# What is the difference between bulk speed and thermal speed in solar wind plasma?

in solar wind plasma different species has different thermal speed but all having same bulk speed. why it is so? and in solar wind is the thermal speed is just the standard deviation around the bulk speed?

## 2 Answers

Think of the atmosphere on Earth. On a calm day, particles in the air are moving; they have a temperature, which, for our purposes, is a measure of the average kinetic energy of the particles, and therefore their average speed. We can think of the thermal speed as the speed of individual particles because of their kinetic energy.

Now let's say things get breezy. Now you have parcels of air moving faster in a given direction. The bulk speed is the speed of this breeze as a whole, not taking into account the motion of each particle.

The analogy holds for the solar wind. A clump as a whole has a certain velocity, the magnitude of which is the bulk speed. Inside that clump, individual particles move around at different speeds depending on their species; these are the thermal speeds.

What is the difference between bulk speed and thermal speed in solar wind plasma?

The short answer is that the former is the first velocity moment of the particle velocity distribution function (e.g., Maxwellian) and the latter derives from the second velocity moment.

I wrote a detailed explaination of the various speeds of sound in space at https://physics.stackexchange.com/a/179057/59023.

in solar wind plasma different species has different thermal speed but all having same bulk speed.

Actually, this is not entirely true. Generally we find that the solar wind, on average, satisfies a so called zero current condition given by: $$\sum_{s} \ q_{s} \ n_{s} \mathbf{v}_{s} = 0$$ where $q_{s}$ is the charge of species $s$, $n_{s}$ is the number density of species $s$, and $\mathbf{v}_{s}$ is the bulk flow velocity of species $s$ in the center of momentum frame for the entire plasma. We find that even for electrons, the cold, dense core drifts relative to the hot, tenuous halo population, i.e., $\mathbf{v}_{ec} \neq \mathbf{v}_{eh}$.

and in solar wind is the thermal speed is just the standard deviation around the bulk speed?

As I stated at https://physics.stackexchange.com/a/179057/59023, the most common form of the thermal speed used is the most probable speed given by: $$V_{Ts}^{mps} = \sqrt{\frac{ 2 \ k_{B} \ T_{s} }{ m_{s} }}$$ where $k_{B}$ is Boltzmann's constant, $T_{s}$ is the average temperature of species $s$, and $m_{s}$ is the mass of species $s$.