Quasi-Two-Dimensional Code for the Calculation of Antenna Impedance of the ICR Heating System

Мұқаба

Дәйексөз келтіру

Толық мәтін

Аннотация

Ion cyclotron resonance heating is considered as one of the methods of additional heating ofplasma and production of the non-inductive current in the T-15MD tokamak. To transfer the maximumpower to the plasma, it is needed to know impedance of an antenna–plasma system, to match it with impedanceof an RF power generator and its transmission line. The work is devoted to the development of a codefor the calculation of antenna impedance of the ICR heating system of plasma in toroidal magnetic traps. Tofind impedance of the antenna–plasma system in the simplified geometry of antenna consisting of conductiveplates, the wave equation is solved in the “cold” plasma approximation, and the spectrum of theRF power emitted by antenna is calculated. The dependences of the impedance of the antenna–plasma systemon distances between antenna and the Faraday screen and between the Faraday screen and the plasmaare obtained for the geometry of the T-15MD tokamak. Two-dimensional distribution of electric field of awave in the plasma is obtained.

Толық мәтін

Рұқсат жабық

Авторлар туралы

P. Naumenko

Moscow Institute of Physics and Technology (National Research University); National Research Centre “Kurchatov Institute”

Хат алмасуға жауапты Автор.
Email: naumenko.pr@phystech.edu
Ресей, Dolgoprudnyi, Moscow oblast, 141701; Moscow, 123098

K. Nedbailov

Moscow Institute of Physics and Technology (National Research University); National Research Centre “Kurchatov Institute”

Email: nedbajlov.ko@phystech.edu
Ресей, Dolgoprudnyi, Moscow oblast, 141701; Moscow, 123098

A. Chernenko

National Research Centre “Kurchatov Institute”

Email: chernenko_as@nrcki.ru
Ресей, Moscow, 123098

Әдебиет тізімі

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Әрекет
1. JATS XML
Жүктеу
2. Fig. 1. Niche with an antenna in isometry. J is the current flowing through the antenna plates. The size d limits the niche (and the calculated space) in the toroidal direction, the size w limits the depth of the niche, the Faraday screen is in the plane X = 0, s and x0 are the coordinates of the antenna position and the plasma separatrix, respectively.

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3. Fig. 2. Section of the antenna in the equatorial plane. The space is divided into 4 regions: 1 – from the outer boundary of the niche in which the antenna unit is located to the plates; 2 – from the plates to the Faraday screen; 3 – from the Faraday screen to the separatrix; 4 – plasma region.

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4. Fig. 3. a) Characteristic form of the polynomial function g (x0 + x) on the left-hand side of equation (15) at kz = 0.08 cm–1 for the conditions of the INTOR tokamak, the transition point from the variable value of the function to the constant value corresponds to the plasma boundary (zero density); b) dependence of the maximum of function (15) on kz on the interval, .

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5. Fig. 4. Dependences of the impedance of the antenna-plasma system on for different positions of the antenna plates in the pipe relative to the Faraday screen s under T-15MD conditions.

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6. Fig. 5. (a) Characteristic form of the integrand function (22) (Fourier harmonics m = 5, n = 2), (b) oscillation region of the integrand function (22) for the conditions of the INTOR tokamak.

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7. Fig. 6. Block diagram of the program.

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8. Fig. 7. Dependences of the real (a) and imaginary (b) parts of the impedance of the antenna-plasma system on the number of harmonics M for the INTOR setup geometry.

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9. Fig. 8. a) Characteristic view of the density profile in the vertical section of the plasma column; b) fragment of the density profile in the vicinity of point x0. The figures were obtained for the INTOR setup conditions at x0 = 10 cm, a = 120 cm, p = 1.2 cm. The Faraday screen is located at point x = 0.

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10. Fig. 9. Dependence of the impedance of the antenna-plasma system on the radial distance between the Faraday screen and the plasma for (a) “cut” and (b) “whole” density profiles. The dotted line is the calculation results, the solid line is the graphs given in [16].

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11. Fig.10. Dependences of the real part of the impedance of the antenna-plasma system on the distance between the Faraday screen and the separatrix for different values of the boundary plasma density (at point x0) for the “cut” density profile. The red color indicates the values of the real part of the impedance for the electron density nx0 on the separatrix in the range (0 ÷ 3) ×1019 m–3, calculated by our program, the black curve is the dependence given in [16].

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12. Fig. 11. Dependence of the real part of the impedance of the antenna-plasma system on the value of the electron density on the separatrix nx0 at x0 = 10 cm.

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13. Fig. 12. Dependence of the impedance of the antenna-plasma system on the depth of the nozzle at x0 = 10 cm, s = 2 cm. The dotted line is the calculation results, the solid line is the graphs given in [16].

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14. Fig. 13. Dependence of the impedance of the antenna-plasma system on the distance between the antenna plates and the Faraday screen at x0 = 10 cm. The dotted line is the calculation results, the solid line is the graphs given in [16].

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15. Fig.14. Comparison of the dependences calculated using formulas (14) and (16) at kz = 0.2 cm–1 (100% H). (a) nx0 = 6 ×1018 m–3, (b) nx0 = 3.5 ×1018 m–3, (c) nx0 =1 ×1018 m–3. The vertical line is drawn at the point x = x0.

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16. Fig.15. Comparison of the dependencies calculated from expressions (14) and (16) at nx0 = 6 ×1018 m–3 (100% H). (a) kz = k0, (b) kz = 0.1 cm–1. The vertical line is drawn at the point x = x0.

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17. Fig. 16. Comparison of the dependence of the impedance of the antenna-plasma system on the distance between the separatrix and the Faraday screen with the mathematical expectation of the perturbed impedance values M[Z} in the T-15MD geometry (100% H).

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18. Fig. 17. Graphs of (a) systematic and (b) random errors for the real part of the impedance ReZ.

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19. Fig.18. Values of the total relative error for (a) the real and (b) the imaginary parts of the impedance.

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20. Fig. 19. Comparison of the dependencies calculated using formulas (14) and (16), with nx0 = 6 ×1018 m–3 (100% H), (a) kz = 0.2 cm–1, (b) kz = k0.

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21. Fig. 20. Dependence of the impedance of the antenna-plasma system on the distance between the Faraday shield and the separatrix (coordinate x0) at a distance between the antenna plates and the Faraday shield of s = 1 cm for (a) 100% H plasma, (b) 95% H – 5% 3He plasma.

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22. Fig. 21. Dependence of the impedance of the antenna-plasma system on the distance between the antenna plates and the Faraday screen (coordinate s) at a distance between the Faraday screen and the separatrix x0 = 6 cm for (a) 100% H plasma, (b) 95% H – 5% 3He plasma.

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23. Fig. 22. Two-dimensional distribution of the modulus of the electric field strength vector of the high-frequency wave at x from 5 to 15 cm, z from 0 to 70 cm for T-15MD (100%).

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