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Old Jul 22nd 2018, 08:03 AM   #1
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computational particle physics

Hi to all,
I have a random number generator in FORTRAN, which gives a random numbers to my particles initial velocity in three dimension (vx,vy,vz). If, I want to make my particles to embark to move with a specific weight (eg. Maxwellian), what should I do?

absv = sqrt(vx*vx+vy*vy+vz*vz)
wt= absv*absv*exp(-(absv*absv)/(a*a))
(a = sqrt(2*k*t/m))

the random generator produce a number between -1 to 1 for the 3 velocity components. I make the arrangement so the velocity would be around -0.35 to 0.35 for each of them (non-relativistic range).
My code is a test particle code, and I could make it work efficiently for each test particle in both constant and dipolar field (with or without Electric field(acc)), but still I am struggling with making the particles to move based on their initial weight. I don't even know, whether I need to use the Maxwell–Boltzmann speed distribution or Maxwell–Boltzmann velocity distribution which in concept, both are telling the same story but giving me different result.
https://en.wikipedia.org/wiki/Maxwel...n_distribution

BTW, if you simply plot any random numbers based on 'wt' you will get the maxwellian speed distribution as an output. I want to know, how can I make the 'wt' to be effective as a probability of particles initial distribution in my code.
any suggestion is appreciated
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Old Jul 23rd 2018, 05:56 AM   #2
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The Fortran (pseudo) random number generator generates a uniform distribution from where 0.0<=R<1.0.
From your description I am guessing you have simply shifted this to give a uniform distribution where -0.35<=R<0.35
While what you actually want is the (Gaussian) shaped distribution indicated by your "wt" function.

I know that this can be done, but I have never actually done it myself...

The links I have found all seem to say "this is simple" but then go on to obfuscate the solution.
Try: <Wikipedia: Box-Muller Transform>
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Old Jul 23rd 2018, 07:06 PM   #3
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Originally Posted by Woody View Post
The Fortran (pseudo) random number generator generates a uniform distribution from where 0.0<=R<1.0.
From your description I am guessing you have simply shifted this to give a uniform distribution where -0.35<=R<0.35
While what you actually want is the (Gaussian) shaped distribution indicated by your "wt" function.

I know that this can be done, but I have never actually done it myself...

The links I have found all seem to say "this is simple" but then go on to obfuscate the solution.
Try: <Wikipedia: Box-Muller Transform>
Thanks for your reply.
I have generated those numbers by using a self made function, Not some pseudo generator. I need to give my particles an specific ID's apart from just giving them random velocity. plus their distribution is not uniform in this domain (-0.35 up to 0.35).

Before I run the code, I need my particle to gain weight initially. If you plot the generated velocity over 'wt', you can find out that they follow the maxwellian, as I mentioned. The question simply comes down to a point that, how to make particles to gain initial weight? what should be done?

Modifying the way that I produce those random numbers won't be the appropriate solution for that. later I may need to change the maxwellian to another type of distribution (eg. loss cone ), So the concept is what I am looking for which can be used in different situation.
please let me know if you have any suggestions.
Thanks.

Last edited by mehdi6; Jul 23rd 2018 at 07:09 PM.
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