title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿ÑÐ¸ÑÑÐµÐ½Ð¾ÑÐ½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð² Ð² ÑÐµÐ¶Ð¸Ð¼Ðµ ÑÐ°ÑÑÐ¸ÑÐ½Ð¾Ð³Ð¾ Ð¾ÑÑÑÐ²Ð°
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: Modelling and analysis of semi-detached tokamak edge plasma
Creators: name: ÐÐ¾Ð»ÐµÑÐ°ÐµÐ²Ð°, ÐÐ½Ð°ÑÑÐ°ÑÐ¸Ñ
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·.)
ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð£ÑÐºÐ¾ÑÐ¸ÑÐµÐ»Ð¸ Ð·Ð°ÑÑÐ¶ÐµÐ½Ð½ÑÑ ÑÐ°ÑÑÐ¸Ñ
ÑÐµÐ¶Ð¸Ð¼ Ð¾ÑÑÑÐ²Ð°
Ð¸Ð·Ð»ÑÑÐ°ÑÑÐ°Ñ Ð¿ÑÐ¸Ð¼ÐµÑÑ
partialÂ detachment
radiating impurity

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¼Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÐºÐ¾Ð´Ð¾Ð¼ SOLPS-ITER Ð¸ ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¾Ð¼Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ñ ÑÐ°Ð·ÑÑÐ´Ð¾Ð² Ñ Ð½Ð°Ð¿ÑÑÐºÐ¾Ð¼Â  Ð¸Ð·Ð»ÑÑÐ°ÑÑÐ¸Ñ Ð¿ÑÐ¸Ð¼ÐµÑÐµÐ¹ Ð°ÑÐ³Ð¾Ð½Ð° (Ar) Ð¸ Ð°Ð·Ð¾ÑÐ° (N) Ð¸ Ð½ÐµÐ¾Ð½Ð° (Ne) Ð² ÑÑÐ»Ð¾Ð²Ð¸ÑÑ H-ÑÐµÐ¶Ð¸Ð¼Ð° Ð´Ð»Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð² ASDEX Upgrade Ð¸ ITER. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ar Ð¸ N ÑÐ¾ÑÐ¾ÑÐ¾ ÑÐ´ÐµÑÐ¶Ð¸Ð²Ð°ÑÑÑÑ Ð² Ð´Ð¸Ð²ÐµÑÑÐ¾ÑÐµ, ÑÑÐ¾ Ð¾Ð±ÑÑÑÐ½ÑÐµÑÑÑ Ð¿Ð¾ÑÑÐ¸ Ð¾Ð´Ð¸Ð½Ð°ÐºÐ¾Ð²ÑÐ¼Ð¸ Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÐ¼Ð¸ Ð¿ÐµÑÐ²Ð¾Ð³Ð¾ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»Ð° Ð¸Ð¾Ð½Ð¸Ð·Ð°ÑÐ¸Ð¸ Ar Ð¸ N Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ Ne. Ð¢Ð°ÐºÐ¶Ðµ, Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð¾ Ð½Ð°Ð¿ÑÑÐºÐ°ÐµÐ¼Ð¾Ð¹ Ð¿ÑÐ¸Ð¼ÐµÑÐ¸ (Ð¸Ð·Ð¼ÐµÑÑÐµÐ¼Ð¾Ðµ ÐºÐ°Ðº ÑÐºÐ¾ÑÐ¾ÑÑÑ Ð³Ð°Ð·Ð¾Ð½Ð°Ð¿ÑÑÐºÐ° Ð² Ð°ÑÐ¾Ð¼Ð°Ñ/Ñ, Ð¸Ð»Ð¸ ÐºÐ°Ðº ÑÑÑÐµÐ´Ð½ÐµÐ½Ð½Ð°Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÑÐ¸ Ð½Ð° ÑÐµÐ¿Ð°ÑÐ°ÑÑÐ¸ÑÐµ), Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾Ðµ Ð´Ð»Ñ Ð´Ð¾ÑÑÐ¸Ð¶ÐµÐ½Ð¸Ñ Ð¾Ð´Ð¸Ð½Ð°ÐºÐ¾Ð²ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ð¹ Ð² Ð´Ð¸Ð²ÐµÑÑÐ¾ÑÐµ, Ð½Ð¸Ð¶Ðµ Ð´Ð»Ñ Ar, ÑÐµÐ¼ Ð´Ð»Ñ N Ð²Ð²Ð¸Ð´Ñ Ð±Ð¾Ð»ÐµÐµ Ð²ÑÑÐ¾ÐºÐ¾Ð¹ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÑÑ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ñ Ar. ÐÑÐ¸ Ð´Ð¾Ð»Ðµ Ð¸Ð·Ð»ÑÑÐ°ÐµÐ¼Ð¾Ð¹ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð² ÑÐ°ÑÑÐµÑÐ½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¿Ð¾ÑÑÐ´ÐºÐ° 50%, ÑÑÐ¾ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾ Ð´Ð»Ñ Ð´Ð¾ÑÑÐ¸Ð¶ÐµÐ½Ð¸Ñ ÑÐµÐ¶Ð¸Ð¼Ð° ÑÐ°ÑÑÐ¸ÑÐ½Ð¾Ð³Ð¾ Ð¾ÑÑÑÐ²Ð° Ð½Ð° Ð²Ð½ÐµÑÐ½ÐµÐ¹ Ð´Ð¸Ð²ÐµÑÑÐ¾ÑÐ½Ð¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ðµ Ð² Ð¾Ð±Ð¾Ð¸Ñ ÑÑÑÑÐ¾Ð¹ÑÑÐ²Ð°Ñ, Ð¿Ð¾ÑÐµÑÐ¸ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ñ Ð¸Ð· Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÑÐ´ÐµÑÐ¶Ð°Ð½Ð¸Ñ Ð´Ð»Ñ ÑÐ°ÑÑÐµÑÐ° ÐÐ¢Ð­Ð  Ñ Ð½Ð°Ð¿ÑÑÐºÐ¾Ð¼ Ar Ð¾ÑÑÐ°ÑÑÑÑ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾ Ð¼Ð°Ð»ÑÐ¼Ð¸ - Ð¾ÐºÐ¾Ð»Ð¾ 6%. Ð£ÑÑÐµÐ´Ð½ÐµÐ½Ð½Ð°Ñ ÐºÐ¾Ð½ÑÐµÐ½ÑÑÐ°ÑÐ¸Ð¸ Ar Ð½Ð° ÑÐµÐ¿Ð°ÑÐ°ÑÑÐ¸ÑÐµ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÐµÑ 0,4%, ÑÑÐ¾ Ð·Ð°Ð¼ÐµÑÐ½Ð¾ Ð¼ÐµÐ½ÑÑÐµ, ÑÐµÐ¼ Ñ N Ð¸ Ne. Ð¢Ð°ÐºÐ¸Ð¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼, Ñ ÑÐ¾ÑÐºÐ¸ Ð·ÑÐµÐ½Ð¸Ñ ÑÐ¼ÐµÐ½ÑÑÐµÐ½Ð¸Ñ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð½Ð° Ð´Ð¸Ð²ÐµÑÑÐ¾ÑÐ½ÑÑ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ð°Ñ, Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÐºÐ¾Ð´Ð¾Ð¼ SOLPS-ITER Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÑÐµÑ, ÑÑÐ¾ Ar Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð¿Ð¾Ð´ÑÐ¾Ð´ÑÑÐµÐ¹ Ð°Ð»ÑÑÐµÑÐ½Ð°ÑÐ¸Ð²Ð½Ð¾Ð¹ Ð¸Ð·Ð»ÑÑÐ°ÑÑÐµÐ¹ Ð¿ÑÐ¸Ð¼ÐµÑÑÑ Ð´Ð»Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ°-ÑÐµÐ°ÐºÑÐ¾ÑÐ° ÐÐ¢Ð­Ð . Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÐºÐ¶Ðµ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð° Ð¿ÑÐ¾ÑÑÐ°Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð´Ð»Ñ Ð¾ÑÐµÐ½ÐºÐ¸ Ð¿ÑÐ¾ÑÐ¸Ð»Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð² ÑÐºÐ²Ð°ÑÐ¾ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¿Ð»Ð¾ÑÐºÐ¾ÑÑÐ¸ Ð½Ð° Ð²Ð½ÐµÑÐ½ÐµÐ¼ Ð¾Ð±Ð²Ð¾Ð´Ðµ Ð² ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐµ. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð¿ÑÐ¾ÑÐ¸Ð»Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½ ÑÑÐµÐ¿ÐµÐ½Ð½Ð¾Ð¹ ÑÑÐ½ÐºÑÐ¸ÐµÐ¹ Ð¾Ñ ÑÐ°Ð´Ð¸Ð°Ð»ÑÐ½Ð¾Ð¹ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°ÑÑ Ð¿ÑÐ¸ Ð¿Ð¾ÑÑÐ¾ÑÐ½Ð½ÑÑ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ°Ñ Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½Ð¾Ð³Ð¾ Ð¿ÐµÑÐµÐ½Ð¾ÑÐ°. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐ¹ Ð¿ÑÐ¾ÑÐ¸Ð»Ñ Ð´Ð°ÐµÑ Ð±Ð¾Ð»ÐµÐµ Ð¼ÐµÐ´Ð»ÐµÐ½Ð½ÑÐ¹ ÑÐ°Ð´Ð¸Ð°Ð»ÑÐ½ÑÐ¹ ÑÐ¿Ð°Ð´ Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ ÑÐºÑÐ¿Ð¾Ð½ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸ÐµÐ¹, ÐºÐ¾ÑÐ¾ÑÐ°Ñ ÑÐ¸ÑÐ¾ÐºÐ¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÑÑÑ Ð´Ð»Ñ Ð¾ÑÐµÐ½ÐºÐ¸ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð² ÑÐºÐ²Ð°ÑÐ¾ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¿Ð»Ð¾ÑÐºÐ¾ÑÑÐ¸. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐµ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¿ÑÐ¾ÑÐ¸Ð»Ð¸ ÑÐ¾Ð³Ð»Ð°ÑÑÑÑÑÑ Ñ Ð¿ÑÐ¾ÑÐ¸Ð»ÑÐ¼Ð¸, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¼Ð¸ Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð´Ð»Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð²Â ITER, JET Ð¸ ASDEX-Upgrade. ÐÐ½Ð¸ ÑÐ°ÐºÐ¶Ðµ ÑÐ¾Ð³Ð»Ð°ÑÑÑÑÑÑ Ñ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð¿ÑÐ¾ÑÐ¸Ð»ÑÐ¼Ð¸ Ð¢Ð¾Ð¼ÑÐ¾Ð½ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ°ÑÑÐµÑÐ½Ð¸Ñ Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ¾Ð² JET Ð¸ ASDEX-Upgrade. ÐÐ½Ð°Ð»Ð¸Ð· Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ SOLPS-ITER Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÐµÑ, ÑÑÐ¾ ÑÑÐµÑ Ð±Ð¾Ð»ÐµÐµ ÑÐ»Ð¾Ð¶Ð½ÑÑ ÑÑÑÐµÐºÑÐ¾Ð², ÑÐ°ÐºÐ¸Ñ ÐºÐ°Ðº Ð¾Ð±Ð¼ÐµÐ½ ÑÐ½ÐµÑÐ³Ð¸ÐµÐ¹ Ñ Ð¸Ð¾Ð½Ð°Ð¼Ð¸, ÐºÐ¾Ð½Ð²ÐµÐºÑÐ¸Ð²Ð½ÑÐ¹ Ð¿ÐµÑÐµÐ½Ð¾Ñ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð¸ Ñ. Ð´. Ð¼Ð¾Ð¶ÐµÑ Ð¸Ð·Ð¼ÐµÐ½Ð¸ÑÑ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð²Ð½Ð¾ÑÑ Ð¿Ð¾Ð¿ÑÐ°Ð²ÐºÐ¸ Ð¿Ð¾ÑÑÐ´ÐºÐ° ÐµÐ´Ð¸Ð½Ð¸ÑÑ, Ð½Ð¾ Ð½Ðµ Ð¸Ð·Ð¼ÐµÐ½Ð¸Ñ ÐµÐ³Ð¾ ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾.
description: The given work is devoted to numerical modelling and analysis of Ar, N and Ne seeded discharges for H-mode conditions on ASDEX Upgrade and for burning plasmas on ITER. It is shown that Ar and N are well retained in the divertor, and the number of radiating impurities (measured as the seeding rate atom/s and as the average impurity density at the separatrix) needed to achieve the same conditions in the divertor is lower for Ar than for N. This is due to almost equal values of the first ionization potential of Ar and N in comparison with Ne and the higher radiation efficiency of Ar. With a fraction of radiating power in the simulation domain of about 50%, which is sufficient to achieve a partial detachment at the outer divertor target for both machines, the radiation losses from the confinement region for ITER with Ar are small, about 6%. The average Ar concentration at the separatrix is 0.4%, which is noticeably lower than for N and Ne. Thus, in terms of outer divertor target power handling, simulations by SOLPS-ITER code demonstrate that Ar can be a alternative radiative impurity for the ITER tokamak-reactor. In this work also a simple analytical model for estimation of the electron temperature profile in the tokamak outer midplane (OMP) is suggested. It is shown that the electron temperature profile can be approximated by a power function of the radial coordinate for constant radial transport coefficients. The obtained profile gives a slower radial decay compared to the exponential approximation, which is widely used to estimate the OMP electron temperature. It is shown that this analytical solution is in good agreement with simulation profiles for ITER, JET and ASDEX-Upgrade (AUG). They also agree with the experimental Thomson scattering profiles from the JET and ASDEX-Upgrade. Analysis based on SOLPS-ITER simulations shows that accounting of more complex effects, such as energy exchange with ions, convective energy fluxes, etc. can change the quantitatively obtained solution of the order of unity but will not change it qualitatively.