title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¡ÐÐ§ Ð²Ð¾Ð»Ð½ Ð² Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÐºÐ¾Ð´Ð¾Ð², Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð½Ð° ÑÐµÑÐµÐ½Ð¸Ð¸ Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð³Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Modeling the propagation of microwaves in a two-dimensional inhomogeneous plasma of a tokamak using numerical codes based on the solution of the wave equation
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: 2021
Subjects: ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð²Ð¾Ð»Ð½Ñ Ð² Ð¿Ð»Ð°Ð·Ð¼Ðµ
Ð¿Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð¹ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐ¹ ÐºÐ¾Ð´
Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ
Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ñ
ÑÑÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ¾ÐºÐ°Ð¼Ð°Ðº ÐÐ»Ð¾Ð±ÑÑ-Ð2
ÑÐ¾ÐºÐ°Ð¼Ð°Ðº Ð¢15-ÐÐ
helicons
numerical modeling
full wave code
waves in plasma
wave equation
spherical tokamak Globys-M2
tokamak T15-MD

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¸ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð±ÑÑÑÑÑÑ Ð¼Ð°Ð³Ð½Ð¸ÑÐ¾Ð·Ð²ÑÐºÐ¾Ð²ÑÑ Ð²Ð¾Ð»Ð½ Ð¿ÑÐ¾Ð¼ÐµÐ¶ÑÑÐ¾ÑÐ½Ð¾Ð³Ð¾ ÑÐ°ÑÑÐ¾ÑÐ½Ð¾Ð³Ð¾ Ð´Ð¸Ð°Ð¿Ð°Ð·Ð¾Ð½Ð° (Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð²) Ð² Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÐºÐ¾Ð´Ð¾Ð². ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. Ð Ð°ÑÑÐµÑ Ð¾Ð´Ð½Ð¾Ð¿ÑÐ¾ÑÐ¾Ð´Ð½Ð¾Ð³Ð¾ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð² Ð² Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ðµ Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ð¼Ð¸, ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐ¸Ð¼Ð¸ ÑÐºÐ²Ð°ÑÐ¾ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¼Ñ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° ÐÐ»Ð¾Ð±ÑÑ-Ð2, Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÐºÐ¾-Ð¾Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÐºÐ¾Ð´Ð° WKBplt Ð¸ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð³Ð¾ ÐºÐ¾Ð´Ð° zimfld. 2. ÐÑÐµÐ½ÐºÐ° Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸, Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð½Ð¾Ð¹ Ð² Ð½Ð¸Ð¶Ð½ÐµÐ³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ð¼ (ÐÐ) ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐµ Ð½Ð° Ð¿ÐµÑÐ¸ÑÐµÑÐ¸Ð¸ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° ÐÐ»Ð¾Ð±ÑÑ-Ð2 Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÐºÐ¾-Ð¾Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÐºÐ¾Ð´Ð° WKBplt Ð¸ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð³Ð¾ ÐºÐ¾Ð´Ð° zimfld. 3. ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð² Ð² ÑÐµÐ°Ð»ÑÐ½Ð¾Ð¹ Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð² Ð¢15-ÐÐ Ð¸ ÐÐ»Ð¾Ð±ÑÑ-Ð2 Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð³Ð¾ ÐºÐ¾Ð´Ð° WaveTOP2D. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÐºÐ¾Ð´Ð¾Ð² Ð±ÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ ÑÐ°ÑÑÐµÑÑ, Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑÐ¸Ðµ, ÐºÐ°Ðº Ð¸Ð·Ð¼ÐµÐ½ÑÐµÑÑÑ Ð¾Ð´Ð½Ð¾Ð¿ÑÐ¾ÑÐ¾Ð´Ð½Ð¾Ðµ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ðµ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð² Ð¸ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ðµ Ð² Ð½Ð¸Ð¶Ð½ÐµÐ³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ð¼ ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐµ Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð½Ð° Ð¿ÐµÑÐ¸ÑÐµÑÐ¸Ð¸ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° ÐÐ»Ð¾Ð±ÑÑ-Ð2. Ð¢Ð°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¾ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð² Ð² Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð² ÐÐ»Ð¾Ð±ÑÑ-Ð2 Ð¸ Ð¢15-ÐÐ, Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÑÑÑÐµ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½Ð¾Ðµ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½Ñ ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð²Ð¾Ð»Ð½Ñ Ð¸ Ð»Ð¾ÐºÐ°Ð»ÑÐ½Ð¾ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð½Ð¾Ð¹ ÐÐ§ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð² Ð¿Ð»Ð¾ÑÐºÐ¾ÑÑÐ¸ Ð¿Ð¾Ð»Ð¾Ð¸Ð´Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¾ Ð¾Ð±Ð½Ð°ÑÑÐ¶ÐµÐ½Ð¾, ÑÑÐ¾ Ð½Ð°Ð¸Ð»ÑÑÑÐµÐ³Ð¾ Ð¾Ð´Ð½Ð¾Ð¿ÑÐ¾ÑÐ¾Ð´Ð½Ð¾Ð³Ð¾ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð² Ð¼Ð¾Ð¶Ð½Ð¾ Ð´Ð¾ÑÑÐ¸ÑÑ, ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÑ Ð¸ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð½ÑÑ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð² ÑÐµÐ½ÑÑÐµ Ð¿Ð»Ð°Ð·Ð¼ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ½ÑÑÐ°, ÑÐ¼ÐµÐ½ÑÑÐ°Ñ Ð²Ð°ÐºÑÑÐ¼Ð½Ð¾Ðµ ÑÐ¾ÑÐ¾Ð¸Ð´Ð°Ð»ÑÐ½Ð¾Ðµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ðµ Ð¿Ð¾Ð»Ðµ Ð½Ð° Ð¾ÑÐ¸, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°Ñ ÑÐ°ÑÑÐ¾ÑÑ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ°. ÐÐ¾Ð´Ð¾Ð±Ð½Ð°Ñ ÑÐµÐ½Ð´ÐµÐ½ÑÐ¸Ñ Ð² Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ð¸ Ð¾Ð´Ð½Ð¾Ð¿ÑÐ¾ÑÐ¾Ð´Ð½Ð¾Ð³Ð¾ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ ÑÐ¾Ð³Ð»Ð°ÑÑÐµÑÑÑ Ñ ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¾ÑÐ¼ÑÐ»Ð¾Ð¹ Ð´Ð»Ñ Ð¼Ð½Ð¸Ð¼Ð¾Ð¹ ÑÐ°ÑÑÐ¸ Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½Ð¾Ð¹ Ðº Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð¼Ñ Ð¿Ð¾Ð»Ñ ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÑ Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð³Ð¾ Ð²ÐµÐºÑÐ¾ÑÐ°. Ð ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸, Ð´Ð»Ñ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ñ Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ð¼Ð¸, ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐ¸Ð¼Ð¸ ÑÐºÐ²Ð°ÑÐ¾ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¼Ñ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° ÐÐ»Ð¾Ð±ÑÑ-Ð2, Ð±ÑÐ»Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾, ÑÑÐ¾ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¸ ÑÑÐ¾Ð¿ÑÐ¾ÑÐµÐ½ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ ÐÐ§ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¼Ð¾Ð¶Ð½Ð¾ Ð´Ð¾Ð±Ð¸ÑÑÑÑ Ð¿ÑÐ¸ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ 6â10^13 ÑÐ¼^(-3), ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐµ 2 ÐºÑÐ, ÑÐ¾ÑÐ¾Ð¸Ð´Ð°Ð»ÑÐ½Ð¾Ð¼ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð¼ Ð¿Ð¾Ð»Ðµ Ð½Ð° Ð¾ÑÐ¸ 8 ÐºÐÑ Ð¸ ÑÐ°ÑÑÐ¾ÑÐµ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ° 200 ÐÐÑ. Ð¢Ð°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾, ÑÑÐ¾ Ð½Ð°Ð¸Ð¼ÐµÐ½ÑÑÐµÐ³Ð¾ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ ÐÐ§ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð² Ð½Ð¸Ð¶Ð½ÐµÐ³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ð¼ ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐµ Ð¿ÑÐ¸ Ð±Ð°Ð·Ð¾Ð²ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ñ Ð¿Ð»Ð°Ð·Ð¼Ñ, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð² ÑÐ°Ð±Ð¾ÑÐµ, Ð¼Ð¾Ð¶Ð½Ð¾ Ð´Ð¾ÑÑÐ¸ÑÑ Ð¿ÑÐ¸ ÑÐ¾ÐºÐµ 500 ÐºÐ. ÐÑÐ¸ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸Ð¸ Ð¶Ðµ ÑÐ¾ÑÐ¾Ð¸Ð´Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ñ 7 ÐºÐÑ Ð´Ð¾ 10 ÐºÐÑ Ð´Ð»Ñ ÑÐ¾ÐºÐ° -500 ÐºÐ Ð½Ð°Ð±Ð»ÑÐ´Ð°Ð»Ð¾ÑÑ ÑÐ¼ÐµÐ½ÑÑÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð² ÐÐ ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐµ Ñ 21% Ð´Ð¾ 12.5%. Ð¡ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð¶Ðµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² Ð´Ð°Ð½Ð½ÑÑ Ð¿ÑÐµÐ´ÐµÐ»Ð°Ñ Ð¿ÑÐ¸ ÑÐ¾ÐºÐµ +500 ÐºÐ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ðµ Ð±ÑÐ»Ð¾ Ð¼Ð°Ð»Ð¾ Ð¸ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÐ»Ð¾ Ð´Ð¾Ð»Ð¸ Ð¿ÑÐ¾ÑÐµÐ½ÑÐ°. Ð¡ ÑÐ¾ÑÑÐ¾Ð¼ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð½Ð° Ð³ÑÐ°Ð½Ð¸ÑÐµ Ð¿ÑÐ¸ ÑÐ¾ÐºÐµ 500 ÐºÐ Ð½Ð°Ð±Ð»ÑÐ´Ð°Ð»ÑÑ ÑÐ¾ÑÑ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð²Ð¿Ð»Ð¾ÑÑ Ð´Ð¾ 10% Ð¿ÑÐ¸ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð½Ð° Ð³ÑÐ°Ð½Ð¸ÑÐµ 2â10^12 ÑÐ¼^(-3), Ð° Ð² ÑÐ»ÑÑÐ°Ðµ ÑÐ¾ÐºÐ° -500 ÐºÐ Ð½Ð°Ð±Ð»ÑÐ´Ð°Ð»Ð¾ÑÑ ÑÐ¼ÐµÐ½ÑÑÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ñ 18% Ð¸ Ð´Ð¾ 10% Ð¿ÑÐ¸ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð½Ð° Ð³ÑÐ°Ð½Ð¸ÑÐµ 3â10^12 ÑÐ¼^(-3). Ð¢Ð°ÐºÐ¶Ðµ Ð½Ð°Ð±Ð»ÑÐ´Ð°Ð»ÑÑ Ð·Ð°Ð¼ÐµÑÐ½ÑÐ¹ ÑÐ¾ÑÑ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¸ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾ Ð±Ð¾Ð»ÑÑÐ¸Ñ ÑÐ¾ÑÐ¾Ð¸Ð´Ð°Ð»ÑÐ½ÑÑ Ð·Ð°Ð¼ÐµÐ´Ð»ÐµÐ½Ð¸ÑÑ. ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¶Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð¾Ð² Ð² ÑÐµÐ°Ð»ÑÐ½Ð¾Ð¹ Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾-Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð² Ð¢15-ÐÐ Ð¸ ÐÐ»Ð¾Ð±ÑÑ-Ð2 Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð¾, ÑÑÐ¾ Ð¿ÑÐ¸ Ð²ÑÐ±ÑÐ°Ð½Ð½ÑÑ Ð² ÑÐ°ÑÑÐµÑÐ°Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ñ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ñ Ð½Ð° ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐµ Ð¢15-ÐÐ Ð¿Ð¾Ð³Ð»Ð¾ÑÐ°ÑÑÑÑ Ð¿Ð¾Ð»Ð½Ð¾ÑÑÑÑ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¸ Ð·Ð° Ð¾Ð´Ð¸Ð½ Ð¿ÑÐ¾ÑÐ¾Ð´, Ð° Ð² ÑÐ»ÑÑÐ°Ðµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° ÐÐ»Ð¾Ð±ÑÑ-Ð2 Ð¿Ð¾Ð»Ð½Ð¾Ð³Ð¾ Ð¿Ð¾Ð³Ð»Ð¾ÑÐµÐ½Ð¸Ñ Ð·Ð° Ð¾Ð´Ð¸Ð½ Ð¿ÑÐ¾ÑÐ¾Ð´ Ð½Ðµ Ð¿ÑÐ¾Ð¸ÑÑÐ¾Ð´Ð¸Ñ, Ð¸Ð·-Ð·Ð° ÑÐµÐ³Ð¾ Ð²Ð¾Ð»Ð½Ð° Ð¼Ð½Ð¾Ð³Ð¾ÐºÑÐ°ÑÐ½Ð¾ Ð¾ÑÑÐ°Ð¶Ð°ÐµÑÑÑ Ð¾Ñ Ð¾ÑÑÐµÑÐµÐº, ÐºÐ¾Ð½ÑÑ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð³ÐµÐ»Ð¸ÐºÐ¾Ð½Ð° ÑÐ°Ð·Ð¼ÑÐ²Ð°ÐµÑÑÑ Ð¸ Ð¸Ð½Ð¾Ð³Ð´Ð° ÑÑÐ°Ð½Ð¾Ð²Ð¸ÑÑÑ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¸ Ð½ÐµÑÐ°Ð·Ð»Ð¸ÑÐ¸Ð¼.
description: The present work is devoted to the study of the propagation and absorption of fast magnetosonic waves in the intermediate frequency range (helicons) in a tokamak plasma using numerical codes. The research sets the following goals: 1. Calculation of single-pass power absorption of helicons in a one-dimensional inhomogeneous plasma with parameters close to those of the Globus-M2 tokamak equatorial plane using the geometric-optical code WKBplt and the one-dimensional full wave code zimfld. 2. Estimation of the power absorbed in the lower hybrid (LH) resonance at the periphery of the one-dimensional inhomogeneous plasma of the Globus-M2 tokamak using the geometric-optical code WKBplt and the one-dimensional full wave code zimfld. 3. Modeling the propagation of helicons in a two-dimensionally inhomogeneous plasma of the T15-MD and Globus-M2 tokamaks using the WaveTOP2D full wave code. In the course of the work, using numerical codes, calculations were performed showing how the single-pass absorption of helicons and absorption in the lower hybrid resonance change depending on the parameters of the one-dimensional inhomogeneous plasma of the Globus-M2 tokamak. A simulation of the propagation of helicons in a two-dimensionally inhomogeneous plasma of the Globus-M2 and T15-MD tokamaks was carried out, which demonstrates the spatial distribution of the components of the wave electric fields and the locally absorbed HF power in the poloidal cross-section. As a result of the work, it was found that the best single-pass absorption of helicons can be achieved by increasing the density and electron temperature at the center of the plasma, decreasing the vacuum toroidal magnetic field on the axis, and also increasing the generator frequency. This tendency in the behavior of single-pass absorption is consistent with the theoretical formula for the imaginary part of the wave vector component transverse to the magnetic field. In particular, for a one-dimensional inhomogeneous plasma of the Globus-M2 tokamak, it was found that almost one hundred percent absorption of RF power can be achieved at a density of 6â10^13 cm^(-3), an electron temperature of 2 keV, a toroidal magnetic field on the axis of 8 kG and a generator frequency of 200 MHz. It was also found that the lowest absorption of RF power in the lower hybrid resonance with the basic plasma parameters used in this work can be achieved at a current of 500 kA. With an increase in the toroidal magnetic field from 7 kG to 10 kG for a current of -500 kA, a decrease in absorption in the LH resonance from 21% to 12.5% was observed. With a change in the magnetic field within these limits at a current of +500 kA, the absorption was small and amounted to fractions of one percent. With an increase in the plasma density at the boundary at a current of 500 kA, an increase in absorption was observed up to 10% at a density at the boundary of 2â10^12 cm^(-3), and in the case of a current of -500 kA, a decrease in absorption was observed from 18% to 10% at a density at the boundary of 3â10^12 cm^(-3). A noticeable increase in absorption was also observed at sufficiently large toroidal wavenumbers. Modeling the propagation of helicons in a two-dimensionally inhomogeneous plasma of the T15-MD and Globus-M2 tokamaks showed that, with the parameters chosen in the calculations, the helicons on the T15-MD tokamak are almost completely absorbed in one pass, and in the case of the Globus-M2 tokamak, the complete absorption in one pass does not occur, due to which the wave experience multiple reflections from the cutoffs and the cone of propagation of the helicon becomes smeared and sometimes practically indistinguishable.