# A CGS units confusions in plasma physics journal papers

1. Feb 8, 2019

### cmb

Hi,

I was wondering of those who might write papers in this field.

What is the convention of units in plasma physics papers, and is this often all screwed around and you have to already understand it to understand it?

I'll give you an example, because I am looking at this paper to understand thermalisation times-
https://descanso.jpl.nasa.gov/SciTechBook/series1/Goebel_AppF_Electron.pdf

In the opening line it says-
Spitzer derived an expression for the slowing-down time of test particles (primary electrons in our case) with a velocity v = root[2Vp/m] , where eVp is the test particle energy....

So what units is that in? If it is cgs units, then is 'e' in MeV, yet the rest of the article references eV? Or maybe it is Rybergs? Or is it statcoulombs? None of those seem to work, MeV is the only unit that works for v in cm/s and Vp in eVs?

What am I missing here?

There is another paper I can link to later that also says it is cgs units, but if you feed in all the numbers in cgs and compare with the graph it shows in the paper, the axes are out by 3 OOM.

I get the impression, please do disabuse me of this idea, that much of plasma physics is 'theoretical' and the equations become sufficiently abstract that they lose all their constants and it is not possible to really know what system of units the equations represent, unless you already understand it.

Would I be overstating the case that any equation involving physical quantities should clearly state what units of measurement those physical variables use?

It is OK in most fields of physics of course, but when it comes to electricity and magnetism that plasma physics papers rel

2. Feb 8, 2019

### jasonRF

To me it looks like that particular equation has a typo. It appears to come from equating kinetic and potential energy: $\frac{1}{2}m\, v^2 = e \, V_p$ where $V_p$ is a voltage, so $v = \sqrt{\frac{2 \, e\, V_p}{m}}$. If you use consistent units you should get the correct result.

Clearly that appendix is from an online book - when I glance at the plasma physics chapter it is clear that the author is using MKS for general equations, and when providing numerical equations seems to be good about specifying the units. But having said that, it is common in plasma physics to use "convenient" units when discussing a plasma. Just because an author indicates that a plasma has a "temperature" of 10 eV doesn't mean that you insert values in eV wherever you see $k_B T$; you use the units that the author uses (in this case, $T$ in Kelvin); it is up to you to convert the convenient units to the units used when deriving the equations. Likewise, it is common to specify densities in $cm^{-3}$ even if using MKS, and the reader just needs to convert the quantity to MKS ($m^{-3}$) before plugging into the equations.

Can it be confusing at times? Sure - especially for authors that don't write well. But usually it is pretty straightforward.

Try re-working your numbers and see what you get. If you still have a problem you should probably look at the Spitzer reference, and show us more detail of your calculations.

jason

3. Feb 8, 2019

### jasonRF

To directly address your concerns/questions:
Not true. My grad work was all in experimental plasma physics, and it was usually straightforward to calculate numbers from the theory to compare with our measurements. Are there some poorly written plasma physics papers that are not clear? Of course. But that is true in every field.

Yes. If they state units after every equation it would be intolerable to read. If an author clearly indicates the units at the appropriate time in the exposition, it shouldn't need to be repeated for every equation thereafter. If an author uses the same units throughout a book, they shouldn't need to specify it all over again in every appendix.

Edit: Now I am thinking that I misunderstood you. Should it be clear what units the author is using? Of course. Does that always happen in plasma physics? No. But still seems unreasonable to expect an author to restate all of the assumptions used throughout a book in every appendix.

jason

Last edited: Feb 8, 2019
4. Feb 9, 2019

### cmb

I already anticipated the absence of the 'e', but what is the 'e'? This is my confusion.

If I calculate, say, velocity of a 10keV proton in what I understand are cgs units, it looks like;
v = sqrt [(2 x 4.8e-10 esu/eV x 10000eV)/(1.6e-24g)] = 2.45e9 cm/s

which is clearly going to be wrong because 'esu's don't relate to eVs

The answer is nice and simple in SI, once converted, and I have no problem with this at all, it is all completely logical
v= sqrt [(2 x 1.6e-19J/eV x 10000eV)/(1.6e-27g)] = 1.4 Mm/s

So I can now calculate this 'cgs unit' and I find it to be;
e = [(1.6e-27g)*(1.4e8cm/s)^2]/[(2 x 10000eV] = 1.6e-12 g.cm^2/eV.s^2

I have not seen "1.6e-12 g.cm^2/eV.s^2" in the description of the elementary charge in cgs units. But unless you use that for 'e' in the equation above, it doesn't give the right answer?

Why use eV at all? I thought the Rydberg the unit of charge in cgs?

5. Feb 9, 2019

### cmb

I guess all I am asking you to tell me is what the consistent set of units are to assume, in physics papers and documents like this, if the units are not clarified in a physics paper (because, as you say, it doesn't always happen)?

6. Feb 13, 2019 at 10:57 AM

### f95toli

Note that you have to be careful here with what you refer to as "system of units".
A paper can be written using the SI system (aka MKS) and still give all numerical values in units of say cm, eV or whatever is convenient. All constants in the equations (e, Kb etc) will still have their SI values.

If the paper is written using the CGS system of units the constants will have different numerical values and the equations will NOT be identical to the equations you would use if the SI system was used (typically the equations differ by factors of c, c^2 and pi; you can't always figure it out from analyzing the dimensions).

Nowadays it is very rare for papers to be written using CGS unit but there are indeed fields where it is still used (e.g. magnetics)
This is not only because of convention; after the re-definition of the SI this spring there will -AFAIK- strictly speaking be no way to convert between the two , in the CGS system of units the permeability of vacuum is equal to unity, but in the new SI (new Ampere with a fixed value of e) it is is a measurable quantity so does not have a precise value. That is, stop using CGS

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