to parameters related to the properties of the plasma within the stellarator, including but not limited to electron density and temperature profiles, ion temperature profiles, minority ion composition and concentration, main ion composition and concentration, and plasma current profiles. Among these, electron density and temperature profiles are calculated using the Thomson scattering method or measured using an interferometer or polarimeter; ion temperature profiles are measured using charge-exchange recombination spectroscopy or passive spectroscopy; minority ion composition and concentration, and main ion composition and concentration are measured using vacuum ultraviolet spectroscopy or soft X-ray spectroscopy; and plasma current profiles are calculated through magnetic measurement inversion.

[0055] Wave parameters are parameters related to the properties of the incident wave, including but not limited to the incident wave frequency and wavelength, which can be obtained through antenna parameter measurement or fast Fourier transform analysis.

[0056] Device parameters are parameters related to the structure of the stellarator, including but not limited to the configuration of the balance magnetic surface, coil current, geometric model of the vacuum chamber, etc., which can be obtained through balance code output or modeling software.

[0057] The single-pass absorption parameter is a key parameter combination that integrates plasma parameters, wave parameters, and device parameters, comprehensively reflecting the plasma's absorption capacity for ion cyclotron resonance waves. The single-pass absorption parameter can be calculated using a formula fitted from a large amount of experimental data, or by employing a characteristic scale normalization method.

[0058] Ionic properties are those related to the properties of the plasma within the stellarator, including but not limited to the relationship between the cyclotron frequency of a few ions and the incident wave, as well as the proportion of ions in the plasma.

[0059] Heating types include, but are not limited to, minority ion fundamental frequency heating, majority ion harmonic heating, mode-switching heating, and direct electronic damping. The criteria for minority ion fundamental frequency heating are that the incident wave frequency is equal to the cyclotron frequency of the minority ions, and the minority ion density is much smaller than the main ion density. The criteria for majority ion harmonic heating are that the incident wave frequency is a multiple of the cyclotron frequency of the main ions. The criteria for mode-switching heating are that the incident wave frequency is approximately equal to the cyclotron frequency of the minority ions and occurs at the plasma edge or in a low-density region. The criteria for direct electronic damping are that the harmonics exceed a preset threshold.

[0060] The specific heating type can be determined as follows: Calculate the cyclotron frequencies of all main ions at the typical magnetic field of the plasma core, and compare the multiple relationship between the incident wave frequency and the cyclotron frequencies of the main ions; then check the types and density ratios of ions whose incident wave frequency is an integer multiple of the cyclotron frequencies of the main ions; next, determine whether the mode transition condition is approaching by combining the antenna emission spectrum; finally, output the heating type based on preset rules. These preset rules include, but are not limited to, threshold rules, which specify the numerical range of the multiple relationship and density ratio corresponding to each heating type, and output the corresponding heating type when it falls within the corresponding range; or a classification algorithm, such as outputting the confidence level corresponding to each heating type based on parameters like the multiple relationship and density ratio, and outputting the heating type with the highest confidence level.

[0061] The calculation of single-pass absorption rate involves calling the corresponding physical model based on the heating type. This physical model can be retrieved from a physical model library, which includes analytical or semi-empirical models optimized for different heating types. Alternatively, it can be generated using a proxy model library. This proxy model library integrates high-fidelity full-wave code and dynamic code, enabling extensive offline calculations in high-dimensional parameter spaces, such as neural network calculations and Gaussian regression, to establish a proxy model.

[0062] Assessing heating efficiency based on single-pass absorptivity involves converting the single-pass absorptivity into an engineering or physical assessment of heating efficiency. For example, the single-pass absorptivity can be directly input into a pre-fitted formula, and the specific value of the heating efficiency can be output. Alternatively, the radial distribution of incident wave power deposited in the plasma can be estimated by combining a wave propagation model. Furthermore, the proportion of ion absorption power can be output based on the single-pass absorptivity, thus providing a data basis for subsequent stellarator optimization.

[0063] This approach, which represents the process of incident wave heating particles using the single-pass absorptivity index, effectively reduces the computational dimensionality, eliminating the need for calculations and solutions across the entire spatial field, thus reducing computational power consumption. Furthermore, the single-pass absorption model in this scheme can output the single-pass absorptivity based solely on the single-pass absorption parameters, wave parameters, and device parameters, enabling standalone operation and improving computational efficiency. Moreover, different heating types are determined based on different ion properties, and corresponding single-pass absorption models are further defined, avoiding distortions caused by inaccurate or oversimplified models and improving the accuracy of single-pass absorptivity calculations. Additionally, the fusion calculation of device parameters, wave parameters, and plasma parameters covers multi-dimensional influencing factors related to particles, incident waves, and the device itself, further enhancing the accuracy of single-pass absorptivity calculations.

[0064] Furthermore, in a preferred implementation, the ion properties include the resonant frequency relationship between minority ions and main ions in the plasma; the heating type includes a first heating type and a second heating type, wherein the first heating type is a synergistic heating mode of minority ion heating and harmonic heating, and the second heating type is a single heating mode of minority ion heating.

[0065] Specifically, the resonance frequency varies depending on the type of ion. The combination of the main ion and the minority ion includes, but is not limited to, the following: the main ion is a deuterium ion and the minority ion is a hydrogen ion (DH); the main ion is a deuterium ion and the minority ion is a helium-3 ion (D-³He); the main ion is a deuterium particle and the minority ion is a tritium ion (DT); and the main ion is a tritium ion and the minority ion is a hydrogen ion (HT).

[0066] Furthermore, in this evaluation method, the heating type of ion cyclotron resonance heating is determined based on the ion properties of the plasma inside the stellarator, including: when the resonance frequency of minority ions and main ions meets the harmonic resonance condition, the heating type is determined as the first heating type; when the resonance frequency of minority ions and main ions does not meet the harmonic resonance condition, the heating type is determined as the second heating type.

[0067] Specifically, the resonance frequency relationship is determined based on the multiple relationship between the charge-to-mass ratio of the minority ions and the charge-to-mass ratio of the main ions. If the charge-to-mass ratio of the minority ions is an integer multiple of the charge-to-mass ratio of the main ions, then the resonance frequencies of the minority ions and the main ions satisfy the harmonic resonance condition; if the charge-to-mass ratio of the minority ions is not an integer multiple of the charge-to-mass ratio of the main ions, then the resonance frequencies of the minority ions and the main ions do not satisfy the harmonic resonance condition. More specifically, in the above ion combinations, in the DH combination, the charge-to-mass ratio of hydrogen is twice that of deuterium, and its cyclotron frequency is also twice that of the deuterium ion; therefore, the DH combination is determined to satisfy the harmonic resonance condition; in the D-³He combination, 3 The charge-to-mass ratio of He is not an integer multiple of that of Deuterium, therefore the D-³He combination is determined not to satisfy the harmonic resonance condition; in the DT combination, the charge-to-mass ratio of Tritium is not an integer multiple of that of Deuterium (3 / 2), therefore the DT combination is determined not to satisfy the harmonic resonance condition; in the HT combination, the charge-to-mass ratio of Hydrogen is 3 times that of Tritium, therefore the HT combination is determined to satisfy the harmonic resonance condition.

[0068] In other words, under synergistic heating mode, the charge-to-mass ratio of minority ions to main ions is an integer multiple. Waves are absorbed not only through the fundamental frequency resonance of minority ions but also indirectly through the higher harmonic resonance of main ions. At this point, energy is generated through a combination of collisional coupling between minority ions and main ions, and wave-particle resonance, forming a synergistic heating effect. Under single heating mode, the charge-to-mass ratio is not an integer multiple. Main ions cannot absorb wave energy through harmonic resonance; only minority ions absorb energy through fundamental frequency resonance and slowly transfer energy to main ions through Coulomb collisions. When classified as the first heating type, the synergistic effect can be further enhanced by adjusting parameters such as wave frequency, magnetic field strength, and ion density, resulting in better heating. When classified as the second heating type, the single energy transfer path can be compensated for by increasing the minority ion concentration or increasing wave power, thus preventing a decrease in heating efficiency.

[0069] In other possible implementation methods, the harmonic resonance condition can be determined based on the engineering parameters related to the magnetic field. For example, if the magnetic field strength is greater than a preset strength threshold (e.g., 15T), it is determined that the condition is met; otherwise, it is not met.

[0070] This approach, by distinguishing between synergistic heating and single heating modes, allows for the quantification of the additional energy absorption resulting from harmonic resonance, reducing the calculation error of the single-pass absorption rate. Furthermore, differentiating heating modes allows for the adjustment of relevant parameters based on the specific heating mode, thereby improving the heating effect.

[0071] Furthermore, in this evaluation method, plasma parameters include the mass, charge, density, and temperature of minority ions and main ions; wave parameters include the parallel beam of the incident wave and the frequency of the incident wave; device parameters include the large radius of the stellarator and the magnetic field strength of the plasma core; and single-pass absorption parameters include the wave cyclotron frequency, ion cyclotron frequency, plasma frequency, thermal velocity, and plasma specific pressure.

[0072] Specifically, the mass and charge of the minority ions and the main ions are known physical constants. The densities of the minority ions and the main ions can be measured using laser interferometers or microwave reflectometers. The temperatures of the minority ions and the main ions can be obtained through charge exchange spectroscopy or Thomson scattering diagnostics. The parallel beam is determined by antenna design and wave propagation models, and can be obtained using wavenumber measurement equipment (such as phase array probes) or simulation software (such as COMSOL). The frequency of the incident wave is set by the wave source, typically in the MHz to GHz range, and can be pre-calculated based on resonance conditions, such as ion cyclotron frequencies; the frequency value can be calibrated in real time using a spectrum analyzer. The large radius is a fixed geometric parameter of the stellarator, obtained from engineering drawings or design specifications, or verified through laser ranging. The magnetic field strength is controlled by the current of the magnet system or measured by sensors.

[0073] Furthermore, in this evaluation method, single-pass absorption parameters for evaluating heating efficiency are calculated based on plasma parameters, wave parameters, and device parameters, including the following:

[0074] The wave cyclotron frequency is calculated based on the frequency of the incident wave; specifically, the wave cyclotron frequency is calculated using the following formula:

[0075]

[0076] in, The cyclotron frequency is the frequency of the wave. denoted as , where is the frequency of the incident wave.

[0077] The ion cyclotron frequency is calculated based on the charge and mass of minority ions and the main ion, the magnetic field strength, and the charge of electrons; the ion cyclotron frequency is calculated using the following formula:

[0078]

[0079] in, The ion cyclotron frequency, For charge, Taking 1 to represent the main ion, Taking 2 indicates a minority of ions. The charge of an electron. The magnetic field strength, For quality, Taking 1 to represent the main ion, The value of 2 indicates a minority of ions.

[0080] The plasma frequency is calculated based on the electron density, mass, and charge; specifically, the plasma frequency is calculated using the following formula:

[0081]

[0082] in, For plasma frequency, For the density of electrons, The charge of an electron. For the mass of electrons, It is the vacuum dielectric constant.

[0083] The thermal rate is calculated based on the temperature and mass of the minority ions and the main ions; wherein, the thermal rate is calculated according to the following formula:

[0084]

[0085] in, For thermal velocity, For temperature, For quality, Taking 1 to represent the main ion, The value of 2 indicates a minority of ions.

[0086] The plasma specific pressure is calculated based on the density and temperature of minority and main ions, as well as the magnetic field strength; the plasma specific pressure is calculated using the following formula:

[0087]

[0088] in, The plasma specific pressure, For pressure, where, , density Boltzmann's constant, For temperature, The magnetic field strength, The permeability of free space, Taking 1 to represent the main ion, The value of 2 indicates a minority of ions.

[0089] By employing this approach and selecting the specific parameters mentioned above, and since the plasma parameters are direct outputs from conventional stellarator diagnostic instruments, the problem of insufficient accuracy and computational difficulty in single-pass absorptivity calculations caused by introducing parameters that are difficult to detect or calculate can be avoided. Furthermore, the selection of wave and device parameters excludes other parameters that can be implicitly characterized by the aforementioned parameters, simplifying the model and further improving computational efficiency while ensuring accuracy. In addition, the selection of these parameters covers the complete process of wave-particle resonance, wave propagation, and energy deposition, ensuring the accuracy of single-pass absorptivity calculations.

[0090] Furthermore, in this evaluation method, the single-pass absorption model corresponding to the first heating type is:

[0091]

[0092] in, The single-pass absorption rate corresponding to the first heating type. For the parallel beam of the incident wave, For the large radius of the stellarator, The intrinsic velocity of electromagnetic wave propagation. .

[0093] Furthermore, in this evaluation method, the single-pass absorption model corresponding to the second heating type is:

[0094]

[0095] in, This represents the single-pass absorption rate corresponding to the second heating type. For the parallel beam of the incident wave, For the large radius of the stellarator, The intrinsic velocity of electromagnetic wave propagation. .

[0096] Furthermore, in this evaluation method, the heating efficiency is assessed based on the single-pass absorption rate, including at least one of multi-parameter analysis, target-driven optimization, and feasibility verification. Multi-parameter analysis includes: estimating the heating efficiency under the same device parameters for different plasma and wave parameters, and identifying the parameters that have the greatest impact on the single-pass absorption rate; target-driven optimization includes: determining the optimal parameter combination using an optimization algorithm based on a preset single-pass absorption rate target value; and feasibility verification includes: determining the feasible range of wave and plasma parameters under the constraint of fixed device parameters.

[0097] Specifically, the steps of multi-parameter analysis include, but are not limited to, parameter construction, single-pass absorptivity evaluation, and sensitivity analysis. Parameter construction involves selecting typical plasma parameters and wave parameters as variables under fixed device parameters (such as magnetic field configuration and antenna structure) to construct a multi-dimensional parameter space and determine the value range of each parameter. Single-pass absorptivity evaluation uses numerical simulation methods to perform sampling calculations within the parameter space, obtaining single-pass absorptivity values ​​under different parameter combinations, forming a database of "parameter-absorptivity" mapping relationships. Sensitivity analysis, based on the database, uses methods such as analysis of variance to calculate the contribution of each parameter to the single-pass absorptivity, identifying the key parameters with the greatest impact, and providing a priority basis for subsequent parameter optimization.

[0098] The steps of goal-driven optimization include, but are not limited to, setting the target value, constructing the optimization model, and solving the optimization algorithm. Setting the target value means setting a target value for the single-pass absorptivity (e.g., ≥60%) based on experimental requirements, such as the target plasma temperature and energy confinement time, combined with the upper limit of the device power and plasma stability conditions. Constructing the optimization model involves using the single-pass absorptivity as the objective function and device parameters (e.g., upper limit of magnetic field strength), plasma parameters (e.g., density range), and wave parameters (e.g., antenna power capacity) as constraints to build a multivariate optimization model. Solving the optimization algorithm involves using algorithms such as genetic algorithms, particle swarm optimization, and simulated annealing to solve the above model, iteratively searching the parameter space to find the optimal parameter combination that makes the single-pass absorptivity reach or approach the target value.

[0099] Feasibility verification steps include, but are not limited to, determining constraints, calculating the feasible region, and boundary verification. Determining constraints includes specifying fixed constraints on device parameters, such as the maximum magnetic field strength, the upper limit of the heat load tolerance of the vacuum chamber walls, and the antenna coupling power threshold; it also considers plasma physics constraints, such as density limits and temperature limits. Calculating the feasible region involves using the "parameter-absorbency" mapping relationship obtained from multi-parameter analysis, combined with the above constraints, to plot the feasible region boundary between wave parameters and plasma parameters using a constraint optimization algorithm, and marking the distribution characteristics of the single-pass absorbency within this region. The distribution characteristics can be specifically represented using contour lines. Figure 2 As shown, Figure 2 The diagram shows a contour plot of the single-pass absorbance in the minority ion mode of the DH experiment. The horizontal axis represents the minority ion concentration, and the vertical axis represents the minority ion temperature. By setting a target single-pass absorbance (e.g., 85%), a corresponding minority ion concentration of approximately 5% and a temperature above 8 keV can be obtained. Boundary validation involves numerical simulation or low-power experiments to verify typical parameter combinations at the feasible region boundary, confirming that they meet the device safety and plasma stability requirements, and ensuring the engineering feasibility of the evaluation results.

[0100] This approach, using single-pass absorption rate as an indicator for evaluation, overcomes the inherent ambiguity of traditional qualitative analysis and achieves a quantitative description of heating efficiency. Through multi-parameter analysis, parameters can be ranked by sensitivity, and parameters with high impact factors can be prioritized for control during actual heating, thereby improving heating efficiency. Goal-driven optimization, using an optimization algorithm to quickly locate the optimal parameter combination, shortens the experimental debugging cycle and reduces resource consumption. Feasibility verification ensures the engineering applicability of the evaluation results and avoids equipment risks caused by parameter exceeding limits.

[0101] Example 2:

[0102] Based on the evaluation method for stellarator ion cyclotron resonance heating efficiency described in Example 1, this embodiment provides another evaluation method. The only difference between this evaluation method and the evaluation method in Example 1 is that when the resonance frequencies of a few ions and the main ion do not meet the harmonic resonance condition, the heating type is not directly determined as the second heating type. Instead, the initiation conditions for mode switching heating are determined based on plasma parameters, wave parameters, and device parameters, and the third heating type or the second heating type is selected based on whether the initiation conditions are met.

[0103] Specifically, in the evaluation method provided in this embodiment, the heating type also includes a third heating type, which is a primary and secondary heating mode of minority ion heating and mode switching heating. Specifically, mode switching heating achieves energy deposition through ion Bernstein wave (IBW) excitation, thereby improving the overall absorption efficiency.

[0104] Plasma parameters also include the concentration of minority ions, which represents the density ratio of minority ions in the plasma; wave parameters also include the incident angle, which represents the angle between the incident wave vector and the direction of the magnetic field, controlled by the antenna phase array; device parameters also include magnetic field shear, which represents the spatial rate of change of the direction of the magnetic field lines, determined by the current configuration of the stellarator coils.

[0105] Specifically, the concentration of a few ions is obtained through scattering, the incident angle is measured using a microwave interferometer, and the magnetic field shear is measured using a magnetic probe array.

[0106] When the resonance frequency of a minority of ions does not meet the harmonic resonance condition with that of the main ions, the following steps are also taken: judging whether the start-up conditions for mode switching heating are met based on plasma parameters, wave parameters, and device parameters.

[0107] If so, the heating type will be determined as the third heating type.

[0108] If not, then the heating type will be determined as the second heating type.

[0109] Furthermore, in this evaluation method, the initiation conditions for mode switching heating include: the concentration of minority ions is below a preset concentration threshold, the angle between the incident angle and the magnetic field is 80° to 100°, and the magnetic field shear is above a preset shear rate threshold. The concentration threshold can be, for example, ≤5%, meaning that a density ratio of minority ions to main ions ≤5% may trigger mode switching heating. The shear rate threshold can be set to > .

[0110] Furthermore, the single-pass absorption model corresponding to the third heating type is:

[0111]

[0112] in, The single-pass absorption rate corresponding to the third heating type. For the parallel beam of the incident wave, For the large radius of the stellarator, The single-pass absorbance corresponding to the mode switching heating was obtained through fitting. The intrinsic velocity of electromagnetic wave propagation. .

[0113] Specifically, The fitting method can be as follows: First, measure the microwave reflectivity and transmittance, and then, according to the law of conservation of energy, separate... The contribution. Establishment A multiple regression model relating the concentration of a few ions, the angle between the incident angle and the magnetic field, and the magnetic field shear.

[0114] This approach, by introducing a synergistic heating model, can significantly improve the accuracy of heating efficiency assessment in non-harmonic resonance scenarios. Furthermore, wave parameters include the incident angle, and device parameters include magnetic field shear. By setting these parameters, the influence of the magnetic field configuration and wave incident angle on heating efficiency can be quantified, thus providing a theoretical basis for optimizing the stellarator's structural design and power coupling scheme.

[0115] Example 3:

[0116] Based on the evaluation method for stellarator ion cyclotron resonance heating efficiency described in Examples 1 and 2, this embodiment provides an electronic device and a computer-readable storage medium.

[0117] The electronic device provided in this embodiment includes: a processor and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the evaluation method for stellarator ion cyclotron resonance heating efficiency as described in Embodiments 1 and 2.

[0118] The computer-readable storage medium provided in this embodiment stores computer-executable instructions, which, when executed by a processor, are used to implement the evaluation method for stellarator ion cyclotron resonance heating efficiency as described in Embodiments 1 and 2.

[0119] While the present invention has been illustrated and described with reference to certain preferred embodiments, those skilled in the art should understand that the above description is a further detailed explanation of the invention in conjunction with specific embodiments, and should not be construed as limiting the specific implementation of the invention to these descriptions. Various changes in form and detail can be made by those skilled in the art, including several simple deductions or substitutions, without departing from the spirit and scope of the invention.

Claims

1. A method for evaluating the ion cyclotron resonance heating efficiency of a stellarator, characterized in that, include: The plasma parameters of the plasma inside the stellarator, the wave parameters of the incident wave used to heat the plasma, and the device parameters of the stellarator are obtained. Based on the plasma parameters, the wave parameters, and the device parameters, a single-pass absorption parameter for evaluating the heating efficiency is calculated, and the heating type of ion cyclotron resonance heating is determined based on the ion properties of the plasma inside the stellarator. Determine the single-pass absorption model corresponding to the heating type, and calculate the single-pass absorption rate corresponding to the heating type based on the single-pass absorption parameters, the wave parameters, and the device parameters using the single-pass absorption model; The heating efficiency is evaluated based on the single-pass absorption rate.

2. The method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in claim 1, characterized in that, The ionic properties include the resonance frequency relationship between minority ions and main ions in the plasma; The heating type includes a first heating type and a second heating type, wherein the first heating type is a synergistic heating mode of minority ion heating and harmonic heating, and the second heating type is a single heating mode of minority ion heating; and The heating type of ion cyclotron resonance heating is determined based on the ionic properties of the plasma within the stellarator, including: When the resonance frequency of the minority ions and the main ions satisfies the harmonic resonance condition, the heating type is determined to be the first heating type. When the resonance frequency of the minority ions and the main ions does not satisfy the harmonic resonance condition, the heating type is determined to be the second heating type; wherein The resonance frequency relationship is determined based on the multiple relationship between the charge-to-mass ratio of the minority ions and the charge-to-mass ratio of the main ions; wherein If the charge-to-mass ratio of the minority ions is an integer multiple of the charge-to-mass ratio of the main ions, then the resonance frequencies of the minority ions and the main ions satisfy the harmonic resonance condition. If the charge-to-mass ratio of the minority ions is not an integer multiple of the charge-to-mass ratio of the main ions, then it is determined that the resonance frequency of the minority ions and the main ions does not satisfy the harmonic resonance condition.

3. The method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in claim 2, characterized in that, The plasma parameters include the mass, charge, density, and temperature of the minority ions and the main ions; The wave parameters include the parallel beam of the incident wave and the frequency of the incident wave; The device parameters include the large radius of the stellarator and the magnetic field strength of the core of the plasma; The single-pass absorption parameters include wave cyclotron frequency, ion cyclotron frequency, plasma frequency, thermal velocity, and plasma specific pressure. and The single-pass absorption parameters for evaluating heating efficiency are calculated based on the plasma parameters, the wave parameters, and the device parameters, including: Calculate the wave cyclotron frequency based on the frequency of the incident wave; The cyclotron frequency of the ions is calculated based on the charge and mass of the minority ions and the main ions, the magnetic field strength, and the charge of the electrons. The plasma frequency is calculated based on the electron density, mass, and charge. The thermal rate is calculated based on the temperature and mass of the minority ions and the main ions; The plasma specific pressure is calculated based on the density and temperature of the minority ions and the main ions, as well as the magnetic field strength.

4. The method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in claim 3, characterized in that, The cyclotron frequency of the wave is calculated using the following formula: in, The cyclotron frequency of the wave is... The frequency of the incident wave; The ion cyclotron frequency is calculated using the following formula: in, The ion cyclotron frequency is [value missing]. For the charge, Let 1 represent the main ion. The number 2 represents the minority ions. The charge of the electron is denoted as . The magnetic field strength is... For the mass, Let 1 represent the main ion. The number 2 represents the minority ions; The plasma frequency is calculated using the following formula: in, The plasma frequency, The density of the electrons, The charge of the electron is denoted as . The mass of the electron, It is the vacuum dielectric constant; The thermal velocity is calculated using the following formula: in, The thermal velocity, The temperature is [temperature value]. For the mass, Let 1 represent the main ion. The number 2 represents the minority ions; The plasma specific pressure is calculated using the following formula: in, The plasma specific pressure, For pressure, where, , For the density Boltzmann's constant, The temperature is [temperature value]. The magnetic field strength is... The permeability of free space, Let 1 represent the main ion. The number 2 represents the minority ions.

5. The method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in claim 4, characterized in that, in, The single-pass absorption model corresponding to the first heating type is: in, The single-pass absorption rate corresponding to the first heating type. The parallel beam of the incident wave. The large radius of the stellarator. The intrinsic velocity of electromagnetic wave propagation. ;and The single-pass absorption model corresponding to the second heating type is: in, This represents the single-pass absorption rate corresponding to the second heating type. The parallel beam of the incident wave. The large radius of the stellarator. The intrinsic velocity of electromagnetic wave propagation. .

6. The method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in claim 5, characterized in that, The heating type also includes a third heating type, wherein the third heating type is a main and auxiliary heating mode of minority ion heating and mode switching heating; The plasma parameters also include the concentration of the minority ions; the wave parameters also include the incident angle; the device parameters also include magnetic field shear; and When the resonance frequency of the minority ions and the main ion does not satisfy the harmonic resonance condition, the following is also included: Determine whether the start-up conditions for the mode switching heating are met based on the plasma parameters, the wave parameters, and the device parameters. If so, the heating type is determined to be the third heating type; If not, then the heating type is determined to be the second heating type; wherein The start-up conditions for the mode switching heating include: the concentration of the minority ions is lower than a preset concentration threshold, the angle between the incident angle and the magnetic field is 80° to 100°, and the magnetic field shear is higher than a preset shear rate threshold. The single-pass absorption model corresponding to the third heating type is: in, The single-pass absorption rate corresponding to the third heating type. The parallel beam of the incident wave. The large radius of the stellarator. The single-pass absorption rate corresponding to the mode conversion heating is obtained through fitting. The intrinsic velocity of electromagnetic wave propagation. .

7. The method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in claim 1, characterized in that, The heating efficiency is evaluated based on the single-pass absorption rate, including at least one of multi-parameter analysis, target-driven optimization, and feasibility verification. in The multi-parameter analysis includes: estimating the heating efficiency corresponding to different plasma parameters and wave parameters under the same device parameters, and identifying the parameters that have the greatest impact on the single-pass absorption rate; The target-driven optimization includes: determining the optimal parameter combination based on a preset single-pass absorption rate target value using an optimization algorithm; The feasibility verification includes: determining the feasible range of the wave parameters and the plasma parameters under the constraint of fixed device parameters.

8. The method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in claim 2, characterized in that, The main ion is a deuterium ion, and the minority ions are hydrogen ions or helium-3 ions.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes the computer execution instructions stored in the memory to implement the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method for evaluating the ion cyclotron resonance heating efficiency of a stellarator as described in any one of claims 1-8.

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