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Particle tracing and incorrect electromagnetic equation of motion

Posted May 9, 2012, 3:28 p.m. EDT 2 Replies

Anthony Ashmore
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Hello all. I was wondering if anyone could clear up a problem concerning the 'Particle Tracing with Mass' plotting. I have computed a background EM field with cylindrical symmetry and I would like to trace the path of an electron through it. However I am slightly uneasy about the equations of motion being used to calculate the force on the particle - these are the equations suggested by COMSOL for EM forces.

Fr = (mf.Er+mf.Bz*r*partv-mf.Bphi*partw)*partq
Fphi = (mf.Ephi-mf.Bz*partu+mf.Br*partw)*partq
Fz = (mf.Ez+mf.Bphi*partu-mf.Br*r*partv)*partq

where,

r component = partu
z component = partv
phi component = partw

Now here is the confusion.

First, the initial velocities are all in units of 'm/s' - this suggests that the phi component is defining 'r * phi dot', would this be correct? Does 'partw' give 'phi dot' or 'r * phi dot'?

Second, the equations above seem off, there is 'mf.Bz*r*partv' in the first one for example. We would not normally expect the z component of velocity to be multiplied by 'r' or indeed be paired with 'Bz' in the cross product. I would expect the first equation should be:

Fr = (mf.Er+mf.Bz*r*partw-mf.Bphi*partv)*partq if 'partw' gives 'phi dot'
or
Fr = (mf.Er+mf.Bz*partw-mf.Bphi*partv)*partq if 'partw' gives 'r * phi dot'

It seem that the definitions of the velocities might be wrong ('partv' and 'partw' should be swapped in the definition of the velocity components) or the equations are wrong. Can anyone help with this? Please do say if I'm being stupid and have missed something elementary as it is my first time using COMSOL

Thanks very much.
2 Replies Last Post Jun 20, 2012, 2:11 a.m. EDT
COMSOL Moderator

Hello Anthony Ashmore

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Anthony Ashmore
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Posted: 1 decade ago Jun 19, 2012, 10:37 p.m. EDT
After doing some experiments I have come to the following conclusions.

COMSOL uses the following definitions: v_z = partw, v_phi=partv, v_r=partu. This is what the pre-defined equations in the post-processing particle tracing suggests, but does not agree with the definitions in the 'Advanced' section of the Settings - these are the problem and need to be changed in a future version.

COMSOL treats partv as 'r phi dot', it has units of m/s. Thus, COMSOL contains extra factors of 'r' in the equations it suggests for EM forces. They should be:

Fr = (mf.Er+mf.Bz*partv-mf.Bphi*partw)*partq
Fphi = (mf.Ephi-mf.Bz*partu+mf.Br*partw)*partq
Fz = (mf.Ez+mf.Bphi*partu-mf.Br*partv)*partq

This can be seen by following a particle track with no external forces and using a 'colour expression' to colour the track according it's speed.. sqrt(partu^2+partv^2+partw^2) gives a track of constant colour, sqrt(partu^2+r^2*partv^2+partw^2) gives a track with varying colour. The first is correct.
After doing some experiments I have come to the following conclusions. COMSOL uses the following definitions: v_z = partw, v_phi=partv, v_r=partu. This is what the pre-defined equations in the post-processing particle tracing suggests, but does not agree with the definitions in the 'Advanced' section of the Settings - these are the problem and need to be changed in a future version. COMSOL treats partv as 'r phi dot', it has units of m/s. Thus, COMSOL contains extra factors of 'r' in the equations it suggests for EM forces. They should be: Fr = (mf.Er+mf.Bz*partv-mf.Bphi*partw)*partq Fphi = (mf.Ephi-mf.Bz*partu+mf.Br*partw)*partq Fz = (mf.Ez+mf.Bphi*partu-mf.Br*partv)*partq This can be seen by following a particle track with no external forces and using a 'colour expression' to colour the track according it's speed.. sqrt(partu^2+partv^2+partw^2) gives a track of constant colour, sqrt(partu^2+r^2*partv^2+partw^2) gives a track with varying colour. The first is correct.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Jun 20, 2012, 2:11 a.m. EDT
Hi

by default, COMSOL maps the (x,y,z) coordinates into (r,phi,z) in 2D-axi, and in that order, if something else appears, it could by indeed an error and you should report it directly to "Support"


--
Good luck
Ivar
Hi by default, COMSOL maps the (x,y,z) coordinates into (r,phi,z) in 2D-axi, and in that order, if something else appears, it could by indeed an error and you should report it directly to "Support" -- Good luck Ivar

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