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I'm wondering what happens when fast electrons (100 - 300 keV) interact with a beam (diameter 1 to 10 μm) of slower electrons (1 to 10 keV), which is at right angles to the trajectories of the fast electrons. The beam of slower electrons is relatively dense with 1 to 10 electrons per μm line density.

I'm mainly interested in the phase shift or modulation of the fast electrons depending on how close they pass the beam of slow electrons.

I've simulated this in two rather classical ways and get very similar results, but I'm uncertain whether experimental results would be very different due to QM effects.

The two simulations I did are:

1. The slow beam is treated as a stationary and continuous charge distribution whereas the fast electrons are treated as a plane and monochromatic wave.

This is pure wave optics, completely ignoring any particle nature.

The phase shift of the fast electron wave is of course completely deterministic and proportional to the projected electrostatic potential produced by the slow beam.

2. Every electron is treated as a classical charged particle and the trajectories are calculated using Runge-Kutta. The slow electrons form a beam, whereas the fast electrons pass this beam at various distances.

The electrostatic potential traversed by each fast electron is summed up and the result agrees very well with simulation 1. Very little randomness in the phase shift of the fast electrons is introduced by the particle nature of the slow beam, but some of the slow electrons do get knocked out of their original trajectory quite a bit.

Is there a more quantum mechanical simulation one could do and would one expect very different results?

Could the phase shift of the fast electrons become very unpredictable in reality?

I'm mainly interested in the phase shift or modulation of the fast electrons depending on how close they pass the beam of slow electrons.

I've simulated this in two rather classical ways and get very similar results, but I'm uncertain whether experimental results would be very different due to QM effects.

The two simulations I did are:

1. The slow beam is treated as a stationary and continuous charge distribution whereas the fast electrons are treated as a plane and monochromatic wave.

This is pure wave optics, completely ignoring any particle nature.

The phase shift of the fast electron wave is of course completely deterministic and proportional to the projected electrostatic potential produced by the slow beam.

2. Every electron is treated as a classical charged particle and the trajectories are calculated using Runge-Kutta. The slow electrons form a beam, whereas the fast electrons pass this beam at various distances.

The electrostatic potential traversed by each fast electron is summed up and the result agrees very well with simulation 1. Very little randomness in the phase shift of the fast electrons is introduced by the particle nature of the slow beam, but some of the slow electrons do get knocked out of their original trajectory quite a bit.

Is there a more quantum mechanical simulation one could do and would one expect very different results?

Could the phase shift of the fast electrons become very unpredictable in reality?

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