[FLASH-USERS] A short note on magnetic field unit [Re: Magnetic field units?]

[dongwook at flash.uchicago.edu]

Dear Nathan,

> Hello,
>
> I'm writing as both a yt developer as well as a user of the unsplit
> staggered mesh solver included in Flash4.  Right now I'm trying to figure
> out the appropriate way to handle unit conversions for the magnetic field.

> It's been brought to my attention that the default parameter choices for
> the unsplit solver will cause FLASH to write the magnetic field to disk in
> 'natural' units (such that mu_0 = 1).  This is different from the value in
> CGS units modulo a factor of order unity.

The FLASH's default unit is cgs for all variables. For example, density,
pressure and velocity are in dyn/cm^2, g/cm^3, cm/sec.  The question is
then what is the unit system for electromagnetic variables?

FLASH uses its convenient unit system "none" for B fields. In this code
unit, factors of 4pi and the speed of light are absorbed into the physical
variables, thus simplifying the Maxwell's equations without mu_0,
epsilon_0, and 4pi. This makes coding lot easier.

In this code unit, B field is not really in gauss, missing sqrt(4pi).
Basically, what you need to do is the conversion as Ji Suoqing replied in
his email (Thanks Suoqing!).

In other words, if you want to answer what is your field strength in FLASH
simulation from reading B_checkpoint, then the answer is

   sqrt(4pi)*B_checkpoint gauss!

The same goes to initial condition. When you initialize in flash.par, say
B_initial = B_x0, then
your initial field in gauss is sqrt(4pi)*B_x0.

> I'd like to know what conversion factor yt should be using internally to
> convert the magnetic fields written to it reads from from plotfiles and
> checkpoint files to CGS units.  According to the user's guide, this is
> controlled by the UnitSystem runtime parameter, so there should be three
> different conversion factors corresponding to the three different choices
> of UnitSystem.

Please find attached a short note I summarized on the units on
electrodynamics.
Hope this helps.

> This conversion is only applicable to the magnetic field in the unsplit
> staggered mesh solver so therefore no such conversion needs to be applied
> for runs using the operator split solvers, correct?

The same rule (as described above) holds for the split 8-wave solver,
including those runtime parameters (e.g., "none", "cgs", "si" in
flash.par) to convert one from the other.

> I'd also like to say that I think it would be better if the unsplit solver
> could handle this conversion internally.  This way outputs would always be
> written in CGS units, as is standard for other FLASH fields, and
> simulations could be initialized with magnetic fields calculated in CGS
> units.

Please have a look at the last two sections in the note. This should
explain what you need to do.

Best,
Dongwook

> Thanks for your help with this,
>
> Nathan Goldbaum
> Graduate Student
> Astronomy & Astrophysics, UCSC
> goldbaum at ucolick.org
> http://www.ucolick.org/~goldbaum
>
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