Accelerating particle photon emission mechanics?

[Jarfi]

It's been a while. But I have always received the help I needed on this forum. I had this question in my head, When a particle accelerates, it creates an oscillating electric field, and a photon. How much does this effect, affect the energy of the particle itself?

Say I had a particle accelerator, and I was accelerating an electron. Would it on each moment be creating a new photon? What if it's accelerating both momentum, and direction(circular accelerator) vs. straight accelerator(straight line).

Does a proportion of the energy put into acceleration turn into photons?

Also, say the electron is constantly accelerating in a circle, what defines the start of one photon and the end of another. It's creating an oscillating electric field, and photons are particles, how many particles are there?

Thank you in advance.

 

[mfb]

When a particle accelerates, it creates an oscillating electric field, and a photon.

It is a possible process. If you continue to accelerate it you'll get some photons, but with a random distribution. It is usually better to think of this in terms of electromagnetic waves. Every acceleration counts. If the acceleration is orthogonal to the direction of motion, this is typically called synchrotron radiation.

Also, say the electron is constantly accelerating in a circle, what defines the start of one photon and the end of another.

There is no such thing. This is one of the reasons an approach via classical waves is better.

 

[Jarfi]

It is a possible process. If you continue to accelerate it you'll get some photons, but with a random distribution. It is usually better to think of this in terms of electromagnetic waves. Every acceleration counts. If the acceleration is orthogonal to the direction of motion, this is typically called synchrotron radiation.There is no such thing. This is one of the reasons an approach via classical waves is better.

Okay. So if I continue to accellerate I'll get some photons. What exactly does that mean, what is the difference between an acceleration forming a photon, and an acceleration which forms an electromagnetic wave. When is it quantized, and when is it not?

There is no such thing. This is one of the reasons an approach via classical waves is better.

Okay, so why are some waves classical while others are quantized, when an electron jumps between orbitals, the wave is still a wave, but it is also a photon. Are there concrete mathematics or defined difference between different forms of photon sources that determines weather or not they can be absorbed as photons?

 

[mfb]

You can (nearly) always describe everything with particles, or express everything as fields - it is a different description for the same thing. Sometimes some descriptions work much better than others.

 

[jartsa]

Let's say we connect a 100 W, 100 MHz AC power source onto an antenna. The antenna emits 100MHz EM-waves, or a huge amount of photons with 100 MHz frequency. Right?

Now let's say we connect a trillion PW, 100 MHz AC power source onto that same antenna. Now we have a particle accelerator that accelerates electrons and emits photons whose frequency has nothing to do with the 100 MHz frequency of the AC that powers the particle accelerator. Right?

 

[vanhees71]

An antenna doesn't emit a huge amount of photons (Fock states of definite photon number to be precise) but coherent states. It's almost always sufficient to think in terms of classical electromagnetic waves in such cases. There's no need for a QFT treatment here.

In the second case you simply vaporize your antenna and produce a plasma plus a lot of em. waves with a wide frequency spectrum. I also don't see any need of QFT to describe this cataclysmic event .

 

[jartsa]

An antenna doesn't emit a huge amount of photons (Fock states of definite photon number to be precise) but coherent states. It's almost always sufficient to think in terms of classical electromagnetic waves in such cases. There's no need for a QFT treatment here.

In the second case you simply vaporize your antenna and produce a plasma plus a lot of em. waves with a wide frequency spectrum. I also don't see any need of QFT to describe this cataclysmic event .

I accidentally used too much power. But my point is that when the power is increased a device that emits EM-waves like an antenna transforms into a device that emits EM-waves like a particle accelerator.

Can we use a synchrotron as an antenna if we keep the particle speeds low?

 

[mfb]

But my point is that when the power is increased a device that emits EM-waves like an antenna transforms into a device that emits EM-waves like a particle accelerator.

What does that mean? Charged particles are accelerated by every electric field, no matter how large the power of an antenna is. Sure, very weak fields are impractical if you want to reach high energies, but this is just a practical issue.

 

[jartsa]

What does that mean? Charged particles are accelerated by every electric field, no matter how large the power of an antenna is. Sure, very weak fields are impractical if you want to reach high energies, but this is just a practical issue.

OP and I want to understand how acceleration and radiation are related, particularly in particle accelerators.

I am particularly interested about how the radiation of an antenna changes when power is increased to such levels that the electrons become relativistic. If that is a dumb idea, then let's just stick to particle accelerators.

So does large acceleration imply large frequency of radiation? Wikipedia says large speed implies large frequency:

The electrons are forced to travel in a closed path by strong magnetic fields. This is similar to a radio antenna, but with the difference that the relativistic speed changes the observed frequency due to the Doppler effect by a factor γ. Relativistic Lorentz contraction bumps the frequency by another factor of γ, thus multiplying the gigahertz frequency of the resonant cavity that accelerates the electrons into the X-ray range.

 

[mfb]

I am particularly interested about how the radiation of an antenna changes when power is increased to such levels that the electrons become relativistic.

No solid material can support that. You can have very fast (potentially relativistic?) oscillations in a plasma. This approach is used in plasma wakefield acceleration.

So does large acceleration imply large frequency of radiation?

In general, yes. But that's not what the quoted Wikipedia article is discussing: It discusses high speeds, not large accelerations.

 

[vanhees71]

I think the trouble is that you mix two levels of description which are not fully compatible. On the one hand you talk about classical bremsstrahlung, i.e., you discuss the radiation of electromagnetic fields due to the acceleration (and of course also "deceleration" is acceleration in the sense of physics, i.e., a change of velocity with time). Then the radiation field is (approximately, i.e., neglecting radiation reaction on the accelerated charges, which is a difficult (in my opinion unsolved) problem of classical electromagnetics, which has to do with the unphysicality of the assumption of classical point charges) then given by the Lienard-Wiechert potentials or equivalently the Jefimenko equations for the electric and magnetic field components (retarded solution of the Maxwell equations).

On the other hand you talk about photons. This is the quantum-field theoretical level of description. Here bremsstrahlung can be described as the emission of a photon when the electron is scattering with something else. This can be treated perturbatively with help of Feynman diagrams, but then also a difficulty occurs, i.e., there are infrared divergences of the corresponding cross sections, and this is overcome by resumming an entire series of Feynman diagrams in the sense of the soft-photon resummation techniques (first used by Bloch and Nordsieck in the 1930ies).

There's of course also another approximation: You can treat the charges as a classical charge-current-density fluctuation and ask for the emission of electromagnetic radiation in terms of the electromagnetic quantum field. It turns out that this problem can be solved exactly, leading to socalled coherent states of the electromagnetic field, showing that the equivalent of bremsstrahlung is not the emission of single photons but the excitation of coherent states, and last but not least that's also the outcome of the quantum-field theoretical treatment, because you can interpret the soft-photon resummation as the correction for having used unphysical asymptotic states. That has to do with the masslessness of the electromagnetic field, i.e., is long-range nature. The naive asymptotic free electron and photon states are in fact not the correct asymptotic free states since the electron carries around it's long-ranged Coulomb field, which has to be taken into account also in the asymptotic-free limit. The corresponding analysis leads, speaking in rough analogies, to an electron surrounded by a soft-photon cloud with the meaning of coherent state of the em. field.

There's a caveat to this hand-waving description: Arnold Neumaier's Insights articles on the myths about virtual particles and vacuum fluctuations (the latter with a long and ongoing discussion!):

https://www.physicsforums.com/insights/misconceptions-virtual-particles/
https://www.physicsforums.com/insights/vacuum-fluctuation-myth/