Method and system for driving double-frequency electron cyclotron current near tokamak medium-radius area

Abstract

The invention discloses a method and a system for driving double-frequency electron cyclotron current near a tokamak medium radius region, and relates to the technical field of tokamak current driving. The method comprises the steps that two electron cyclotron waves with different frequencies in a double-frequency electron cyclotron wave system arranged on a Tokamak device are used for simultaneously driving off-axis current in a medium-radius area and off-axis current outside the medium-radius area, and the electron cyclotron wave with the higher frequency drives the off-axis current in the medium-radius area in a top emission mode; the low-frequency electron cyclotron waves drive off-axis current outside a middle radius area in an outer middle plane emission mode. According to the invention, electron cyclotron waves with two different working frequencies of a dual-frequency system can be simultaneously and effectively used for off-axis current driving near a tokamak medium radius area.

Description

Technical Field

[0001] This invention relates to the field of tokamak current driving technology, and in particular to a dual-frequency electron cyclotron current driving method and system near the radius region in a tokamak. Background Technology

[0002] Tokamak is a highly promising type of magnetically confined fusion reactor. Non-inductive current drive is crucial for the long-pulse operation of tokamaks and for maintaining steady-state, high-performance operation of future reactor-scale tokamak devices. Traditional electron cyclotron current drive (ECCD), due to its narrow current profile and ease of radial position control, is widely used to control plasma current profiles and suppress various magnetohydrodynamic instabilities. Numerous numerical simulations based on tokamak fusion reactors have shown that efficiently driving off-axis currents in the mid-radius region to form a broad current distribution with negative central magnetic shear plays a vital role in optimizing plasma operating conditions and controlling instabilities.

[0003] Single-frequency electron cyclotron resonant heating and current-driven (ECRH&CD) systems limit the circumferential magnetic field range of tokamak operation. Dual-frequency ECRH&CD systems, however, can output two high-power microwaves at different frequencies. These microwaves can effectively drive current within different magnetic field ranges, thus broadening the applicable magnetic field range for ECRH&CD in tokamaks. Many existing tokamaks are equipped with dual-frequency or even multi-frequency ECRH&CD systems, with the 105 / 140 GHz dual-frequency system being a typical example. The Korean KSTAR and Czech COMPASS Upgrade devices use a 105 / 140 GHz dual-frequency cyclotron and a 170 GHz single-frequency cyclotron, while the German ASDEX Upgrade uses a 140 GHz single-frequency cyclotron and a 140 GHz / 105 GHz dual-frequency cyclotron. The Chinese HL-3 ECRH system includes a 105 GHz single-frequency cyclotron and a 140 GHz / 105 GHz dual-frequency cyclotron.

[0004] The dual-frequency ECRH&CD system allows for a wider range of magnetic fields that can be applied in tokamaks, but the range of magnetic fields that can be matched by different operating frequencies varies, and in most cases only one operating frequency is used. How to enable the two different operating frequencies of the electron cyclotron waves in the dual-frequency system to be used simultaneously and effectively for off-axis current driving near the radius region in the tokamak has become an urgent technical problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a dual-frequency electron cyclotron current driving method near the radius region in a tokamak, enabling two electron cyclotron waves with different operating frequencies in a dual-frequency system to be used simultaneously and effectively for off-axis current driving near the radius region in a tokamak.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A dual-frequency electron cyclotron current driving method near the radius region in a tokamak includes the following steps:

[0008] The tokamak device utilizes a dual-frequency electron cyclotron wave system (referred to as "dual-frequency system") equipped with two electron cyclotron waves of different frequencies to simultaneously drive off-axis currents in the middle radius region and outside the middle radius region. The higher frequency (i.e., high frequency) electron cyclotron wave drives the off-axis current in the middle radius region through top emission, while the lower frequency (i.e., low frequency) electron cyclotron wave drives the off-axis current outside the middle radius region through outer plane emission.

[0009] The phrase "near the mid-radius area" includes both the "mid-radius area" and "outside the mid-radius area".

[0010] Top-level launch is achieved through the top launch window, while outer-middle-plane launch is achieved through the outer-middle-plane launch window.

[0011] Furthermore, the higher frequency electron cyclotron wave drives the off-axis current in the mid-radius region in a Fisch-Boozer-dominant manner (i.e., the Fisch-Boozer mechanism is the dominant mechanism); the lower frequency electron cyclotron wave drives the off-axis current outside the mid-radius region in an Ohkawa-dominant manner (i.e., the Ohkawa mechanism is the dominant mechanism).

[0012] Furthermore, the higher frequency electron cyclotron wave is a 140 GHz electron cyclotron wave; the lower frequency electron cyclotron wave is a 105 GHz electron cyclotron wave.

[0013] The power of the 140 GHz electron cyclotron wave is deposited on the high-field side, while the power of the 105 GHz electron cyclotron wave is deposited on the low-field side.

[0014] Furthermore, the magnetic field B when the two electron cyclotron waves of different frequencies simultaneously drive the off-axis current near the mid-radius region (i.e., both within and outside the mid-radius region) T The value range is: 2.1 T ≤ B T ≤ 2.35 T. Preferably 2.15 T ~ 2.35 T, for example 2.15 T, 2.2 T, 2.25 T, 2.3 T or 2.35 T.

[0015] Furthermore, when the higher frequency electron cyclotron wave drives the off-axis current in the mid-radius region through top emission, its emission angle (α, β) is (232.5 ~ 248°, 154 ~ 242°), for example (α, β) = (232.5°, 160°).

[0016] When the lower frequency electron cyclotron wave drives the off-axis current outside the mid-radius region through the outer mid-plane emission mode, its emission angle (α, β) is (140 ~ 170°, 78 ~ 90°), for example (α, β) = (155°, 80°).

[0017] Furthermore, the injection power ratio of the higher frequency (140 GHz) electron cyclotron wave to the lower frequency (105 GHz) electron cyclotron wave is ≥ 2.

[0018] Furthermore, the electron temperature when the two electron cyclotron waves of different frequencies simultaneously drive off-axis currents near the mid-radius region (i.e., the mid-radius region and outside the mid-radius region) is 4.0 ~ 8.0 keV.

[0019] Furthermore, the electron density when the two electron cyclotron waves of different frequencies simultaneously drive off-axis currents near the mid-radius region (i.e., within and outside the mid-radius region) is 2.0 ~ 7.0 × 10⁻⁶. 19 m -3 .

[0020] Furthermore, the present invention also relates to a dual-frequency electron cyclotron current driving system for use near the radius region in a tokamak, the system being used to implement the aforementioned dual-frequency electron cyclotron current driving method near the radius region in a tokamak, and comprising:

[0021] A dual-frequency electron cyclotron wave system is configured to generate and emit two electron cyclotron waves of different frequencies to simultaneously drive off-axis currents in the mid-radius region and outside the mid-radius region.

[0022] The dual-frequency electronic cyclotron wave system includes:

[0023] A high-frequency wave transmitting subsystem, whose transmitting antenna is arranged in the top region of the tokamak device and configured to transmit high-frequency electron cyclotron waves in a top-emitting manner to drive off-axis current in the mid-radius region;

[0024] The low-frequency wave transmitting subsystem has its transmitting antenna located in the outer mid-plane region of the tokamak device and configured to transmit low-frequency electron cyclotron waves in an outer-mid-plane transmission mode to drive off-axis currents outside the mid-radius region.

[0025] This invention utilizes a higher-frequency electron cyclotron wave in a dual-frequency system, emitted from the top, to drive the off-axis current in the middle radius region. Simultaneously, it utilizes a lower-frequency electron cyclotron wave in the dual-frequency system, emitted from the outer middle plane, to drive the off-axis current outside the middle radius region. This enables two electron cyclotron waves with different operating frequencies in a dual-frequency system to be used simultaneously and effectively for driving off-axis currents near the middle radius region of a tokamak. Attached Figure Description

[0026] Figure 1 A schematic diagram illustrating the definitions of the poloidal emission angle β and the circumferential emission angle α of an ECCD;

[0027] Figure 2 The emission position, second harmonic resonance layer position, and electron density n of the ECCD. e Electronic temperature T e and effective ionic charge Z eff The distribution diagram shows (a) the emission location and the location of the second harmonic resonance layer, and (b) the electron density n. e Electronic temperature T e and effective ionic charge Z eff Distribution;

[0028] Figure 3 Here is a contour plot of TL-ECCD as a function of emission angle. (a) is the normalized current drive efficiency, (b) is the normalized radial position of the peak drive current, (c) is the total drive current, and (d) is the peak value of the drive current density.

[0029] Figure 4 This is a schematic diagram of a TL-ECCD trace, with a wave frequency of 140 GHz, α = 232.5 °, and β = 160 °.

[0030] Figure 5 The diagram shows the radial distribution of driving current and power deposition in a TL-ECCD, with a wave frequency of 140 GHz, a total injected power of 1 MW, α = 232.5 °, and β = 160 °.

[0031] Figure 6 Here is a contour plot of EL-OKCD as a function of emission angle. (a) is the normalized current drive efficiency, (b) is the normalized radial position of the peak drive current, (c) is the total drive current, and (d) is the peak value of the drive current density.

[0032] Figure 7 The diagram shows the EL-OKCD trace with a wave frequency of 105 GHz, α = 155 °, and β = 80 °.

[0033] Figure 8The diagram shows the radial distribution of the driving current density and power deposition of the EL-OKCD, with a wave frequency of 105 GHz, a total injected power of 1 MW, α = 155 °, and β = 80 °.

[0034] Figure 9 The diagram shows the dual-wave joint drive trajectory. The TL-ECCD parameters are: electron cyclotron wave frequency of 140 GHz, α = 232.5 °, β = 160 °; the EL-OKCD parameters are: electron cyclotron wave frequency of 105 GHz, α = 155 °, β = 80 °.

[0035] Figure 10 A schematic diagram of the radial distribution of driving current density and power deposition in dual-wave joint drive;

[0036] Figure 11 Schematic diagrams of current density and power deposition profiles for 105 / 140 GHz dual-frequency electron cyclotron wave combined current drive; (a) current density, (b) power deposition profile; injection power P of EL-OKCD. ec For 1 MW, the TL-ECCD injection power P ec They are 1 MW, 2 MW, and 3 MW respectively;

[0037] Figure 12 The normalized current drive efficiency of TL-ECCD, EL-OKCD, and their combined drive varies with B. T A diagram illustrating the trend of value changes;

[0038] Figure 13 Schematic diagram of TL-ECCD driving current density and power deposition distribution under different circumferential magnetic fields;

[0039] Figure 14 A schematic diagram showing the driving current density and power deposition distribution of EL-OKCD under different circumferential magnetic fields;

[0040] Figure 15 A schematic diagram showing the driving current density and power deposition distribution under dual-wave joint drive in different circumferential magnetic fields;

[0041] Figure 16 The diagram shows the current profile of a TL-ECCD at different electron temperatures and electron densities. (a) represents the electron temperature, and (b) represents the electron density.

[0042] Figure 17 The diagram shows the EL-OKCD current profiles at different electron temperatures and electron densities. (a) represents the electron temperature, and (b) represents the electron density.

[0043] Figure 18The diagram shows the effects of electron temperature and electron density on the normalized current driving efficiency of TL-ECCD, EL-OKCD, and dual-wave joint drive. (a) represents electron temperature, and (b) represents electron density. Detailed Implementation

[0044] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0045] Tokamas are typically equipped with dual-frequency or even multi-frequency electron cyclotron resonant heating and current-driven (ECRH&CD) systems, with the 105 / 140 GHz dual-frequency system being a typical example. The dual-frequency ECRH&CD system increases the range of circumferential magnetic fields applicable to the tokamak, enhancing its application flexibility. However, different frequencies of electron cyclotron waves match different magnetic field ranges, and in most cases, only one frequency is used. To overcome this technical bottleneck, this invention, by selecting a suitable emission method and utilizing different current-driven mechanisms, enables the simultaneous and effective driving of off-axis currents near the radial region of the tokamak by 105 / 140 GHz dual-frequency electron cyclotron waves.

[0046] Based on the above concept, this invention proposes a novel electron cyclotron wave current driving scheme, enabling a dual-frequency ECRH&CD system to simultaneously drive effective off-axis current near the mid-radius region of a tokamak to achieve negative central magnetic shear. Specifically, a higher-frequency electron cyclotron wave is emitted from the top to drive the off-axis current in the mid-radius region, while a lower-frequency electron cyclotron wave is emitted from the outer mid-plane to drive the off-axis current outside the mid-radius region. The high-frequency and low-frequency electron cyclotron waves drive the off-axis current primarily through the Fisch-Boozer and Ohkawa mechanisms, respectively, meaning that two different current driving mechanisms of electron cyclotron waves are used to simultaneously drive the off-axis current near the mid-radius region of the tokamak. In this embodiment, "near the mid-radius region" refers to both the mid-radius region and the area outside it; the higher-frequency (i.e., high-frequency) electron cyclotron wave refers to a 140 GHz electron cyclotron wave; and the lower-frequency (i.e., low-frequency) electron cyclotron wave refers to a 105 GHz electron cyclotron wave. Among them, the 140 GHz electron cyclotron wave, emitted from the top, drives the off-axis current in the middle radius region in a Fisch-Boozer-dominant manner, exhibiting a wide driving current profile and high current driving efficiency. The 105 GHz electron cyclotron wave, emitted from the outer middle plane, drives the off-axis current outside the middle radius region in an Ohkawa-dominant manner, exhibiting a localized driving current profile and lower efficiency.

[0047] It should be noted that there are three methods for achieving off-axis current driving near the radius region in a tokamak using electron cyclotron waves. The first is top-emitting electron cyclotron current driving (TL-ECCD), which has a wide driving current profile and high efficiency. The second is current driving through the outer mid-plane or upward-sloping window, dominated by the Fisch-Boozer mechanism, i.e., the traditional ECCD. The third is outer mid-plane emission Ohkawa mechanism-dominated current driving (EL-OKCD). The current driving efficiency of these three methods varies significantly near the radius region in the tokamak. TL-ECCD has high current driving efficiency and a wide driving current profile in this region. Traditional ECCD has a narrow driving current profile, but due to the very strong electron trapping effect in the mid-radius region and beyond, even depositing wave power on the high-field side of the device cannot effectively reduce the detrimental effects of electron trapping; its current driving efficiency rapidly decreases to zero as the normalized small radius increases. By depositing the power of the electron cyclotron wave on the low-field side and ensuring that the quasi-linear diffusion region of the electron cyclotron wave in the velocity space is located exactly below the capture / passage boundary, the OKCD can effectively drive local currents outside the mid-radius region, and its current driving efficiency can even exceed that of the traditional ECCD.

[0048] Traditional ECCDs and TL-ECCDs require wave power to be deposited on the high-field side of the tokamak to effectively suppress harmful Ohkawa currents, necessitating higher electron cyclotron wave frequencies. EL-OKCDs, however, fully utilize the electron trapping effect to drive off-axis currents, requiring wave power to be deposited on the low-field side. Compared to traditional ECCDs and TL-ECCDs with high-field deposition, EL-OKCDs have lower wave frequencies. Therefore, for dual-frequency electron cyclotron wave systems with one high and one low frequency, TL-ECCDs and EL-OKCDs may be able to effectively drive off-axis currents near the radius region in the tokamak simultaneously. To address this, this invention proposes a novel scheme for driving off-axis currents near the radius region in the tokamak and conducts numerical simulation studies on an HL-3 type tokamak device equipped with a 105 / 140 GHz dual-frequency electron cyclotron wave system to determine the circumferential magnetic field (Bo) required to effectively drive off-axis currents in the target region under this scheme. T The range of electron cyclotron waves, as well as the influence of power ratios and electron temperature and density at different frequencies.

[0049] This embodiment employs coupled ray tracing and the Fokker-Planck quasi-linear program—GENRAY / CQL3D—to numerically simulate the off-axis current drive of a dual-frequency electron cyclotron wave near the mid-radius region in a tokamak. The GENRAY program calculates the propagation and power deposition of the radio frequency wave in the plasma by solving the trace equation. The CQL3D program receives the radio frequency wave data calculated by the GENRAY program, constructs the quasi-linear diffusion coefficient of the radio frequency wave, then solves the bounce-averaged Fokker-Planck equation to calculate the electron distribution function, and finally calculates the radio frequency wave current drive from the electron distribution function. The position of the electron cyclotron wave in the tokamak plasma power deposition and drive current profile can be achieved by changing the wave emission angle, thereby realizing the simultaneous off-axis current drive of the dual-frequency electron cyclotron wave near the mid-radius region. In the GENRAY program, the poloidal emission angle β is defined as the angle between the projection of the wave vector onto the tokamak poloidal section and Z, and the circumferential emission angle α is defined as the angle between the wave vector and the large-radius direction of the tokamak. (See [link to relevant documentation]). Figure 1 .

[0050] Considering that dual-frequency electron cyclotron waves are simultaneously driven by off-axis currents near the radius region in the tokamak, the propagation and power deposition of electron cyclotron waves of different frequencies in the plasma are first calculated using the GENRAY program. Then, these calculations are either coupled separately to the CQL3D program, or both are coupled to the CQL3D program. Assuming that the wave parameters of the dual-frequency electron cyclotron waves calculated by the GENRAY program are coupled to the CQL3D program, the solved Fokker-Planck equations are:

[0051]

[0052] In the formula, Let be the electron distribution function. and Let be the normalized velocities parallel and perpendicular to the magnetic field, respectively; ρ be the normalized radius; and t be time. The first term on the right-hand side of the equation (equal sign) represents this. The second term on the right-hand side of the equation (equal sign) is the Coulomb collision term. and the third item For the quasi-linear diffusion term of the dual-frequency electron cyclotron wave, D EC1 and D EC2 It is the quasi-linear diffusion coefficient of two electron cyclotron waves of different frequencies.

[0053] In numerical simulation studies on HL-3 type tokamak devices, a high-frequency 140 GHz electron cyclotron wave is emitted from the top and drives the off-axis current in the mid-radius region using the Fisch-Boozer mechanism; a low-frequency 105 GHz electron cyclotron wave is emitted from the outer mid-plane and drives the off-axis current outside the mid-radius region using the Ohkawa mechanism. If only one type of electron cyclotron wave current driving is considered, then only the collision term and its corresponding quasi-linear diffusion term in equation (1) need to be retained. However, when the two drive together, all three terms are retained. Unlike the traditional single-wave independent driving, this embodiment adopts dual-wave joint driving, that is, retaining three terms (the collision term and two quasi-linear diffusion terms in equation (1)).

[0054] To eliminate the effects of device geometry and collisional effects originating from electron density and temperature, a normalized current drive efficiency ζ is typically employed. CD However, due to the wide radial distribution of the TL-ECCD drive current, this embodiment uses the integral form of the current drive efficiency.

[0055]

[0056] Where, dI EC It is the infinitesimal driving current element of the electron cyclotron wave from ρ to ρ + dρ, R0 is the large radius of the device, P0 is the injected power of the electron cyclotron wave, and n e and T e These represent the electron density and temperature, respectively.

[0057] The HL-3 device has a large radius R0 = 178.1 cm, a small radius a = 65.5 cm, a ring diameter ratio A = R / a = 2.7, and a circumferential magnetic field B. T ≤ 3.0 T, plasma current I p ≤ 3.0 MA. The magnitude of its resonant magnetic field is calculated from the frequency and harmonic wavenumber of the electron cyclotron wave. When the unusual second harmonic (X2 mode) is selected, the resonant magnetic field at the 140 GHz operating frequency is 2.5 T. When the fundamental ordinary mode (O1 mode) is selected, the resonant magnetic field at 140 GHz is 5 T, which is much larger than the circumferential magnetic field range of HL-3. For the 105 GHz electron cyclotron wave, only the X2 mode is selected, and the corresponding resonant magnetic field is approximately 1.88 T. Therefore, for both 105 and 140 GHz electron cyclotron waves, the X2 mode is selected in the simulation. Based on the resonant magnetic fields of both modes, the approximate magnetic field range for driving off-axis currents simultaneously at the 140 GHz and 105 GHz operating frequencies near the mid-radius region is determined to be 1.8 T to 2.5 T.

[0058] According to the resonance layer Rec With circumferential magnetic field B T and electron cyclotron frequency f ec Relationship between them:

[0059]

[0060] With B T The value increases from 2.15 T to 2.35 T, such as Figure 2 As shown in (a), the 140 GHz second harmonic resonant layer is located on the high-field side and gradually approaches the magnetic axis, while the 105 GHz second harmonic resonant layer is located on the low-field side and gradually moves away from the magnetic axis. Both the 140 GHz and 105 GHz second harmonic resonant layers are located near the mid-radius region (ρ ~ 0.5). Since the power of the 140 GHz electron cyclotron wave is deposited on the high-field side, it can effectively drive the off-axis current in the mid-radius region through top emission in a Fisch-Boozer mechanism-dominated manner. For the 105 GHz electron cyclotron wave, whose power is deposited on the low-field side, it is more effective to drive the off-axis current outside the mid-radius region through outer mid-plane emission in an Ohkawa mechanism-dominated manner.

[0061] Based on the above analysis, for a 105 / 140 GHz dual-frequency electron cyclotron wave system, by selecting a suitable transmission method and utilizing different current driving mechanisms, the dual-frequency electron cyclotron waves can simultaneously and effectively drive the off-axis current near the radius region in the tokamak. In this embodiment, the position of the top transmission window is determined to be (R... i = 1.83 m, Z i = 1.33 m), the position of the external mid-plane transmission window is (R i = 2.65 m, Z i = 0.0 m), such as Figure 2 As shown in (a), the electron density n e Electronic temperature T e and effective ionic charge Z eff The distribution is as follows Figure 2 As shown in (b).

[0062] Based on the previously obtained circumferential magnetic field B T In this embodiment, the scope is selected as B. TThe emission angle of the electron cyclotron wave was scanned at 2.25 T to determine the emission angle range in which both TL-ECCD and EL-OKCD can effectively drive off-axis currents near the mid-radius region. Furthermore, the current driving of the 105 / 140 GHz dual-frequency electron cyclotron wave near the mid-radius region in the tokamak is likely to be affected by the circumferential magnetic field, injection power, and plasma temperature and density. Therefore, this embodiment also analyzes these factors and determines the appropriate ranges or values ​​for these factors (circumferential magnetic field, injection power, and plasma temperature and density).

[0063] In B T At a T = 2.25 T, a two-dimensional parameter scan of the emission angle (α, β) was performed on a 140 GHz TL-ECCD. The scan results are as follows: Figure 3 As shown. Figure 3 Figures (a)-(d) present contour plots of the TL-ECCD normalized current drive efficiency, normalized radial position of peak drive current, total drive current, and peak magnitude of drive current density, respectively. Figure 3 The results in (a)-(c) show that the total current I of the TL-ECCD ec and normalized current drive efficiency ζ CD It increases with the normalized radial radius ρ, and decreases after reaching a certain radial position ρ. To enable the TL-ECCD to effectively drive the off-axis current in the mid-radius region, according to... Figure 3 Based on the scan results, selecting one set of emission angles (α, β) = (232.5°, 160°), the TL-ECCD exhibits good driving efficiency. CD = 0.2017, deposition location ρ = 0.475, located near the mid-radius region. In f ec At 140 GHz, I ec >0, initial parallel refractive index during wave injection , In this case, the current drive is dominated by the Fisch-Boozer mechanism, i.e., ECCD. For example... Figure 4 As shown, the projection of wave rays into the tokamak poloidal section propagates close to the resonant layer, indicating that this is a typical TL-ECCD situation. The driving current and power deposition profiles of the TL-ECCD under this condition are shown in the figure below. Figure 5 As shown, the driving current profile is relatively wide, mainly because the electron cyclotron wave emitted from the top propagates close to the wave resonant layer, and the wave power is gradually deposited in the plasma along the wave track, driving ionization. At an injection power of 1 MW, the total driving current I... ec = 45.31 kA, peak current density The driving current profile is located near the mid-radius ρ = 0.5, and the wave power absorption share is... The electron cyclotron wave power is completely absorbed by the plasma. Among them, P... abs and P ec These are the total absorbed power and the total injected power, respectively.

[0064] In B T =2.25 T, Figure 6 The results of EL-OKCD at 105 GHz as a function of emission angle (α, β) are presented. To enable EL-OKCD to effectively drive off-axis currents near the mid-radius region, the emission angle was chosen such that the driving ionization profile is located near ρ ~ 0.65, resulting in good driving performance. Selecting one set of emission angles: (α, β) = (155°, 80°), EL-OKCD exhibits high ionization driving efficiency, and its normalized current driving efficiency ζ... CD = 0.102, the deposition location is at ρ = 0.63. Figure 7 The trace of the electron cyclotron wave is shown at an emission angle of (α, β) = (155°, 80°). In this case, I ec > 0, I ec ·N ||0 > 0, the drive current is Ohkawa mechanism dominated current drive (OKCD). Under this condition, the radial distribution of drive current density and power deposition of EL-OKCD is as follows: Figure 8 As shown, the drive current profile is relatively localized. At a 1 MW injection power, the total drive current I... ec =20.86 kA, peak current density = 9.64 A·cm -2 Peak position of driving current ρ = 0.625. Similarly, in this case, the electron cyclotron wave power is also completely absorbed by the plasma.

[0065] The waveforms corresponding to the combined current-driven results analysis of TL-ECCD and EL-OKCD are as follows: Figure 9 As shown. From Figure 10 As can be seen, the power of TL-ECCD and EL-OKCD is deposited near the mid-radius. The driving current and power deposition profiles under dual-wavelength combined drive are basically equal to the algebraic sum of the two. The total driving current of the combined drive is 66.26 kA, and the algebraic sum of the two is 45.31 + 20.86 = 66.17 kA, therefore there is no synergistic effect between the two.

[0066] While a combined 105 / 140 GHz dual-frequency electron cyclotron wave drive can achieve off-axis current drive near the radius region in the HL-3 tokamak, from... Figure 10As can be seen, the peak positions of current density and power deposition are not near ρ ~ 0.5, but rather biased towards the peak current density position of EL-OKCD. To maintain the peak positions of power deposition and driving current profile under combined current drive near ρ ~ 0.5, the influence of injected power on off-axis current drive near the radius region of the tokamak is analyzed below. Since the TL-ECCD has a wider radial current density distribution and higher current drive efficiency, while the EL-OKCD has a more localized radial current density distribution and relatively lower current drive efficiency, more injected power is allocated to the TL-ECCD, thus enabling the dual-frequency electron cyclotron wave to simultaneously drive off-axis current near the radius region of the tokamak. Similarly, under a 2.25 T circumferential magnetic field, while keeping the EL-OKCD injection power at 1 MW, increasing the TL-ECCD injection power... Figure 11 The combined current density and power deposition profiles of dual-frequency waves are presented for TL-ECCD injection powers of 1 MW, 2 MW, and 3 MW. From... Figure 11 As can be seen, as the injection power of TL-ECCD increases, when the injection power ratio of TL-ECCD and EL-OKCD is greater than or equal to 2, the current profile driven by the 105 / 140 GHz dual-frequency electron cyclotron wave returns to the medium radius region around ρ ~ 0.5.

[0067] Based on the preceding analysis, although the circumferential magnetic field B can be determined... T The scanning range is 1.8 T ~ 2.35 T, but this range is only approximate. Within this range, there may be circumferential magnetic field regions or B that prevent TL-ECCD and EL-OKCD from effectively driving off-axis currents simultaneously near the mid-radius region. T Value. Therefore, this embodiment also analyzes the numerical simulation results of TL-ECCD, EL-OKCD, and their combined drive, setting the injection power of both waves to 1 MW, and determining the circumferential magnetic field range that enables TL-ECCD and EL-OKCD to effectively drive off-axis currents simultaneously in the mid-radius region. For example... Figure 12 As shown, when B T At 2.0 T, the normalized current drive efficiency of EL-OKCD approaches zero. T In the case of < 2.0 T, the current drive of the outer plane emission is no longer dominated by the Ohkawa mechanism, but by the Fisch-Boozer mechanism of ECCD. Figure 12 B is not shown in the text. T The normalized current drive efficiency of EL-OKCD at < 2.0 T. And in the circumferential magnetic field B... TAt T = 2.3, the normalized current drive efficiency of TL-ECCD, EL-OKCD, and their combined drive reaches a peak. When B T At a current >2.3 T, the normalized current drive efficiency of all three decreased significantly. Figure 12 It can be determined that, near the radius region in the tokamak, a 140 GHz TL-ECCD can effectively drive the off-axis current B. T The value range is 1.8 T ~ 2.35 T, while the 105 GHz EL-OKCD corresponds to B. T The values ​​are 2.1 T ~ 2.35 T. In summary, the 105 / 140 GHz dual-frequency electron cyclotron wave can effectively drive the off-axis current in the radius region of the tokamak within a range of 2.1 T ~ 2.35 T.

[0068] Figures 13-15 The radial distribution of driving current density and power deposition for TL-ECCD, EL-OKCD, and their combined current drive are shown for magnetic field ranges of 2.15 T to 2.35 T. Their optimal emission angle, total driving current, driving efficiency, and radial position are shown in Tables 1-3. These results also indicate that, under different B... T At this value, there is no synergistic effect between the dual-frequency electron cyclotron wave combined current drive. The current drive efficiency of TL-ECCD is higher than that of EL-OKCD. TL-ECCD has a wider current profile, while EL-OKCD has a more localized current profile. Therefore, for dual-frequency electron cyclotron waves to simultaneously drive currents near the mid-radius region, a larger injection power needs to be allocated to TL-ECCD so that the peak current density of the dual-frequency wave simultaneous drive is located at the mid-radius (ρ ~ 0.5).

[0069]

[0070]

[0071]

[0072] Since electron temperature and density both affect the propagation and power deposition of electron cyclotron waves in tokamak plasma, they alter the efficiency of electron cyclotron wave current driving. Therefore, this embodiment also analyzes the influence of these factors on off-axis current driving of dual-frequency electron cyclotron waves near the mid-radius region and determines suitable ranges for electron temperature and density. Specifically, the suitable electron temperature range for effectively driving off-axis current with 105 / 140 GHz dual-frequency electron cyclotron waves simultaneously near the mid-radius region of the tokamak is 4.0 ~ 8.0 keV, and the electron density range is 2.0 ~ 7.0 × 10⁻¹⁰. 19 m-3 .

[0073] In this embodiment, the circumferential magnetic field B is selected. T The magnetic balance remains unchanged at 2.25 T. Figure 2 The electron temperature and density distribution shape shown in (b) remains unchanged, and the emission angle is not altered; the magnitudes of the electron temperature and density are changed by a calibration factor. That is: in Figure 2 The electron temperature and density distributions shown in Figure (b) are multiplied by a given temperature calibration factor and a density calibration factor, respectively. In the simulation calculations, the injection power of both TL-ECCD and EL-OKCD is 1 MW.

[0074] For TL-ECCD, the electron temperature T at the plasma center e0 The variation range is 4.0 ~ 10.0 keV, and the central density n e0 The variation range is 2.0 ~ 8.0 × 10 19 m -3 .from Figure 16 As can be seen in (a), when n e0 Unchanged, with T e0 As the current gradually increases, the peak value of the driving current density gradually rises, and the deposition location gradually moves away from the axis; Figure 16 In (b), when T e0 Unchanged, as n e0 As n gradually increases, the peak value of the driving current density gradually decreases. e0 ≥ 6.0×10 19 m -3 At that time, its current density peak shifted to around ρ ~ 0.25 and the peak value increased significantly, as n e0 As the current density continues to increase, the peak current density gradually decreases.

[0075] The temperature and density scan results of EL-OKCD are as follows: Figure 17 As shown. When n e0 Unchanged, with T e0 As T increases, the peak value of the driving current density gradually rises, and the deposition location gradually moves away from the axis; when T... e0 Unchanged, as n e0 As n gradually increases, the peak value of the driving current density gradually decreases, and the deposition location also gradually moves away from the axis; when n e0 = 8.0×10 19 m -3 At that time, EL-OKCD is almost unable to effectively drive the current.

[0076] Figure 18 The normalized current-driven efficiency ζ of the dual-frequency electron cyclotron wave is shown in the mid-radius region. CDWith changes in electron temperature and density. (By) Figure 18 The results in (a) show that keeping n e0 The ζ of TL-ECCD remains unchanged as the electron temperature increases. CD The value gradually decreases, and the ζ of EL-OKCD CD The value first increases and then decreases. The dual-frequency electron cyclotron wave joint drive is more affected by TL-ECCD, ζ CD Similarly, with T e0 The amplitude decreases as the wave emission angle increases. Since the wave emission angle remains constant, TL-ECCD and EL-OKCD each have a ζ... CD The main reason for the change in the value with electron temperature is that the Doppler frequency shift effect affects wave-particle resonance, which causes the radial position of the driving current profile to shift in the direction of increasing ρ value, such as... Figure 17 (a) and Figure 18 As shown in (a), this further affects ζ. CD Value. (By) Figure 18 The result in (a) shows the electron temperature T suitable for the dual-frequency electron cyclotron wave to effectively drive off-axis currents near the radius region in the tokamak. e0 The range is 4.0 ~ 8.0 keV, which is mainly due to the limitation of the current drive efficiency of EL-OKCD.

[0077] Figure 18 Figure (b) shows the effect of electron density. While maintaining T... e0 With n remaining constant, e0 With the increase of ζ, the normalization efficiency of TL-ECCD CD The efficiency initially increases and then decreases. This is because as electron density increases, electron specific pressure increases, thus reducing the impact of electron trapping on the ECCD, causing the current-driven efficiency of the TL-ECCD to increase with increasing density. However, the TL-ECCD has a larger parallel refractive index, so even if the electron density does not reach its cutoff density... The propagation path of waves in plasma is more easily deflected at high densities, causing some of their power to remain unabsorbed by electrons, thus reducing the current-driven efficiency. Figure 18 ζ of TL-ECCD in (b) CD Value in n e0 = 8.0×10 19 m -3 The reason for the sudden and significant drop in EL-OKCD value ζ. CD The value decreased slightly after a slow rise, but at n e0 > 7.0×10 19 m -3 Then it drops rapidly, when n e0 = 8.0×10 19 m-3 At that time, EL-OKCD's ζ CD The value is even less than 0. Electron density n e0 Between 4.0 and 7.0 × 10 19 m -3 Within the range, the power absorption share η of the 105 GHz EL-OKCD wave is > 99%, indicating that the wave power is completely absorbed. The decrease in Ohkawa current caused by the increase in electron specific voltage is its ζ. CD The reason why the value decreases slightly with increasing density. When n e0 > 7.0×10 19 m -3 At that time, the electron density at the 105 GHz electron cyclotron resonance position may have already approached its cutoff density of 6.83 × 10⁻⁶. 19 m -3 This causes most of the wave power to be reflected and unable to propagate to the vicinity of the resonant layer. In n e0 = 8.0×10 19 m -3 At this point, due to the cutoff density effect, the power absorption share η of the 105 GHz wave is 28.2%, and the current driving efficiency of the EL-OKCD decreases significantly. Therefore, the electron density range suitable for effectively driving off-axis currents in the radius region of a tokamak using a dual-frequency electron cyclotron wave of 105 / 140 GHz is 2.0 ~ 7.0 × 10⁻⁶. 19 m -3 .

[0078] In summary, this embodiment proposes a novel electron cyclotron wave off-axis current driving scheme to enable two waves of different frequencies in a dual-frequency electron cyclotron wave system to simultaneously drive off-axis currents near the radial region in a tokamak. In this scheme, the higher-frequency electron cyclotron wave drives the off-axis current in the radial region through top emission, while the lower-frequency electron cyclotron wave drives the off-axis current outside the radial region through outer mid-plane emission. In this scheme, the high-frequency and low-frequency electron cyclotron waves dominate the off-axis current driving through the Fisch-Boozer and Ohkawa mechanisms, respectively, thus utilizing the dominance of two different current driving mechanisms to simultaneously drive the off-axis current near the radial region in the tokamak.

[0079] Based on this scheme, this embodiment conducts numerical simulation studies on an HL-3 type tokamak. For the 105 / 140 GHz electron cyclotron system equipped on the HL-3 tokamak device, the 140 GHz electron cyclotron can achieve a circumferential magnetic field of 1.8 T ≤ B. T Within a range of ≤ 2.35 T, the off-axis current in the mid-radius region is effectively driven by top emission, and the 105 GHz electron cyclotron wave operates within a narrower circumferential magnetic field range (2.1 T ≤ B).T Within ≤ 2.35 T, the off-axis current can be effectively driven in the region outside the central radius by emission from the outer midplane. Taking all the above factors into consideration, the 105 / 140 GHz dual-frequency electronic cyclotron wave system, under the new current driving scheme, can simultaneously and effectively drive the circumferential magnetic field range of off-axis current near the central radius region of the HL-3 tokamak in the range of 2.1 T ~ 2.35 T.

[0080] The 140 GHz top-emission electron cyclotron current drive (TL-ECCD) produces a wide current profile and high normalized current drive efficiency. In contrast, the 105 GHz out-of-center emission Ohkawa mechanism-dominated current drive (OKCD) produces a narrow current profile and relatively low normalized current drive efficiency. When simultaneously driving off-axis currents near the mid-radius region using a 105 / 140 GHz dual-frequency electron cyclotron system, the power ratio of TL-ECCD to EL-OKCD should be greater than or equal to 2 (i.e., ≥ 2). This embodiment also investigated the effects of electron temperature and density on this current drive scheme, finding that electron temperature and density are optimal at 4.0 ~ 8.0 keV and 2.0 ~ 7.0 × 10⁻⁶ keV, respectively. 19 m -3 Within their respective regions of interest, both TL-ECCD and EL-OKCD can effectively drive current.

[0081] This invention is not limited to the above embodiments. Those skilled in the art will understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of this invention. The scope of this invention is defined by the claims and their equivalents.

Claims

1. A method for driving a tokamak using a dual-frequency electron cyclotron current near the radius region, characterized in that, Includes the following steps: The tokamak device utilizes a dual-frequency electron cyclotron wave system equipped with two electron cyclotron waves of different frequencies to simultaneously drive off-axis currents in the mid-radius region and outside the mid-radius region. The higher-frequency electron cyclotron wave drives the off-axis current in the mid-radius region through top emission, while the lower-frequency electron cyclotron wave drives the off-axis current outside the mid-radius region through outer mid-plane emission.

2. The dual-frequency electron cyclotron current driving method near the radius region in a tokamak according to claim 1, characterized in that, The higher frequency electron cyclotron waves drive the off-axis current in the mid-radius region in a Fisch-Boozer-dominated manner. The lower frequency electron cyclotron wave drives the off-axis current outside the mid-radius region in a manner dominated by the Ohkawa mechanism.

3. The dual-frequency electron cyclotron current driving method near the radius region in a tokamak according to claim 1 or 2, characterized in that, The higher frequency electron cyclotron wave is a 140 GHz electron cyclotron wave; The lower frequency electron cyclotron wave is a 105 GHz electron cyclotron wave.

4. The dual-frequency electron cyclotron current driving method near the radius region in a tokamak according to claim 3, characterized in that, The two electron cyclotron waves of different frequencies simultaneously drive the off-axis current in magnetic field B within the mid-radius region and outside the mid-radius region. T The value is: 2.1 T ≤ B T ≤ 2.35 T.

5. The dual-frequency electron cyclotron current driving method near the radius region in a tokamak according to claim 3, characterized in that, The ratio of the injection power of the higher frequency electron cyclotron wave to that of the lower frequency electron cyclotron wave is ≥ 2.

6. The dual-frequency electron cyclotron current driving method near the radius region in a tokamak according to claim 3, characterized in that, The electron temperatures of the two electron cyclotron waves of different frequencies that simultaneously drive off-axis currents in the mid-radius region and outside the mid-radius region are 4.0 ~ 8.0 keV.

7. The dual-frequency electron cyclotron current driving method near the radius region in a tokamak according to claim 3, characterized in that, The electron density of the two electron cyclotron waves of different frequencies simultaneously driving off-axis currents in the mid-radius region and outside the mid-radius region is 2.0 ~ 7.0 × 10⁻⁶. 19 m -3 .

8. A dual-frequency electronic cyclotron current drive system for use in the radius region of a tokamak, characterized in that, The system for implementing the method as described in any one of claims 1-7 includes: A dual-frequency electron cyclotron wave system is configured to generate and emit two electron cyclotron waves of different frequencies to simultaneously drive off-axis currents in the mid-radius region and outside the mid-radius region. The dual-frequency electronic cyclotron wave system includes: A high-frequency wave transmitting subsystem, whose transmitting antenna is arranged in the top region of the tokamak device and configured to transmit high-frequency electron cyclotron waves in a top-emitting manner to drive off-axis current in the mid-radius region; The low-frequency wave transmitting subsystem has its transmitting antenna located in the outer mid-plane region of the tokamak device and configured to transmit low-frequency electron cyclotron waves in an outer-mid-plane transmission mode to drive off-axis currents outside the mid-radius region.

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