Relativistic electron Moving through toroidal superconductor

[Samson4]

I understand the electron in the situation to be rapidly accelerated away from the torroid. If this is true, my question is:
Will the electron emmit radiation following the synchrotron formula?
Also, would the radiation travel through the torroid?

 

[mfb]

Toroid.

I guess you mean a toroidal field produced by a superconducting coil?

In which direction does the electron travel? If the magnetic field has a component orthogonal to the direction of motion, it will emit synchrotron radiation, sure. For ultrarelativistic electrons, this radiation is emitted along the direction of motion.

 

[Samson4]

I mean a toroidal superconductor with a relativistic electron traveling towards the center of the toroid. Wouldn't the superconductor produce an equal and opposite magnetic field, causing the electron to rapidly accelerate in the direction it approached from?

In the picture, the electron is traveling from the left towards the right. However, a current is induced in the superconductor that exactly mirrors the magnetic field, thus accelerating it right to left. The abrupt acceleration of the electron emits radiation along the electron's path. However, the electron has lost much of it's velocity. The radiation arrives at the right side of the page before the electron but they take the same path. This; of course, is only because the electron was traveling both perfectly perpendicular to the toroid and centrally to it's circumference.

 

[mfb]

The electromagnetic field of the electron points in the wrong way to induce any current in toroidal direction.

 

[Samson4]

I'm expecting the magnetic field to be induced toroidally and the current to flow from the outer diameter to the inner diameter; inside the superconductor.. Or are you saying the superconductor would not react to the magnetic field in this situation?

 

[mfb]

There would be a tiny radial current flow. So what? A radial current flow, which is negligible anyway, won't lead to a magnetic field orthogonal to the electron motion. It cannot, just from symmetry.

 

[Samson4]

If the opening was sufficiently small, and the superconductor was cylindrical; would the proposed situation be possible?

 

[mfb]

Emission of synchrotron radiation? I don't see why there should be synchrotron radiation.

 

[Samson4]

Because the electron is moving at a speed close to c and experiencing a great loss of energy as it approached the superconductor. I thought synchrotron radiation was emitted when a relativistic electron is accelerated by a magnetic field, either radially or in a straight line.

 

[ZapperZ]

Because the electron is moving at a speed close to c and experiencing a great loss of energy as it approached the superconductor. I thought synchrotron radiation was emitted when a relativistic electron is accelerated by a magnetic field, either radially or in a straight line.

http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/synchrotron.html

Radially or in a straight line? By a magnetic field?! Where did you learn the Lorentz force law from? A magnetic field cannot accelerate a charge particle "in a straight line".

It would be nice if you first check if you have the concept correct before trying to apply it to such complicated situation.

Zz.

 

[Samson4]

I did type that a little weird, this is what I meant to say:

Classically, any charged particle which moves in a curved path or is accelerated in a straight-line path will emit electromagnetic radiation.
...accelerated to very high speeds, the radiation is referred to as synchrotron radiation.

http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/synchrotron.html

I don't understand why an electron moving towards a superconductor at relativistic speeds wouldn't emit radiation. It would be rapidly "decelerated" by a changing magnetic field created by the superconductor.

 

[mfb]

and experiencing a great loss of energy as it approached the superconductor.

I don't see any argument why it should do so. Induced charges in the superconductor can lead to a completely negligible electric force.