The solar wind is a supersonic, hydromagnetic flow of plasma originating in the solar corona. At the radius of Earth’s orbit, the wind’s density is ρ ∼ 6 × 10⁻²¹ kgm⁻³, its velocity is v ∼ 400 km s⁻¹, its temperature is T ∼ 10⁵ K, and its magnetic field strength is B ∼ 1nT.

(a) By balancing the wind’s momentum flux with the magnetic pressure exerted by Earth’s dipole magnetic field, estimate the radius above Earth at which the solar wind passes through a bow shock (Fig. 17.2).

(b) Consider a strong perpendicular shock at which the magnetic field is parallel to the shock front. Show that the magnetic field strength will increase by the same ratio as the density, when crossing the shock front. Do you expect the compression to increase or decrease as the strength of the field is increased, keeping all of the other flow variables constant?

Figure 17.2.

Transcribed Image Text:

Sun 400 km s-¹ Earth bow shock