# Relativistic electron Moving through toroidal superconductor

• Samson4
In summary: The radiation is emitted along the electron's path, just like if the electron was moving in a straight line.
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?

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.

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.

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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?

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.

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

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

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.

Samson4 said:
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.

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.

Samson4 said:
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.

## 1. How does a toroidal superconductor affect the movement of relativistic electrons?

A toroidal superconductor creates a strong magnetic field that can significantly affect the movement of relativistic electrons passing through it. This magnetic field can cause the electrons to follow a curved path, known as a cyclotron motion, resulting in a change in their trajectory.

## 2. What is the difference between a toroidal superconductor and a regular superconductor?

A toroidal superconductor is a type of superconductor that is shaped like a ring or torus, while a regular superconductor can have various shapes. Additionally, a toroidal superconductor creates a magnetic field that is confined within the ring, whereas a regular superconductor can create a magnetic field that extends beyond its physical boundaries.

## 3. Can relativistic electrons pass through a toroidal superconductor without any resistance?

Yes, relativistic electrons can pass through a toroidal superconductor without experiencing any resistance, as long as the superconductor is cooled below its critical temperature. This is because a superconductor has zero electrical resistance, allowing for the electrons to move through it with minimal energy loss.

## 4. What are the potential applications of using toroidal superconductors in relation to relativistic electron movement?

Toroidal superconductors have potential applications in particle accelerators and fusion reactors, where the movement of relativistic electrons is crucial. The strong magnetic field created by the toroidal superconductor can help guide and control the trajectory of the electrons, allowing for more efficient and precise movement.

## 5. How does the speed of the relativistic electrons affect their movement through a toroidal superconductor?

The speed of the relativistic electrons can affect their movement through a toroidal superconductor in two ways. Firstly, faster-moving electrons will experience a greater force from the magnetic field, causing them to follow a more curved path. Secondly, as the electrons approach the speed of light, their mass increases, making it more difficult to manipulate their trajectory using magnetic fields.

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