On the Effect of Two-Dimensional Plasma Inhomogeneity in a Magnetic Island on the Parametric Excitation Threshold of Trapped Upper Hybrid Waves and the Level of Anomalous Absorption in ECRH Experiments

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Abstract

The effect of two-dimensional localization of an upper hybrid (UH) wave in a magnetic island is found. The influence of this effect on the threshold and saturation level of the absolute parametric decay instability of an extraordinary wave, which results in the excitation of two two-dimensional localized UH waves, is investigated.

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A. Yu. Popov

Ioffe Institute

Author for correspondence.
Email: a.popov@mail.ioffe.ru
Russian Federation, St. Petersburg

E. Z. Gusakov

Ioffe Institute

Email: a.popov@mail.ioffe.ru
Russian Federation, St. Petersburg

N. V. Teplova

Ioffe Institute

Email: a.popov@mail.ioffe.ru
Russian Federation, St. Petersburg

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Supplementary files

Supplementary Files
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1. JATS XML
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2. Fig. 1. The trajectory of the upper hybrid wave (solid line, fm = 69.71 GHz, mx = 45) is shown in the poloidal section of the TEXTOR tokamak [29]. The magnetic surfaces are shown as dashed lines. The zoomed-in window shows the trajectory of the VG-wave in the magnetic island

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3. Fig. 2. The trajectory of the upper hybrid wave (solid line, fm = 69.71 GHz, mx = 45) is shown in the magnetic surface plane of the TEXTOR tokamak [29]. The magnetic force lines are shown as dashed lines

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4. Fig. 3. The wave vector component qx(x) obtained numerically by the ray-tracing procedure is indicated by the arrow. The analytical solution is shown by dots and indicated by the arrow

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5. Fig. 4. The wave vector component qζ(ζ) obtained numerically from ray tracing is indicated by the arrow. The analytical solution is shown by the dashed curve and indicated by the arrow

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6. Fig. 5. The wave number of the VG-wave fm = 69.71 GHz, qξmn = 0.43 cm-1, m = (40.3), shifted down by the value of the wave number of the extraordinary wave, is the solid line. The wave number of the second VG wave is the dashed line. The VG-frequency profile is the thick solid curve. Te = 700 eV, Ti = 350 eV - on the discharge axis. B = 2.1T - in the magnetic island

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7. Fig. 6. Sum of the wave numbers of the primary (fn = 70.29 GHz, n = (12.4)) and secondary (fl = 69.67 GHz, qξnp = 0.52 cm-1, l = (47.3)) WG-waves - solid line. The wave number of the secondary IB wave fI = 0.62 GHz, qIξ = 0.09 cm-1 is the dashed curve. The VG-frequency profile is the thick solid curve. The parameters are the same as in Fig. 4

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8. Fig. 7. Temporal evolution of the energies of the primary HG waves and the secondary HG wave in the beam spot. The dependences are indicated by arrows. The thin horizontal lines give the saturation levels predicted by equations (18)-(20). P0 = 1 MW, w = 1 cm

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9. Fig. 8. Dependence of the primary instability increment on the pumping power. The solid line shows the analytical dependence (16). Symbols are the result of numerical solution of equations (13). The zoomed-in window shows the dependence in the vicinity of the threshold power

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10. Fig. 9. Time dependence of the energy of all VG-waves within the box in the region of WΣ calculation in the saturation mode for different pumping power

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11. Fig. 10. Dependence of the anomalous absorption level on the pump power. The symbols show the result of the numerical solution ΔP = dWΣ/dt. The solid line shows the analytical dependence (21)

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