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Superconductivity at room temperature??

Have you done the experiment and determined whether you do not get radiation?

Not personally. But it's hardly the difficult enterprise that you claimed. And if I'm wrong about the results, then the textbooks are wrong too, and you've got yourself a rather easy way to make your mark in physics without even worrying about the superconductivity folks.

But even if you did, which I doubt, since I have found you are very liable to claim things which do not happen, it is not the same as accelerating charge-carriers by using an electric field: WHICH IS THE ISSUE WE ARE DISCUSSING HERE! I have NEVER spoken about mechanical acceleration and you know it. Talking about being intellectually dishonest! You take the cake.

Except that the acceleration of the current around the bend of a wire IS electrical. It's not mechanical. You get a net charge difference between the inside edge and outside edge of the bend, and that accelerates the charges around the bend. It's all electrical. There's no mechanical acceleration in this scenario. Which should be obvious, since there are no moving parts (other than the electrons) involved.
 
"As far as I know" means you're just guessing.
I am just not so arrogant to not allow for being wrong: But so far I am correct.
Anyway, it's easy. Take an electron in a Penning trap, like one of Gabrielse's experiments. It obeys Maxwell's Equations. Your naive intuition might say "of course it should radiate, it's an accelerating electron"---but Gabrielse was able to suppress the radiation by surrounding the electron with a resonant cavity tuned away from the cyclotron resonance. Maxwell's Equations are still true and the electron did not radiate. (Or not much---the suppression depends on the cavity Q factor.)
Obviously you can surround any emitter which radiate with other emitters that cancel the radiation since they are out of phase. This does not prove that the accelerating electron does not radiate.
Similarly: in a dry room, take an acrylic disk and put a point charge Q at one point on the circumference. Spin the disk at 1000 rpm; the moving charge will radiate at 1 kHz, enough to pick up (in a near-field sense anyway) in basic lab amplifiers. Now, draw a line of conducting paint around the edge of the disk, and dump the same charge Q on it. It's no longer a point charge, it's a line charge. Spin the disk at 1000 rpm; it's the same amount of charge undergoing the same acceleration, but the oscilloscope now sees no kHz signal.
Obviously, the center of charge is now stationary at the center of the disk: Are you REALLY so stupid?
The point being: take any system of electrons and forces. There is no single magic rule-of-thumb governing radiation. The only thing that tells you whether a system radiates or not is Maxwell's Equations.
Correct.
Sometimes---often, in fact, like it or not, Maxwell's Equations tell you that an ensemble of charges behaves differently than a point charge.
Not under conditions where the assembly of charges is accelerated without scattering by an electric-field, as they must do in a superconductor if your claim is true that they are accelerated.
Do you know engineers whose products violate Maxwell's Equation? Seriously?
No I do not: I only know "professionals" on superconducting who believe that they can violate Maxwell's equations. People like you!
"Dear engineering friend, does your radiation-emitting-system violate Maxwell's Equations?" If so, please have them log in here, that would be a much more interesting discussion than your confused picture of superconductivity.
Why should I ask them? You are the people who are violating Maxwell's equations, not the electrical engineers.
Take your AM loop antenna and run a DC current around it.
If the charges accelerate they will emit EM radiation. The wavelengths might be long, but they will radiate.
Radio, TV, microwaves are emitted by carefully setting up time-varying accelerating charges. The time-varying part is important.
What do you think happens to the fields of accelerating charges: Do you think they are time-independent? In your case you should forget to try and understand Maxwell's laws since you do not even understand elementary dynamics.

See you all again later so that we can proceed with your farcical arguments: Maybe tomorrow!
 
Obviously, the center of charge is now stationary at the center of the disk: Are you REALLY so stupid?

The center of mass is also stationary at the center of the disk.

Yet both the actual charge and mass are moving, and each bit of charge and mass is accelerating. Constantly. That's basic circular motion.
 
Please do not waste my valuable time. We have NEVER talked about a ring with a constant charge density. It is probably not even possible to create such a ring experimentally. We are talking about charges, each having a center of charge, being accelerated around a circle. So I am not even going to waste my time on your non-relevant arguments.

Speaking of the ring example only:

Classically speaking: yes, there are two size scales to consider. First, what is the characteristic wavelength of the radiation? Second, what is the size scale at which the charges stop looking continuous? Look at the case of my spinning disk. Let's make it 10cm diameter and place 1 nC (10^10 electrons) onto it. Spinning at 1000rpm, its radiation would be at wavelengths of 300000 m, but the charges involved look continuous (in the relevant projection) down to 3x10^-11 m. So there's a factor of 10^16 suppressing the classical radiation of this system. My intuition says that QED suppresses it even further, but I could be wrong on that point.

Note that a bent wire involves much much slower motion, and lower accelerations, than this rather fast-spinning disk.

Is that the factor that you guess that engineers find so important? Do you know electrical engineers whose circuit-designs include a classical one-part-per-sextillion corrections for radiation? No you don't, you made up the existence of such engineers because you were so sure that your argument was right.
 
Obviously you can surround any emitter which radiate with other emitters that cancel the radiation since they are out of phase. This does not prove that the accelerating electron does not radiate.

If you have a system of emitters where one emitter cancels the radiation of the others: YES, this is a system that does not radiate.

An ensemble of electrons moving through a bent wire is an example of such a system. An ensemble of electrons arranged symmetrically around a spinning ring is another example of such a system.
 
Hey folks,

I have a proposal. The entire discussion of acceleration is relevant to Johan's understanding (or not) of the meaning of the statement "E=0 and B=0 in a superconductor".

Meanwhile, we have left hanging the fact that Johan STILL thinks that this circuit:

Code:
ground --- power supply ----------- junction ---------- ground

                                    ___   . . . . . . . . V=3
                                    |    |
                                    |    |  .  . . . . . . V=2
                                    |    | 
                  __________________|    | . .  . . . . . V=1
                 /                       |
________________/                        |_______________ V=0

emits radiation with energy 2qV every time an electron goes through it.

This is confirmed in your "chapter 28" diagram. In figure 28-6, on the left, you show an electron starting at voltage V, climbing up to voltage 2V, and emitting a photon of energy 2qV on the way down. Analyze the energy budget around the loop of the circuit---you STILL haven't done this after twenty requests---and you will see that your picture violates energy conservation.
 
Another way to say the same thing: in your figure 28-6, you have drawn a power source in the junction. Inside the junction, you have drawn an increase of qV in the electron's potential energy---as though the junction was itself a battery. This is nonsense. The junction is not a battery, it contains no storehouse of chemical energy that gets depleted to do work on any charge passing through it.

On the left-hand side of the diagram, a charge's potential energy is qV. On the right-hand side, the charge's potential energy is 0. A battery has to do work qV, precisely, to move the electron from right to left (via the battery you drew in 28-1, for example.) Yet you say the electron can do 2qV work (emitting a photon) in going from left to right. Do you see the problem?

I would also point out that your diagram in 28-1 is exactly what I drew in Post 191---at the time you objected to this fifteen different ways, leading to Skwinty drawing a two-battery circuit (quoted in post 257) that you partially agreed to. Were those objections some sort of bluff, or diversion, or ... ?
 
As soon as you read "order parameter" or "phase-angle" scalar field; run for cover before you get trapped in Alice's Wonderland!:D

Johan,
After reviewing the posts in this thread, these are the comments you made about a paper which I referenced. http://arxiv.org/abs/0912.4810.

I have read this paper and the author seems to be postulating the same as you, wrt cooper pairs.

I quote:

"We have shown that the AC Josephson frequency 2|e|V/h actually means that the charge on the superconducting order parameter is e. The conventional interpretation that it is the evidence of the tunneling of 2e-carriers is reversed. The present result indicates that although the BCS theory based on the Cooper-pair formation explains bulk properties of
superconductors very well, it fails to explain the persistent current flow which occurs predominantly in the surface region. We speculate that some of the Cooper-pairs are broken or Cooper-pairs are not formed in the surface region, and spin-vortices are created there; then, the phase of the order parameter arises as a Berry phase effect due to the spin-vortex
formation. This also indicates that Cooper pairs are not an absolutely necessary ingredient of superconductivity"
 
"Modifying" is not a good descriptor. What they did was create an equation to describe the current in a superconductor. This doesn't change Maxwell's equations, but is used in addition to Maxwell's equations.

Except that the London brothers used as input what they have to explain. Their equations are based on the assumption that the charge-carriers do not dissipate energy by either scattering or EM radiation, whereas the latter is what one needs to prove in order to model superconduction. The effect that one measures cannot be the cause of what one is measuring: If you assume that the effect is also the cause you are doing paranormal physics.

Furthermore their derivation is only valid when there is a magnetically induced CIRCULAR electric-field. But they end up claiming it is still valid when there is no such field and even valid in the case where the charge-carriers follow a linear path: Now this is REAL VOODOO.

But that doesn't mean Maxwell's equations are different for superconductors and regular conductors. They aren't. They're still the same.
At least here we agree: This means that if charge-carriers are accelerated without scattering, as you claim they are in a superconductor, EM waves will be radiated; unless Maxwell's equation are now different; which we must agree that they are not!
 
There is little reason to discuss non-classical phenomena so long as johanfprins continues to misrepresent the classical consequences of Maxwell's equations.
As Ziggurat noted in another post, johanfprins has been claiming that accelerated charges always radiate, but that's not true in the simple situation described by Ziggurat.
Talk about intellectual dishonesty: You are the expert here. We were NOT arguing about distributed charges spinning on disks etc; but about charge-carriers being accelerated along a ring by an applied electric-field.

The two cases are obviously different, since each charge carrier has its own center of charge at which the applied electric-field acts. In Ziggurtats case the distributed charge has a single center of charge at which an applied electric-field does not act; and which in addition does not accelerate since the distributed charge is spinning around this center. If, however, you apply an electric-field so that the latter center of charge is being accelerated, you will generate EM radiation.
It appears that johanfprins is just plain wrong about the classical consequences of Maxwell's equations. I suspect he's just repeating something he heard in primary school, without devoting enough of his valuable time to consider it carefully.
I challenge you to an open debate about Maxwell's equations in front of a learned audience; but of course persons like you are always cowards who hide behind anonymity and then throw unfounded insults around. I would not be surprised if my goldfish knows more about Maxwell's equations than you do.
You're wrong about that. Ziggurat talked about it when he described his counterexample to your absolute claim, and you talked about it when you dismissed Ziggurat's counterexample out of hand.
Where did I talk about distributed charges being rotated before Ziggurat in desperation brought up this irrelevant "counter example"? You are the most dishonest person I have ever come along in my life. Not even Joseph Goebbels could have distorted the truth better than you are doing.
As both ben m and Ziggurat have explained, it's downright easy.
I have never done the experiment and do not know how easy it will be. Maybe it is; maybe I am again being lied to? In either case it is irrelevant to our initial discussion of superconducting charge-carriers being accelerated around a ring by an applied electric-field.
I thought you were fed up with the physics-literate and had begun to plead your case to the illiterate.
You missed that I am fed-up with the people who think they are physics-literate even though they have no common sense: So I am looking for those people who still have common sense. As you, Ben m, Ziggurat and Sol Invictus have demonstrated, the probability to find common sense amongst the "professionals" working on superconduttion is zero.
 
The second half of Ben's spinning disk scenario is exactly the same as mine. He put the charge on a ring of conducting paint, I put it on a metal ring, the idea and the results are the same.
Exactly and they are both irrelevant to our initial discussion where you claimed that superconducting charge carriers are accelerated by an electric-field around a ring without emitting EM radiation. This is physically impossible.
And this doesn't require a superconductor.
But the argument is about a superconductor within which you claim that non-scattering charge-carriers can be accelerated without generating EM radiation.
In fact, it's simpler to consider a conducting but non-superconducting ring. That way, the charges will distribute themselves uniformly around the ring (unlike in the first half of Ben's example where the disk is insulating), but they're also guaranteed to rotate with the ring (since resistance will drag the charges along with the ring) if you wait a while after spinning it up.
Of course it is simpler for you to duck and dive by bringing up irrelevant examples like spinning discs and non-superconducting rings. You are just plain intellectually dishonest.
 
Not personally. But it's hardly the difficult enterprise that you claimed. And if I'm wrong about the results, then the textbooks are wrong too, and you've got yourself a rather easy way to make your mark in physics without even worrying about the superconductivity folks.
I have not claimed anywhere that you are wrong about what you claim here but consistently pointed out that the example is irrelevant since it has NOTHING to do with non-scattering superconducting charge-carriers being accelerated around a ring by an applied electric-field. Stop being so utterly dishonest: PLEASE!
Except that the acceleration of the current around the bend of a wire IS electrical. It's not mechanical. You get a net charge difference between the inside edge and outside edge of the bend, and that accelerates the charges around the bend. It's all electrical. There's no mechanical acceleration in this scenario. Which should be obvious, since there are no moving parts (other than the electrons) involved.
So now you are writing exactly what I have been saying all along as if it supports your case! It does not support your claim that non-scattering superconducting charge-carriers can be accelerated without emitting EM -radiation. If they accelerate electrically they will radiate. That is what we know from REAL physics!
 
The center of mass is also stationary at the center of the disk.

Yet both the actual charge and mass are moving, and each bit of charge and mass is accelerating. Constantly. That's basic circular motion.

It seems that you have never heard about the rotational motion of rigid bodies; and I am not going to even try and explain primary school physics to you.

So you claim that the distributed charge is moving under the action of an electric-field. I cannot see where this happening; Let me try again: Maybe the penny will finally drop! We are talking about your claim that non-scattering superconducting charges can accelerate under the action of an applied electric field without emitting EM radiation. Mechanically spinning a distributed charge on a disc or on the side of a disc has NOTHING in common to the initial discussion. So again: PLEASE STOP BEING SO DISHONEST!
 
Speaking of the ring example only:

Classically speaking: yes, there are two size scales to consider. First, what is the characteristic wavelength of the radiation? Second, what is the size scale at which the charges stop looking continuous? Look at the case of my spinning disk. Let's make it 10cm diameter and place 1 nC (10^10 electrons) onto it. Spinning at 1000rpm, its radiation would be at wavelengths of 300000 m, but the charges involved look continuous (in the relevant projection) down to 3x10^-11 m. So there's a factor of 10^16 suppressing the classical radiation of this system. My intuition says that QED suppresses it even further, but I could be wrong on that point.

Note that a bent wire involves much much slower motion, and lower accelerations, than this rather fast-spinning disk.
You are again being dishonest since a fast spinning disc as you want to bring into the discussion has NOTHING in common with non-scattering charges being accelerated by an applied electric field around a ring. No matter how slow the acceleration, they will emit EM radiation. Thus, since it is experimentally found that in a superconducting ring such radiation is not emitted, it can only mean one logical non-paranormal conclusion: The charge-carriers are not accelerating: The latter is what has to be explained to model superconductors and it has not been explained by any traditional model like BCS etc. Also not by the paranormal concepts you are stating on this thread.
Is that the factor that you guess that engineers find so important? Do you know electrical engineers whose circuit-designs include a classical one-part-per-sextillion corrections for radiation? No you don't, you made up the existence of such engineers because you were so sure that your argument was right.
Well I did challenge you to do an experiment where you accelerate non-scattering charges by an applied electric field around a ring without generating EM radiation. All you could come up with was claptrap involving spinning discs with distributed charges and no acceleration caused by an electric field. So it is clear that you cannot design any experiment to refute the fact that non-scattering charge-carriers being accelerated around a ring must emit EM radiation.
 
If you have a system of emitters where one emitter cancels the radiation of the others: YES, this is a system that does not radiate.
An ensemble of electrons moving through a bent wire is an example of such a system.
Charges which do not scatter and are accelerated around a bent wire is NOT such a system: They will emit radiation as we all know they do when we use magnetic fields to plot out Fermi-levels.

I must first stop here; but will be back since it is important for the future of physics to oppose the paranormal concepts which have entered physics with increasing frequency since 1927. Oh why did they not listen to Einstein?
 
Talk about intellectual dishonesty: You are the expert here.
Not really, but I appreciate your flattery.

We were NOT arguing about distributed charges spinning on disks etc; but about charge-carriers being accelerated along a ring by an applied electric-field.
You may not have been arguing about that, but your fictional EE was:
I also challenge Sol's "supra-pro's" to get down from pipe-dreaming in their ivory towers and visit an engineering faculty, where they will meet the true professionals who, in contrast to the supra-pro's, have common sense. I can well imagine that a discussion between a supra-pro and an electrical engineer with common sense can be as follows:

Supra-pro: We believe that charges can accelerate without emitting EM-radiation: Have you also observed such an effect.

EE: NEVER!!! It is consistently found by us that accelerating charges must radiate. If you say it can be otherwise you must be a crackpot or an illusionist-magician to demonstrate this.
Notice the absolute and unqualified nature of your fictional EE's claim. He said "accelerating charges must radiate", and anyone who says otherwise "must be a crackpot".

He's calling Maxwell a crackpot. If you thought your fictional EE had limited his claim to accelerations "along a ring by an applied electric-field", then you misread his claim.

Ziggurat's counterexample proves that your fictional EE was wrong. You shouldn't take that personally. It's about your fictional EE, not you.

I challenge you to an open debate about Maxwell's equations in front of a learned audience; but of course persons like you are always cowards who hide behind anonymity and then throw unfounded insults around. I would not be surprised if my goldfish knows more about Maxwell's equations than you do.
That wouldn't surprise me either.

I'd be delighted to amuse a learned audience while defending the honor of anonymous cowards everywhere by debating your goldfish, Bjarne's cow, and a couple of fictional EEs, but I think we should start a new thread for that. Let's ask Michael Mozina to frame the question.

Where did I talk about distributed charges being rotated before Ziggurat in desperation brought up this irrelevant "counter example"?
As explained above, your fictional EE made an incorrect claim for which Ziggurat produced a relevant counterexample.

Although Ziggurat's counterexample was relevant to the claim made by the fictional EE you quoted, his counterexample may not have been relevant to your argument. If that's the case, then your fictional EE's claim was also irrelevant to your argument.

But you've raised a good point: None of us should blame you for any of the opinions expressed by your fictional EE. You were just using that EE to ridicule the ignorance of arrogant know-it-alls.

You are the most dishonest person I have ever come along in my life. Not even Joseph Goebbels could have distorted the truth better than you are doing.
Ah, shucks. I like you too.

You missed that I am fed-up with the people who think they are physics-literate even though they have no common sense: So I am looking for those people who still have common sense.
A noble quest. How will you recognize them?

As you, Ben m, Ziggurat and Sol Invictus have demonstrated, the probability to find common sense amongst the "professionals" working on superconduttion is zero.
Although I am both flattered and amused that you would group me with such credible scientists, you're over-estimating my contribution. I'm not a professional working on "superconduttion", so my nonsense can't be relevant.
 
Talk about intellectual dishonesty: You are the expert here. We were NOT arguing about distributed charges spinning on disks etc; but about charge-carriers being accelerated along a ring by an applied electric-field.

No no no---accelerating "along" a ring? No, we were specifically talking about how charge-carriers can negotiate a curve, a particular type of motion that involves acceleration. When a charge carrier moving at velocity {vx,vy} = {1,0} um/s turns left and ends up moving at {0,1} um/s, that is an acceleration. That is what we are talking about. That is why the spinning-disk example is relevant---it's an example of an ensemble of charges, all accelerating, that do not emit radiation.

We are not talking about a charge accelerating from {1,0} to {2,0}, for example.

but of course persons like you are always cowards who hide behind anonymity and then throw unfounded insults around. I would not be surprised if my goldfish knows more about Maxwell's equations than you do.

This is the twentieth or thirtieth time: Johan, nobody is insulting you. Several people are saying that you've made physics mistakes, and we are trying to explain those mistakes to you. You are the one leaping to insults. For example:

Not even Joseph Goebbels could have distorted the truth better than you are doing.

You need to take a long, long, close look at your way of arguing.
 
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Summary

It is clear that I am encountering people on this forum which will do anything in their power to distort anything I am saying and to in this way avoid looking at reality. Even though their paranormal arguments and distortions are wasting everybody's valuable time, I am forced to answer all their postings in the interest of physics.

I will thus do so; but as anybody with common sense will realize I do not have the time to sit in front of my computer day and night to try and teach physics to people who do not want to understand what is possible and what is not possible in physics. I will thus return to this forum regularly when time permits to answer each and every posting. Obviously people will be able to inundate this thread with irrelevant postings as Clinger, Ben m, Ziggurat and previously Sol Invictus did. This will prolong the time I need to answer each of these assinine arguments: But I will try and do so for as long as I am alive!

I will be back when time permits

Thus before I sign off for the day I just want to summarize what the initial argument is about: I claimed that the electron charge-carriers in a superconductor must transfer charge without being accelerated by an electric field since an electric-field cannot be present within a superconductor.

My opponents claim that the charge-carriers within a superconductor are accelerated by an electric field which is somehow supernaturally induced by the static magnetic field that is produced around the superconducting current.

So all along the arguments was whether electrons are being accerated when a supercurrent flows. I say no since Onnes found that the voltage dropped to zero. One might want to argue that it is not zero. If so the definition of superconduction normally found in the physics literature is a lie. If it is, however, zero, which I assume it is in my arguments, its absence is impeccable prove that the charge-carriers are moving without being accelerated by an electric field.

It was also argued on this forum that a supercurrent around a ring is caused by acceleration of charge-carriers within a superconductor. I pointed out consistently that if charge-carriers are not accelerated by an applied voltage across two contacts, they will also not be accelerated by an induced electric field around a ring: Indeed that they motion around a ring has nothing to do with acceleration.

We have now ended up discussing fictional rotating discs with distributed charge on the disc: This has nothing to do with superconducting charge-carriers moving around a ring. The fact that we could stray so far from the initial topic illustrates that my opponents on this thread are dishonest for some reason: Maybe because they might have to admit that the main stream models on superconduction have all along been wrong? Why can they not be wrong? Are Bardeen, Cooper and Schrieffer saints from heaven? I doubt it! Whatever I might think of William Schockley in other ways, he was not very flattering about the physics abilities of Bardeen: An I am starting to understand why.
 
Exactly and they are both irrelevant to our initial discussion where you claimed that superconducting charge carriers are accelerated by an electric-field around a ring without emitting EM radiation. This is physically impossible.

You have declared this to be so, but your reasoning is wrong. Charge carriers can and do accelerate without emitting radiation.

But the argument is about a superconductor within which you claim that non-scattering charge-carriers can be accelerated without generating EM radiation.

The scattering is irrelevant to the question of whether or not accelerating charges must emit radiation. So is the superconductivity.

Of course it is simpler for you to duck and dive by bringing up irrelevant examples like spinning discs and non-superconducting rings. You are just plain intellectually dishonest.

I find that picked the simplest example to prove a point is a good thing. And it's not irrelevant. You made an absolute claim. Either the claim is true, or it is false. Since the claim is absolute, any counterexample will disprove it. I provided a counterexample, thereby disproving your claim. There's nothing irrelevant or intellectually dishonest about that. That's how rigorous, logical debate proceeds.

I have not claimed anywhere that you are wrong about what you claim here but consistently pointed out that the example is irrelevant since it has NOTHING to do with non-scattering superconducting charge-carriers being accelerated around a ring by an applied electric-field.

Why should the superconductivity or the lack of scattering make any difference? It doesn't. In fact, an exact parallel to my example of a spinning ring exists for superconductors. Get a superconducting ring, apply a magnetic field to the ring, and you'll induce a current around the ring. The current is persistent and time-independent. The charge carriers in the superconducting ring are traveling around a circle. Circular motion 101: they're constantly accelerating.

Do they radiate? No, they do not. They could not, not without violating energy conservation.

So now you are writing exactly what I have been saying all along as if it supports your case! It does not support your claim that non-scattering superconducting charge-carriers can be accelerated without emitting EM -radiation. If they accelerate electrically they will radiate. That is what we know from REAL physics!

You write as if scattering prevented charge carriers from radiating. But that's nonsense. It has no basis in theory or experiment. Furthermore, the exact same situation arises in non-scattering superconductors as well. And I've already pointed out the example to you. When a current passes through a superconducting wire with a bend in it, the charge carriers must accelerate to move around the bend. Just like with a copper wire, that acceleration is due to an electric field, which is created by a charge carrier density imbalance between the outside and inside edge of the bend.

It seems that you have never heard about the rotational motion of rigid bodies; and I am not going to even try and explain primary school physics to you.

I'm very much aware of the physics of rigid body motion. I'm also quite aware that rotation of rigid bodies involves acceleration of each part of that rigid body. That's why objects break apart if you spin them too fast.

So you claim that the distributed charge is moving under the action of an electric-field.

I claim that it doesn't MATTER why the charge distribution is accelerating, the fact remains that it accelerates. In fact, due to linearity, Maxwell's equations require that the cause of the acceleration be irrelevant. Whether or not a background electric field exists will make no difference to the field produced by the charge in question.

But yes, you can construct an exactly equivalent scenario in which the acceleration of non-scattering charges is from an electric field.
 

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