The solar wind is a quasi-spherical outflow of plasma from the Sun. At the radius of Earth’s orbit, the mean proton and electron densities are n_p ∼ n_e ∼ 4 × 10⁶ m⁻³, their temperatures are T_p ∼ T_e ∼ 10⁵ K, and their common radial fluid speed is ∼400 km s⁻¹. The mean magnetic field strength is ∼1nT. Eventually, the radial momentum flux in the solar wind falls to the value of the mean interstellar pressure, ∼10⁻¹³Nm⁻², and a shock develops.

(a) Estimate the radius where the shock develops.

(b) The solar system moves through the interstellar medium with a speed∼30 kms⁻¹. Sketch the likely flow pattern near this radius.

(c) How do you expect the magnetic field to vary with radius in the outflowing solar wind? Estimate its value at the termination shock.

(d) Estimate the electron plasma frequency, the ion-acoustic Mach number, and the proton Larmor radius just ahead of the termination shock front, and comment on the implications of these values for the shock structure.

(e) The Voyager 1 spacecraft was launched in 1977 and is traveling radially away from the Sun with a terminal speed ∼17 km s⁻¹. It was observed to cross the termination shock in 2004, and in 2012 it passed beyond the limit of the shocked solar wind into the interstellar medium. The Voyager 2 spacecraft passed through the termination shock a few years after Voyager 1. How do these observations compare with your answer to part (a)?