title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÑÑÑÐºÑÑÑÑ Ð³Ð¾Ð»Ð¾Ð²Ð½Ð¾Ð¹ ÑÐ´Ð°ÑÐ½Ð¾Ð¹ Ð²Ð¾Ð»Ð½Ñ ÐÐµÐ¼Ð»Ð¸ Ð² Ð¿ÐµÑÐ¸Ð¾Ð´Ñ ÑÐ»Ð°Ð±Ð¾Ð³Ð¾ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»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 structure of the Earths bow shock wave during periods of weak magnetic field
Creators: name: ÐÐ°ÑÑÐ¾ÑÐ¾Ð²Ð°, ÐÐ°ÑÑ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: 2024
Subjects: ÑÐ´Ð°ÑÐ½ÑÐµ Ð²Ð¾Ð»Ð½Ñ
Ð¼Ð°Ð³Ð½Ð¸ÑÐ¾ÑÑÐµÑÐ° ÐÐµÐ¼Ð»Ð¸
Ð±ÐµÑÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²Ð¸ÑÐµÐ»ÑÐ½Ð°Ñ Ð¿Ð»Ð°Ð·Ð¼Ð°
Ð³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ðµ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ ÑÐµÐ¾ÑÐ¸Ñ
Ð¸Ð¾Ð½Ð½Ð°Ñ Ð²ÐµÐ¹Ð±ÐµÐ»ÐµÐ²ÑÐºÐ°Ñ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ
Ð°Ð»ÑÑÐ²ÐµÐ½Ð¾Ð²ÑÐºÐ°Ñ Ð¸Ð¾Ð½Ð½Ð¾-ÑÐ¸ÐºÐ»Ð¾ÑÑÐ¾Ð½Ð½Ð°Ñ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ
shock waves
Earths magnetosphere
collisionless plasma
hybrid kinetic modeling
linear theory
ion Weibel instability
Alfven ion-cyclotron instability

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¸ÑÐ¾Ð´Ñ ÑÐ¸Ð»ÑÐ½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð²Ð±Ð»Ð¸Ð·Ð¸ ÑÑÐ¾Ð½ÑÐ° Ð³Ð¾Ð»Ð¾Ð²Ð½Ð¾Ð¹ ÑÐ´Ð°ÑÐ½Ð¾Ð¹ Ð²Ð¾Ð»Ð½Ñ ÐÐµÐ¼Ð»Ð¸ Ð² Ð¾Ð±Ð»Ð°ÑÑÑÑ ÑÐ¾ ÑÐ»Ð°Ð±ÑÐ¼ (Ð¼ÐµÐ½ÐµÐµ 10 Ð½Ð¢) Ð¼ÐµÐ¶Ð¿Ð»Ð°Ð½ÐµÑÐ½ÑÐ¼ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÐ¼ Ð¿Ð¾Ð»ÐµÐ¼. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»Ð¾ÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ð³Ð¾ ÐºÐ¾Ð´Ð° âMaximusâ, Ð² ÐºÐ¾ÑÐ¾ÑÐ¾Ð¼ Ð´Ð»Ñ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ Ð±ÐµÑÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð¹ Ð¿Ð»Ð°Ð·Ð¼Ñ ÑÐ°Ð¼Ð¾ÑÐ¾Ð³Ð»Ð°ÑÐ¾Ð²Ð°Ð½Ð½Ð¾ ÑÐµÑÐ°ÑÑÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐÐ»Ð°ÑÐ¾Ð²Ð° Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÐÐ°ÐºÑÐ²ÐµÐ»Ð»Ð° Ð½Ð° ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð´ÐµÐºÐ°ÑÑÐ¾Ð²Ð¾Ð¹ ÑÐµÑÐºÐµ. ÐÐ¾Ð´ÐµÐ»Ñ Ð¾ÑÐ½Ð¾Ð²ÑÐ²Ð°Ð»Ð°ÑÑ Ð½Ð° Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ñ ÑÐ´Ð°ÑÐ½ÑÑ Ð²Ð¾Ð»Ð½, Ð½Ð°Ð±Ð»ÑÐ´ÐµÐ½Ð½ÑÑ ÑÐ¿ÑÑÐ½Ð¸ÐºÐ°Ð¼Ð¸ MMS. ÐÑÐ»Ð¸ ÑÐ¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ñ ÑÑÐ¸ ÑÐ´Ð°ÑÐ½ÑÐµ Ð²Ð¾Ð»Ð½Ñ, Ð¿ÐµÑÐ²Ð°Ñ Ð¸Ð· ÐºÐ¾ÑÐ¾ÑÑÑ Ð¸Ð¼ÐµÐ»Ð° Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ðµ ÑÐµÐ¿Ð»Ð¾Ð²Ð¾Ð³Ð¾ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ðµ Ðº Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð¼Ñ Ð¿ÐµÑÐµÐ´ ÑÑÐ¾Ð½ÑÐ¾Ð¼ Î² = 68, Ð° Ð´Ð²Ðµ Ð´ÑÑÐ³Ð¸Ðµ Ð¸Ð¼ÐµÐ»Ð¸ Î² = 3, Ð¸ Ð¾ÑÐ»Ð¸ÑÐ°Ð»Ð¸ÑÑ ÑÐ³Ð»Ð°Ð¼Ð¸ Ð½Ð°ÐºÐ»Ð¾Ð½Ð° Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ðº Ð½Ð¾ÑÐ¼Ð°Ð»Ð¸ ÑÑÐ¾Ð½ÑÐ° (Î¸ = 50Â° Ð¸ Î¸= 75Â°). Ð¡Ð¾Ð¿Ð¾ÑÑÐ°Ð²Ð»ÑÑ Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°Ð½Ð¸Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸ Ð¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ (Ð´Ð¸ÑÐ¿ÐµÑÑÐ¸Ð¾Ð½Ð½ÑÐµ ÐºÑÐ¸Ð²ÑÐµ, Ð¿Ð¾Ð»ÑÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð¸ ÑÐºÐ¾ÑÐ¾ÑÑÑ Ð²Ð¾Ð»Ð½ Ð²Ð±Ð»Ð¸Ð·Ð¸ ÑÑÐ¾Ð½ÑÐ°), ÑÐ´Ð°Ð»Ð¾ÑÑ Ð¸Ð´ÐµÐ½ÑÐ¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°ÑÑ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸, Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÑÑÐ¸Ðµ ÑÑÑÑÐºÑÑÑÑ ÑÑÐ¾Ð½ÑÐ°. ÐÑÐ»Ð¾ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð² Ð¿Ð¾Ð´Ð½Ð¾Ð¶Ð¸Ð¸ ÑÐ´Ð°ÑÐ½Ð¾Ð¹ Ð²Ð¾Ð»Ð½Ñ Ð¼Ð¾Ð³ÑÑ ÑÐ°ÑÐºÐ°ÑÐ¸Ð²Ð°ÑÑÑÑ Ð¾Ð´Ð½Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾ Ð¸Ð¾Ð½Ð½Ð°Ñ Ð²ÐµÐ¹Ð±ÐµÐ»ÐµÐ²ÑÐºÐ°Ñ Ð¸ Ð°Ð»ÑÑÐ²ÐµÐ½Ð¾Ð²ÑÐºÐ°Ñ Ð¸Ð¾Ð½Ð½Ð¾-ÑÐ¸ÐºÐ»Ð¾ÑÑÐ¾Ð½Ð½Ð°Ñ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸, ÑÐ¾Ð·Ð´Ð°ÑÑÐ¸Ðµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð°Ñ Ð²ÐµÑÐ²Ñ, Ð²ÑÐ·ÑÐ²Ð°ÑÑÐ°Ñ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¸ ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ. ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð¾, ÑÑÐ¾ ÑÑÑÑÐºÑÑÑÐ° ÑÑÐ¾Ð½ÑÐ° Ð¾ÑÐ»Ð¸ÑÐ°ÐµÑÑÑ Ð´Ð»Ñ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ ÑÐ³Ð»Ð° Ð½Ð°ÐºÐ»Ð¾Ð½Ð° Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ðº Ð½Ð¾ÑÐ¼Ð°Ð»Ð¸ Ðº ÑÑÐ¾Ð½ÑÑ 50Â° Ð¸ 75Â°, ÑÐ¾ ÐµÑÑÑ Ð´Ð¾Ð¼Ð¸Ð½Ð¸ÑÑÑÑÐ°Ñ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ Ð·Ð°Ð²Ð¸ÑÐ¸Ñ Ð½Ðµ ÑÐ¾Ð»ÑÐºÐ¾ Ð¾Ñ Î², Ð½Ð¾ Ð¸ Ð¾Ñ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸Ð¸ ÑÐ´Ð°ÑÐ½Ð¾Ð¹ Ð²Ð¾Ð»Ð½Ñ.
description: The given work is devoted to the study of the nature of strong fluctuations in the magnetic field near the front of the Earths bow shock wave in areas with a weak (less than 10 nT) interplanetary magnetic field. The study was carried out using the kinetic hybrid code âMaximusâ, in which the Vlasov equation and Maxwell equations are self-consistently solved on a three-dimensional Cartesian grid to describe a collisionless plasma. The model was based on the parameters of shock waves observed by MMS satellites. Three shock waves were modeled, the first of which had the ratio of thermal pressure to magnetic in front of the front Î² = 68, and the other two had Î² = 3, and differed in the angles of inclination of the magnetic field to the front normal (Î¸ = 50Â° and Î¸= 75Â°). By comparing the predictions of linear theory and the results of modeling (dispersion curves, polarization and wave velocity near the front), it was possible to identify the instabilities that determine the structure of the front. It has been shown that at the foot of the shock wave, the ion Weibel and Alfven ion-cyclotron instability can swing simultaneously, creating fluctuations in the magnetic field, as well as a potential branch causing fluctuations in density and electric field. Modeling has shown that the structure of the front differs for the values of the angle of inclination of the magnetic field to the front normal of 50Â° and 75Â°, that is, the dominant instability depends not only on Î², but also on the geometry of the shock wave.