Most of us see the tech help procedure from the recipient end, but I wanted to share the view from the giver perspective. I recently got a succession of E mail and telephone messages from a user who was trying to complete a Trak solution for electron flow under an intense deadline set by his funding agency (this always seems to be the case). Apparently, Trak did not recognize the presence of a strong magnetic field. As with many tech help complaints, the user felt that the program failed to anticipate his desires. An equivalent situation would be if sporting-goods store owner got a telephone call: "I took your skis down a black diamond run and they wrapped me around a tree! Get out here immediately!"
In passing, the user mentioned a 3.5 tesla field! Knowing that the device he was working on was several meters long, I sensed a disconnect. Let's check the math. The gyrofrequency for a particle with mass m in a field B is
ωg = eB/γm
and the gyroradius is
R = γmβc/eB.
Consider the motion of a 1 MeV electron (γ = 2.96, β = 0.941) in a field B = 3.5 T. Putting in the numbers,
ωg = 2.08 × 1011 1/s and R = 1.4 × 10-3 m. To resolve magnetic motion accurately, there should be at least ~12 steps per revolution or
Δt < 1/2ωg
For the calculation, Δt should be less than 2.5E-12 s. Based on the element size and electron velocity in his meter-scale system, the user's time step was about 100 times longer. Magnetic kicks occurred at random and the field did not appear to be present.
A literal solution would be to choose an extremely small time step and wait hours, running the risk of accumulated numerical errors. The resolution I suggested was simply to lower the field and pick a reasonable time step. With regard to assigning space charge and finding distributions, there is no point to resolving gyration orbits to a size smaller than the element dimensions or the distance between model electrons. Even with a reduced field, electrons would be tied closely to field lines. Furthermore, magnetic mirroring effects depend only on relative field differences. The only purpose to a literal solution would be to calculate 10's of thousands of little circles. I made my suggestion. but the user had to reject it. His military sponsor was emphatic that the field must be 3.5 tesla! As of today, the user is still in the tree.
On the topic of magnetic fields and time steps in Trak and OmniTrak, there have been several instances where users walked over the edge, despite public-spirited warning signs in the instruction manuals. To reduce rescues in the future, I have installed safety fences in the codes. They provide active checking with negligible overhead. At the beginning of each particle orbit, the code calculates the quantity
F = m/2 q Δt,
where m, q and Δt are the mass, charge and assigned time step of the current particle. The codes stop and issue an error message if the quantity (B/γ) exceeds F.
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