# Electron trajectory in B field with random energy kick

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1. Feb 26, 2015

### jasonpatel

So I wanted to get some second opinions on this situation I have thinking about.Lets say an electron enters, normally, a section of bfield that is perpendicular to its motion such that the electron will undergo circular motion. This is the simple part and is labeled as "E0" in the picture attached below (in both case A and B).

Lets say that at the midpoint of the electrons journey it absorbs a photon and now has a new energy of "E+" (as dipicted in the red in the picture below). Now, there are two options in my head for the trajectory:

A. The radius of the electron at the midpoint immediately increases to a larger radius. But the radius extends ALONG the original "E0" radius and the electron follows a trajectory that is somewhat concentric( http://www.powerframeworks.com/series/SG/034/sg022-and-sg034-differences.jpg ), but larger radius, with that of the "E0" trajectory at exactly the midpoint where the photon was absorbed.

B. The radius of the electron at the midpoint immediately increases to a larger radius. But the radius is measured with respect to the entrance of the bfield section just as the radius of the "E0" is measured, the only difference is that it is longer now.

So, which one is correct? Well, we know that the electrons trajectory should be continuous. Thereofre, the x position and the angle of the electron (x') should be continuous before and after the photon is absorbed; boundary conditions. It is in my opinion that this is only satisfied in case A with the concentric trajectories.

Any thoughts? Disagreements?

2. Feb 26, 2015

### Staff: Mentor

first, since you posted in the classical physics section, I assume that you are actually not interested in all of the quantum weirdness and wave functions and uncertainty principle and so forth. You probably what to just consider it like a classical point particle.

Then, the collision with the photon causes a change in the electrons momentum, which means the path has a sharp bend in it. After this sharp bend, the electron travels on a completely different circular path than the one it was on previously. The circles must intersect at the point of the collision, but do not have to have the same center or radius or tangent.

3. Feb 26, 2015

### jasonpatel

HI thanks for the reply. Actually I guess I didn't clarify the situation to completeness.

The photon is actually emitted from the electron. The electron is considered ultrarelativistic so the change in momentum can be considered opposite of the electrons original momentum vector. Hence, my assumption that the electron's position and angle does not change after the emission of a photon, only its energy changes.

Any thoughts?

4. Feb 27, 2015

### jasonpatel

Also if you could refer me to some readings on the "quantum effects" of such a system I would be very interested on reading, thanks!

5. Feb 27, 2015

### Staff: Mentor

OK, so no sharp bend. Just a sudden change in the radius. Both circles would be tangent to the momentum at emission.