When solar wind encounters a magnetosphere and is spread out into the bow shock, what happens to the introduced magnetized plasma when it reaches the end of said bow shock? Does it just float there on the magnetosphere? Having plasma just chilling there seems somewhat bad, or is that fine?
The Earth’s bow shock deflects the solar wind. Once the solar wind reaches the end of the bow shock, it speeds back up, so it is always in motion. The solar wind doesn’t pose any serious threat to us on Earth. Even when large solar storms occur (like coronal mass ejections), these don’t pose any danger to us directly because high-energy particles in the storm are deflected by Earth’s atmosphere. However, large solar storms can temporarily disturb Earth’s magnetic field, which can disrupt satellites, telecommunications, and power grids. Such large storms are only rare events, and are not representative of the solar wind.