title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð½Ð¸Ð¶Ð½ÐµÐ³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ð³Ð¾ ÑÐ¾ÐºÐ° ÑÐ²Ð»ÐµÑÐµÐ½Ð¸Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÐºÐ¾Ð´Ð° FRTC Ð¸ ÐºÐ¾Ð´Ð° ASTRA
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: Numerical modelling of the lower hybrid current drive using the dynamic FRTC and ASTRA codes
Creators: name: Ð¥Ð°Ð²Ð¸Ð½, ÐÐ°ÑÐ¸Ð»Ð¸Ð¹
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: 2020
Subjects: ÑÐ¾ÐºÐ°Ð¼Ð°Ðº
Ð¿Ð»Ð°Ð·Ð¼Ð°
Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ñ ÑÐ¾ÐºÐ°
Ð½Ð¸Ð¶Ð½ÐµÐ³Ð¸Ð±ÑÐ¸Ð´Ð½ÑÐµ Ð²Ð¾Ð»Ð½Ñ
ÑÑÐ½ÐºÑÐ¸Ñ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð¾Ð²
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¤Ð¾ÐºÐºÐµÑÐ° - ÐÐ»Ð°Ð½ÐºÐ°
Ð¼ÐµÑÐ¾Ð´ ÐÑÐ°Ð½ÐºÐ° - ÐÐ¸ÐºÐ¾Ð»ÑÐ¾Ð½Ð°
tokamak
plasma
current generation
lower hybrid waves
electron distribution function
Fokker - Planck equation
Crank - Nicolson method

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð° ÐÑÐ°Ð½ÐºÐ° â ÐÐ¸ÐºÐ¾Ð»ÑÐ¾Ð½Ð° Ð´Ð»Ñ ÑÐµÑÐµ-Ð½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¤Ð¾ÐºÐºÐµÑÐ° â ÐÐ»Ð°Ð½ÐºÐ°, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼Ð¾Ð³Ð¾ Ð² ÐºÐ¾Ð´Ðµ Fast Ray Tracing Code (FRTC). ÐÐ°Ð½Ð½Ð°Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð°Ñ ÑÑÐµÐ¼Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð° Ð² Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ð¼ Ð²Ð¸Ð´Ðµ. Ð ÑÐ°-Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð¼ÐµÑÐ¾Ð´Ð° Ñ Ð¿ÑÐµÐ´ÑÐµÑÑÐ²ÑÑÑÐ¸Ð¼, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¼ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼. ÐÑÐ¸Ð²ÐµÐ´ÐµÐ½Ñ Ð¿ÑÐ¸Ð¼ÐµÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð´Ð»Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð² Ð¤Ð¢ â 2 Ð¸ ÐÐ»Ð¾Ð±ÑÑ Ð â 2. ÐÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¾, ÑÑÐ¾ ÑÑÐ° ÑÑÐµÐ¼Ð° Ð¾Ð±Ð»Ð°Ð´Ð°ÐµÑ Ð²ÑÑÐ¾ÐºÐ¾Ð¹ ÑÐ¾ÑÐ½Ð¾ÑÑÑÑ, Ð½Ð¾ Ð² ÑÐ¾ Ð¶Ðµ Ð²ÑÐµÐ¼Ñ Ð½Ðµ Ð²ÑÐµÐ³Ð´Ð° ÑÐ¿Ð¾ÑÐ¾Ð±Ð½Ð° Ð²ÑÐ´Ð°ÑÑ ÐºÐ¾ÑÑÐµÐºÑÐ½ÑÐ¹ Ñ ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¾ÑÐºÐ¸ Ð·ÑÐµÐ½Ð¸Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°Ñ. Ð ÑÐ²ÑÐ·Ð¸ Ñ ÑÐµÐ¼ Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÑÑÑÑ Ð°Ð»ÑÑÐµÑÐ½Ð°ÑÐ¸Ð²Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ñ. Ð¢Ð°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¾ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¸ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÐºÐ¾Ð´Ð° FRTC. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÐ¹ ÑÐ°ÑÑÐµÑ Ð½Ðµ ÑÑÐ¸ÑÑÐ²Ð°ÐµÑ ÑÐ²Ð¾Ð»ÑÑÐ¸Ñ ÑÑÐ½ÐºÑÐ¸Ð¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ, Ð¸Ð· â Ð·Ð° ÑÐµÐ³Ð¾ ÑÐ¾Ðº Ð·Ð°Ð¼ÐµÑÐ°ÐµÑÑÑ Ñ Ð¾Ð¿ÐµÑÐµÐ¶ÐµÐ½Ð¸ÐµÐ¼. ÐÐ¾ÑÑÐ¾Ð¼Ñ ÑÐ°ÑÑÐµÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÐºÐ¾Ð´Ð° Ð´Ð»Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð², Ð²ÑÐµÐ¼Ñ Ð²ÑÑÐ¾Ð´Ð° Ð½Ð° ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°Ñ ÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÐµÑ Ð¿Ð¾ÑÑÐ´ÐºÐ° Ð²ÑÐµÐ¼ÐµÐ½Ð¸ ÑÐ°Ð·ÑÑÐ´Ð°, Ð¼Ð¾Ð¶ÐµÑ Ð²ÑÑÑÑÐ¿Ð°ÑÑ ÑÐ¾Ð»ÑÐºÐ¾ Ð² ÑÐ¾Ð»Ð¸ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ° Ð´Ð»Ñ ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð¹ Ð¾ÑÐµÐ½ÐºÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð².
description: The given work devoted to the description of the Crank-Nicholson method for solving the Fokker-Planck equation used in Fast Ray Tracing Code (FRTC). This numerical scheme is obtained in analytical form. The paper demonstrates comparison of this method with the previous one as well as comparison with the analytical solution. Examples of calculations for tokamaks FT - 2 and Globeus M - 2 are given. It is demonstrated that this scheme has high accuracy, but at the same time it is not always able to give a physically correct result. Therefore, alternative methods for solving the problem are proposed. We also compared the work of dynamic and stationary FRTC code. The work demonstrates that the stationary calculation doesn't take into account the evolution of the distribution function, that's why the current is substituted ahead of time. That's why the stationary code calculation for tokamaks, for which the time of going to the stationary is the order of discharge time, can only act as a tool for qualitative evaluation of results.