Full-wave modeling of electron cyclotron plasma heating at the fundamental and second harmonics for the GDMT facility

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Abstract

Possible scenarios of auxiliary electron cyclotron plasma heating in various configurations of the next-generation open magnetic trap GDMT (Gas-Dynamic Multiple-mirror Trap) designed at the Budker Institute of Nuclear Physics are considered. For this purpose, a full-wave impedance approach is used to model the interaction of electromagnetic waves with hot plasma, which allows taking into account the interaction of electromagnetic and quasi-electrostatic modes in the vicinity of the electron cyclotron resonance in an axisymmetric magnetic configuration. Heating scenarios using the ordinary electromagnetic mode at the fundamental harmonic and extraordinary mode at the second harmonic are considered. For each case, the ranges of the setup parameters in which such a heating scheme can be effective are determined; optimal for the heating efficiency focusing parameters of the quasi-optical microwave beam are analyzed.

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E. D. Gospodchikov

A.V. Gaponov-Grekhov Institute of Applied Physic of the Russian Academy of Sciences

Author for correspondence.
Email: egos@ipfran.ru
Russian Federation, Nizhny Novgorod

P. A. Chuvakin

A.V. Gaponov-Grekhov Institute of Applied Physic of the Russian Academy of Sciences

Email: egos@ipfran.ru
Russian Federation, Nizhny Novgorod

A. L. Solomakhin

A.V. Gaponov-Grekhov Institute of Applied Physic of the Russian Academy of Sciences; G.I. Budker Institute of Nuclear Physics, Siberian Branch of the Russian Academy of Sciences

Email: egos@ipfran.ru
Russian Federation, Nizhny Novgorod; Novosibirsk

A. G. Shalashov

A.V. Gaponov-Grekhov Institute of Applied Physic of the Russian Academy of Sciences

Email: egos@ipfran.ru
Russian Federation, Nizhny Novgorod

References

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Supplementary files

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2. Fig. 1. Microwave radiation input ports on the general plan of the starting configuration of the GDML installation (a) and the magnetic plug module, into which it is proposed to build the ECR heating system [1] (b): 1 – magnetic field line, 2 – transition coil, 3 – microwave beam input port, 4 – cryostat vacuum chamber, 5 – cryostat thermal screen, 6 – magnetic plug solenoid.

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3. Fig. 2. The surface of the cold resonance ωc = ω for a frequency of 85 GHz at various currents through the coils of C6 - C7, determined by the parameter α = 102 (i - i0) / i0: 1 - α = 0; 2 - 0.05; 3 - 0.1; 4 - 0.2; 5 - 0.35; 6 - 0.5; 7 - 0.75; 8 - 1.0; 9 - 1.4; 10 - 1.8; 11 - –0.05; 12 - –0.12. In Figure ρ is the distance from the axis of the trap, and Z coordinate along the axis of the trap.

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4. Fig. 3. Dependence of the normalized gyrofrequency ωc / ω on the distance to the axis in three sections z for the magnetic configuration corresponding to α = 0.35. Radiation frequency is 85 GHz.

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5. Fig. 4. Model profiles of plasma density and electron temperature at the GDML facility [10], recalculated for a trap cross-section of z = 430 cm.

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6. Fig. 5. Dependences of the field intensity ρ │ E(ρ) │2 and the absorbed power density QX(ρ) on the radial coordinate, corresponding to the azimuthal harmonic with m = 0, calculated using the impedance method in the cross section z = 430 cm for the electron temperature on the trap axis Tmax = 300 eV (black curves) and Tmax = 600 eV (red curves). The magnetic configuration of the GDML corresponds to α = 0.35, the concentration on the trap axis Nmax = 1013 cm–3.

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7. Fig. 6. Sections of the distribution of the absorbed power density by the plane z = 430 cm (a) and the plane φ = 0 (b). The direction φ = 0 corresponds to the direction of the input beam axis. The configuration of the magnetic field of the GDML corresponds to α = 0.35, Tmax = 300 eV, Nmax = 1013 cm–3. The red dashed line indicates the cold gyroresonance surface.

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8. Fig. 7. Dependences of the total absorption efficiency (a) and the mismatch coefficient (b) on the current I in coils C6–C7, determined by the parameter α = 102 (I – I0) / I0. The value I = I0 corresponds to the X-point for the ECR surfaces. The black curves correspond to the electron temperature on the axis Tmax = 300 eV, the red curves correspond to the temperature Tmax = 600 eV. The simulation results for heating at the first harmonic of the ordinary wave are shown as circles, for the extraordinary wave at the second harmonic – as crosses. The plasma density on the trap axis Nmax = 3.6×1013 cm–3.

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9. Fig. 8. Dependences of the total absorption efficiency on the plasma concentration. Red curves correspond to α = 0.35, black curves correspond to α = 1.0. The electron temperature on the trap axis is Tmax = 600 eV. The simulation results for heating at the first harmonic of the ordinary wave are shown by circles, for the extraordinary wave at the second harmonic – by crosses.

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10. Fig. 9. Partial absorption efficiency Am(z) for an ordinary wave at the first harmonic (a, b) and for an extraordinary wave at the second harmonic (c, d) for two different values ​​of the plasma concentration on the trap axis: Nmax = 8.8×1013 cm–3 (a, c) and Nmax = 0.4×1013 cm–3 (b, d). The magnetic configuration corresponds to α = 0.35. The electron temperature on the trap axis Tmax = 600 eV.

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