A Velocity Verlet for relativistic simulation

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Philip Koeck
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I'm simulating a situation that's partly relativistic and I'm wondering if it's wise to use Velocity Verlet.

A fast electron (200 keV or roughly 208 000 000 m/s) travels along the z-axis and intersects a beam of slower electrons (1 keV or roughly 20 000 000 m/s) that are moving along the x-axis.

I treat the slower electrons as non-relativistic.

For the fast electron I assume it's travelling essentially in the z-direction at all times, which is very accurate as far as I can see.
So I use the parallel corrected mass in the z-direction and the orthogonal in x and y to get the acceleration of the fast electron at every time step.

I realise that velocity verlet is not intended for accelerations that are velocity-dependent, but in this case the velocity of the fast electron is almost constant so γ and γ3 are almost constant during the whole simulation.

Does it sound okay to use Velocity Verlet in this case or should I consider a different algorithm?
 
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I don't know the answer to your question about the integrator, but you could try working with four-vectors. The four velocity has a constant magnitude by definition and the Lorentz force law relates to it via the four momentum which is the invariant mass times the four velocity.
 
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