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Warning Trajectory in dipole field independent of energy ! 

Forum: Fields: Magnetic and Otherwise
Date: 13 Jul, 2005
From: Tim Chambers <Tim Chambers>

So I have my Earth with its dipole working, and running pretty speedily.  
Now comes the big problem: the paths of charged particles in the field 
are independent of energy!  I have gone through the following steps, 
changing no code except the GetFieldValue() function...

First, uniform B-field along z axis.  As expected, the radius of curvature
of the particle's path increases with energy.  As a side note, I found 
that above a certain energy, about 8.5MeV for an electron in a 3 nT field,
the particle would go absolutely straight, zero curvature.
Then, a B-field along the z-axis where field strength is a function of the
particle's z coordinate.  Again, radius of curvature increases with energy.
Now, a more complicated function, looking like
Bfield[0] = y
Bfield[1] = z
Bfield[2] = x

And still the path depends on energy.  Adding another layer of complexity:
Bfield[0] = y*z
Bfield[1] = z*x
Bfield[2] = x*y

And as always, more energy makes the particle take larger loops with less
curvature.  

So then I implemented my dipole field:
Bfield[0] = 3*coeff*z*x
Bfield[1] = 3*coeff*z*y
Bfield[2] = coeff*(3*z*z - r*r)

and suddenly, the trajectory becomes independent of energy.  For the same 
starting position and direction, an electron ranging anywhere from 10 
eV to 10 TeV will take exactly the same path.  The initial direction has 
a small effect; it determines whether the particle travels forward or 
backward along the field line trapping it but otherwise does not matter.
For example, these two run macros:

/gps/position -8000. -8000. -8000. km
/gps/energy 100 eV
/gps/direction 1. 0. 0.

and

/gps/position -8000. -8000. -8000. km
/gps/energy 10 MeV
/gps/direction 1. 0. 1.

produce identical output.  What is the cause of this problem?

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1 None: Addendum to above...   (Tim Chambers - 14 Jul, 2005)
(_ None: Re: Trajectory in dipole field ... what is happening ?   (John Apostolakis - 15 Jul, 2005)
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