Coupling simulation method suitable for radio frequency wave heating of linear device
By employing a self-consistent iterative simulation method involving coupled multi-physics processes, the design optimization challenge of a linear device's radio frequency wave heating system was solved, achieving efficient and accurate simulation applicable to various linear devices and complex conditions.
Patent Information
- Application Number
- CN202511043867.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-28
- Publication Date
- 2025-11-14
AI Technical Summary
Existing numerical simulation methods cannot effectively integrate the coupled behavior of multiple physical processes in linear devices, resulting in low computational efficiency and error accumulation, making it difficult to achieve design optimization and performance verification of radio frequency wave heating systems.
By employing a step-by-step iterative approach, a coupled simulation method for radio frequency wave heating of a linear device is constructed through the self-consistent coupling of key physical processes such as neutral gas diffusion, electromagnetic wave propagation, particle source and energy source calculation, and plasma transport. Modular design and optimal algorithms are used to reduce computational complexity.
It achieves systematic simulation at the entire device scale, improves computational efficiency and accuracy, provides reliable design and experimental guidance, and is applicable to various linear devices and complex boundary conditions.
Smart Images
Figure CN120951722A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of data processing technology, and specifically relates to a coupling simulation method suitable for radio frequency wave heating of linear devices. Background Technology
[0002] Linear plasma devices play a crucial role in aerospace propulsion, nuclear fusion research, and industrial plasma applications. Their axially symmetric geometry enables stable confinement and efficient acceleration of plasma, making them particularly suitable for deep-space propulsion missions requiring continuous thrust output. In the field of nuclear fusion, linear devices serve as a simplified platform for plasma physics research, used to verify theoretical models of heating and transport. Furthermore, linear devices demonstrate unique application potential in industrial scenarios such as material surface modification and semiconductor etching. Compared to toroidal devices (such as tokamaks), linear devices avoid complex circumferential magnetic field configuration designs, reducing engineering complexity; however, their open geometry places higher demands on the coordinated control of plasma generation, heating, and transport.
[0003] In linear devices, radio frequency (RF) heating (such as electron cyclotron resonance heating (ECRH) and ion cyclotron resonance heating (ICRF)) is the mainstream method for plasma generation and heating. However, existing numerical simulation methods generally adopt a partial and targeted simulation strategy, that is, they construct models independently for specific physical processes (such as plasma transport, wave-plasma interaction, etc.), lacking a systematic description of the coupled behavior of multiple processes in the entire device. This fragmented simulation approach leads to the following problems:
[0004] Modeling multiple coupled processes is difficult: Plasma dynamic evolution involves three heterogeneous physical processes: ionization, transport and wave heating. Their spatiotemporal scales differ greatly. Traditional simulation methods are difficult to establish a unified numerical description system due to the mutual exclusion of algorithm frameworks.
[0005] Computing bottleneck: If a single high-fidelity method (such as a full 3D electromagnetic PIC) is used to cover all processes, the amount of computation will far exceed the current computing power limit, resulting in low simulation efficiency or even failure to achieve simulation.
[0006] Therefore, there is an urgent need for a coupled simulation method that can integrate multiple physical processes and balance computational efficiency and accuracy to solve the design optimization and performance verification challenges of linear device radio frequency wave heating systems. Summary of the Invention
[0007] To address the aforementioned technical problems, this invention provides a coupled simulation method applicable to radio frequency wave heating of linear devices, offering an efficient and reliable theoretical tool for the optimized design and performance verification of radio frequency wave heating systems of linear devices, and filling the technical gap in multi-process coupled simulation in this field.
[0008] To achieve the above objectives, the present invention adopts the following technical solution:
[0009] A coupling simulation method for radio frequency wave heating of a linear device, comprising:
[0010] Step 1: Construct the geometric model of the linear device;
[0011] Step 2: Initialize the parameters of the geometric structure model;
[0012] Step 3: Update the neutral gas density distribution based on the neutral gas diffusion equation and the initialized parameters;
[0013] Step 4: Calculate the propagation characteristics of electromagnetic waves in the plasma based on the electromagnetic wave propagation equation and the neutral gas density distribution.
[0014] Step 5: Calculate the energy deposition power of electromagnetic waves in the plasma based on the dielectric tensor and electric field distribution;
[0015] Step 6: Calculate the particle, energy, and momentum transport behavior of the plasma using the magnetohydrodynamic transport equation, and update the parameters of the geometric model.
[0016] Step 7: Iterate through steps 3-6 until the plasma parameters converge, and output the final plasma distribution and heating characteristics.
[0017] Furthermore, in step 1, the geometric structure model includes a quartz tube, a vacuum system, and a radio frequency antenna.
[0018] Furthermore, the initialization parameters include plasma temperature, density, and neutral gas density distribution.
[0019] Furthermore, in step 3, the neutral gas diffusion equation is:
[0020] (1)
[0021] Where, n n D is the density distribution function of a neutral gas. n =0.19 cm 2 / s is the diffusion coefficient of argon gas, and t represents time; For the source distribution of neutral gases, and The distribution functions for ionization and recombination are respectively:
[0022] (2)
[0023] (3)
[0024] Where, n eand T e For plasma density and temperature, E th =15.76 eV is the energy threshold for the ionization of argon atoms (Ar) into first-order argon ions (Ar+). and These are the ionization rate and the recombination rate;
[0025] Solving the equation yields the density distribution of the neutral gas.
[0026] Furthermore, step 4 includes calculating the propagation characteristics of electromagnetic waves in the plasma based on the constructed geometric model and the initial plasma temperature and density, as well as the neutral gas density obtained in step 3, where E is the electric field vector. The frequency of the electromagnetic waves emitted by the antenna. Let c be the electromagnetic wave number, c be the speed of light, and K be the equivalent dielectric tensor. Gradient operator in three-dimensional space:
[0027] (4).
[0028] Furthermore, step 5 includes calculating the deposition power distribution of electromagnetic waves in the plasma based on the constructed geometric model and the initialized plasma temperature and density, the neutral gas density obtained in step 3, and the electric field vector E obtained in step 4. subscript It is a plasma component. The input parameter is a component The dielectric tensor, The vacuum permittivity is indicated by an asterisk. Represents the conjugate transpose of a matrix and a vector:
[0029] (15).
[0030] Furthermore, step 6 includes, based on the constructed geometric model and the initialized plasma temperature and density, the neutral gas density obtained in step 3, the electric field vector E obtained in step 4, and the deposition power distribution obtained in step 5. The transport of particles, energy, and momentum in the plasma is calculated using formulas (16), (17), and (18), respectively:
[0031] (16)
[0032] (17)
[0033] (18)
[0034] In the formula, n e Let be the plasma density, u represent the average plasma velocity, and D represent the plasma diffusion coefficient. and These are the distribution functions for ionization and recombination, respectively. subscript Indicates plasma composition, Time represents electron, Time represents ions, , k is the Boltzmann constant. , and Each represents a component The density, temperature and thermal conductivity, T e For electron temperature, T i m is the ion temperature. i For ion mass. , Indicates the parallel and vertical transport coefficients. and These represent the gradient along the direction of the magnetic field and the gradient perpendicular to the direction of the magnetic field, respectively.
[0035] Furthermore, step 7 includes calculating the convergence of the parameter distribution as follows:
[0036] (19)
[0037] Where f represents the distribution function of the parameters, including n e T e T i and n n m is the current iteration step, f m Let f be the parameter distribution at the current iteration step. m-1 Given the parameter distribution of the previous iteration, x g This represents the coordinates of grid point g. N represents the summation over all grid points in space. g This represents the total number of grid points, therefore This represents the average difference between the previous step and the current step when the number of iterations is m. The calculation is considered to have converged when the value is less than the threshold, and the calculation ends.
[0038] In a second aspect, the present invention provides an electronic device comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned coupling simulation method for radio frequency wave heating of a linear device.
[0039] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned coupling simulation method for radio frequency wave heating of a linear device.
[0040] The beneficial effects of this invention are as follows:
[0041] Self-consistent coupling of multiple physics processes: By using a step-by-step iterative approach, key physical processes such as neutral gas diffusion, electromagnetic wave propagation, particle source and energy source calculation, and plasma transport are dynamically coupled, achieving systematic simulation at the entire device scale and avoiding error accumulation caused by model fragmentation in traditional methods.
[0042] Computationally efficient and accurate: It adopts a modular design and selects the optimal algorithm for each physical process (such as diffusion equation, electromagnetic field wave equation, magnetohydrodynamic transport equation), which significantly reduces computational complexity while ensuring accuracy and breaks through the computing power limitation of a single high-fidelity method.
[0043] It is highly instructive for experiments: the input parameters only require experimentally measurable data (such as the amount of neutral gas and the power of the radio frequency antenna), and the other physical parameters (such as plasma temperature and density distribution) are obtained through self-consistent calculations without the need for human assumptions. The results are highly reliable and can provide direct reference for the design and experimentation of linear devices.
[0044] Versatility and scalability: The method framework is applicable to a variety of linear devices (such as VASIMR and industrial plasma equipment) and can be flexibly extended to other wave heating mechanisms or complex boundary conditions, with broad application potential. Attached Figure Description
[0045] Figure 1 This is a flowchart of a coupling simulation method for radio frequency wave heating of a linear device. Detailed Implementation
[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0047] like Figure 1 As shown, this invention provides a coupling simulation method suitable for radio frequency wave heating of linear devices. It employs an iterative approach using multiple simulation methods to self-consistently calculate the plasma parameter distribution in the linear device. The specific method is as follows:
[0048] Step 1. Construct the geometric model: Establish the geometric structure model of the linear device, specifically including the quartz tube (the quartz tube is a container for containing plasma), the vacuum system, and the radio frequency antenna.
[0049] Step 2. Parameter Initialization. The relevant parameters that need to be calculated for this geometric model include plasma temperature, density, and the density distribution of the neutral gas. Based on the constructed geometric model, the parameters are initialized. Initialization does not affect the final result, but better initial parameters can reduce the number of iterations. Generally, parameters close to those in the experiment or with constant distributions are chosen.
[0050] Step 3. Neutral gas diffusion modeling. Based on the constructed geometric model and initialization parameters, the density distribution of the neutral gas is updated. This step involves calculating equations (1) to (3) to obtain the density distribution of the neutral gas by solving the diffusion equation. The input parameters for this step are plasma density, temperature, neutral gas filling rate, and background pressure.
[0051] (1)
[0052] Equation (1) describes the diffusion properties of neutral argon gas, where n n Let be the density distribution function of a neutral gas. For the source distribution of neutral gases, and These are the distribution functions for ionization and recombination, respectively (i.e., the number of particles generated by ionization and the number of particles lost during recombination, in units of / m). 3 / s). D n =0.19 cm 2 / s represents the diffusion coefficient of argon. t represents time. Since the velocity of neutral gases is low, convection effects are neglected here.
[0053] The plasma density and temperature are obtained in the plasma transport step, which will be discussed later. The neutral gas filling rate... The background pressure p0 was set according to the experimental parameters. A fixed flow rate boundary condition was used at the inflation port. ( (The gas flow rate is used), and a Dirichlet boundary condition (i.e., constant gas pressure boundary condition) is applied at the exhaust port, with a neutral gas density at the outlet. For a fixed value, where p0 = 10 -4 Pa, T n = 25℃, R0 represents the background pressure, neutral gas temperature, and ideal gas constant, respectively. This step uses the commercial software COMSOL for calculation.
[0054] and The calculation is performed using equations (2) and (3). Where n e For plasma density, T e E represents the electron temperature. th=15.76 eV is the energy threshold for the ionization of argon atoms (Ar) into first-order argon ions (Ar+). and For ionization rate and recombination rate, which are functions of plasma density and temperature. Specific expressions are obtained from the OPEN-ADAS database.
[0055] (2)
[0056] (3)
[0057] Step 4. Electromagnetic wave propagation modeling. Based on the constructed geometric model and the initial plasma temperature and density, as well as the neutral gas density obtained in Step 3, the propagation characteristics of electromagnetic waves in the plasma are calculated. The propagation of electromagnetic waves is determined by equation (4), where E is the electric field vector. The frequency of the electromagnetic waves emitted by the antenna. Let c be the electromagnetic wave number, c be the speed of light, and K be the equivalent dielectric tensor. This represents the gradient operator in three-dimensional space.
[0058] (4)
[0059] The input parameter for this step is the plasma density n. e Electronic temperature T e Ion temperature T i Neutral gas density n n Antenna power P and magnetic field B. Electromagnetic wave frequency, antenna power, and magnetic field are device parameters, and these parameters vary between different devices. Taking a VASIMR-type thruster (linear device) as an example, it employs two antenna systems: a helical wave heating system and an ion cyclotron heating system, with wave frequencies of [missing information]. = 13.56 MHz and 0.5 MHz. This step uses the RF module of the commercial software COMSOL for calculation.
[0060] The propagation characteristics of electromagnetic waves in plasma using the dielectric tensor K characteristic in equation (4) can be expressed as:
[0061] (5)
[0062] in, For unit tensors, i.e. , For particles The dielectric tensor is expressed as:
[0063] (6)
[0064] (7)
[0065] (8)
[0066] (9)
[0067] in, Summation index Includes all plasma components (electrons, ions). , , ,and For particles The plasma frequency, cyclotron frequency, thermal velocity, and collision frequency. n = -1, 0 or 1, is a calculation parameter. j is the imaginary unit (…). ). Let z be the wave number in the z-direction. , where d a This represents the length of the antenna along the z-direction. The z-direction is the axial direction. It is the modulus; for ordinary electromagnetic wave modes, l is 1. , , , For particles Density, charge, mass, and temperature. Electron collision frequency. Including electron-ion collisions Collision with electrons and neutral gas ,based on ,have:
[0068] (10)
[0069] (11)
[0070] Ion collision frequency Including ion-electron collisions :
[0071] (12)
[0072] and m i Typical collision cross-sections and ion masses, Z(x) is the plasma dispersion function:
[0073] (13)
[0074] (14)
[0075] Where Im(.) represents the imaginary part of the parameter.
[0076] Step 5. Energy Deposition Modeling. Based on the constructed geometric model and the initial plasma temperature and density, as well as the neutral gas density n obtained in Step 3. n The electric field E calculated in step 4 is used to calculate the deposition power distribution of electromagnetic waves in the plasma using formula (15). subscript The plasma composition is the input parameter for this step. dielectric tensor Electric field vector E. The vacuum permittivity is indicated by an asterisk. This represents the conjugate transpose of a matrix and a vector.
[0077] (15)
[0078] Step 6. Plasma transport modeling. Based on the constructed geometric model and the initial plasma temperature and density, as well as the neutral gas density n obtained in Step 3. n and the electric field E calculated in step 4, and the power deposition obtained in step 5. The transport behavior of particles, energy, and momentum in the plasma is calculated using formulas (16), (17), and (18), respectively. , and Let D and u represent the density, temperature, and thermal conductivity of component a, respectively. , This represents the plasma diffusion coefficient, the average plasma velocity (velocity in a fluid sense), and the parallel and perpendicular transport coefficients. Due to the quasi-electroneutrality of plasma, the density of different particles is equal, i.e., n. e =n i . , Where k is the Boltzmann constant. The input parameters for this step are the neutral gas density and the external magnetic field. The output parameter is the particle density n. e (Equation 16) Particle temperature (Equation 17) and parallel velocity u (Equation 18). The density of the neutral gas is used to calculate the value in equation (16). and This step uses the magnetohydrodynamic calculation program EMC3 for calculations. , The calculation is self-consistent with the EMC3 program. and These represent the gradient along the magnetic field direction and the gradient perpendicular to the magnetic field direction, respectively. The transport coefficient D is proportional to... ,in denoted as ionic gyrocyclotron radius. It is the velocity component of the ions perpendicular to the magnetic field, thermal conductivity. .
[0079] (16)
[0080] (17)
[0081] (18)
[0082] Step 7: Iterate through steps 3-6 until the plasma parameters converge, and output the final plasma distribution and heating characteristics.
[0083] In principle, to ensure the integrity of convergence, the convergence of all parameters should be checked, specifically including the neutral gas density n. n Ionization source Recombination source Electric field E, various components dielectric tensor ,Element Power deposition distribution Plasma density n e Electronic temperature T e Ion temperature T i Distribution. However, due to the coupling characteristics between parameters, when the plasma density n e Electronic temperature T e Ion temperature T i and neutral gas density n n When the distribution is determined, other parameters can be obtained through the corresponding formula (Equation 1-16). Therefore, in actual calculations, the plasma density n is guaranteed. e Electronic temperature T e Ion temperature T i and neutral gas density n n The convergence of the distribution is sufficient. The convergence of a distribution with a certain parameter is calculated as follows:
[0084] (19)
[0085] Where f represents the distribution function of a certain parameter (n e T e T i and n n ), m is the current iteration step, f m Let f be the parameter distribution at the current iteration step. m-1 Given the parameter distribution of the previous iteration, x g This represents the coordinates of grid point g. N represents the summation over all grid points in space. g This represents the total number of grid points, therefore This represents the average difference between the previous step and the current step when the number of iterations is m. When the value is less than a certain threshold (usually set at 5% or 1%, depending on the required precision), the calculation is considered to have converged and can be terminated.
[0086] In a second aspect, the present invention provides an electronic device comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned coupling simulation method for radio frequency wave heating of a linear device.
[0087] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned coupling simulation method for radio frequency wave heating of a linear device.
[0088] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A coupling simulation method suitable for radio frequency wave heating of linear devices, characterized in that, include: Step 1: Construct the geometric model of the linear device; Step 2: Initialize parameters, including plasma density n e Electronic temperature T e Ion temperature T i and neutral gas density n n distributed; Step 3: Update the neutral gas density distribution based on the neutral gas diffusion equation and the initialized parameters; Step 4: Calculate the propagation characteristics of electromagnetic waves in the plasma based on the electromagnetic wave propagation equation and the neutral gas density distribution. Step 5: Calculate the energy deposition power of electromagnetic waves in the plasma based on the dielectric tensor and electric field distribution; Step 6: Calculate the particle, energy, and momentum transport behavior of the plasma using the magnetohydrodynamic transport equations, and update the plasma density n. e Electronic temperature T e Ion temperature T i ; Step 7: Iterate through steps 3-6 until the plasma parameters converge, and output the final plasma distribution and heating characteristics.
2. The coupling simulation method for radio frequency wave heating of a linear device according to claim 1, characterized in that, In step 1, the geometric model includes a quartz tube, a vacuum system, and a radio frequency antenna.
3. The coupling simulation method for radio frequency wave heating of a linear device according to claim 1, characterized in that, In step 2, the initialization parameters include plasma temperature, density, and neutral gas density distribution.
4. The coupling simulation method for radio frequency wave heating of a linear device according to claim 1, characterized in that, In step 3, the neutral gas diffusion equation is: (1) Where, n n D is the density distribution function of a neutral gas. n =0.19 cm 2 / s is the diffusion coefficient of argon gas, and t represents time; For the source distribution of neutral gases, and The distribution functions for ionization and recombination are respectively: (2) (3) Where, n e and T e For plasma density and temperature, E th =15.76 eV is the energy threshold for the ionization of argon atoms (Ar) into first-order argon ions (Ar+). and These are the ionization rate and the recombination rate; Solving the equation yields the density distribution of the neutral gas.
5. The coupling simulation method for radio frequency wave heating of a linear device according to claim 1, characterized in that, Step 4 includes calculating the propagation characteristics of electromagnetic waves in the plasma based on the constructed geometric model, the initial plasma temperature and density, and the neutral gas density obtained in step 3, where E is the electric field vector. The frequency of the electromagnetic waves emitted by the antenna. Let c be the electromagnetic wave number, c be the speed of light, and K be the equivalent dielectric tensor. Gradient operator in three-dimensional space: (4)。 6. The coupling simulation method for radio frequency wave heating of a linear device according to claim 5, characterized in that, Step 5 includes calculating the deposition power distribution of electromagnetic waves in the plasma based on the constructed geometric model and the initialized plasma temperature and density, the neutral gas density obtained in step 3, and the electric field vector E obtained in step 4. subscript It is a plasma component. The input parameter is a component. The dielectric tensor, The vacuum permittivity is indicated by an asterisk. Represents the conjugate transpose of a matrix and a vector: (15)。 7. The coupling simulation method for radio frequency wave heating of a linear device according to claim 6, characterized in that, Step 6 includes, based on the constructed geometric model and the initialized plasma temperature and density, the neutral gas density obtained in step 3, the electric field vector E obtained in step 4, and the deposition power distribution obtained in step 5. The transport of particles, energy, and momentum in the plasma is calculated using formulas (16), (17), and (18), respectively: (16) (17) (18) In the formula, n e Let be the plasma density, u represent the average plasma velocity, and D represent the plasma diffusion coefficient. and These are the distribution functions for ionization and recombination, respectively. subscript Indicates plasma composition, Time represents electron, Time represents ions, , k is the Boltzmann constant. , and Each represents a component The density, temperature and thermal conductivity, T e For electron temperature, T i m is the ion temperature. i For ion mass. , Indicates the parallel and vertical transport coefficients. and These represent the gradient along the direction of the magnetic field and the gradient perpendicular to the direction of the magnetic field, respectively.
8. The coupling simulation method for radio frequency wave heating of a linear device according to claim 1, characterized in that, Step 7 includes calculating the convergence of the parameter distribution as follows: (19) Where f represents the distribution function of the parameters, including n e T e T i and n n m is the current iteration step, f m Let f be the parameter distribution at the current iteration step. m-1 Given the parameter distribution of the previous iteration, x g This represents the coordinates of grid point g. N represents the summation over all grid points in space. g This represents the total number of grid points, therefore This represents the average difference between the previous step and the current step when the number of iterations is m. The calculation is considered to have converged when the value is less than the threshold, and the calculation ends.
9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the coupling simulation method for radio frequency wave heating of a linear device as described in any one of claims 1-8.
10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the coupling simulation method for radio frequency wave heating of a linear device as described in any one of claims 1-8.