title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð¾Ð»Ð½ Ð² Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ð² Ð¿ÑÐ¾Ð¼ÐµÐ¶ÑÑÐ¾ÑÐ½Ð¾Ð¼ Ð´Ð¸Ð°Ð¿Ð°Ð·Ð¾Ð½Ðµ ÑÐ°ÑÑÐ¾Ñ Ñ ÑÑÑÑÐ¾Ð¼ Ð½ÐµÐ¼Ð°ÐºÑÐ²ÐµÐ»Ð»Ð¾Ð²ÑÐºÐ¾Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð¾Ð²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Modeling of waves in tokamak plasma in the lowerhybrid frequency range, taking into account the non-Maxwellian electron distribution function
Creators: name: ÐÐµÑÐ°ÐµÐ², Ð¡ÐµÑÐ³ÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: ÐÐ»Ð°Ð·Ð¼Ð° (ÑÐ¸Ð·.) Ð²ÑÑÐ¾ÐºÐ¾ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐ½Ð°Ñ
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Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ñ
waves in plasma
wave equation
tokamak
full-wave code
non-Maxwellian electron distribution
helicons

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÑÐµÑÑ Ð½ÐµÐ¼Ð°ÐºÑÐ²ÐµÐ»Ð»Ð¾Ð²ÑÐºÐ¾Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð¾Ð² Ð¿Ð¾ ÑÐºÐ¾ÑÐ¾ÑÑÑÐ¼ Ð¿ÑÐ¸ Ð¿Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð¼ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¸ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð²Ð¾Ð»Ð½ Ð¿ÑÐ¾Ð¼ÐµÐ¶ÑÑÐ¾ÑÐ½Ð¾Ð³Ð¾ ÑÐ°ÑÑÐ¾ÑÐ½Ð¾Ð³Ð¾ Ð´Ð¸Ð°Ð¿Ð°Ð·Ð¾Ð½Ð° Ð² Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ¾Ð´Ð° WaveTOP2D. Ð£ÑÐµÑ Ð½ÐµÐ¼Ð°ÐºÑÐ²ÐµÐ»Ð»Ð¾Ð²cÐºÐ¾Ð³Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»ÑÑ Ð´Ð»Ñ ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÑ ÑÐµÐ½Ð·Ð¾ÑÐ° Ð´Ð¸ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¿ÑÐ¾Ð½Ð¸ÑÐ°ÐµÐ¼Ð¾ÑÑÐ¸, ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐµÐ¹ Ð·Ð°ÑÑÑÐ°Ð½Ð¸Ñ Ð¿Ð¾ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ñ ÐÐ°Ð½Ð´Ð°Ñ. ÐÑÑÐ¸ÑÐ»ÐµÐ½Ð¸ÐµÂ  Ð² ÑÐ»ÑÑÐ°Ðµ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð»ÑÐ½Ð¾Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ²ÐµÐ»Ð¾ÑÑ Ðº Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ Ð½ÐµÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ Ð¾Ð±Ð¾Ð±ÑÐµÐ½Ð½Ð¾Ð¹ Ð´Ð¸ÑÐ¿ÐµÑÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¸ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð²Ð¼ÐµÑÑÐ¾ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð´Ð¸ÑÐ¿ÐµÑÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¸ Ð¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð² ÑÐ»ÑÑÐ°Ðµ ÐÐ°ÐºÑÐ²ÐµÐ»Ð»Ð¾Ð²ÑÐºÐ¾Ð³Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð¼ÐµÑÐ¾Ð´Ð° Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ Ð³Ð»Ð°Ð²Ð½Ð¾Ð³Ð¾ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐµÐ³ÑÐ°Ð»Ð°, Ð²ÑÐ¾Ð´ÑÑÐµÐ³Ð¾ Ð² Ð²ÐµÑÐµÑÑÐ²ÐµÐ½Ð½ÑÑ ÑÐ°ÑÑÑÂ  Ð±ÑÐ» Ð²ÑÐ±ÑÐ°Ð½ Ð¼ÐµÑÐ¾Ð´, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÐ¹ Ð½Ð° Ð¼ÐµÑÐ¾Ð´Ðµ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÐÐ°ÑÑÑÐ°. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ°Ð±Ð¾ÑÑ ÑÑÐµÑ Ð½ÐµÐ¼Ð°ÐºÑÐ²ÐµÐ»Ð»Ð¾Ð²ÑÐºÐ¾Ð³Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð±ÑÐ» Ð¾ÑÑÑÐµÑÑÐ²Ð»ÐµÐ½, ÐºÐ¾Ð´ Ð±ÑÐ» Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½ Ð¸ Ð±ÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð¿ÐµÑÐ²ÑÐµ Ð¿Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð»Ð½Ð¾Ð²ÑÐµ ÑÐ°ÑÑÐµÑÑ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¸ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ ÐºÐ°Ðº Ð½Ð¸Ð¶Ð½ÐµÐ³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ð¹ Ð²Ð¾Ð»Ð½Ñ Ð² Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ð¤Ð¢-2, ÑÐ°Ðº Ð¸ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð² Ð² Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° ÐÐ»Ð¾Ð±ÑÑ-Ð2. ÐÑÐ¸ ÑÑÐ¾Ð¼ Ð½ÐµÐ¼Ð°ÐºÑÐ²ÐµÐ»Ð»Ð¾Ð²ÑÐºÐ°Ñ ÑÑÐ½ÐºÑÐ¸Ñ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð¾Ð² Ð¿Ð¾ ÑÐºÐ¾ÑÐ¾ÑÑÑÐ¼, Ð¸Ð¼Ð¸ÑÐ¸ÑÑÑÑÐ°Ñ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð»Ð°ÑÐ¾ Ð¸Ð·-Ð·Ð° ÐºÐ²Ð°Ð·Ð¸Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ð² Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ ÑÐºÐ¾ÑÐ¾ÑÑÐµÐ¹ Ð·Ð° ÑÑÐµÑ Ð·Ð°ÑÑÑÐ°Ð½Ð¸Ñ Ð¿Ð¾ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ñ ÐÐ°Ð½Ð´Ð°Ñ, Ð·Ð°Ð´Ð°Ð²Ð°Ð»Ð°ÑÑ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸. ÐÐ¾Ð»Ð½Ð¾Ð²Ð¾Ð»Ð½Ð¾Ð²ÑÐµ ÑÐ°ÑÑÐµÑÑ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð¸, ÑÑÐ¾ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð»Ð°ÑÐ¾ Ð½Ð° ÑÑÐ½ÐºÑÐ¸Ð¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð¶ÐµÑ ÑÑÑÐµÑÑÐ²ÐµÐ½Ð½ÑÐ¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼ Ð²Ð»Ð¸ÑÑÑ Ð½Ð° Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ðµ Ð²Ð¾Ð»Ð½. Ð ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸, Ð´Ð»Ñ ÐÐ Ð²Ð¾Ð»Ð½Ñ Ð² ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐµ Ð¤Ð¢-2 Ð¿ÑÐ¸ÑÑÑÑÑÐ²Ð¸Ðµ Ð¿Ð»Ð°ÑÐ¾ Ð¿ÑÐ¸Ð²Ð¾Ð´Ð¸Ð»Ð¾ Ðº ÑÐ¼ÐµÑÐµÐ½Ð¸Ñ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð¿Ð¾ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ñ ÐÐ°Ð½Ð´Ð°Ñ Ð² ÑÑÐ¾ÑÐ¾Ð½Ñ Ð¿ÐµÑÐ¸ÑÐµÑÐ¸Ð¸ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð¸ Ð±Ð¾Ð»ÐµÐµ Ð¿Ð¸ÐºÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¼Ñ Ð¿ÑÐ¾ÑÐ¸Ð»Ñ ÑÐ°Ð´Ð¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐ½ÐµÑÐ³Ð¾Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð² Ð¾ÑÐ»Ð¸ÑÐ¸Ðµ Ð¾Ñ ÑÐ»ÑÑÐ°Ñ ÐÐ°ÐºÑÐ²ÐµÐ»Ð»Ð¾Ð²ÑÐºÐ¾Ð³Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ. ÐÐ½Ð°Ð»Ð¾Ð³Ð¸ÑÐ½Ð¾Ðµ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¸ Ð½Ð°Ð»Ð¸ÑÐ¸Ð¸ Ð¿Ð»Ð°ÑÐ¾ Ð½Ð° ÑÑÐ½ÐºÑÐ¸Ð¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð¾Ð² Ð½Ð°Ð±Ð»ÑÐ´Ð°Ð»Ð¾ÑÑ Ð¸ Ð¿ÑÐ¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð² Ð² ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐµ ÐÐ»Ð¾Ð±ÑÑ-Ð2 Ð¿ÑÐ¸Â Ð¸ 16, ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐ¸Ñ Ð½Ð¸Ð¶Ð½ÐµÐ¹ Ð³ÑÐ°Ð½Ð¸ÑÐµ Ð¿Ð»Ð°ÑÐ¾ .
description: The given work is devoted to taking into account the non-Maxwellian electron velocity distribution function in full-wave modeling of the propagation and absorption of waves in the lowerhybrid frequency range in a two-dimensional inhomogeneous tokamak plasma using the WaveTOP2D code. The non-Maxwellian distribution was taken into account for the component of the plasma dielectric tensorÂ corresponding to the Landau damping mechanism. The calculation in the case of an arbitrary distribution function has been reduced to the calculation of some generalized plasma dispersion function instead of the classical dispersion function of a homogeneous plasma in the case of a Maxwellian distribution. As a method for calculating the principal value of the integral, which is included in the real part of , a method based on the Gaussian integration method was chosen. As a result of the work, the non-Maxwellian distribution was taken into account, the code was modified, and the first full-wave modeling of the propagation and absorption of both the lower hybrid wave in the FT-2 tokamak plasma and helicons in the Globus-M2 tokamak plasma were carried out. In this case, the non-Maxwellian electron velocity distribution function, which simulates the formation of a plateau due to quasilinear diffusion in velocity space due to the Landau damping mechanism, was specified analytically. Full-wave calculations have shown that the formation of a plateau in the distribution function can significantly affect the absorption of waves. In particular, for the lowerhybrid wave in the FT-2 tokamak, the presence of a plateau led to a shift in absorption by the Landau mechanism towards the plasma periphery and a more peaked radial energy absorption profile, in contrast to the case of the Maxwellian distribution. A similar absorption behavior in the presence of a plateau in the electron distribution function was also observed in the simulation of helicons in the Globus-M2 tokamak atÂ  and 16, corresponding to the lower boundary of the plateau.