A design method for double-saddle antenna used in Xuanlong-50 device

Abstract

The present invention discloses a design method for a dual-saddle antenna applied to a Xuanlong-50 device, the design method comprising the following steps: determining basic parameters; establishing a physical model; using electromagnetic wave theory to derive the Maxwell equations and boundary conditions satisfied when the dual-saddle antenna interacts with the Xuanlong-50 device plasma in cylindrical coordinates; using the finite element method to solve the Maxwell equations to obtain the electromagnetic field distribution in the vacuum and plasma regions, as well as the power deposition of the dual-saddle antenna transmission wave in the plasma; simulating the influence of the dual-saddle antenna structure and position on the coupling power during discharge. The beneficial effects of the present invention are as follows: a spiral wave discharge plasma is achieved under the conditions of low radio frequency source power (30-80KW) of a fusion device, effectively reducing the operating cost of a fusion device using radio frequency wave discharge plasma; the antenna design is simple, and the density and uniformity of the spiral wave-heated plasma are high.

Description

Technical field

[0002] The present invention relates to the technical field of research on spiral wave discharge plasma emitted by a spherical tokamak device antenna, and in particular to a design method for a double-saddle antenna used in a Xuanlong-50 device. [Background Technology]

[0004] International exploration of the peaceful uses of fusion energy has been underway for nearly 70 years. Fusion energy releases a million times more energy per unit than fossil fuels, and fusion fuel is abundant on Earth. Fusion energy is an ideal clean energy source and driving force for development for humanity. Breakthroughs in fusion technology will transform the world's energy landscape. Currently, there are two methods for achieving controlled nuclear fusion energy worldwide: magnetic confinement and inertial confinement. Inertial confinement methods include laser target fusion and Z-pinch fusion. Both methods have extremely short durations (on the order of nanoseconds), far short of the requirements for controlled nuclear fusion as a commercial energy source. Therefore, magnetic confinement fusion is currently the most promising method for achieving controlled nuclear fusion energy. Within the field of magnetic confinement fusion, the main devices that utilize magnetically confined thermonuclear plasma to achieve nuclear fusion reactions include tokamaks and stellarators. Significant progress has been made worldwide in tokamaks, leading to the launch of the International Thermonuclear Experimental Reactor (ITER) project, whose goal is to demonstrate the scientific and technological feasibility of the peaceful uses of fusion energy. China joined the ITER project in 2006. China's fusion research has gone through a process from technical learning and cooperation to leading research and development in some aspects.

[0005] The spherical tokamak, also known as a spherical ring or low-ratio tokamak, is a high-temperature plasma fusion device. Unlike traditional tokamaks, its tokamak has a very small tokamak ratio (larger radius / smaller radius of the plasma ring), giving the entire plasma a spherical shape. This allows for more efficient use of magnetic energy and improves performance in magnetohydrodynamic instabilities. This type of fusion reactor is expected to be smaller and less expensive than traditional tokamaks. In 2018, ENN Technology Development Co., Ltd. officially launched construction of the "Xuanlong-50" spherical tokamak. Through systematic organization and coordinated division of labor, the design, manufacture, installation, and commissioning of the device were completed in approximately 10 months. On August 8, 2019, the ENN "Xuanlong-50," a medium-scale spherical tokamak fusion experimental device independently designed and built by ENN Group, was completed in Langfang, Hebei Province. The first plasma discharge was achieved, officially initiating physical experiments.

[0006] Helicon waves are low-frequency electromagnetic waves (between the ion cyclotron frequency and the electron cyclotron frequency) excited by radio frequency antennas and propagating in high-conductivity media. Helicon waves can propagate to the core of the plasma and have no density limit, low electron damping, and can directly heat ions. Therefore, helicon wave discharge plasma has the advantages of high ionization rate, high density, uniformity and stability, and controllable particle energy. It is widely used in thin film deposition, plasma rocket propulsion, semiconductor etching, nuclear fusion and other fields.

[0007] In 2019, the Xinao "Xuanlong-50" device mainly uses electron cyclotron wave discharge plasma. Although the plasma density can reach 10 18 m -3 , but the uniformity of density needs to be further improved.

[0008] Electron cyclotron waves (20-170 GHz) have excellent propagation capabilities and localized wave energy deposition. However, due to the strong damping of electrons, under reactor-level plasma conditions, these waves can only propagate to the plasma center at very high frequencies; otherwise, they are refracted before reaching the plasma center. Long-second pulse, high-power gyrotrons are expensive, making the construction and operation of electron cyclotron heating systems relatively expensive. Furthermore, the uniformity of the electron cyclotron discharge plasma in the ENN Xuanlong-50 device needs to be further improved. [Summary of the invention]

[0010] The present invention discloses a design method for a double-saddle antenna applied to a Xuanlong-50 device, which generates relatively uniform high-density plasma with low operating costs, thereby solving the technical problems involved in the background technology.

[0011] To achieve the above object, the technical solution of the present invention is:

[0012] A design method for a double-saddle antenna for a Xuanlong-50 device, the design method comprising the following steps:

[0013] Step 1: Determine basic parameters, including the size parameters of the Xuanlong-50 device, the current intensity and wave frequency of the double-saddle antenna, the plasma type, density, temperature, and magnetic field;

[0014] Step 2: Based on the determined basic parameters, a physical model and Maxwell's equations are established to describe the interaction between the dual-saddle antenna and the plasma. The finite element method is then used to solve the Maxwell equations to obtain the electromagnetic field distribution in the vacuum and plasma regions, as well as the power deposition of the dual-saddle antenna's transmitted wave in the plasma.

[0015] Step 3: Based on the Maxwell equations and the obtained electromagnetic field distribution and power deposition, simulate the influence of the double-saddle antenna structure and position on the coupling power during discharge, adjust the distance from the inner boundary of the double-saddle antenna to the axis center of the Xuanlong-50 device, the central angle of the double-saddle antenna arc relative to the center of the Xuanlong-50 device, and the arc of the feeder end to the plasma center. 、 The width, thickness and spacing of the double saddle antenna are used to obtain the optimal design parameters of the double saddle antenna.

[0016] Step 4: Design a double-saddle antenna based on the obtained optimal design parameters and the actual antenna installation space of the Xuanlong-50 device.

[0017] As a preferred improvement of the present invention, in step 1, the Xuanlong-50 device is cylindrical, with a height H of 281cm and a distance b from its outer wall to the center of the cylinder of 155.5cm; the magnetic field is uniformly distributed and the size is , the direction is along the axial direction of the Xuanlong-50 device.

[0018] As a preferred improvement of the present invention, the double saddle antenna extends along the circumferential direction of the Xuanlong-50 device, and includes a first arcuate side AB extending along the circumferential direction of the Xuanlong-50 device, a second arcuate side FC extending along the circumferential direction of the Xuanlong-50 device and arranged parallel to the first arcuate side AB, a feeder end E and an output end D arranged on the second arcuate side FC, and a first short side AF and a second short side BC connecting the first arcuate side AB and the second arcuate side FC and parallel to the axial direction of the Xuanlong-50 device.

[0019] As a preferred improvement of the present invention, the current intensity of the double saddle antenna is , frequency .

[0020] As a preferred improvement of the present invention, assuming that the plasma is evenly distributed and fills the entire Xuanlong-50 device, the radius of the columnar plasma is , neutral hydrogen atom density , the electron density is , the temperature of the electrons , ion temperature .

[0021] As a preferred improvement of the present invention, in step 2, the physical model includes a cold plasma model and a three-dimensional antenna model, the plasma is assumed to be a linear medium, and the disturbance of the electromagnetic field is expressed as expi( mq + kz - wt ) form changes, among which, w = 2 pf is the circular frequency of the double saddle antenna.

[0022] As a preferred improvement of the present invention, step 2 specifically includes:

[0023] According to Maxwell's equations, the electromagnetic field in cylindrical coordinate plasma and the current density of the double saddle antenna j and charge density r The satisfied relationship is:

[0024] (1)

[0025] (2)

[0026] (3)

[0027] (4)

[0028] In the formula represents the magnetic field in the plasma, is the electric field in the plasma, is an imaginary unit, k 0 = wc is the vacuum wave number, c is the speed of light, ε is the dielectric tensor of the plasma satisfying:

[0029] (5)

[0030] (6) (7) (8)

[0031] In the formula 、 、 is the plasma dielectric tensor component, , is the wave vector of the spiral wave in the z direction, is the thermal velocity of the particle, and are the temperature and mass of the particle, is the plasma dispersion function; 、 and are the plasma frequency, particle cyclotron frequency, and particle collision frequency, respectively; is the electron-neutral particle collision frequency, is the electron-ion collision frequency, is the ion-electron collision frequency, which satisfies:

[0032] (9) (10) (11)

[0033] in 、 are the plasma electron temperature and density, is the ion mass, is the electron-neutral particle collision cross section;

[0034] According to the definition of electromagnetic field vector potential and scalar potential, magnetic field and electric field are respectively expressed as vector magnetic potential. and scalar potential It is expressed as follows:

[0035] (12) (13)

[0036] The vector magnetic potential satisfies the Coulomb criterion:

[0037] , (14)

[0038] Vector magnetic potential at the outer wall of the device and Directional component 、 and scalar potential The following boundary conditions are met:

[0039] (15)

[0040] (16)

[0041] (17)

[0042] Using boundary conditions (15)-(17), the Maxwell equations (1)-(14) are numerically solved by finite element method to obtain the approximate values of the vector magnetic potential and scalar potential of each node, and then the electric and magnetic field distributions in the plasma region are obtained;

[0043] The plasma dielectric tensor in Maxwell's equations (3) and (4) is Replaced by the vacuum dielectric tensor , we can get the field distribution in vacuum. The wave excited by the double saddle antenna is deposited on the surface with a radius of The coupled power in the columnar plasma is:

[0044] (18)

[0045] In the formula , and are the Fourier transforms of the electric field in the plasma , and .

[0046] As a preferred improvement of the present invention, step 4 specifically includes:

[0047] Adjust the distance s from the inner boundary of the double-saddle antenna to the center of the device axis to determine the optimal distance s for high coupling power during discharge;

[0048] Adjust the central angle of the first arc side AB of the double saddle antenna relative to the center O of the Xuanlong-50 device θ s , the arc of the feeder end E to the plasma center is θ a , determine the best arc with high coupling power during discharge θ s and θ a ;

[0049] Adjust the width 2L of the double-saddle antenna to determine the optimal antenna width with high coupling power during discharge;

[0050] Adjust the thickness d of the double-saddle antenna to determine the optimal antenna thickness for high coupling power during discharge;

[0051] Adjust the distance between the double saddle antennas 2S1 to determine the optimal antenna distance for radiation field strength.

[0052] As a preferred improvement of the present invention, the dual-saddle antenna is a 13.56 MHz dual-saddle antenna.

[0053] The beneficial effects of the design method of the double-saddle antenna applied to the Xuanlong-50 device provided by the present invention are as follows:

[0054] 1. By optimizing the design of a 13.56MHz dual-saddle antenna structure, the present invention achieves helicon discharge plasma in a fusion device under low RF source power (30-80kW). The construction and operating costs of a 20-170GHz electron cyclotron heating system generally range from several million to tens of millions of yuan. The 13.56MHz dual-saddle antenna helicon heating system designed by the present invention costs between tens and several million yuan, effectively reducing the operating costs of a fusion device using RF wave discharge plasma.

[0055] 2. The 13.56 MHz double-saddle antenna designed by the present invention is simple in design, and the density and uniformity of the helical wave-heated plasma are high.

Brief Description of the Drawings

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive work, among which:

[0058] Figure 1 It is a schematic diagram of the three-dimensional structure of the Xuanlong-50 device and the double-saddle antenna of the present invention;

[0059] Figure 2 This is a schematic diagram of the cross-sectional structure of the Xuanlong-50 device and the double-saddle antenna of the present invention;

[0060] Figure 3 Graph showing the relationship between the coupling power P and s of the dual-saddle antenna of the present invention;

[0061] Figure 4 (a) to (f) are the coupling power P and 、 θ s The change relationship diagram;

[0062] Figure 5 Graph showing the relationship between the coupling power P and the half-width L of the dual-saddle antenna of the present invention;

[0063] Figure 6 This is a graph showing the relationship between the thickness d of the double-saddle antenna of the present invention and the coupling energy;

[0064] Figure 7 This is a diagram showing the relationship between the spacing between the double-saddle antennas and the radiated electric field of the present invention;

[0065] Figure 8 Schematic diagram of the structure of the double saddle antenna of the present invention;

[0066] Figure 9 This is a schematic diagram of the installation of the dual-saddle antenna of the present invention in the Xuanlong-50 device;

[0067] Figure 10 This is a diagram showing the experimental results of the 11816 gun of the present invention, which shows the discharge of Xuanlong-50 plasma using a dual-saddle antenna;

[0068] Figure 11 (a) to (d) are the experimental results of discharge of #11785--#11820. [Specific implementation method]

[0070] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0071] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in this field can implement it. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0072] The present invention provides a design method for a double-saddle antenna applied to a Xuanlong-50 device, the design method comprising the following steps:

[0073] Step 1: Determine basic parameters, including the size parameters of the Xuanlong-50 device, the current intensity and wave frequency of the double-saddle antenna, the plasma type, density, temperature, and magnetic field;

[0074] For details, see Figure 1 and 2 As shown, the Xuanlong-50 device is cylindrical, with a height H of 281cm and a distance b from its outer wall to the center of the cylinder of 155.5cm; the magnetic field is uniformly distributed and the size is , the direction is along the z-axis direction of the Xuanlong-50 device.

[0075] The double-saddle antenna (i.e., the "antenna" in the figure) extends along the circumferential direction of the Xuanlong-50 device, and includes a first arc-shaped side AB extending along the circumferential direction of the Xuanlong-50 device, a second arc-shaped side FC extending along the circumferential direction of the Xuanlong-50 device and arranged parallel to the first arc-shaped side AB, a feeder end E and an output end D arranged on the second arc-shaped side FC, and a first short side AF and a second short side BC connecting the first arc-shaped side AB and the second arc-shaped side FC and parallel to the z-axial direction of the Xuanlong-50 device.

[0076] The current intensity of the double saddle antenna , frequency .

[0077] Assuming that the plasma is evenly distributed and fills the entire Xuanlong-50 device, the radius of the columnar plasma is , neutral hydrogen atom density , the electron density is , the temperature of the electrons , ion temperature .

[0078] Step 2: Based on the determined basic parameters, a physical model and Maxwell's equations are established to describe the interaction between the dual-saddle antenna and the plasma. The finite element method is then used to solve the Maxwell equations to obtain the electromagnetic field distribution in the vacuum and plasma regions, as well as the power deposition of the dual-saddle antenna's transmitted wave in the plasma.

[0079] Specifically, the physical model includes a cold plasma model and a three-dimensional antenna model. The plasma is assumed to be a linear medium, and the disturbance of the electromagnetic field is expressed as expi( mq + kz - wt ) form changes, among which, w = 2 pf is the circular frequency of the double saddle antenna.

[0080] Furthermore, step 2 specifically includes:

[0081] According to Maxwell's equations, the electromagnetic field in cylindrical coordinate plasma and the current density of the double saddle antenna j and charge density r The satisfied relationship is:

[0082] (1)

[0083] (2)

[0084] (3)

[0085] (4)

[0086] In the formula represents the magnetic field in the plasma, is the electric field in the plasma, is an imaginary unit, k 0 = wc is the vacuum wave number, c is the speed of light, ε is the dielectric tensor of the plasma satisfying:

[0087] (5)

[0088] (6) (7) (8)

[0089] In the formula 、 、 is the plasma dielectric tensor component, , is the wave vector of the spiral wave in the z direction, is the thermal velocity of the particle, and are the temperature and mass of the particle, is the plasma dispersion function; 、 and are the plasma frequency, particle cyclotron frequency, and particle collision frequency, respectively; is the electron-neutral particle collision frequency, is the electron-ion collision frequency, is the ion-electron collision frequency, which satisfies:

[0090] (9) (10) (11)

[0091] in 、 are the plasma electron temperature and density, is the ion mass, is the electron-neutral particle collision cross section;

[0092] According to the definition of electromagnetic field vector potential and scalar potential, magnetic field and electric field are respectively expressed as vector magnetic potential. and scalar potential It is expressed as follows:

[0093] (12) (13)

[0094] The vector magnetic potential satisfies the Coulomb criterion:

[0095] , (14)

[0096] Vector magnetic potential at the outer wall of the device and Directional component 、 and scalar potential The following boundary conditions are met:

[0097] (15)

[0098] (16)

[0099] (17)

[0100] Using boundary conditions (15)-(17), the Maxwell equations (1)-(14) are numerically solved by finite element method to obtain the approximate values of the vector magnetic potential and scalar potential of each node, and then the electric and magnetic field distributions in the plasma region are obtained;

[0101] The plasma dielectric tensor in Maxwell's equations (3) and (4) is Replaced by the vacuum dielectric tensor , we can get the field distribution in vacuum. The wave excited by the double saddle antenna is deposited on the surface with a radius of The coupled power in the columnar plasma is:

[0102] (18)

[0103] In the formula , and are the Fourier transforms of the electric field in the plasma , and .

[0104] Step 3. According to the Maxwell equations and the obtained electromagnetic field distribution and power deposition, simulate the influence of the double-saddle antenna structure and position on the coupling power during discharge, adjust the distance from the inner boundary of the double-saddle antenna to the axis center of the Xuanlong-50 device, the central angle of the double-saddle antenna arc relative to the center of the Xuanlong-50 device, the arc of the feeder end to the plasma center, the double-saddle antenna width, the double-saddle antenna thickness and the double-saddle antenna spacing to obtain the optimal design parameters of the double-saddle antenna;

[0105] Specifically include:

[0106] Adjust the distance s from the inner boundary of the double-saddle antenna to the center of the device axis to determine the optimal distance s for high coupling power during discharge;

[0107] For details, see Figure 3 As shown in the figure, when the distance s from the inner boundary of the double saddle antenna to the center of the device axis changes in the range of 143.0cm-155.00cm, the variation law of the coupling power with s is as follows: Figure 3 As shown (other simulation parameters: , , , Simulation results show that, when other parameters remain constant, the coupling power gradually decreases as the coupling distance s increases. The spiral wave coupling power is maximum when the antenna spacing is 143.00cm, 143.50cm, and 144.00cm. Considering practical installation requirements, it is recommended to install the antenna at s = 143.5cm, if feasible.

[0108] Adjust the central angle of the first arc side AB of the double saddle antenna relative to the center O of the Xuanlong-50 device θ s , the arc of the feeder end E to the plasma center is θ a , determine the best arc with high coupling power during discharge θ s and θ a ;

[0109] See Figure 4 As shown, the central angle of the saddle antenna arc AB relative to the device center O is θ s When the angle changes from 0.2617rad to 0.5233rad (corresponding to the central angle of 15° to 30°), the coupling power θ s The changing rules of Figure 4 (a) to (f) (other simulation parameters , , ), the simulation results show that: when other parameters are constant, θ s The larger the coupling power, the greater the θ s At a certain time, The smaller the value, the greater the coupling power. , .

[0110] Adjust the width 2L of the double-saddle antenna to determine the optimal antenna width with high coupling power during discharge;

[0111] See Figure 5 As shown in the figure, when the width 2L of the double saddle antenna changes in the range of 0.0cm to 15.0cm, the variation law of the coupling power with the width is as follows: Figure 5 As shown (other simulation parameters: , , , ). According to the simulation results, when other parameters are constant, the coupling power of the double saddle antenna increases with the increase of antenna width. Considering the installation space of the antenna, the width of the antenna is designed to be .

[0112] Adjust the thickness d of the double-saddle antenna to determine the optimal antenna thickness for high coupling power during discharge;

[0113] See Figure 6 As shown in the figure, when the thickness d of the double saddle antenna changes in the range of 0.60cm-1.20cm, the variation rules of coupling power and coupling resistance are as follows: Figure 6 As shown (other simulation parameters: , , , ). The simulation results show that the thickness of the antenna has little effect on the coupling power of the double saddle antenna. Based on the simulation results and the design experience of other device antennas, the antenna thickness is selected. .

[0114] Adjust the distance between the double saddle antennas 2S1 to determine the optimal antenna distance for radiation field strength.

[0115] See Figure 7 As shown, when the distance 2S1 between the double saddle antennas changes from 3.0cm to 7cm, the far field diagram of the antenna radiating into the air is as follows: Figure 7 As shown (other simulation parameters: , , , , Simulation results show that when the circuits are fed in phase, increasing the antenna spacing 2S1 slightly increases the antenna radiation field, but the overall radiation trend is minimally affected. Based on the simulation results and the actual antenna installation space, the spacing between the two saddle antennas is designed to be 2S1 = 4.00 cm.

[0116] Step 4: Based on the obtained optimal design parameters and the actual installation space of the Xuanlong-50 antenna (see Figure 9 As shown in Figure 3), a double-saddle antenna is designed.

[0117] The double saddle antenna is a 13.56MHz double saddle antenna. Figure 10 ) shows that the electron density in the center of the plasma is the highest at the beginning of the discharge. The main reason for the high electron density in the center may be the strong magnetic field in the center. Figure 11 (a) to (d) in the figure show that spiral waves are generated in the 13.56MHz double-saddle antenna discharge plasma and resonant absorption occurs ( Figure 11 As shown in (d) in the figure), this resonant absorption may be the second harmonic absorption of the ion cyclotron wave, or it may be because the density gradient forms a potential well, in which the spiral wave repeatedly reflects and propagates back and forth, heating the electrons.

[0118] The beneficial effects of the design method of the double-saddle antenna applied to the Xuanlong-50 device provided by the present invention are as follows:

[0119] 1. By optimizing the design of a 13.56MHz dual-saddle antenna structure, the present invention achieves helicon discharge plasma in a fusion device under low RF source power (30-80kW). While the construction and operating costs of a 20-170GHz electron cyclotron heating system typically range from several million to tens of millions of yuan, the 13.56MHz dual-saddle antenna helicon heating system designed by the present invention costs between tens and several million yuan, effectively reducing the operating costs of a fusion device using RF discharge plasma.

[0120] 2. The 13.56 MHz double-saddle antenna designed by the present invention is simple in design, and the density and uniformity of the helical wave-heated plasma are high.

[0121] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and the embodiments. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A design method for a double-saddle antenna used in a Xuanlong-50 device, characterized in that: The design method includes the following steps: Step 1: Determine basic parameters, including the size parameters of the Xuanlong-50 device, the current intensity and wave frequency of the dual-saddle antenna, the plasma type, density, temperature, and magnetic field. The dual-saddle antenna extends along the circumferential direction of the Xuanlong-50 device and includes a first arcuate side AB extending along the circumferential direction of the Xuanlong-50 device, a second arcuate side FC extending along the circumferential direction of the Xuanlong-50 device and arranged parallel to the first arcuate side AB, a feeder end E and an output end D arranged on the second arcuate side FC, and a first short side AF and a second short side BC connecting the first arcuate side AB and the second arcuate side FC and parallel to the axial direction of the Xuanlong-50 device. Step 2: Based on the determined basic parameters, a physical model and Maxwell's equations are established to describe the interaction between the dual-saddle antenna and the plasma. The finite element method is then used to solve the Maxwell equations to obtain the electromagnetic field distribution in the vacuum and plasma regions, as well as the power deposition of the dual-saddle antenna's transmitted wave in the plasma. Step 3: Based on the Maxwell equations and the electromagnetic field distribution and power deposition, simulate the influence of the double-saddle antenna structure and position on the coupling power during discharge, adjust the distance from the inner boundary of the double-saddle antenna to the axis center of the Xuanlong-50 device, the central angle of the double-saddle antenna arc relative to the center of the Xuanlong-50 device, and the arc of the feeder end to the plasma center. 、 The width, thickness and spacing of the double saddle antenna are used to obtain the optimal design parameters of the double saddle antenna. Step 4: Based on the obtained optimal design parameters and the actual installation space of the Xuanlong-50 device antenna, a double-saddle antenna is designed, specifically including: Adjust the distance s from the inner boundary of the double-saddle antenna to the center of the device axis to determine the optimal distance s for high coupling power during discharge; Adjust the central angle of the first arc side AB of the double saddle antenna relative to the center O of the Xuanlong-50 device θ s , the arc of the feeder end E to the plasma center is θ a , determine the best arc with high coupling power during discharge θ s and θ a ; Adjust the width 2L of the double-saddle antenna to determine the optimal antenna width with high coupling power during discharge; Adjust the thickness d of the double-saddle antenna to determine the optimal antenna thickness for high coupling power during discharge; Adjust the distance between the double saddle antennas 2S1 to determine the optimal antenna distance for radiation field strength.

2. The design method for the double-saddle antenna used in the Xuanlong-50 device according to claim 1 is characterized in that: In step 1, the Xuanlong-50 device is cylindrical, with a height H of 281 cm and a distance b from its outer wall to the center of the cylinder of 155.5 cm; the magnetic field is uniformly distributed and the size is , the direction is along the axial direction of the Xuanlong-50 device.

3. The design method of a double-saddle antenna for a Xuanlong-50 device according to claim 2, characterized in that: The current intensity of the double saddle antenna , frequency .

4. The design method for the double-saddle antenna used in the Xuanlong-50 device according to claim 3 is characterized in that: Assuming that the plasma is evenly distributed and fills the entire Xuanlong-50 device, the radius of the columnar plasma is , neutral hydrogen atom density , the electron density is , the temperature of the electrons , ion temperature .

5. The design method for the double-saddle antenna used in the Xuanlong-50 device according to claim 1 is characterized in that: In step 2, the physical model includes a cold plasma model and a three-dimensional antenna model. The plasma is assumed to be a linear medium, and the disturbance of the electromagnetic field is expressed as expi( mq + kz - wt ) form changes, among which, w = 2 pf is the circular frequency of the double saddle antenna.

6. The design method for the double-saddle antenna used in the Xuanlong-50 device according to claim 5, characterized in that: Step 2 specifically includes: According to Maxwell's equations, the electromagnetic field in cylindrical coordinate plasma and the current density of the double saddle antenna j and charge density r The satisfied relationship is: （1） （2） （3） （4） In the formula represents the magnetic field in the plasma, is the electric field in the plasma, is an imaginary unit, k 0 = wc is the vacuum wave number, c is the speed of light, ε is the dielectric tensor of the plasma satisfying: （5） （6） （7） （8） In the formula 、 、 is the plasma dielectric tensor component, , is the wave vector of the spiral wave in the z direction, is the thermal velocity of the particle, and are the temperature and mass of the particle, is the plasma dispersion function; 、 and are the plasma frequency, particle cyclotron frequency, and particle collision frequency, respectively; is the electron-neutral particle collision frequency, is the electron-ion collision frequency, is the ion-electron collision frequency, which satisfies: （9） （10） （11） in 、 are the plasma electron temperature and density, is the ion mass, is the electron-neutral particle collision cross section; According to the definition of electromagnetic field vector potential and scalar potential, magnetic field and electric field are respectively expressed as vector magnetic potential. and scalar potential It is expressed as follows: （12） （13） The vector magnetic potential satisfies the Coulomb criterion: ， （14） Vector magnetic potential at the outer wall of the device and Directional component 、 and scalar potential The following boundary conditions are met: （15） （16） （17） Using boundary conditions (15)-(17), the Maxwell equations (1)-(14) are numerically solved by finite element method to obtain the approximate values of the vector magnetic potential and scalar potential of each node, and then the electric and magnetic field distributions in the plasma region are obtained; The plasma dielectric tensor in Maxwell's equations (3) and (4) is Replaced by the vacuum dielectric tensor , we can get the field distribution in vacuum. The wave excited by the double saddle antenna is deposited on the surface with a radius of The coupled power in the columnar plasma is: （18） In the formula , and are the Fourier transforms of the electric field in the plasma , and .

7. The design method for the double-saddle antenna used in the Xuanlong-50 device according to claim 1, characterized in that: The double-saddle antenna is a 13.56 MHz double-saddle antenna.

Images