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 $1.5 \times 10^{5}$ K and ion temperature $5\times 10^{4}$ 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 $\nu_{c}$ for Coulomb collisions (i.e., electromagnetic scattering by point charges) of thermal electrons and ions (Use $\nu_{c,\alpha}^{-1} = 0.27 T_{\alpha}^{3/2} (m_{\alpha}/m_{e})^{1/2} / (\ln \Lambda_{\alpha} n_{\alpha})$, where $\Lambda_{\alpha}$ is the Gaunt factor given by $8\times 10^{6} T_{\alpha} / n_{\alpha}^{1/2}$ and $n_{\alpha}$ 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 $10 c/\omega_{pe}$.

(a)

Sketch this situation.

(b)

Calculate the direction and magnitude of the solar wind's convection electric field and the associated $E\times B$ drift velocity.

(c)

Calculate the direction and magnitudes of any plasma drifts undergone by an electron which initially has $v_{\parallel} = 3 v_{\perp} = 5 \times 10^{6}$ 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 $v_{\perp}$ after interacting with the shock?