# "Thermal speed"--need a definition



## Macfury (Feb 3, 2006)

When one speaks of "thermal speed"of a particle, how does it differ from plain old speed? I've looked for a definition online but haven't found anything basic enough. Any physic types ou there?


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## gordguide (Jan 13, 2001)

You usually see it when discussing some unusual subatomic phenomenae; it's part of the Big Bang Theory, and you see it when discussing Plasmas, Particle Accelerators, Space Travel, etc.

For example with accelerators is the speed at which some very short lived particles can be observed, and since that involves firing particles at a target, it's probably some plasma effect anyway.

In formulas it's usually:
V
<i>th</i>

I think it refers to one of the possible wave speeds (there is the sound speed, the light speed, and the thermal speed); you see it referred to when there are multiple waves at different speeds acting on something, eg "three wave interactions in warm plasmas".

I don't really understand how exactly it differs from the two more common ones but Plasmas always gave me trouble anyway. I do know that Plasmas need more than the "normal" three parameters you need to define (pressure, density, temperature), so my guess is thermal speed is one of the other parameters. It's probably not an issue with normal states of matter, which is perhaps why you don't see it much. That should give you a start, though.

UPDATE: Found this:
" ...
According to a general principle of statistical mechanics called the H-theorem, the Maxwellian distribution is the unique distribution function that arises when a gas is in thermal equilibrium [Huang, 1963]. For a plasma in thermal equilibrium, not only should the distribution function for each species be a Maxwellian but the temperature of all species must be equal. However, because collisions occur very infrequently in a tenuous plasma, the approach to thermal equilibrium is often very slow. Therefore, non-equilibrium effects are quite common in plasmas. Since the electron and ion masses are very different, the rate of energy transfer between electrons and ions is much slower than between electrons or between ions. Therefore, when a plasma is heated, substantial temperature differences often develop between the electrons and ions. Non-equilibrium distributions also occur when an electron beam or an ion beam is injected into a plasma. Under these circumstances the velocity distribution function of the beam usually cannot be represented by a Maxwellian distribution. Such non-thermal distributions produce many interesting effects that will be discussed later.
..."

So, it would seem, the "normal state" thermal speed is at equilibrium, but you have to account for the distribution of thermal speeds with Plasma states.


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## Macfury (Feb 3, 2006)

Thanks, Gord, that gives me a lead. Most of the internet references go right into it without framing the meaning.


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## MacDoc (Nov 3, 2001)

Some info here

http://idol.union.edu/~malekis/ESC24/KoskywebModules/sl_nano4.htm

But mostly plasma related elsewhere - even Wiki is MIA.

This problem might give a direction at least



> Consider a disk of large planetesimals, containing a large number of Moon-sized bodies. All planetesimals exert gravitational perturbations on their neighbors, who from time to time fly by close to their surface. Estimate the typical vertical component of the post-encounter velocity, (let it approximately equal the escape speed from the surface of the perturbing bodies). Estimate minimum thickness of the disk of meteoroids (small bodies that can be detected in infrared), assuming that their inclinations are not damped by any effects (gas drag, collisions).
> 
> Hint: recall the relation between the disk scale height H (thickness) and (vertical) *velocity dispersion of disk particles, that velocity being called "thermal speed v_T" or "soundspeed c" in case of gas but playing the same role*


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## da_jonesy (Jun 26, 2003)

Macfury said:


> When one speaks of "thermal speed"of a particle, how does it differ from plain old speed? I've looked for a definition online but haven't found anything basic enough. Any physic types ou there?


from the source you love to hate...

http://en.wikipedia.org/wiki/Ambipolar_diffusion

http://en.wikipedia.org/wiki/Plasma_oscillation

By referring to the context of galactic disks, we find another important element that is generally overlooked in the discussion of the energy balance equations for accretion disks. This is the distinction between thermal speed and _effective_ thermal speed. In practice, the effective thermal speed entering the dynamical equations may be higher than the thermal speed entering the radiation equations. The interstellar medium of galaxy disks is a cloudy medium, for which the thermal speed associated with the temperature of the clouds is much smaller than the velocity dispersion of the cold gas clouds. It is the latter that sets the appropriate effective thermal speed relevant to the dynamics of the disk. When a fluid model of the interstellar medium is adopted, in studies of disk dynamics, the numbers that are used for the equivalent acoustic speed are then those applicable to the turbulent speed characteristic of the cloudy medium. Therefore, one important cooling mechanism is that associated with the inelastic collisions between gas clouds. Mechanisms of this kind may operate also in accretion disks, but they are usually ignored (but see Quataert & Chiang 2000).


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## Macfury (Feb 3, 2006)

Thanks guys, much appreciated.


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