title: Ð Ð°Ð´Ð¸Ð°ÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð¿Ð¾ÑÐµÑÐ¸ Ð¸Ð· Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐ¼Ñ ÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð¹ Ð²ÑÑÐ¾Ñ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: Radiation losses from a finite potential well
Creators: name: ÐÐ°Ð³Ð¾Ð²Ð¸ÑÑÐ½, ÐÐ½Ð´ÑÐµÐ¹
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»ÐµÐºÑÑÐ¾Ð½-ÑÐ¸ÐºÐ»Ð¾ÑÑÐ¾Ð½Ð½ÑÐ¹ ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐ½ÑÐ¹ Ð½Ð°Ð³ÑÐµÐ²
Ð°Ð±ÑÐ¾Ð»ÑÑÐ½Ð°Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐ°ÑÐ¿Ð°Ð´Ð½Ð°Ñ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ
ÑÑÑÐµÐºÑ ÑÑÐ½Ð½ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ
Ð²ÐµÑÑ Ð½ÐµÐ³Ð¸Ð±ÑÐ¸Ð´Ð½ÑÐ¹ ÑÐµÐ·Ð¾Ð½Ð°Ð½Ñ
electron-cyclotron resonance heating
absolute parametric decay instability
tunneling effect
upper hybrid resonance

description: ÐÐ° Ð¼Ð½Ð¾Ð³Ð¸Ñ ÑÑÑÐ°Ð½Ð¾Ð²ÐºÐ°Ñ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐ´ÐµÑÐ¶Ð°Ð½Ð¸Ñ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÑÑÑ Ð¼ÐµÑÐ¾Ð´ Ð­Ð¦Ð Ð. Ð¡ÐÐ§ Ð²Ð¾Ð»Ð½Ñ Ð½Ð°ÐºÐ°ÑÐºÐ¸, ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÑÐ¸ÐµÑÑ Ð² Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ðµ, Ð¼Ð¾Ð³ÑÑ Ð¿ÑÐµÑÐµÑÐ¿ÐµÐ²Ð°ÑÑ ÑÐ°ÑÐ¿Ð°Ð´ Ð½Ð° Ð´Ð¾ÑÐµÑÐ½Ð¸Ðµ Ð²Ð¾Ð»Ð½Ñ. ÐÐµÐ´Ð°Ð²Ð½Ð¾ Ð±ÑÐ»Ð¾ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ ÑÑÐ¾Ñ ÑÐ°ÑÐ¿Ð°Ð´ Ð¼Ð¾Ð¶ÐµÑ Ð¿ÑÐ¸Ð²ÐµÑÑÐ¸ Ðº Ð½Ð¸Ð·ÐºÐ¾Ð¿Ð¾ÑÐ¾Ð³Ð¾Ð²Ð¾Ð¼Ñ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð¸Ñ Ð¾Ð¿Ð°ÑÐ½Ð¾Ð¹ Ð°Ð±ÑÐ¾Ð»ÑÑÐ½Ð¾Ð¹ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ°ÑÐ¿Ð°Ð´Ð½Ð¾Ð¹ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ (ÐÐÐ Ð). Ð­ÑÐ¾ ÑÐ²Ð»ÐµÐ½Ð¸Ðµ ÑÑÐ°Ð½Ð¾Ð²Ð¸ÑÑÑ Ð½ÐµÐ¸Ð·Ð±ÐµÐ¶Ð½ÑÐ¼, ÐµÑÐ»Ð¸ Ð¾Ð´Ð½Ð° Ð¸Ð»Ð¸ Ð¾Ð±Ðµ Ð´Ð¾ÑÐµÑÐ½Ð¸Ñ Ð²Ð¾Ð»Ð½Ñ Ð¾ÐºÐ°Ð·Ð°Ð»Ð¸ÑÑ Ð·Ð°Ð¿ÐµÑÑÑ Ð² Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐ¼Ðµ. ÐÐÐ Ð Ð¼Ð¾Ð¶ÐµÑ Ð¿ÑÐ¸Ð²ÐµÑÑÐ¸ Ðº ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐ¼ Ð°Ð½Ð¾Ð¼Ð°Ð»ÑÐ½ÑÐ¼ ÑÐ²Ð»ÐµÐ½Ð¸ÑÐ¼, ÑÐ°ÐºÐ¸Ð¼ ÐºÐ°Ðº Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ðµ Ð¾ÑÑÐ°Ð¶ÐµÐ½Ð¸Ðµ Ð³ÑÐµÑÑÐµÐ¹ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¸ ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ðµ Ð¸Ð¾Ð½Ð¾Ð². ÐÐ° ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½ÑÐµ Ð¸ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²ÐµÐ½Ð½ÑÐµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð¸ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÑÐ¸Ñ Ð°Ð½Ð¾Ð¼Ð°Ð»ÑÐ½ÑÑ ÑÐ²Ð»ÐµÐ½Ð¸Ð¹ Ð²Ð»Ð¸ÑÐµÑ ÑÐ¾, Ð½Ð° ÐºÐ°ÐºÐ¾Ð¼ ÑÑÐ¾Ð²Ð½Ðµ Ð½Ð°ÑÑÑÐ°ÐµÑÑÑ ÑÑÐ° Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ Ð¸ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ°ÐºÐ¸Ñ ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¸Ñ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ð¾Ð² Ð½Ð°ÑÑÑÐµÐ½Ð¸Ðµ Ð´Ð¾ÑÑÐ¸Ð³Ð°ÐµÑÑÑ. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ» Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½ ÐµÑÑ Ð¾Ð´Ð¸Ð½ Ð¸Ð· Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼Ð¾Ð², ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¾ÑÐ²ÐµÑÑÑÐ²ÐµÐ½Ð½Ñ Ð·Ð° Ð½Ð°ÑÑÑÐµÐ½Ð¸Ðµ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸. Ð­ÑÐ¾Ñ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¼ ÑÐ²ÑÐ·Ð°Ð½ Ñ ÑÐµÐ¼, ÑÑÐ¾ Ð²ÑÑÑÐ¸Ðµ ÑÐ²ÑÐ·Ð°Ð½Ð½ÑÐµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð¸ÑÐ¿ÑÑÑÐ²Ð°ÑÑ ÑÐ¸Ð»ÑÐ½ÑÐµ Ð¿Ð¾ÑÐµÑÐ¸ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð¸Ð·-Ð·Ð° ÑÑÐ½Ð½ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐµÑÐµÐ· Ð¾Ð±Ð»Ð°ÑÑÑ Ð½ÐµÐ¿ÑÐ¾Ð·ÑÐ°ÑÐ½Ð¾ÑÑÐ¸. Ð­ÑÐ¾Ñ ÑÑÑÐµÐºÑ ÐµÑÐµ Ð½Ðµ Ð±ÑÐ» ÑÑÑÐµÐ½ Ð¿ÑÐ¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ðµ Ð¸ Ð¼Ð¾Ð¶ÐµÑ ÑÑÐ³ÑÐ°ÑÑ Ð²Ð°Ð¶Ð½ÑÑ ÑÐ¾Ð»Ñ Ð² Ð¿ÐµÑÐµÑÐ¾Ð´Ðµ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð² ÑÐµÐ¶Ð¸Ð¼ Ð½Ð°ÑÑÑÐµÐ½Ð¸Ñ. ÐÑÐ»Ð¾ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ ÑÐµÐ´ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐµÐµ ÑÑÐ½Ð½ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÐµÑÑÐ½ÐµÐ³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ð¹ Ð²Ð¾Ð»Ð½Ñ ÑÐµÑÐµÐ· Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÐ¹ Ð±Ð°ÑÑÐµÑ. Ð¡ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð½ÐµÐ³Ð¾ Ð±ÑÐ»Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ Ð¿ÑÐ°Ð²Ð¸Ð»Ð¾ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð»Ñ ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÑ ÑÐ°ÑÑÐ¾Ñ Ñ ÑÑÑÑÐ¾Ð¼ Ð½Ð°Ð±ÐµÐ³Ð° ÑÐ°Ð·Ñ Ð´Ð»Ñ Ð¾ÑÑÐ°Ð¶ÑÐ½Ð½ÑÑ Ð²Ð¾Ð»Ð½. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð´ÐµÐºÑÐµÐ¼ÐµÐ½ÑÑ Ð´Ð»Ñ Ð·Ð°Ð¿ÐµÑÑÑÑ ÐÐ Ð²Ð¾Ð»Ð½.
description: Electron cyclotron resonance heating (ECRH) is a method that is widely utilized in current magnetic fusion devices. Microwaves propagating in inhomogeneous magnetized plasma can decay into two daughter waves. It has recently been shown that this decay can lead to the low threshold excitation of most dangerous absolute parametric decay instability (APDI). This phenomenon becomes inevitable if one or both of the daughter waves are trapped in a potential well. The qualitative and quantitative characteristics and features of these phenomena are determined by the saturation level of instability and the way in which this saturation is achieved. In this paper, we investigated another physical mechanism, which may be responsible for the instability saturation and controlling the saturation level. This mechanism is related to the fact that the higher bound states in a finite tower of eigen modes suffers strong energy losses due to tunneling through an evanescent region, making the trapped waves corresponding to these bound states heavily damped. This effect has not yet been accounted for and may play an important role in the transition of instability into the saturation mode. A reduced equation describing the tunneling of an upper hybrid wave through a potential barrier was obtained analytically. It was used to obtain a quantization rule for the eigenfrequencies, taking into account the phase shift for the reflected waves. As a result of the work, the decrements for the locked UH waves were numerically obtained.