Electron in constant acceleration

[Quantum9999]

If I throw the electron from electron gun with some acceleration .Will it maintain it's constant acceleration? If yes then it radiates photons from where will the electron gets energy to constantly radiate photon? If not then why?

 

[vanhees71]

If an electron is accelerated, it will radiate electromagnetic waves, and of course it looses the corresponding energy.

 

[Quantum9999]

If an electron is accelerated, it will radiate electromagnetic waves, and of course it looses the corresponding energy.

So, what will to electron if it radiates all of it's energy. Will it vanishes from existence.

 

[vanhees71]

It'll simply come to rest. It's not so easy to get rid of the electron since there are several conservation laws forbidding it to simply vanish (energy, momentum, and electric charge are all conserved). One possible way would be to let it annihilate with a positron, its antiparticle. This would result in two photons. Also note that the electron can't simply radiate all of its energy (only its kinetic energy). What remains as energy when it comes to rest is its rest energy $E=m c^2$ (where $m$ is the rest mass of the electron).

 

[ZapperZ]

So, what will to electron if it radiates all of it's energy. Will it vanishes from existence.

It will lose its energy in motion, the energy that it gained from the field that accelerated it. Nothing that it is radiating comes from its "mass", so why should it loses that?

Zz.

 

[Ibix]

If I throw the electron from electron gun with some acceleration .Will it maintain it's constant acceleration?

Once it leaves the gun, no. It will move with constant speed.

 

[Dale]

Will it maintain it's constant acceleration?

After leaving the electron gun it will no longer accelerate.

If not then why?

Because of Newton's first law.

 

[vanhees71]

It depends. If you shoot it into a charged capacitor it'll be accelerated ;-)). BTW the main problem in accelerating electrons is that they are so light. When you accelerate the electrons in a ring accelerator they radiate a lot of em. wave, which is an energy loss making it expensive to accelerate them. That's why electron accelerators for high are usually built as linear accelerators, but that needs a lot of space.

 

[ZapperZ]

It depends. If you shoot it into a charged capacitor it'll be accelerated ;-)). BTW the main problem in accelerating electrons is that they are so light. When you accelerate the electrons in a ring accelerator they radiate a lot of em. wave, which is an energy loss making it expensive to accelerate them. That's why electron accelerators for high are usually built as linear accelerators, but that needs a lot of space.

Actually, that isn't a "main problem" if that is what you want out of those electrons. That's why we have synchrotron light sources. We want them to radiate.

Zz.

 

[vanhees71]

Sure, but for accelerator physicists it's a nuisance.

Of course those who like to use the synchrotron light for studying or a X-ray FEL light source as at DESY, the radiation is the interesting thing.

 

[tech99]

If an electron is accelerated, it will radiate electromagnetic waves, and of course it looses the corresponding energy.

It looks as if this particular electron, subject to continuous uni-directional acceleration, is trying to radiate half a wave. I don't think the wave will let go of the electron and be radiated until the electron reverses its acceleration - it will hang on to the the charge. We cannot have DC radiation so far as I am aware. What is the answer here?

 

[Dale]

I don't think the wave will let go of the electron and be radiated until the electron reverses its acceleration - it will hang on to the the charge.

This is not correct. From the Lienard-Wiechert potential you can see that there is a radiative term.
$$ \frac{q \mathbf n \times ((\mathbf n-\beta)\times \dot \beta)}{c(1-\mathbf n \cdot \beta)^3|\mathbf r - \mathbf r_s |} $$
This term is non-zero even under a constant $\dot \beta$

 

[ZapperZ]

It looks as if this particular electron, subject to continuous uni-directional acceleration, is trying to radiate half a wave. I don't think the wave will let go of the electron and be radiated until the electron reverses its acceleration - it will hang on to the the charge. We cannot have DC radiation so far as I am aware. What is the answer here?

Radiate half a wave? That makes no sense! If that is true, then Bremsstrahlung radiation, which is a deceleration, will also "radiate half a wave". Do you think this is what we observe?

Zz.

 

[A.T.]

It looks as if this particular electron, subject to continuous uni-directional acceleration, is trying to radiate half a wave.

The case of a constant proper acceleration has been discussed here many times. If you go to the rest frame of he electron you have a static E-field, so no radiation. See diagram (b) here:

https://www.physicsforums.com/threa...in-a-gravitational-field.950608/#post-6020064

 

[vanhees71]

Constant proper acceleration is pretty complicated and has a long history of debate. Even Pauli got it wrong! The problem, of course, is that it's not a very physical situation to have constant proper acceleration for an infinite time. The mathematical problem is that the world lines are hyperbolae with the light cone as asymptotic lines. This leads to singular ($\delta$-distribution like) terms which get easily forgotten without applying a careful regularization procedure (e.g., assuming proper accerleration only over a finite time interval) and then taking the limit to the somewhat artificial situation (e.g., making the finite time interval infinite). The best treatments I know about is

http://rspa.royalsocietypublishing.org/content/229/1178/416

https://arxiv.org/abs/1405.7729
https://doi.org/10.1119/1.4875195 (Erratum: https://doi.org/10.1119/1.4906577)