# Thread: Thermal speed versus bulk speed

1. ## Thermal speed versus bulk speed

This paper "The Solar Wind and Heliosphere" (PDF) mentions on page 5, regarding the Solar Wind:
An ion’s thermal speed is small (~45 km·s-1) so its bulk speed (~450 km·s-1) determines the time (4 days) it takes to reach Earth.
• What's the difference between thermal speed and bulk speed? (the physics, not numerically)
• Is the thermal speed a component of the bulk speed?
• Or are they measuring different physical properies?

2. The thermal speed is how fast proton are bouncing off other solar wind protons. Bulk speed, is how fast they are collectively traveling away from the Sun.

3. Makes sense. Thanks.

4. The bulk speed is basically what you would normally consider to be the flow speed of the gas. It is basically the average of the velocities of all of the particles. The thermal speed is the residual once the bulk speed component is removed. It is basically the random motion due to temperature, and as such, the thermal speed determines the temperature of the gas.

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That would make complete sense to me in a dense gas like
Earth's atmosphere, where atoms are bumping into each other
frequently, but as I understand it (and what the linked PDF says),
the solar wind is exceedingly rarefied. The PDF says 6.6 protons
per cubic centimetre. It also explicitly states that "proton-proton
collision times are long compared to the transit time from the sun"
and gives that average time as 4 x 10^6 s (four million seconds,
or 46 days). With such infrequent collisions, how can it have a
thermal speed that is distinguishable from the bulk speed?

-- Jeff, in Minneapolis

6. Originally Posted by Jeff Root
With such infrequent collisions, how can it have a
thermal speed that is distinguishable from the bulk speed?
I'm guessing that the thermal speed is superimposed on the bulk speed, and is acquired in the Sun's denser atmosphere.

7. Originally Posted by Jeff Root
how can it have a thermal speed that is distinguishable from the bulk speed?
Whether in a given situation it has time to undergo many collisions, in principle one can define the two velocities from the distribution of individual values for the particles - essentially, bulk flow is the mean velocity, thermal velocity is the standard deviation about the mean. So you could have a flow of particles which is at high speed in some reference frame, while in comparison the internal velocities are tiny so that in its own frame the material is "cold". An example would be the jets of SS 433, which have a bulk velocity of 0.26c and a thermal velocity no more than tens of km/s.

8. Even in an extremely rarefied gas, you can still take the mean velocity of all of the particles. That is always the bulk velocity. Once you have determined this mean, you can then subtract it from each particle's individual velocity, and the remaining velocity component is the thermal velocity. Collisions aren't actually necessary to define a thermal speed.

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Since the numbers I quoted from the PDF (for the plasma as
it passes Earth's orbit) suggest that collisions are extremely
rare, I surmise that the thermal speed is a measure of how
fast the cloud is expanding. As the cloud expands, the thermal
speed goes down because it is subsumed into the bulk speed,
even if the actual speeds of the particles are unchanged.

-- Jeff, in Minneapolis

10. Greetings,

Originally Posted by ngc3314
Whether in a given situation it has time to undergo many collisions, in principle one can define the two velocities from the distribution of individual values for the particles - essentially, bulk flow is the mean velocity, thermal velocity is the standard deviation about the mean. So you could have a flow of particles which is at high speed in some reference frame, while in comparison the internal velocities are tiny so that in its own frame the material is "cold". An example would be the jets of SS 433, which have a bulk velocity of 0.26c and a thermal velocity no more than tens of km/s.
Quite so. This is the identical situation that one encounters utilizing atomic and molecular beam expansions. The bulk motion is highly collimated in one direction typically propagating at supersonic speeds. Yet the system is cold because of the low dispersion of the particle velocities and is free of collisions. When probed perpendicular to the direction of bulk propagation this allows for sub-Doppler spectral resolution as well as efficient cooling of the vibrational and rotational degrees of freedom of a molecular species. The system is sufficiently cool to allow formation and investigation of van der Waals complexes.

Best regards,
EigenState

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In the case of a solar plasma, the bulk speed is the speed of the bulk, and the thermal speed is the distribution around that bulk. For a blob of solar plasma, the expansion is pretty much controlled by the magnetic field, so it dosent really expand much. The way the variation in bulk speed of each particle is distributed around the bulk speed is the temperature. At absolute zero all particles are travelling at the bulk speed, then as the temperature rises, the velocity distribution becomes gaussian (bell curve) around the bulk speed, with the width of the gaussian being the temp.

Temperature is a pretty iffy concept in a plasma tho. If you have multi-species plasma, all the individual species may have a different temp. At the very least, the ion temp and the electron temp will be different, and if you have more than one type of ion they can have all different temps also.

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The different particles will have different speeds, just like different
atoms in Earth's air, but won't they have the same temperature, just
like Earth's air? (I suspect that you're right, they won't, because
they are ions, not atoms.)

-- Jeff, in Minneapolis

13. In a dense mixture like Earth's air, different species of different mass will have different velocities; collisions drive the combination toward energy equipartition rather than velocity equality. In the absence of other processes, higher-mass particles have a smaller scale height (or the equivalent for star clusters, mass segregation), which enters into the rapid escape of hydrogen and helium from the Earth. However, in complex systems, other processes are very often important. Speaking of "the" temperature is a simplification that doesn't often work very well away from everyday situations. Brightness temperature, ionization temperature, electron temperature, effective temperature, spin temperature...

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Originally Posted by Jeff Root
The different particles will have different speeds, just like different
atoms in Earth's air, but won't they have the same temperature, just
like Earth's air? (I suspect that you're right, they won't, because
they are ions, not atoms.)

-- Jeff, in Minneapolis
They wont have the same temp. In a non-collisional plasma with a set bulk velocity and multiple species, the temp of each individual species can be very different. You should see a relationship between temp and mass with the heavier ions usually being lower temp. It does kinda depend on the mechanism that accelerates the plasma tho. What makes any blob of gas come to a specific temperature is collisions bringing the mix to thermodynamic equilibrium. If you dont have the collisions, you can have different temps.

15. To add to that point, often species with very different masses don't share energy very well, whereas collisions at the same mass do share energy well. So that's why each species can come to its own temperature, without it being the same for other species.

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