**Assignment 1 for the course Solar and Space Physics**

- 1.
- Typical parameters for the solar wind at 1 AU are: speed 450 km s
^{-1}, number density 7 cm^{-3}, magnetic field strength 3 nT, electron temperature K and ion temperature K. Looking up any required definitions, calculate the following quantities:- (a)
- the solar wind plasma frequency,
- (b)
- the electron and ion thermal speeds,
- (c)
- the electron and ion Debye lengths,
- (d)
- the gyrofrequency and gyroperiod for thermal electrons and ions,
- (e)
- the frequencies
for Coulomb collisions (i.e., electromagnetic scattering
by point charges) of thermal electrons and ions (Use
,
where
is the Gaunt factor given by
and
is given in cm
^{-3}.), - (f)
- the mean free path for thermal electrons and ions in the solar wind,
- (g)
- and the distance the solar wind convects during one collision time for each species.
- (h)
- Finally, comment on the collisionality of the solar wind at 1 AU and the number of electrons per Debye sphere.

- 2.
- For one period the solar wind is flowing radially away from the Sun
with a speed of 450 km s
^{-1}and number density of 7 cm^{-3}. The solar wind magnetic field strength is 3 nT directed at a 45 degree angle to the Earth-Sun line in the ecliptic plane. Consider the portion of Earth's bow shock closest to the Sun and assume a locally planar approximation. Suppose that the magnetic field increases by a factor of 4 across the shock with constant normal component, in a distance of .- (a)
- Sketch this situation.
- (b)
- Calculate the direction and magnitude of the solar wind's convection electric field and the associated drift velocity.
- (c)
- Calculate the direction and magnitudes of any plasma drifts undergone by
an electron which initially has
m s
^{-1}as it moves up the shock ramp. - (d)
- How far and in what direction must the electron drift to increase its kinetic energy by a factor of 4?
- (e)
- Is this electron reflected from the shock or is it transmitted? What is its value of after interacting with the shock?