Hello friends, I recently, was reading all about the accelerating charges and radiation, but somehow the classical electrodynamics treatment is still inadequate, that is, the radiation reaction force(derived for oscillating charges) vanishes for uniformly accelerating charges. In this view, people tried to investigate self interaction during acceleration, but all in vain because of undefinable quantities at the position of the charge. Now, in between all this do we even have any experiment that confirms the presence of radiation for uniformly accelerated charges. If yes, then does it stick to the Larmor's formula of power dissipation ? Thanks in advance
Hi universal_101. I'm pretty certain there is zero experimental proof. Apart from the vexed matter of gravitational influence, one can never achieve indefinitely sustained uniform acceleration for obvious reasons. But it is possible to achieve it for sufficient time such that transient effects (starting and stopping) are not present or at least minimal. However just try a back-of-the-envelope calculation and it's clear any possible radiation field from uniform acceleration achievable in any laboratory situation will be far too small to detect. How would one measure the Coulombic, let alone any radiative field, of say a single electron accelerating between two charged capacitor plates!? As far as theory goes, there is still much debate - one example right here at PF:https://www.physicsforums.com/showthread.php?t=72035
Thanks Q-reeus, The thing is, I'm not interested in the gravitational portion of the problem, that is, the violation of equivalence principle, or motion of charged particle under gravitation. Of-course having put that aside, we have the accelerating charges in EM fields and radiation due to acceleration. Now, you are right in saying that if there is some radiation due to uniformly accelerating electrons it is extremely small and cannot be detected(radiation). But I think there could be ways around it, if instead of the radiation we track the energy of these charge particles in uniform acceleration and deceleration experiments. Whereas, on the other hand, the term uniform acceleration itself is quite complicated, when we include relativity(increase in mass) in static fields, the acceleration should converge to zero when we approach the speed 'c' , Moreover, if there is any radiation during uniform acceleration and therefore radiation reaction force, it would most probably depend on the magnitude of acceleration which would again make the original acceleration non-uniform. And if we extend it further, this non-uniform acceleration again induce radiation and radiation reaction by the known formula. In this light how good is the question about uniform acceleration and radiation ?
Still a no-go for absolutely uniform acceleration owing to the extreme feebleness of any energy loss. You may find appealing a fairly simple argument based on conservation of energy given here: http://arxiv.org/abs/gr-qc/9811030 Not saying I endorse it though. Not sure on this, but think that in a frame where the accelerating q is relativistic, feebler acceleration is exactly countered by Lorentz contraction of charge's field lines, intensifying transverse field that matters re radiation. Assuming there is any radiation to start with. Right, and how possible is it to achieve any useful level of uniform acceleration in the first place, quite apart from those higher order feedback issues? Seems to be purely a theorist's playground, interesting though it is.
Alright, let me have another shot, suppose we have a electrostatic linear accelerator which can accelerate charges to speeds approaching 'c', Now if there is present a radiation reaction force then the speed of the particle approaching the end of the accelerator would be less than the expected speed without radiation. i.e. [itex]E - (e^2 a c^2/6{\pi}) = m_e c^2(γ-1)[/itex] and for appropriately chosen E of the accelerator and its length, it seems the other two energy comes close for 1.05≤γ≤1.1 and normal accelerations(a). If I did everything correctly. Therefore, now by injecting these accelerated particles in a magnetic fields and separating them by their energies can easily show if the particles radiated or not. If I assume my calculations are correct. Before we go further, is there any straight forward proof of the intensification (synchrotron should not be included), that is, do we experience intensified electric field near a CRT or any other linear motion ? I think classical electrodynamics has more potential than Maxwell's equations, but to have any arguments we should have observations, which we are lacking here.
Are we talking uniform in magnitude and direction? Or magnitude only? Because for later, an electron passing through a bend in an accelerator (E.g. J-Lab) is a fine example.
Without checking veracity of your calculations, just ask you to consider the practicalities here. A linear accelerator as used at say Stanford is not electrostatic in nature but uses a phased arrays of cavity Klystrons etc. that always induces some significant back-and-forth accelerations en-route. A pure electrostatic accelerator would be of the electron-gun cold-cathode type, and accelerations are far from uniform. Nearest one might suppose would be a parallel-plate capacitor with tiny holes in the middle of each plate. Firing a charge through both holes and one would have near-uniform acceleration in between plates. But then there is the matter of induced currents and back-reaction fields as the charge enters and exits the hole regions. Some tricky calculations needed but my guess is those back reaction effects will swamp any conceivable pure uniform radiation component. Nothing much to speak of in CRT case (a few tens of KV only mildly relativistic). It is part and parcel of SR that such contraction exists though. Got me there - can you explain how classical electrodynamics is different from Maxwell's eqn's?
I just thought it would be very nice to have an experimental proof, but even though I think that charges accelerating in EM fields(uniform or not) would/should radiate. Ofcourse, it is this contraction which is sometimes used to explain the magnetic field as a relativistic effect of electric field. But the only problem is we don't have any scientific experimental proof of the contraction, but it is off topic, even though SR is supposed to be the consequence of Maxwell's equations, in other words, ME's are Lorentz invariant. A vague answer would be, We did not have point charges when Maxwell's equations were formulated ! and classical electrodynamics is all about point charges.
There has by now been quite some decades of experience involving particle accelerators of the cyclotron/synchrotron type. Specially designed versions of the latter now supply high intensity x-rays as primary objective. To explain x-ray output frequencies given fundamental 'jiggle' frequencies in the MHz range requires SR, or something exactly equivalent to it. The Lienard-Wiechert potentials, fully consistent with Maxwell's eqn's and SR, provide extraordinary accurate predictions for the entire frequency spectrum and angular intensity distribution of emitted radiation. There is a viable alternative? It's true afaik the notion of electron wasn't used by Maxwell, but isn't that putting things the wrong way around? A point charge cannot be explained classically - certainly not given high energy particle-smashing experiments. Must go. :zzz:
you can see some theoretical arguments here.however it is really messy.http://www.mathpages.com/home/kmath528/kmath528.htm
Exactly, besides synchrotron, that is, simple linear constant acceleration. Do we have any experiments?
I may not know the term for constant magnitude and direction, but I meant exactly that by uniform acceleration. On the other hand, why not!
Thanks Q-reeus for the effort, on the other hand it seems that non-radiating uniform acceleration can also be a valid scenario, as long as Larmor's formula is characterized as "only applicable for bound charges".
Yes that is a valid viewpoint given how the the derivation of radiative back-reaction force F_{rad} is obtained from Larmor formula applied to periodic oscillations:http://en.wikipedia.org/wiki/Abraham–Lorentz_force#Derivation F_{rad} is proportional only to da/dt, hence formally vanishes for uniform a = du/dt. My feeling is the problem stems from the unrealistic assumption uniform acceleration has 'always been there'. Drop that, and radiation must be happening. But as to what extent, too much subtle arguing either way for me to place any bets.
Whereas, Power radiated is essentially dependent on (acceleration)^{2} only(that is independent of da/dt), which was(Larmor formula) essentially can be derived from the consideration of uniform rectilinear acceleration!! That is, there is NO restriction whatsoever on the type of acceleration even on the derivation of Larmor formula itself. This is a big problem !! This somehow suggests we should reanalyze our fundamentals.
When harmonic motion occurs, it all sorts out nicely enough with power having a^{2} dependency ~ E_{rad}^{2} and reaction force having da/dt phasing opposing velocity as required. More difficult to get consistency in uniform case for sure. There is a lot of talk about any radiation being observer-frame dependent when it comes to uniform acceleration in particular - as per that link in #2. Another that may or may not help: http://physics.fullerton.edu/~jimw/general/radreact/ Keep searching!