Tungsten fluff thickness prediction method based on surface temperature rise condition

Abstract

The invention discloses a tungsten fluff thickness prediction method based on a surface temperature rise condition, and belongs to the technical field of tungsten surface nanostructure evolution under helium ion irradiation. The method comprises the following steps: establishing a tungsten fluff growth rate prediction formula considering a growth-annealing synergistic effect on the basis of an adsorption particle migration mechanism and an annealing kinetics theory; constructing an SURO-FUZZ model in order to simulate the growth dynamic process of tungsten villus and obtain simulation data required by fitting unknown parameters of a prediction formula; through comparison with an experiment, the accuracy of the SURO-FUZZ model is verified; and fitting unknown parameters of a prediction formula through simulation data of SURO-FUZZ. According to the analysis formula provided by the invention, two inhibition effects are fully considered, compared with the prior art, the integrating degree with experimental data under the long-term irradiation condition is higher, and compared with numerical simulation, the consumption of computing resources is greatly reduced, and the growth conditions of tungsten fluff under different surface temperature conditions can be efficiently predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of the evolution of tungsten (W) surface nanostructures under helium (He) ion irradiation, and in particular to a research method for simulating the growth of tungsten fuzz and predicting an analytical formula at different surface temperatures. Background Art

[0002] In the field of nuclear fusion, the performance of plasma-facing materials (PFMs) in the fusion plasma environment has always been a research focus attracting much attention. PFMs are directly exposed to the harsh environment of high particle flux and strong heat load, and such environmental conditions pose great challenges to the performance and durability of PFMs. Among them, tungsten (W) has become a candidate material for the divertor target plate due to its high melting point, low sputtering yield, and low tritium retention rate. However, under helium (He) plasma irradiation, a porous nanostructure, namely "fuzz", will form on the tungsten surface, which may cause the generation of impurities and dust, affecting the long-term stable operation and energy utilization efficiency of the fusion device. Therefore, in-depth research on the characteristics of PFMs in such an extreme environment, especially the growth characteristics of tungsten fuzz, is of crucial significance for ensuring the safe and efficient operation of future fusion devices. At present, the generally recognized formation mechanism of tungsten fuzz is closely related to the diffusion of helium particles in the tungsten substrate, the aggregation of helium clusters, and the rupture of helium bubbles. And in the later stage of fuzz growth, tungsten adsorbed particles will migrate along the fuzz fibers towards the tips, and this behavior promotes the elongation of the fibers, thereby increasing the overall thickness of the fuzz layer. Generally, an increase in temperature will accelerate the migration of adsorbed particles, resulting in an increase in the overall thickness of the fuzz layer. However, under the condition of a relatively high surface temperature, a shrinkage phenomenon of the fuzz nanostructure, namely the "annealing" phenomenon, has been observed on experimental platforms such as NAGDIS-I and LP-MIES. Generally speaking, as a key factor affecting the growth of tungsten fuzz, the specific influence mechanism and effect of the surface temperature still need to be further explored and clarified.

[0003] At present, numerical simulation and analytical models are two common research approaches for studying the growth characteristics of tungsten fuzz. Among them, numerical simulation, such as using the self-developed three-dimensional (3D) kinetic Monte Carlo (KMC) code SURO-FUZZ, is suitable for studying complex microscopic processes, including helium particle diffusion, helium cluster aggregation, and tungsten fuzz growth. Therefore, it can more comprehensively simulate the growth process of tungsten fuzz. However, numerical simulation usually requires a large amount of computing resources. Especially when dealing with complex problems such as long-term irradiation, it requires a greater amount of calculation, and various parameters in the model need to be finely set, which has high requirements for the establishment and operating environment of the model. This greatly increases the calculation cost and reduces the calculation efficiency. In addition, in addition to numerical simulation, the analytical model is also a commonly used method. Through mathematical derivation and theoretical analysis, it can obtain analytical formulas for calculating the growth of tungsten fuzz, which has the advantage of high calculation efficiency and is suitable for quickly predicting the growth of tungsten fuzz. However, the analytical model is usually based on some idealized assumptions, such as ignoring some microscopic details and simplifying the growth process, and has limited processing ability for complex actual growth situations. Therefore, it cannot fully and accurately reflect the true growth status of tungsten fuzz under different conditions. Therefore, there is an urgent need to propose a method with low calculation cost and high accuracy for predicting the growth of tungsten fuzz under different surface temperatures. Summary of the Invention

[0004] The main object of the present invention is to provide an effective method for predicting the growth thickness of tungsten fuzz under different surface temperatures and long-term irradiation conditions, aiming to solve the technical problem that the numerical simulation method requires too much computing resources to calculate the thickness of tungsten fuzz under long-term irradiation.

[0005] The technical solution of the present invention:

[0006] S1. Based on the adsorption particle migration mechanism and annealing kinetics theory, establish a prediction formula for the growth rate of tungsten fuzz considering the synergistic effect of growth-annealing.

[0007] The growth and annealing kinetics of tungsten fuzz can both be described by diffusion-like kinetics laws. Further, in the step S1, it specifically includes:

[0008] Step S1.1. Derive the annealing term in the prediction formula:

[0009] In the annealing stage, the evolution of the fuzz thickness z fuzz with time is expressed as:

[0010]

[0011] where z fuzz represents the fuzz thickness at the current moment, z0 is the initial fuzz thickness, t represents the irradiation time, D anneal(T) is the annealing diffusion coefficient related to temperature. By differentiating Equation (1), the decreasing rate of the tungsten fluff thickness is obtained when only considering the annealing effect:

[0012]

[0013] Step S1.2: Derive the growth term in the prediction formula:

[0014] Under helium ion bombardment, the diffusion process of tungsten adsorbed particles is described by Fick's first law, and the diffusion flux at the tip of the nanofiber is expressed as:

[0015]

[0016] Among them, J represents the diffusion flux of tungsten adsorbed particles, that is, the number of adsorbed particles passing through a unit area per unit time, D(T) is the diffusion coefficient of tungsten adsorbed particles varying with temperature. C(z) is the concentration of tungsten adsorbed particles on the surface of the nanofiber. The growth rate of the fluff thickness depends on the number of adsorbed particles diffusing to the tip and staying, which is expressed as:

[0017]

[0018] Among them, N J represents the number of adsorbed particles reaching the tip of the fluff fiber and staying, N s represents the total number of adsorbed particles at the tip of the nanofiber. Assuming the nanofiber is a cylinder, the ratio of its surface area to the tip area is:

[0019]

[0020] In the formula, A fiber represents the lateral area per unit length of the tip of the nanofiber, A tip is the cross-sectional area of the tip of the nanofiber, and R is the radius of the nanofiber. Formula (5) characterizes the contribution ratio of the lateral surface to transporting tungsten adsorbed particles to the tip. Under the assumption that the lateral surface of the fiber provides the main diffusion contribution, the total adsorption particle residence rate at the tip of the nanofiber is expressed as:

[0021]

[0022] Among them, is the concentration gradient on the surface of the nanofiber. Substituting Equation (6) into Equation (4), the growth rate expression of the nanofiber can be obtained:

[0023]

[0024] The concentration gradient of tungsten adsorbed particles along the nanofiber is expressed as:

[0025]

[0026] Among them, represents the concentration of tungsten adsorption particles at the tip of the nanofiber, and C0(z fuzz ) represents the concentration of tungsten adsorption particles at the bottom of the nanofiber.

[0027] Since the concentration of tungsten adsorption particles C0(z fuzz ) decreases with the increase of the fluff thickness, it is assumed to follow a simple exponential decay function: where C 00 is the initial concentration of adsorption particles, and A is the decay parameter. Under the action of the annealing effect, the concentration of bottom adsorption particles will further decay, and this decay term is assumed to be described by a cubic exponential function form. Finally, the concentration of tungsten adsorption particles at the bottom of the nanofiber is where B is the decay parameter related to the annealing effect.

[0028] Let The gradient of the tungsten adsorption particle concentration along the nanofiber is expressed as:

[0029]

[0030] Integrate the prefactor in formula (9) into D growth (T), and the final expression of the growth term in the prediction formula can be obtained:

[0031]

[0032] Step S1.3. Finally, integrate the derived growth term and annealing term to obtain the prediction formula for the growth rate of tungsten fluff with the synergistic effect of growth and annealing:

[0033]

[0034] S2. To simulate the growth kinetic process of tungsten fluff and obtain the simulation data required to fit the unknown parameters in the prediction formula (11), a three-dimensional kinetic Monte Carlo model, namely the SURO-FUZZ model, is constructed.

[0035] The SURO-FUZZ model discretizes the simulation region using a three-dimensional cubic grid of Nx×Ny×Nz, with the side length of each unit grid being d. Among them, the grids are classified into tungsten grids: grids containing tungsten particles inside; helium grids: grids composed entirely of helium particles; and vacuum grids: grids containing neither tungsten particles nor helium particles. Under the initial conditions, a flat tungsten target plate is set, and each unit grid has the same number of tungsten particles. As the simulation progresses, under the action of the physical mechanisms in steps S2.1 and S2.2, the tungsten particles in the grids migrate, leading to the dynamic evolution of the entire grid structure and finally forming a tungsten fluff structure at the macroscopic scale.

[0036] The core mechanisms causing the evolution of the tungsten fluff morphology in the SURO-FUZZ model include two sub-models: (1) Growth model: Simulates the growth phenomenon of tungsten fluff caused by the interaction between incident particles and the surface of the tungsten target plate. (2) Annealing model: An independent high-temperature kinetic model used to simulate the contraction phenomenon of tungsten fluff caused by the self-repair process on the surface of tungsten fluff under high-temperature conditions.

[0037] Among them, the growth model and the annealing model in the SURO-FUZZ model specifically include the following in step S2:

[0038] Step S2.1, the growth model, simulates the following physical processes: the injection of helium particles, the migration of adsorbed particles, and the formation and rupture of helium bubbles.

[0039] At the beginning of the simulation, the parameters of the incident particles need to be initialized. The incident particles will continuously bombard the surface of the tungsten target plate at a specific angle and energy distribution (the specific angle and energy distribution are derived from experimental measurement data) and move along a straight-line trajectory in the simulation region. When the particles reach the boundary of the simulation region, different processing methods are adopted according to the boundary type. It is set that the periodic boundary conditions are used for the particle movement in the X and Y coordinate axes directions, while the upper and lower boundaries of the Z coordinate axis are absorption boundaries.

[0040] When the incident particles collide with the surface of the target plate, the model calls the physical model of the interaction between plasma and the material surface to simulate the growth process of tungsten fluff. Once a helium particle hits a tungsten grid, the model uses the Monte Carlo method to determine whether the helium ion is reflected, and the reflection probability is calculated by the open-source SRIM (The Stopping and range of ions in Matter) model. When the helium particle is reflected, the ions will continue to be traced in a specular reflection manner and lose half of their energy until they run out of energy or touch a new boundary and then the tracing stops.

[0041] When the incident helium particles are not reflected, their injection into the tungsten substrate will be considered. The injected helium particles migrate randomly within the tungsten grids until they migrate into the vacuum grids and overflow, or combine with other injected helium particles within a certain tungsten grid to form clusters. The time step dt for helium particle migration is calculated by the Einstein diffusion formula:

[0042]

[0043] where l (= 5 nm) represents the length of each grid in the x, y, and z directions, and m (= 3) represents the dimension of the model. The diffusion coefficient (D) of helium particles is calculated by the Arrhenius expression:

[0044]

[0045] where the pre-exponential factor D0 and the activation energy E d are listed in Table 1, and k b is the Boltzmann constant. As helium particles continue to accumulate within the tungsten grids, once the number of helium particles in a certain tungsten grid approaches its maximum value in the tungsten grid, this tungsten grid will transform into a helium grid. At this time, all the tungsten particles in the original tungsten grid will transform into movable adsorbed particles and then move to the surface of the tungsten target for migration. As the helium bubbles grow continuously, the rupture of the helium bubbles will cause the tungsten grid above them to peel off and randomly scatter onto adjacent surface grids. Among them, the maximum value of helium particles in the tungsten grid is calculated based on the ideal gas law.

[0046] Step S2.2, the annealing model, simulates the self-healing phenomenon caused by particle aggregation on the surface of tungsten fluff under high-temperature conditions. Based on the principle of thermodynamics, at high temperatures, tungsten surface atoms obtain sufficient kinetic energy to overcome the potential barrier and achieve particle aggregation through migration, ultimately leading to the densification and shrinkage of the fluff structure.

[0047] Based on the pseudo-potential model in the lattice Boltzmann method, this study innovatively constructs an improved model applicable to the annealing process of tungsten fluff, aiming to describe the shrinkage process of fluff under high-temperature conditions. The pseudo-potential model was initially designed to describe the interactions within fluids. The improved model is adaptively adjusted to depict the aggregation behavior of tungsten particles in a high-temperature environment. Specifically, the pseudo-potential interaction force at position is expressed as follows:

[0048]

[0049] where is the unit direction vector in the α direction (for example, ), and ω α is the weight factor in the α direction, and its specific value is given in the literature. The item represents the position of the pseudopotential at while represents the pseudopotential at the adjacent lattice points in the direction. Let the value of the pseudopotential

[0050] be equal to the number of tungsten particles in the corresponding grid. Therefore, the interaction force tends to point to the position with a higher concentration of tungsten particles, which reflects the attraction between tungsten particles. Once the calculation of the interaction force of the pseudopotential of the tungsten grid in the entire fluff layer is completed, the number of tungsten particles located at the position

[0051]

[0052] and migrating in the α direction can be calculated by the following formula: βT where H(T) is a temperature-related parameter that affects the number of migrating particles, enabling the pseudopotential model to simulate the annealing process at different temperatures. The relationship between H(T) and temperature is described by H(T) = μe α + γT, where μ, β, and γ are fitting parameters. It should be noted that tungsten particles will migrate only when n and the included angle between them is less than 90 degrees; otherwise, there will be no particle migration phenomenon.

[0053] After calculating the number of tungsten particles migrating in each direction, the tungsten particles in the fluff layer start to migrate to the surrounding grids simultaneously. If the target grid is a vacuum grid, it will be converted into a tungsten grid; if there are no tungsten particles remaining in a grid, the grid will be converted into a vacuum grid.

[0054] By integrating the growth model and the annealing model through the SURO - FUZZ model, the full - cycle simulation of tungsten fluff under different temperature conditions is realized. In the SURO - FUZZ model, the growth dynamics of tungsten fluff are quantitatively characterized by real - time monitoring of the change in fluff thickness over time. Specifically, a thickness calculation method based on porosity distribution is adopted: First, the porosity P(z) is calculated layer by layer along the z - direction, which is defined as the ratio of the number of vacuum grids in the layer to the total number of grids; then, by identifying the continuous layer region within a predefined porosity interval, the maximum height difference is defined as the characteristic thickness of the fluff layer.

[0055] S3. Verify the accuracy of the SURO - FUZZ model by comparing with experiments.

[0056] Specifically, in step S3 includes:

[0057] To verify the accuracy of the SURO - FUZZ model, the growth process of tungsten fluff is simulated using this model, and the simulation results are compared and analyzed with the existing experimental data.

[0058] Select the low-energy helium plasma irradiation experiment. On the platform of the high-power material irradiation experiment system (LP-MIES), polycrystalline tungsten samples at different temperatures are observed, and the evolution law of tungsten surface nanostructures within a certain temperature range (1100 - 1830K) is systematically compared. After the experiment, the cross-section of the irradiated sample is analyzed by means of a scanning electron microscope to quantify the thickness and radius of tungsten nanofibers formed under different conditions. By analyzing the experimental observation data of the fluff growth kinetics, it is confirmed that the annealing effect has a great influence on the evolution of tungsten fluff thickness.

[0059] Carry out SURO-FUZZ simulation work and compare it with the above experimental results to verify the accuracy of the SURO-FUZZ model.

[0060] When the SURO-FUZZ model reaches the required accuracy, it is used to predict the thickness of W fluff growth under surface heating conditions; when it does not meet the requirements, the temperature-related parameter H(T) in the annealing model is dynamically adjusted to optimize the model fitting effect until a tungsten fluff growth curve consistent with the experimental data is obtained. This adaptive modeling method effectively improves the prediction reliability of the model under different temperature zone conditions.

[0061] S4. Fit the unknown parameters of the prediction formula with the simulation data of SURO-FUZZ.

[0062] In the step S4 specifically includes:

[0063] In the process of parameter fitting of the prediction formula, in order to accurately obtain each parameter, it is necessary to separately investigate the evolution law of fluff under the action of a single mechanism: by separately enabling the growth model to simulate the pure growth process and separately enabling the annealing model to simulate the pure annealing process, so as to separately fit and obtain the growth parameters A, D growth (T) and the annealing parameter D anneal (T). Finally, both the growth model and the annealing model are used, and an iterative algorithm is adopted to fit the unknown parameter B in the prediction formula.

[0064] S4.1. Determine the parameters A and D anneal (T) when not considering the annealing process (i.e., D growth (T) = 0). At this time, the prediction formula (11) is simplified to:

[0065]

[0066] By integrating formula (16), an implicit function relationship between fluff thickness and irradiation time is established, which can be expressed as:

[0067] e Az (Az - 1) = A2 D growth (T)t-1 (17)

[0068] To calibrate formula (17), with the parameter settings remaining the same as those in the LP-MIES experiment, the annealing model in SURO-FUZZ was not enabled, and only the growth model was used for simulation to obtain the evolution data of the fluff thickness over time. Subsequently, using the simulation data of SURO-FUZZ, the D in formula (17) was determined by the nonlinear least squares method. growth (T) and A.

[0069] S4.2. To determine the unknown parameter D in prediction formula (11) anneal (T), with D growth (T) set to 0, it was simplified to a form that only considered the annealing effect:

[0070] z fuzz (t) = z fuzz (0) - (2D anneal (T)t) 1 / 2 (18)

[0071] Since the annealing effect is only related to the temperature effect and is not affected by the particle flow irradiation. Therefore, to study the annealing process separately, the growth model was turned off and the particle flow irradiation was stopped in the SURO-FUZZ model, and only the annealing model was enabled to simulate the evolution of the tungsten fluff thickness over time in this state. In addition, to exclude the influence of the initial morphology difference on the simulation results, at the initial moment of the simulation, a consistent initial fluff morphology was set for the samples under all temperature conditions.

[0072] On the premise that other simulation parameters were consistent with the LP-MIES experiment conditions, the SURO-FUZZ model was used to simulate the annealing process at different surface temperatures. Subsequently, using the simulation data of SURO-FUZZ, the D in formula (18) was determined by the linear least squares method. anneal (T).

[0073] S4.3. Fitting the unknown parameter B in formula (11) requires considering the combined effect of growth and annealing phenomena. Therefore, the SURO-FUZZ model enabled both the growth model and the annealing model to obtain the required fitting data. Among them, the simulation conditions remained the same as those in the LP-MIES experiment. Combining the parameters A, D growth (T) and D anneal (T) determined in steps 4.1 and 4.2, the B in formula (18) was determined by the nonlinear least squares method.

[0074] S4.4. Since the D obtained by fitting in steps 4.1 and 4.2 growth(T) and D anneal (T) shows a discrete distribution at different temperature points and cannot be directly used to continuously predict the tungsten fluff thickness value within the temperature range of (1100 - 2000K). Therefore, in order to effectively predict the fluff growth thickness over the entire surface temperature range, the Arrhenius formula (19)-(20) that can describe the law of diffusion-like kinetics needs to be introduced to fit the D growth (T) and D anneal (T).

[0075]

[0076]

[0077] In the formula, D growth,0 and D anneal,0 are the pre-exponential diffusion parameters, E growth and E anneal represent the activation energy, and k is the Boltzmann constant. Finally, the variation laws of the growth and annealing diffusion parameters with temperature are obtained through fitting.

[0078] Finally, the coefficients A, D growth (T), D anneal (T) and B obtained in steps 4.1 to 4.4 are substituted into formula (11) in step 1 to obtain a complete prediction formula. Based on the complete prediction formula, under the condition of a given incident particle flux, the fluff thickness at different times under any temperature condition (1000 - 2000K) can be accurately calculated, providing a reliable quantitative basis for the service life assessment and scientific formulation of the maintenance cycle of tungsten components in plasma devices.

[0079] Advantages of the present invention:

[0080] (1) The analytical formula proposed by the present invention fully considers two inhibition effects. Compared with the previously proposed analytical formula, it has a higher degree of agreement with experimental data in the case of long-term irradiation, and compared with numerical simulation, it greatly reduces the consumption of computing resources, improves the computing efficiency, and can efficiently predict the growth of tungsten fluff under different surface temperature conditions;

[0081] (2) By integrating the newly constructed annealing model into the SURO-FUZZ program, the present invention more accurately describes the shrinkage process of the fluff nanostructure, making the simulation results have good consistency with experimental data and improving the accuracy of the numerical simulation of the tungsten fluff growth process by SURO-FUZZ;

[0082] (3) By fitting and validating the temperature-related coefficients and suppression parameters, the analytical formula of the present invention can be applied to complex situations with different surface temperatures and long-term irradiation, verifying the flexible applicability of the method and providing a more effective tool for studying the growth of tungsten fuzz. Description of the Drawings

[0083] Figure 1 It is the particle tracking flow chart of the growth model in the SURO-FUZZ model;

[0084] Figure 2 It is the schematic diagram of the interaction between particles and the material surface in the growth model of the SURO-FUZZ model. Among them, (a) is the schematic diagram of particles bombarding the material surface, (b) is the schematic diagram of helium particles diffusing on the surface, (c) is the schematic diagram of the migration of tungsten adsorbed particles, and (d) is the schematic diagram of the rupture of helium bubbles;

[0085] Figure 3 It is the comparison diagram of the evolution of the fuzz thickness with time between the results of the SURO-FUZZ model and the LP-MIES experimental device at different surface temperatures. Among them, (a) is the temperature = 1100K, (b) is the temperature = 1240K, (c) is the temperature = 1400K, (d) is the temperature = 1515K, (e) is the temperature = 1640K, and (f) is the temperature = 1830K;

[0086] Figure 4 It is the fitting diagram of the SURO-FUZZ model results by Formula 17 at different surface temperatures and only considering the growth process. Among them, (a) is the temperature = 1100K, (b) is the temperature = 1240K, (c) is the temperature = 1400K, (d) is the temperature = 1515K, (e) is the temperature = 1640K, and (f) is the temperature = 1830K;

[0087] Figure 5 It is the fitting diagram of the SURO-FUZZ model results by Formula 18 at different surface temperatures and only considering the annealing process. Among them, (a) is the temperature = 1100K, (b) is the temperature = 1240K, (c) is the temperature = 1400K, (d) is the temperature = 1515K, (e) is the temperature = 1640K, and (f) is the temperature = 1830K;

[0088] Figure 6 It is the fitting diagram of the SURO-FUZZ model results by Formula 11 at different surface temperatures and considering both the growth and annealing processes. Among them, (a) is the temperature = 1100K, (b) is the temperature = 1240K, (c) is the temperature = 1400K, (d) is the temperature = 1515K, (e) is the temperature = 1640K, and (f) is the temperature = 1830K;

[0089] Figure 7It is the fitting image of the growth and annealing diffusion coefficients with the Arrhenius formula, where (a) is the growth diffusion coefficient D growth (T), and (b) is the annealing diffusion coefficient D anneal (T);

[0090] Figure 8 It is the comparison diagram of the final prediction formula and the evolution of tungsten fluff thickness obtained by the LP-MIES experimental device at different surface temperatures, where (a) is the temperature = 1100K, (b) is the temperature = 1240K, (c) is the temperature = 1400K, (d) is the temperature = 1515K, (e) is the temperature = 1640K, and (f) is the temperature = 1830K. Specific implementation manners

[0091] It should be understood that the specific embodiments described below are only used to explain the present invention and are not used to limit the application scope of the present invention. The purpose realization, implementation manner, functional characteristics, and advantages of the present invention will be further described with reference to the embodiments and the accompanying drawings.

[0092] S1. Based on the adsorption particle migration mechanism and annealing kinetics theory, establish a prediction formula for the growth rate of tungsten fluff considering the synergistic effect of growth and annealing.

[0093] The growth and annealing kinetics of tungsten fluff can both be described by the diffusion-like kinetics law. Further, the specific content of step S1 includes:

[0094] Step S1.1. Derive the annealing term in the prediction formula:

[0095] In the annealing stage, the evolution of the fluff thickness z fuzz with time is expressed as:

[0096]

[0097] where z fuzz represents the fluff thickness at the current moment, z0 is the initial fluff thickness, t represents the irradiation time, and D anneal (T) is the temperature-dependent annealing diffusion coefficient. By differentiating formula (1), the decrease rate of the tungsten fluff thickness when only considering the annealing effect is obtained:

[0098]

[0099] Step S1.2. Derive the growth term in the prediction formula:

[0100] Under the bombardment of helium ions, the diffusion process of tungsten adsorbed particles is described by Fick's first law, and the diffusion flux at the tip of the nanofiber is expressed as:

[0101]

[0102] Among them, J represents the diffusion flux of tungsten adsorbed particles, that is, the number of adsorbed particles passing through a unit area per unit time, D(T) is the diffusion coefficient of tungsten adsorbed particles varying with temperature. C(z) is the concentration of tungsten adsorbed particles on the surface of the nanofiber. The growth rate of the fluff thickness depends on the number of adsorbed particles diffusing to the tip and staying, and is expressed as:

[0103]

[0104] Among them, N J represents the number of adsorbed particles reaching the tip of the fluff fiber and staying, and N s represents the total number of adsorbed particles at the tip of the nanofiber. Assuming the nanofiber is a cylinder, the ratio of its surface area to the tip area is:

[0105]

[0106] In the formula, A fiber represents the lateral area per unit length at the tip of the nanofiber, and A tip is the cross-sectional area of the tip of the nanofiber, and R is the radius of the nanofiber. Formula (5) characterizes the contribution ratio of the lateral surface to the transport of tungsten adsorbed particles to the tip. Under the assumption that the lateral surface of the fiber provides the main diffusion contribution, the total residence rate of adsorbed particles at the tip of the nanofiber is expressed as:

[0107]

[0108] Among them, is the concentration gradient on the surface of the nanofiber. Substituting formula (6) into formula (4), the growth rate expression of the nanofiber can be obtained:

[0109]

[0110] The concentration gradient of tungsten adsorbed particles along the nanofiber is expressed as:

[0111]

[0112] Among them, represents the concentration of tungsten adsorbed particles at the tip of the nanofiber, and C0(z fuzz ) represents the concentration of tungsten adsorbed particles at the bottom of the nanofiber.

[0113] Since the concentration C0(z fuzz ) of tungsten adsorbed particles at the bottom decreases with the increase of the fluff thickness, it is assumed to follow a simple exponential decay function: Among them, C 00is the initial concentration of adsorbed particles, and A is the decay parameter. Under the action of the annealing effect, the concentration of adsorbed particles at the bottom will further decay, and this decay term is assumed to be described by a cubic exponential function. Finally, the concentration of tungsten adsorbed particles at the bottom of the nanofiber is where B is the decay parameter related to the annealing effect.

[0114] Let C zfuzz <<C0(z fuzz ), the gradient of the tungsten adsorbed particle concentration along the nanofiber is expressed as:

[0115]

[0116] Integrate the prefactor in formula (9) as D growth (T), and the final expression of the growth term in the prediction formula can be obtained:

[0117]

[0118] Step S1.3. Finally, integrate the derived growth term and annealing term to obtain the prediction formula for the growth rate of tungsten villi with the synergistic effect of growth and annealing:

[0119]

[0120] S2. To simulate the growth kinetics process of tungsten villi and obtain the simulation data required to fit the unknown parameters in the prediction formula (11), a three-dimensional kinetic Monte Carlo model, namely the SURO-FUZZ model, is constructed.

[0121] The SURO-FUZZ model discretizes the simulation area using a three-dimensional cubic grid of Nx×Ny×Nz, and the side length of each unit grid is d. Among them, the grids are classified into tungsten grids: grids containing tungsten particles inside; helium grids: grids composed entirely of helium particles; vacuum grids: grids that contain neither tungsten particles nor helium particles; under the initial conditions, a flat tungsten target plate is set, and each unit grid has the same number of tungsten particles. As the simulation process progresses, under the physical mechanisms of step S2.1 and step S2.2, the tungsten particles in the grids migrate, which leads to the dynamic evolution of the entire grid structure and finally forms a tungsten villi structure at the macroscopic scale.

[0122] The core mechanisms causing the morphological evolution of tungsten villi in the SURO-FUZZ model include two sub-models: (1) Growth model: Simulate the growth phenomenon of tungsten villi caused by the interaction between incident particles and the surface of the tungsten target plate. (2) Annealing model: An independent high-temperature kinetic model used to simulate the contraction phenomenon of tungsten villi caused by the self-repair process on the surface of tungsten villi under high-temperature conditions.

[0123] Among them, the growth model and annealing model in the SURO-FUZZ model specifically include the following in the step S2:

[0124] Step S2.1, the growth model, simulates the following physical processes: the injection of helium particles, the migration of adsorbed particles, and the formation and rupture of helium bubbles.

[0125] At the beginning of the simulation, it is necessary to initialize the parameters of the incident particles. The incident particles will continuously bombard the surface of the tungsten target plate at a specific angle and energy distribution (the specific angle and energy distribution are derived from experimental measurement data) and move along a straight-line trajectory in the simulation area. As Figure 1 shown, when the particles reach the boundary of the simulation area, different processing methods are adopted according to the boundary type. It is set that the periodic boundary conditions are used in the X and Y coordinate axes directions for the particle movement, while the upper and lower boundaries of the Z coordinate axis are absorption boundaries.

[0126] When the incident particles collide with the surface of the target plate ( Figure 1 boundary 3 in), the model calls the physical model of the interaction between the plasma and the material surface to simulate the growth process of tungsten fluff. The schematic diagram of the general principle of the physical model is as Figure 2 shown. Figure 2 (a) in shows the interaction between the incident helium particles and the tungsten target plate. Once the helium particles hit the tungsten grid, the model uses the Monte Carlo method to judge whether the helium ions are reflected, and the reflection probability is calculated by the open-source SRIM (The Stopping and range of ions in Matter) model. When the helium particles are reflected, the ions will continue to be tracked in the way of specular reflection and lose half of their energy until they run out of energy or touch a new boundary and stop tracking.

[0127] When the incident helium particles are not reflected, their injection into the tungsten substrate will be considered, as Figure 2 (b) in shows. The injected helium particles randomly migrate in the tungsten grid until they migrate out of the vacuum grid or combine with other injected helium particles to form clusters in a certain tungsten grid. The time step dt used for the migration of helium particles is calculated by the Einstein diffusion formula:

[0128]

[0129] where l (=5nm) represents the length of each grid in the x, y, and z directions, and m (=3) represents the dimension of the model. The diffusion coefficient (D) of helium particles is calculated by the Arrhenius expression:

[0130]

[0131] Among them, the pre-exponential factor D0 and the activation energy E d are listed in Table 1, and k b is the Boltzmann constant. As helium particles continuously accumulate within the tungsten grid, once the number of helium particles in a certain tungsten grid approaches its maximum value within the tungsten grid, this tungsten grid will transform into a helium grid. As shown in Figure 2 (c), at this time, all the tungsten particles within the original tungsten grid will transform into movable adsorbed particles, and then move to the surface of the tungsten target plate for migration. In addition, as shown in Figure 2 (d), as the helium bubbles continuously grow, the rupture of the helium bubbles will cause the tungsten grid above them to peel off and randomly scatter onto adjacent surface grids. Among them, the maximum value of helium particles within the tungsten grid is calculated based on the ideal gas law.

[0132] Table 1.

[0133]

[0134] Step S2.2, the annealing model simulates the self-repair phenomenon caused by the aggregation of particles on the surface of tungsten fluff under high-temperature conditions. Based on the principle of thermodynamics, at high temperatures, tungsten surface atoms obtain sufficient kinetic energy to overcome the potential barrier and achieve particle aggregation through migration, ultimately leading to the densification and contraction of the fluff structure.

[0135] Based on the pseudo-potential model in the lattice Boltzmann method, this study innovatively constructs an improved model applicable to the annealing process of tungsten fluff, aiming to describe the contraction process of fluff under high-temperature conditions. The pseudo-potential model was initially designed to describe the interactions within a fluid. The improved model is adaptively adjusted to depict the aggregation behavior of tungsten particles in a high-temperature environment. Specifically, the pseudo-potential interaction force at position is expressed as follows:

[0136]

[0137] Among them, is the unit direction vector in the α direction (for example, ), ω α is the weighting factor in the α direction, and its specific value is given in the literature. The term represents the pseudo-potential at position , and represents the pseudo-potential at the adjacent lattice point in the direction. Let the value of the pseudo-potential be equal to the number of tungsten particles within the corresponding grid. Therefore, the interaction force tends to point to the position with a higher concentration of tungsten particles, which reflects the attraction between tungsten particles.

[0138] Once the calculation of the pseudo-potential interaction forces of the tungsten grids within the entire fluff layer is completed, at position And the number of tungsten particles migrating in the α direction can be calculated by the following formula:

[0139]

[0140] where H(T) is a temperature-related parameter that affects the number of migrating particles, enabling the pseudopotential model to simulate the annealing process at different temperatures. The relationship between H(T) and temperature is described by H(T) = μe βT +γT, where μ, β, and γ are fitting parameters. It should be noted that only when n α is greater than zero (i.e., when the angle between and is less than 90 degrees), will the tungsten particles migrate; otherwise, there will be no particle migration phenomenon.

[0141] After calculating the migration numbers of tungsten particles in each direction, the tungsten particles in the fluff layer start to migrate to the surrounding grids simultaneously. If the target grid is a vacuum grid, it will be converted into a tungsten grid; if there are no tungsten particles remaining in a grid, the grid will be converted into a vacuum grid.

[0142] By integrating the growth model and the annealing model through the SURO-FUZZ model, the full-cycle simulation of tungsten fluff under different temperature conditions is achieved. In the SURO-FUZZ model, the growth dynamics of tungsten fluff are quantitatively characterized by real-time monitoring of the change in fluff thickness over time. Specifically, a thickness calculation method based on porosity distribution is adopted: First, the porosity P(z) is calculated layer by layer along the z direction, which is defined as the ratio of the number of vacuum grids in this layer to the total number of grids; subsequently, by identifying the continuous layer region within a predefined porosity interval, its maximum height difference is defined as the characteristic thickness of the fluff layer.

[0143] S3. Verify the accuracy of the SURO-FUZZ model by comparing it with experiments.

[0144] Specifically, the step S3 includes:

[0145] To verify the accuracy of the SURO-FUZZ model, the growth process of tungsten fluff is simulated using this model, and the simulation results are compared and analyzed with the existing experimental data.

[0146] A brief description of the experimental part is as follows: On the platform of the Large Power-Materials Irradiation Experimental System (LP-MIES), low-energy (50 eV) helium plasma irradiation was carried out on polycrystalline tungsten (W) samples to explore the evolution law of nanostructures with temperature. The tungsten samples used had a size of 1 cm × 1 cm × 2 mm and a purity of 99.95%. During the experiment, inductively coupled plasma technology was used to control the surface temperature within the range of 1100 to 1830 K. The change in the tungsten surface temperature during the experiment corresponded to the change in the helium ion flux density controlled by the equipment from 6.3×10 21 changing to 4.7×10 22 ions / m 2 ·s, and the helium plasma pressure was constantly maintained at 5.0 Pa during the experiment.

[0147] The low-energy helium plasma irradiation experiment was selected. On the platform of the Large Power-Materials Irradiation Experimental System (LP-MIES), polycrystalline tungsten samples at different temperatures were observed, and the evolution law of the tungsten surface nanostructures within a certain temperature range (1100 - 1830 K) was systematically compared. After the experiment, the cross-section of the irradiated sample was analyzed by means of a scanning electron microscope to quantify the thickness and radius of the tungsten nanofibers formed under different conditions. By analyzing the experimental observation data of the fluff growth kinetics, it was confirmed that the annealing effect had a great influence on the evolution of the tungsten fluff thickness.

[0148] The SURO-FUZZ simulation work was carried out and compared with the above experimental results to verify the accuracy of the SURO-FUZZ model.

[0149] When the SURO-FUZZ model reaches the required accuracy, it is used to predict the thickness of W fluff growth under surface heating conditions; when the requirement is not met, the temperature-related parameter H(T) in the annealing model is dynamically adjusted to optimize the model fitting effect until a tungsten fluff growth curve consistent with the experimental data is obtained. This adaptive modeling method effectively improves the prediction reliability of the model under different temperature zone conditions.

[0150] To simulate the experiment on the LP-MIE platform, the parameter settings of the SURO-FUZZ model were kept consistent with the experimental environment. The surface temperatures for the SURO-FUZZ model to conduct simulations were set at 1100, 1240, 1400, 1515, 1640, and 1830 K respectively. Helium ions bombarded the surface of the tungsten target plate vertically with an energy of 50 eV. Since this ion energy is lower than the physical sputtering threshold (~115 eV), the erosion effect of the fluff layer can be ignored.

[0151] In the SURO-FUZZ model, the initially set flat tungsten target plate morphology consists of a 50×50×720 cubic grid, with the side length d of each grid being 5 nm. By continuously adjusting the temperature-related parameter H(T) of the annealing model in the experimental SURO-FUZZ model, the appropriate coefficients are found: μ = 7.7×10 -17 , β = 1.4×10 -2 , and γ = 8.8×10 -7 . Given the limitation of computing power, the simulation time in SURO-FUZZ is set to 2500 s, which is shorter than the exposure time (~3×10 4 s) in the LP-MIES experiment.

[0152] Figure 3 shows the evolution of the tungsten fuzz thickness over time obtained from SURO-FUZZ simulations, as well as the experimental data measured on LP-MIES at different surface temperatures. It can be observed that the vast majority of the simulation results are in good agreement with the experimental data. When at a low temperature of 1100 K, the simulated tungsten fuzz thickness is slightly higher than the measured value in (a) of Figure 3 . For other substrate temperatures, the simulated tungsten fuzz thickness fits well with the measured values in (b)-(f) of Figure 3 . At a high temperature of 1830 K, the annealing effect plays a key role in suppressing the growth of tungsten fuzz in Figure 3 (f). It can be concluded from Figure 3 that the SURO-FUZZ model can effectively reproduce the results of the LP-MIES experiment, and the accuracy of its model is verified.

[0153] On this basis, the simulation data of the SURO-FUZZ model provides a complete thickness-time evolution relationship dataset for the prediction formula, ensuring the accuracy and reliability of parameter fitting.

[0154] S4. Fit the unknown parameters of the prediction formula using the simulation data of SURO-FUZZ.

[0155] Specifically, the step S4 includes:

[0156] In the process of parameter fitting of the prediction formula, to accurately obtain each parameter, it is necessary to separately examine the fuzz evolution law under the action of a single mechanism: simulate the pure growth process by enabling the growth model alone, and simulate the pure annealing process by enabling the annealing model alone, so as to separately fit and obtain the growth parameters A, D growth (T) and the annealing parameter D anneal (T). Finally, simultaneously use the growth model and the annealing model, and adopt an iterative algorithm to fit the unknown parameter B in the prediction formula.

[0157] S4.1. Determine the parameters A and D anneal without considering the annealing process (i.e., D growth (T)=0). At this time, the prediction formula (11) is simplified to:

[0158]

[0159] By integrating formula (16), an implicit function relationship between the fluff thickness and the irradiation time is established, which can be expressed as:

[0160] e Az (Az - 1)=A 2 D growth (T)t - 1 (17)

[0161] To calibrate formula (17), under the same parameter settings as the LP - MIES experimental conditions, without enabling the annealing model in SURO - FUZZ, only the growth model is used for simulation to obtain the evolution data of the fluff thickness over time. Subsequently, using the simulation data of SURO - FUZZ, the D growth (T) and A in formula (17) are determined by the non - linear least - squares method.

[0162] Table 2.

[0163]

[0164] Figure 4 shows the evolution of the fluff thickness (represented by red balls) obtained by SURO - FUZZ simulation over time. The simulation results show that, considering only the growth effect, the growth rate of tungsten fluff increases significantly with the increase of temperature. And in Figure 4 , by fitting the simulation results of SURO - FUZZ, the values of D growth (T) and A in formula (17) at different surface temperatures can be obtained. As shown in Table 2, D growth (T) shows a diffusion - like variation law with temperature, while the value of A(=1×10 -3 ) remains unchanged at all surface temperatures. The parameter A is determined by minimizing the error through the non - linear least - squares method to ensure that the calculation result of formula (17) is consistent with the data of SURO - FUZZ. Based on the calibrated parameters D growth (T) and A, the prediction result of formula (17) is consistent with Figure 4 the result of the SURO - FUZZ model in

[0165] S4.2. To determine the unknown parameter D anneal (T) in the prediction formula (11), by setting D growthUnder the condition of (T) = 0, it is simplified to a form that only considers the annealing effect:

[0166] z fuzz (t) = z fuzz (0)-(2D anneal (T)t) 1 / 2 (18)

[0167] Since the annealing effect is only related to the temperature effect and is not affected by the particle flux irradiation. Therefore, in order to study the annealing process separately, the growth model is turned off and the particle flux irradiation is stopped in the SURO - FUZZ model, and only the annealing model is enabled to simulate the evolution of the tungsten fluff thickness over time in this state. In addition, in order to exclude the influence of the initial morphology difference on the simulation results, at the initial moment of the simulation, a consistent initial fluff morphology of the samples under all temperature conditions is set.

[0168] On the premise that other simulation parameters are consistent with the LP - MIES experimental conditions, the SURO - FUZZ model is used to simulate the annealing process at different surface temperatures. Subsequently, using the simulation data of SURO - FUZZ, D in formula (18) is determined by the linear least - squares method anneal (T).

[0169] The results are as Figure 5 shown. The simulation results show that when only considering the annealing effect, the decreasing rate of the tungsten fluff thickness increases significantly with the increase of temperature. Subsequently, using formula (18), by fitting Figure 5 the simulation results of SURO - FUZZ in it, the values of D anneal (T) at different surface temperatures are obtained. These values are summarized in Table 2. As Figure 5 shown, the prediction results of formula (18) are in good agreement with Figure 5 the simulation results of SURO - FUZZ in it.

[0170] S4.3. To fit the unknown parameter B in formula (11), the combined effects of growth and annealing phenomena need to be considered simultaneously. Therefore, the SURO - FUZZ model enables both the growth model and the annealing model to obtain the required fitting data. Among them, the simulation conditions remain the same as the LP - MIES experimental conditions. Combining the parameters A, D growth (T) and D anneal (T) determined in steps 4.1 and 4.2, B in formula (18) is determined by the nonlinear least - squares method.

[0171] As Figure 6 shown, SURO - FUZZ simulates the evolution of the fluff thickness over time. Combining the parameters (A = 1×10 -3 , Dgrowth (T) and D anneal (T)), the optimal value of B was obtained as 6.3×10 by fitting the simulation results of SURO - FUZZ -4 . Using the calibrated parameter B, the prediction results of formula (11) are consistent with Figure 6 the simulation results of SURO - FUZZ in

[0172] S4.4. Since the D growth (T) and D anneal (T) obtained by fitting in steps 4.1 and 4.2 show a discrete distribution at different temperature points and cannot be directly used to continuously predict the tungsten fluff thickness values in the temperature range (1100 - 2000K). Therefore, in order to achieve an effective prediction of the fluff growth thickness over the entire surface temperature range, the Arrhenius formulas (19) - (20) that can describe the law of diffusion - like kinetics need to be introduced to fit the D growth (T) and D anneal (T) obtained by fitting in steps 4.1 and 4.2

[0173]

[0174]

[0175] where D growth,0 and D anneal,0 are the pre - exponential diffusion parameters, E growth and E anneal represent the activation energy, and k is the Boltzmann constant. Finally, the variation laws of the growth and annealing diffusion parameters with temperature are obtained by fitting

[0176] Figure 7 (a) in Figure 7 and growth (b) in anneal respectively give the Arrhenius fitting results for D growth,0 (T) and D 5 (T). In terms of the growth process, the optimal values of D 2 = 1.89×10 -1 nm growth s anneal,0 and E 2 s -1 and E anneal = 0.27eV are determined. For the annealing process, the optimal values of D

[0177] Finally, the coefficients A = 1×10 -3 nm -1 , and B = 6.3×10 -4 nm -6 s 3 Substituting into formula (11), a complete prediction formula is obtained. To prove the correctness of the prediction formula, we compare the prediction formula with the LP-MIES experiment for example verification. Through the prediction formula (i.e., formula (11)), the final evolution of the tungsten fuzz thickness at different surface temperatures is obtained. Figure 8 The comparison between the improved prediction results and the experimental data from LP-MIES is shown. Compared with the existing prediction formulas, the prediction formula proposed in the present invention has a better fit with the experimental measurement results, especially in the later stage of fuzz growth and at higher surface temperatures.

[0178] Finally, the coefficients A, D growth (T), D anneal (T) and B are substituted into formula (11) in step 1 to obtain a complete prediction formula. Based on the complete prediction formula, under the condition of a given incident particle flux, the fuzz thickness at different times under any temperature condition (1000 - 2000K) can be accurately calculated, providing a reliable quantitative basis for the service life evaluation of tungsten components in plasma devices and the scientific formulation of maintenance cycles.

[0179] In addition, a major advantage of this complete prediction model is that it can not only be applied to the prediction of fuzz thickness under different incident helium particle flux conditions, but also significantly reduces the dependence on high-performance numerical simulations, thus saving a large amount of computing resources. Further, through the inversion of model parameters, the competition mechanism between D_growth(T) and D_anneal(T) can be analyzed, thereby deepening the understanding of the action mechanism of the high-temperature annealing effect in the process of tungsten fuzz growth.

Claims

1. A method for predicting the thickness of tungsten fluff under the condition of surface temperature rise, characterized in that, The steps are as follows: S1. Based on the adsorption particle migration mechanism and annealing kinetics theory, establish a prediction formula for the growth rate of tungsten villi considering the synergistic effect of growth-annealing; S2. To simulate the growth kinetics process of tungsten villi and obtain the simulation data required to fit the unknown parameters of the formula in step S1, construct a three-dimensional kinetic Monte Carlo model, namely the SURO-FUZZ model; S3. Verify the accuracy of the SURO-FUZZ model by comparing with experiments; S4. Use the simulation data of SURO-FUZZ to fit the unknown parameters of the prediction formula.

2. The thickness prediction method of tungsten fluff under the condition of surface temperature rise according to claim 1, wherein, The specific content of step S1 includes: Both the growth and annealing kinetics of tungsten villi can be described by diffusion-like kinetics laws; Step S1.

1. Derive the annealing term in the prediction formula: During the annealing stage, the villus thickness z fuzz is expressed as the evolution over time: Among them, z fuzz represents the thickness of the fluff at the current moment, z0 is the initial fluff thickness, t represents the irradiation time, and D anneal (T) is the temperature-dependent annealing diffusion coefficient; by differentiating formula (1), the rate of decrease in the tungsten fluff thickness when only considering the annealing effect is obtained: Step S1.

2. Derive the growth term in the prediction formula: Under the bombardment of helium ions, the diffusion process of tungsten adsorption particles is described by Fick's first law, and the diffusion flux at the tip of the nanofiber is expressed as: where J represents the diffusion flux of tungsten adsorption particles, that is, the number of adsorption particles passing through a unit area per unit time, D(T) is the diffusion coefficient of tungsten adsorption particles varying with temperature; C(z) is the concentration of tungsten adsorption particles on the surface of the nanofiber; the growth rate of the villi thickness depends on the number of adsorption particles diffusing to the tip and staying, which is expressed as: Among them, N J represents the number of adsorbed particles that reach the tip of the villous fiber and stay, and N s represents the total number of adsorbed particles at the tip of the nanofiber; assuming that the nanofiber is a cylinder, the ratio of its surface area to the tip area is: In the formula, A fiber represents the lateral area per unit length at the tip of the nanofiber, and A tip is the cross-sectional area at the tip of the nanofiber, and R is the radius of the nanofiber; Equation (5) characterizes the contribution ratio of the lateral surface to the transport of tungsten adsorbed particles to the tip; Under the assumption that the fiber lateral surface provides the main diffusion contribution, the total residence rate of adsorbed particles at the tip of the nanofiber is expressed as: Among them, is the concentration gradient on the surface of the nanofiber; substituting Equation (6) into Equation (4), the growth rate expression of the nanofiber can be obtained: The concentration gradient of tungsten adsorption particles along the nanofiber is expressed as: Among them, C zfuzz represents the concentration of tungsten adsorption particles at the tip of the nanofiber, and C0(z fuzz ) represents the concentration of tungsten adsorption particles at the bottom of the nanofiber; Since the tungsten adsorption particle concentration C0(z fuzz ) decreases with the increase of the fluff thickness, it is assumed that it follows a simple exponential decay function: where C 00 is the initial adsorption particle concentration, and A is the decay parameter; under the action of the annealing effect, the bottom adsorption particle concentration will further decay, and this decay term is assumed to be described by a cubic exponential function; finally, the tungsten adsorption particle concentration at the bottom of the nanofiber is where B is the decay parameter related to the annealing effect; Let The gradient of the tungsten adsorption particle concentration along the nanofiber is expressed as: Integrate the leading coefficient in Equation (9) into D growth (T), and the final expression of the growth term in the prediction formula can be obtained: Step S1.

3. Finally, integrate the derived growth term and annealing term to obtain a prediction formula for the growth rate of tungsten villi with the synergistic effect of growth-annealing:

3. A method for predicting the thickness of tungsten villi under the condition of surface temperature rise according to claim 1, characterized in that, The specific content of step S2 includes: The SURO-FUZZ model discretizes the simulation region using a three-dimensional cubic grid of Nx×Ny×Nz, and the side length of each unit grid is d; among them, the grid types are tungsten grids: grids containing tungsten particles inside, helium grids: grids entirely composed of helium particles, and vacuum grids: grids containing neither tungsten particles nor helium particles; under the initial conditions, a flat tungsten target plate is set, and each unit grid has the same number of tungsten particles; as the simulation process progresses, under the physical mechanisms of step S2.1 and step S2.2, the tungsten particles in the grid migrate, which leads to the dynamic evolution of the entire grid structure and finally forms a tungsten villi structure at the macroscopic scale; The core mechanisms causing the morphological evolution of tungsten villi in the SURO-FUZZ model include two sub-models: (1) Growth model: Simulate the tungsten villi growth phenomenon caused by the interaction between incident particles and the surface of the tungsten target plate; (2) Annealing model: An independent high-temperature kinetics model used to simulate the tungsten villi shrinkage phenomenon caused by the self-repair process on the surface of tungsten villi under high-temperature conditions; Among them, the growth model and annealing model in the SURO-FUZZ model specifically include in step S2: Step S2.

1. The growth model simulates the following physical processes: the injection of helium particles, the migration of adsorption particles, and the formation and rupture of helium bubbles; At the beginning of the simulation, the parameters of the incident particles need to be initialized. The incident particles will continuously bombard the surface of the tungsten target plate with a specific angular and energy distribution and move along a straight-line trajectory in the simulation region. When the particles reach the boundary of the simulation region, different treatment methods are adopted according to the boundary type. Periodic boundary conditions are set for the particle motion in the X and Y coordinate axes directions, while the upper and lower boundaries of the Z coordinate axis are absorption boundaries. When the incident particles collide with the surface of the target plate, the model calls the physical model of the interaction between the plasma and the material surface to simulate the growth process of tungsten fuzz. Once a helium particle hits the tungsten grid, the model uses the Monte Carlo method to determine whether the helium ion is reflected, and the reflection probability is calculated by the open-source SRIM model. When the helium particles are reflected, the ions will continue to be tracked in the form of specular reflection and lose half of their energy until they run out of energy or touch a new boundary and stop tracking. When the incident helium particles are not reflected, their injection into the tungsten substrate will be considered. The injected helium particles randomly migrate within the tungsten grid until they migrate into the vacuum grid and overflow, or combine with other injected helium particles to form clusters in a certain tungsten grid. The time step dt used for the migration of helium particles is calculated by the Einstein diffusion formula: where l represents the length of each grid in the x, y, and z directions, and m represents the dimension of the model. The diffusion coefficient (D) of helium particles is calculated by the Arrhenius expression: Among them, the pre-exponential factor D0 and the activation energy E d are listed in Table 1, and k b is the Boltzmann constant; as helium particles continuously accumulate within the tungsten grid, once the number of helium particles in a certain tungsten grid approaches its maximum value in the tungsten grid, this tungsten grid will transform into a helium grid; at this time, all the tungsten particles originally within this tungsten grid will transform into movable adsorbed particles and then move to the surface of the tungsten target plate for migration; as the helium bubbles grow continuously, the rupture of the helium bubbles will cause the tungsten grid above them to peel off and randomly scatter onto adjacent surface grids; among them, the maximum value of helium particles in the tungsten grid is calculated according to the ideal gas law; Step S2.2, the annealing model, simulates the self-healing phenomenon caused by the aggregation of particles on the surface of tungsten fuzz under high-temperature conditions. Based on the thermodynamic principle, at high temperatures, the tungsten surface atoms gain enough kinetic energy to overcome the potential barrier and achieve particle aggregation through migration, ultimately leading to the densification and shrinkage of the fuzz structure. Based on the pseudo-potential model in the lattice Boltzmann method, this study innovatively constructs an improved model applicable to the annealing process of tungsten fluff, aiming to describe the contraction process of fluff under high-temperature conditions; the pseudo-potential model was initially designed to describe the interactions within a fluid; the improved model is adaptively adjusted to characterize the aggregation behavior of tungsten particles in a high-temperature environment; specifically, the pseudo-potential interaction force located at position is expressed as follows: Among them, is the unit direction vector in the α direction, and ω α is the weight factor in the α direction, and its specific value is given in the literature; The term represents the pseudo-potential at the position ; then represents the pseudo-potential at the adjacent lattice point in the direction; assume that the value of the pseudo-potential is equal to the number of tungsten particles in the corresponding grid; thus, the interaction force tends to point to the position with a higher concentration of tungsten particles, which reflects the attraction between tungsten particles; Once the calculation of the pseudo-potential interaction force of the tungsten grid within the entire villous layer is completed, the number of tungsten particles located at position and migrating in the α direction can be calculated by the following formula: Among them, H(T) is a temperature-related parameter that affects the number of migrating particles, enabling the pseudo-potential model to simulate the annealing process at different temperatures; the relationship between H(T) and temperature is described by H(T) = μe βT +γT, where μ, β, and γ are fitting parameters; it should be noted that tungsten particles will migrate only when n α is greater than zero; otherwise, there will be no particle migration phenomenon; After calculating the migration numbers of tungsten particles in all directions, the tungsten particles in the fuzz layer start to migrate to the surrounding grids simultaneously. If the target grid is a vacuum grid, it will be converted into a tungsten grid. If there are no tungsten particles remaining in a grid, the grid will be converted into a vacuum grid. By integrating the growth model and the annealing model with the SURO-FUZZ model, the full-cycle simulation of tungsten fuzz under different temperature conditions is realized. In the SURO-FUZZ model, the growth dynamics of tungsten fuzz are quantitatively characterized by real-time monitoring of the change in fuzz thickness over time. Specifically, a thickness calculation method based on the porosity distribution is adopted: First, the porosity P(z) is calculated layer by layer along the z direction, which is defined as the ratio of the number of vacuum grids in this layer to the total number of grids. Subsequently, by identifying the continuous layer region within a predefined porosity interval, its maximum height difference is defined as the characteristic thickness of the fuzz layer.

4. A method for predicting the thickness of tungsten villi under the condition of surface temperature rise according to claim 1, characterized in that, The specific steps of step S3 include: To verify the accuracy of the SURO-FUZZ model, the growth process of tungsten fuzz is simulated using this model, and the simulation results are compared and analyzed with the existing experimental data. Select the low-energy helium plasma irradiation experiment. On the high-power material irradiation experimental system platform, observe polycrystalline tungsten samples at different temperatures, and systematically compare the evolution law of the tungsten surface nanostructure within a certain temperature range. After the experiment, analyze the cross-section of the irradiated sample with a scanning electron microscope to quantify the thickness and radius of the tungsten nanofibers formed under different conditions. By analyzing the experimental observation data of the fluff growth kinetics, it is confirmed that the annealing effect has a great influence on the evolution of the tungsten fluff thickness. Carry out SURO-FUZZ simulation work and compare it with the above experimental results to verify the accuracy of the SURO-FUZZ model. When the SURO-FUZZ model reaches the required accuracy, it is used to predict the thickness of W fluff growth under surface heating conditions. When the requirement is not met, the temperature-related parameter H(T) in the annealing model is dynamically adjusted to optimize the model fitting effect until a tungsten fluff growth curve consistent with the experimental data is obtained. This adaptive modeling method effectively improves the prediction reliability of the model under different temperature zone conditions.

5. A method for predicting the thickness of tungsten villi under surface heating conditions according to claim 1, characterized in that, The specific steps of step S4 include: In the process of parameter fitting for the prediction formula, to accurately obtain various parameters, it is necessary to separately investigate the evolution law of villi under the action of a single mechanism: simulate the pure growth process by enabling the growth model alone, and simulate the pure annealing process by enabling the annealing model alone, so as to separately fit and obtain the growth parameters A, D growth (T) and the annealing parameter D anneal (T); finally, simultaneously use the growth model and the annealing model, and adopt an iterative algorithm to fit the unknown parameter B in the prediction formula; S4.

1. Without considering the annealing process, i.e., D anneal (T) = 0, determine the parameters A and D growth (T); at this time, the prediction formula (11) is simplified to: By integrating formula (16), an implicit function relationship between the fluff thickness and the irradiation time is established, which can be expressed as: e Az (Az-1) = A 2 D growth (T)t-1 (17) To calibrate Equation (17), with the parameter settings remaining the same as those in the LP-MIES experiment, the annealing model in SURO-FUZZ is not enabled, and only the growth model is used to simulate the evolution data of the villus thickness over time. Subsequently, the simulation data of SURO-FUZZ are used to determine D growth (T) and A in Equation (17) through the nonlinear least squares method. S4.

2. To determine the unknown parameter D in the prediction formula (11) anneal (T), under the condition of setting D growth (T) = 0, simplify it to a form that only considers the annealing effect: z fuzz z(t) = fuzz z(0) - (2D anneal z(T)t) 1 / 2 (18) Since the annealing effect is only related to the temperature effect and is not affected by the particle flux irradiation. Therefore, in order to study the annealing process alone, the growth model is turned off and the particle flux irradiation is stopped in the SURO-FUZZ model, and only the annealing model is enabled to simulate the evolution of the tungsten fluff thickness over time in this state. In addition, in order to exclude the influence of the initial morphology difference on the simulation results, at the initial moment of the simulation, the same initial fluff morphology of the samples under all temperature conditions is set. Under the premise that other simulation parameters are consistent with the LP-MIES experimental conditions, the SURO-FUZZ model is used to simulate the annealing process at different surface temperatures; subsequently, the simulated data of SURO-FUZZ are used to determine D anneal (T) in formula (18) by linear least squares method S4.

3. The unknown parameter B in the fitting formula (11) needs to simultaneously consider the combined effects of growth and annealing phenomena. Therefore, the SURO-FUZZ model simultaneously enables the growth model and the annealing model to obtain the required fitting data. Among them, the simulation conditions are kept the same as those of the LP-MIES experiment. Combining the parameters A, D growth (T) and D anneal (T) determined in Steps 4.1 and 4.2, the value of B in formula (18) is determined by the nonlinear least squares method. S4.

4. Since the D growth (T) and D anneal (T) obtained by fitting in steps 4.1 and 4.2 show a discrete distribution at different temperature points and cannot be directly used to continuously predict the tungsten fluff thickness values within the temperature range (1100 - 2000K); therefore, in order to effectively predict the fluff growth thickness over the entire surface temperature range, it is necessary to introduce the Arrhenius equations (19)-(20) that can describe the law of diffusion-like kinetics to fit the D growth (T) and D anneal (T) obtained by fitting in steps 4.1 and 4.2; where D growth,0 and D anneal,0 are pre-exponential diffusion parameters, E growth and E anneal represent the activation energy, k is the Boltzmann constant; finally, the variation laws of the growth and annealing diffusion parameters with temperature are obtained by fitting; Finally, substitute the coefficients A, D growth (T), D anneal (T) and B obtained in Steps 4.1 to 4.4 into formula (11) in Step 1 to obtain a complete prediction formula; based on the complete prediction formula, under the condition of a given incident particle flux, the fluff thickness at different times under any temperature condition can be accurately calculated, providing a reliable quantitative basis for the service life assessment of tungsten components in plasma devices and the scientific formulation of maintenance cycles.

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