How is energy conserved in an accelerator?

[lilrex]

I have a problem, something that I should know but slipped through the cracks.

I have posted this in another thread but I will re-post it here in truncate. the other thread is https://www.physicsforums.com/showthread.php?t=185203 (I hope I referenced this right.) anyway I do not intend to duplicate the same questions but I have questions more appropriate to ask in an engineering forum.

Here is the question:

If a particle is accelerated within a field it will have the energy imparted on it to the proportion of the potential of the field. This field (of which I see as static) is removed before the particle reaches the plate accelerating it. It then passes through a hole in the plate. How is the energy in the field dissipated? By what method does current flow from the cathode to the anode thus completing the circuit and allowing energy to be consumed? Like I said it seems to be static to me and thus no energy is used to accelerate the particle. I could just assume that the field will be damped and go on with life but I can no longer take it!

My second question is also to satisfy my curiosity:(edit) but it was a retarded question.

 

[vanesch]

I have a problem, something that I should know but slipped through the cracks.

I have posted this in another thread but I will re-post it here in truncate. the other thread is https://www.physicsforums.com/showthread.php?t=185203 (I hope I referenced this right.) anyway I do not intend to duplicate the same questions but I have questions more appropriate to ask in an engineering forum.

Here is the question:

If a particle is accelerated within a field it will have the energy imparted on it to the proportion of the potential of the field. This field (of which I see as static) is removed before the particle reaches the plate accelerating it. It then passes through a hole in the plate. How is the energy in the field dissipated? By what method does current flow from the cathode to the anode thus completing the circuit and allowing energy to be consumed? Like I said it seems to be static to me and thus no energy is used to accelerate the particle. I could just assume that the field will be damped and go on with life but I can no longer take it!

The answer is: induced charge ! The movement of the charged particle induces charge movement on the field-generating plates which correspond exactly to the consumed energy (the energy transferred from the voltage source to the accelerated particle).
Look op the Shockley-Ramo theorem.

As to your second question, I don't really understand what you're asking...

 

[lilrex]

As to your second question, I don't really understand what you're asking...

(Edit): don’t worry about it, it was a retarded question. Thank you for the direction in my previous question.

 

[lilrex]

What problems would one expect with high current accelerated beams?

I was wondering when reading a paper on neutron spallation experiments where the beam current was 10ma @ 2-4 GeV (an assumtion). He quoted transmutation times of 3 to 201mg/month depending on what the target element is.

It appears of course that higher current would be desirable but what is the cost? Where is the practical limit to the current of 100 to 500 MeV accelerators that could be used for ADS for the purpose of waste destruction? I haven’t looked at all of the accelerators published but I have not found impressive performers in terms of current at energy high enough to use for spallation.

That paper referenced is doi:10.1088/1742-6596/41/1/053(Experienced gained during 10 years transmutation experiments in Dubna)

 

[vanesch]

It appears of course that higher current would be desirable but what is the cost? Where is the practical limit to the current of 100 to 500 MeV accelerators that could be used for ADS for the purpose of waste destruction? I haven’t looked at all of the accelerators published but I have not found impressive performers in terms of current at energy high enough to use for spallation.

That's indeed a very smart remark. I personally have my doubts about the practical and economical feasibility of ADS systems. It makes me think a bit about fusion research. Of course it is possible in principle, and with enough engineering, one will eventually succeed. The question is, however, if the ultimate system is going to be practical. For a scientific experiment, one doesn't care, because only one or a few prototypes have to be built, and one only needs to obtain the result a few times (to get confirmation). But for industrial purposes, this is different.

In as much as I understand it, practical ADS machines need accelerator technology that is yet far from what is currently done in scientific settings, mainly because of:
- the high current
- the stability in time (because in a subcritical reactor, you cannot permit yourself to have fluctuations of a factor of 3 or so in thermal power over a time lapse of minutes: this strains the thermal load far too much on many critical components)

The closest one comes is with the SINQ facility in Zurich but that's still miles from the design values.

Maybe these engineering difficulties can be overcome, but, as you say, at what price ?

 

[ZapperZ]

I reread the OP and I don't quite understand the question.

I work in accelerator physics so I know a bit about the acceleration scheme here. In practically all the high-energy accelerators (and even low energy ones used at SNS and light sources), you have an RF source from a Klystron that is fed to an accelerating cavity via a series of waveguides. The accelerating cavity then will have either a standing wave mode, or a traveling wave mode (depending on what it is for). It is this RF field that induces the charged particle to accelerate. A typical EM field geometry would be a TM01 mode, where the E-field amplitude is largest along the axis of the cavity. In a LINAC, you can stack a series of these cavities, so as the charged particle passes through from one to the other, it continues to be accelerated.

So there really isn't a charge accumulation on the walls of the cavities that is causing the field for acceleration. While there are induced charges and induced currents in the walls, these are not something we want in the first place since they can cause power loss.

Zz.

 

[Morbius]

This field (of which I see as static) is removed before the particle reaches the plate accelerating it. It then passes through a hole in the plate. How is the energy in the field dissipated?

lilrex,

If I understand your question properly - when one changes the magnetic field - for example reverses
the polarity - where does the energy in the field go when it was decreased to zero before being reversed.

When the field collapses; that energy induces current in the coil that creates the field in the first place.

An elementary example of this is the ignition coil on your car. A secondary winding in the coil is
energized and creates a magnetic field. The secondary current is then interupted [ by the "points" in
the distributor in older cars - and by a computer controlled system in newer cars.].

The magnetic field then collapses. Anytime the magnetic field is changing in the vicinity of a coil
or other loop of conductor - it induces a current in that conductor. In the case of the ignition coil, the
field collapse induces current in the primary coil. Since the primary coil has a many more turns than
the secondary - the voltage induced in the primary is much greater than the 12 Volts in the secondary;
and that's how you get the high voltage that generates the sparks in the spark plugs.

Dr. Gregory Greenman
Physicist

 

[lilrex]

I am aware of the current accelerating technologies in a typical Linac and the such (Though I do not fully understand them yet). I understand that my question is simplified in terms of operating principle but I wanted to know "mechanically" how power is transferred from the electrostatic field to the particle. Since the older types of accelerators are a bit more ‘strait forward’ in there operation it would help me understand the mode of energy transfer more clearly. My question would apply to the cyclotron where you have D plates providing the accelerating field and of course the old accelerators based on Van de Graff generators. I suspect that the operation principles are the same with the high energy linacs they are just more cleverly applied.

 

[lilrex]

If I understand your question properly - when one changes the magnetic field - for example reverses
the polarity...

I am not sure how to properly word the question for the best communication of meaning but I was looking at pure electrostatic attraction. Like fields oppose and opposite fields attract. Being that the particle is charged in the case of a proton positively, it will be attracted to a negative plate and appose a positive plate. The charged particle will undergo a translation towards the negative plate the magnitude of which is proportional to the potential of the plate. A plate which has a -1 volt potential will impart 1eV of energy to the particle. This increase in energy will be transferred from the plate. vanesch suggested induced charge is responsible for this effect, which to me is still a little fuzzy, I will investigate it further. Assuming no other losses in the system this relationship will represent the power consumption of the accelerator.

Perhaps this expresses the question better. Cheers!

 

[Morbius]

I am not sure how to properly word the question for the best communication of meaning but I was looking at pure electrostatic attraction.

lilrex,

In any case; the answer is the same. If your static electric field is created by some conductors;
and you turn off the power - the field collapses into the conductors that created it.

Dr. Gregory Greenman
Physicist

 

[vanesch]

The way I understood the OP's question was as follows:
you have essentially a kind of parallel-plate capacitor with a hole in one plate (the anode). An electron starts its journey close to the cathode, and accelerates towards the anode, and passes through the hole, to go on, accelerated as it is, at high speed in free space.
I thought that the question was: the electron has gained energy, and the E-field is still the same, where did this energy come from ?
And my answer was: from the voltage source that keeps the capacitor plates at equal potential, because, even though the electron didn't enter physically the circuit, it did induce a charge into the anode when moving through the field, which involved the voltage source give off a certain current during this time, and hence delivering an amount of energy, which equals the energy gained by the electron.

 

[lilrex]

Vanesch, according to your post you understood my post perfectly. I knew that the energy transferred was conserved I just didn’t know the process. At first glance the Shockley-Ramo theorem deals with capacitive entities I still need to study it further. Vanesch thank you for your reply as it was informative.

Morbius, thank you for your replies also. ZapperZ I hope to pick your brain further!

 

[lilrex]

If one had an idea for a PA that could produce say a (insert optimistic power here)MW beam where would they start on getting it built? I ask this because of all the restrictions on building a radiation producing machines. If someone had a bright idea they couldn’t even build a scaled version of it to prove the concepts. I am sure that the situation is not uncommon though I just wonder what procedure one would go though to make an idea in this field a reality.