# Radio Frequency Acceleration in Particle Accelerators

So, I've been really interested in Particle Physics since 6th grade when I did a project on particle accelerators. I understand most of it, except for one thing, the radio frequency cavities which are used for acceleration. I just want to ask, how do the Superconducting Radio Frequency Cavities accelerate particles and do they have to be superconducting?

BvU
Homework Helper
The superconducting isn't needed in first principle, but it allows a certain energy efficiency that makes these big accelerators feasible in the first place.

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As far as I understand the radio waves get amplified by the resonance of the cavity which somehow accelerates the ions. What I am asking is what does superconductivity do, how is the resonance calculated, and how resonance can accelerate ions. Thanks for your time.

ZapperZ
Staff Emeritus
First of all, do you understand how normal RF cavities work in particle accelerators? It has nothing to do with amplification. You need to understand this first before tackling superconducting cavities.

Zz.

mfb
Mentor
The cavities "just" reduce the losses. You could accelerate the beams with simple electromagnetic radiation in vacuum but it would be horribly inefficient. In cavities you get a resonance and losses can be quite small. Loss comes (among other things) from resistance in the walls -> superconducting cavities have smaller losses.

sophiecentaur
Gold Member
2020 Award
the radio waves get amplified by the resonance of the cavity
What happens is that the cavity acts as a transformer. At resonance, there are peaks of voltage in some places in the cavity (the gap) so the bursts of accelerating Field are higher than you would get with the straight (50Ω) output of the transmitter amplifier.

But doesn't the pumping in a radio wave that matches the resonance frequency amplify the radio wave? As far as I know, the resonance frequency is supposed to be a key part of the system. How would you calculate the resonance frequency of the cavity and find out what that optimal resonance frequency is given the velocity of the particle?

sophiecentaur
Gold Member
2020 Award
But doesn't the pumping in a radio wave that matches the resonance frequency amplify the radio wave?
Amplification is a term tat generally applies to adding Power from a supply, to make a signal bigger. You don't get any more Power out of a resonator than you put in it. A transformer is not an amplifier. A resonator is just a form of transformer.
To use a resonator in an accelerator, you 'just' need to make sure that the bunches of particles going through the gap arrive at the same rate as the resonance maxima of Volts across the gap. (And that the RF feed is the right frequency.)

General Scientist
ZapperZ
Staff Emeritus
But doesn't the pumping in a radio wave that matches the resonance frequency amplify the radio wave? As far as I know, the resonance frequency is supposed to be a key part of the system. How would you calculate the resonance frequency of the cavity and find out what that optimal resonance frequency is given the velocity of the particle?
A cavity is designed so that it has a particular resonant frequency that matches the power source, such as from a klystron. But the klystron itself produced RF with a rather broader band. This is not good for particle acceleration, because the wider the frequency range, the poorer the quality of the accelerated beam (i.e. it will be accelerated over a larger energy spread).

So the RF from the klystron goes into a resonant cavity (or a series of resonant cavities such as in a LINAC) that has been tuned to a particular frequency that matches the central frequency from the power source. Depending on how narrow of a band the resonant cavity can accept, there will be a narrow frequency range that can exist inside the cavity. All the other frequencies from the power source will be reflected back or will not make it into the cavity.

One calculates the resonant frequency via the design of the geometry of the system. We have to do that first, because these things are horribly expensive to build. Even after one has been built, we still have to do fine adjustments to it via the built-in divots and also by adjusting the temperature of the structure to match exactly the frequency that we want.

Zz.

Klystron, mfb and General Scientist
Zapper, are particle accelerators with RF cavities still using klystrons today as the primary RF output source which is then narrowed down to a more precise frequency range with the help of cavities as you said?

What do you mean when you say "the power source is matched to the cavity in terms of frequency" ? Does that mean that the ions are produced or the ones already produced accelerated into the cavity at the exact rate which matches the field peaks in the cavity much like a surfer can accelerate if he matches the peak of the wave?

ZapperZ
Staff Emeritus
Zapper, are particle accelerators with RF cavities still using klystrons today as the primary RF output source which is then narrowed down to a more precise frequency range with the help of cavities as you said?
If you ever get a chance to visit a synchrotron light source, you'll see a bank of kylstrons humming along doing their thing.

Note that there are a huge number of particle accelerators in the world, and more than 95% of them have nothing to do with high energy physics or particle collider experiments. Your doctor's office may have one when they have to take a x-ray. Many of these do not need something as large as a klystron, since they only require, say, keV of electron energies. But big facilities such as particle colliders, synchrotron light sources, FELs, etc... will use these klystrons.

What do you mean when you say "the power source is matched to the cavity in terms of frequency" ? Does that mean that the ions are produced or the ones already produced accelerated into the cavity at the exact rate which matches the field peaks in the cavity much like a surfer can accelerate if he matches the peak of the wave?
When you build an accelerator, you specify not only the level of power out of your power source, but also the frequency that you'll be operating. So your power source will come with such output power and frequency. However, these are not as narrow of a band as required by most accelerator. They tend to be wider than what we need them for. So while your accelerating structures (such as these cavities) also will have a design to operate at that same frequency, these structures then to be more refined and accurate in their design based on what the accelerator is used for. Electron beams for FELs, for example, have very high and narrow tolerance in terms of energy and emittance, for example. No raw RF from a klystron can satisfy such narrow tolerance.

Zz.

I just read in LHC page that LHC also uses klysrons and cavities, why semiconductors are not used , is it because they can't handle the very high energies required for these applications? Or is there a specific need for a physical electron beam which I doubt?

Is there a schematic anywhere where one could see in detail how the klystron and cavity work more precisely?

thanks.

Staff Emeritus
why semiconductors are not used
How would semiconductors help?

ZapperZ
Staff Emeritus
I just read in LHC page that LHC also uses klysrons and cavities, why semiconductors are not used , is it because they can't handle the very high energies required for these applications? Or is there a specific need for a physical electron beam which I doubt?

Is there a schematic anywhere where one could see in detail how the klystron and cavity work more precisely?

thanks.
As Vanadium has asked, when you ask why not use such-and-such, you need to explain why, rather than wait for someone to give contrary views.

In producing accelerating structures, one must consider not just the physics, but also the engineering and economic aspects. Machining copper structures is easier (Cu is a rather soft metal), and it is quite robust for what they are used for. And remember when I mentioned about these structures having divots and also us being able to slightly change their temperatures to get the exact frequency or most power into the structure that we need. You can't do that with semiconductors, at least not as easily and not as cheaply. You also need them to be large, and it is often difficult to have a uniform, homogeneous solid semiconductor of such size (you can't braise them the way you can Cu or other metals).

But the other issue that we have with semiconductor structures is that, the RF pulse from the klystron is typically long (order of ms). From our experience, long RF pulses at very high gradient tend to induce not only breakdown in these structures, but also have ample opportunities to create multipactor events on the semiconductor surfaces, which is not something that we want (semiconductors tend to have a higher secondary emission than metals).

Having said all of that, there are advanced accelerator concepts that used semiconducting structures to generate wakefields that are then used to accelerate bunches of electrons. The wakefields are generated by very short and very large charge electron bunches. Such technique is still in research and development stage, although we have seen several proof-of-principle demonstrations.

But the workhorse of normal accelerating structures is still Cu, with Nb being the superconducting counterpart.

Zz.

I’ve also been interested in the LHC. The following may be of interest and do a good job of explaining things, although you or someone may be able to find something newer. You might look for some books by Don Lincoln on the LHC as well...really good read.

Accelerating: Radio Frequency cavities (with excellent video)

RF Power Generation in LHC
http://accelconf.web.cern.ch/Accelconf/p03/PAPERS/ROAA005.PDF

The LHC Superconducting RF System
https://cds.cern.ch/record/410377/files/lhc-project-report-316.pdf

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sophiecentaur
Gold Member
2020 Award
I just read in LHC page that LHC also uses klysrons and cavities, why semiconductors are not used , is it because they can't handle the very high energies required for these applications? Or is there a specific need for a physical electron beam which I doubt?

Is there a schematic anywhere where one could see in detail how the klystron and cavity work more precisely?

thanks.
This needs clearing up, I think.
The source of RF power is nothing to do with the effect of the RF field in a (not the klystron) cavity on the ion / electron beam in the experiment. It just so happens that the way the electrons in a klystron are also interacting with the RF field across a gap in the cavity.
Klysrons amplify by modulating the velocities of an electron beam on the input cavity. This causes 'bunching' of electrons as the fast ones catch up with the slow ones on each cycle of RF. This mechanism transfers DCPower from the beam into RF power 'on the beam'. The RF power is extracted from the beam with a second cavity and is fed to whatever device it's being used for. The klystron cavities are much wider bandwidth than the original source / driver circuit, which will be synthesised; they are just tuned for maximum / optimum setting. Google how a Klystron works but not the obsolete 10mW? reflex klystron which used to be used in school before Gunn diodes etc. became available.

ZapperZ
Staff Emeritus
This needs clearing up, I think.
The source of RF power is nothing to do with the effect of the RF field in a (not the klystron) cavity on the ion / electron beam in the experiment. It just so happens that the way the electrons in a klystron are also interacting with the RF field across a gap in the cavity.
Klysrons amplify by modulating the velocities of an electron beam on the input cavity. This causes 'bunching' of electrons as the fast ones catch up with the slow ones on each cycle of RF.
Er, no. The klystrons do not do this. The injection phase is what causes the tightening of the bunch. If, say, the charge bunch enters the beam at 70 degree phase of the RF, then early part of the bunch will not be accelerated as fast as the later part. If the bunch enters at 90-180 degrees, the bunch will be elongated.

This is simply a property of charge bunch interaction with a RF field.

Zz.

ZapperZ
Staff Emeritus
I sense a possibility of a huge misunderstanding here. So I'm going to clarify a bit what I've written.

I consider a "klystron" as a RF power source. The RF from this unit is then "piped" to the accelerator itself. So it can go to the charge source cavity, or to the accelerating structures (such as a linac). All of these accelerator units are connected, but not part, of the klystron. The klystron could easily be situated outside of the accelerator bunker/shielded area.

So the "cavities" or accelerating structures that I mentioned are part of the accelerator itself, since this is what was asked in the beginning of this thread (superconducting rf cavities). I was not taking about "cavities" in the klystron unit itself.

Zz.

sophiecentaur
Gold Member
2020 Award
Er, no. The klystrons do not do this. The injection phase is what causes the tightening of the bunch. If, say, the charge bunch enters the beam at 70 degree phase of the RF, then early part of the bunch will not be accelerated as fast as the later part. If the bunch enters at 90-180 degrees, the bunch will be elongated.

This is simply a property of charge bunch interaction with a RF field.

Zz.
That's an interesting comment. Are you referring to a straight amplifying Klystron? I worked on Klystrons some years ago and went through the theory fairly thoroughly of a simple two cavity (UHF ) Klystron. The only place where the electrons can be velocity modulated will be as they pass through the gap in the input cavity and the sinusoidal voltage across the gap is what modifies the velocity. During the passage through the drift tube, the beam becomes density modulated and the spectrum of the waveform is described pretty well in terms of Bessel Functions. It was all pretty much accepted technology so I think you must be describing something else. I can't remember coming across an "injection phase". Where would this occur? I'm pretty sure that UHF TV transmitters can't have changed much in the thirty or so years since I was involved with them. Broadcast Analogue TV klystrons used three or four cavities with offset tuning to produce the 7MHz or so bandwidth needed for the TV signal but that's steam age stuff and different techniques would apply for digital TV multiplex signals. But that's incidental to the basic principle of velocity modulation to density modulation of a beam (ditto for Travelling Wave Amplifiers )
I would expect some phase shift relative to the RF input due to the resonance in the cavity and the physical separation between the input loop coupling and the gap.
I looked at various sites and I couldn't find anything to contradict significantly what I though I knew already. Where are we 'adrift'?

ZapperZ
Staff Emeritus
That's an interesting comment. Are you referring to a straight amplifying Klystron? I worked on Klystrons some years ago and went through the theory fairly thoroughly of a simple two cavity (UHF ) Klystron. The only place where the electrons can be velocity modulated will be as they pass through the gap in the input cavity and the sinusoidal voltage across the gap is what modifies the velocity. During the passage through the drift tube, the beam becomes density modulated and the spectrum of the waveform is described pretty well in terms of Bessel Functions. It was all pretty much accepted technology so I think you must be describing something else. I can't remember coming across an "injection phase". Where would this occur? I'm pretty sure that UHF TV transmitters can't have changed much in the thirty or so years since I was involved with them. Broadcast Analogue TV klystrons used three or four cavities with offset tuning to produce the 7MHz or so bandwidth needed for the TV signal but that's steam age stuff and different techniques would apply for digital TV multiplex signals. But that's incidental to the basic principle of velocity modulation to density modulation of a beam (ditto for Travelling Wave Amplifiers )
I would expect some phase shift relative to the RF input due to the resonance in the cavity and the physical separation between the input loop coupling and the gap.
I looked at various sites and I couldn't find anything to contradict significantly what I though I knew already. Where are we 'adrift'?
Read Post #18. I was not describing the klystron. I was describing the RF that came from the klystron (or, for that matter, ANY RF power source) and being used in accelerating structures of an accelerator.

Zz.

sophiecentaur
Gold Member
2020 Award
The klystrons do not do this
I interpreted this as how they work (which had been what I wrote in my post)

Read Post #18. I was not describing the klystron. I was describing the RF that came from the klystron (or, for that matter, ANY RF power source) and being used in accelerating structures of an accelerator.

Zz.
That's a relief. My post was describing Klystron operation and I was trying to differentiate between the action of cavities in klystrons and in accelerators and pointing out that they are different pieces of hardware. The OP seemed to be lumping them together and also seemed to assume that the klystron would be generating its own RF - like the old types used in schools etc.

(or, for that matter, ANY RF power source)
Absolutely

ZapperZ
Staff Emeritus
Addendum: Maybe a figure will illustrate this clearer.

See this proceedings paper:

http://inspirehep.net/record/1363733/files/mop036.pdf

Look at Fig. 2. This is an example of an RF accelerating structure. It is a multicell structure, meaning that there is a series of cavities that is filled with RF field. Particles being accelerated are transferred from one cell to the next as it moves through the structure, being accelerated as they pass through the cell.

On the right end of the figure is the RF input, designated by the RF input coupler. This is where RF from whatever RF power source enters the structure. I mentioned klystron in the beginning because that is a common RF power source. I did not intend to discuss the workings of a klystron, since that isn't the issue here. This can easily be a microwave accelerating structure, and will need a microwave power source. Or it can be powered by a gerbil running in a cage.

Zz.

ParticleMan
Parts of this video about the LHC may also be of interest from a visual perspective or for something to talk to, specifically the parts around 1m in and around 7m in for those with limited time.

Tom.G
Ok, I watched an older video explaining klysrons to refresh what I knew, so a klystron is a high power high frequency switch made back in the days when semiconductors were no where near those power levels. So a DC power source both creates (thermal emission) and accelerates (PD across cathode-anode) an electron beam which is then "kicked" or disturbed by an electric field made from a magnetic field inside what looks to me as a one turn "current transformer" like cavity,
so it looks to me that this disturbance makes the electrons bunch up instead of going in a uniformly static beam but since they are still accelerated by the DC power applied to cathode-anode these bunches are still gaining energy and as they reach the second or third or any number of cavities they can now induce a AC field in that cavity with the designed frequency.

Is it true that a particular klystron can only have a small output frequency variation since part of the frequency determining factor is its shape and size both the cavities and drift tubes?

so in a particle accelerator such a klystron is made to inject what, physical electron beams into the accelerator cavities or EM waves with certain frequency?

So the cavities in the accelerator loop serve the same function as the cavities in a klystron , they accelerate passing particles only instead of electrons as in a klystron they accelerate ions? But in a klystron the electrons receive their energy from the PD across cathode-anode what then drives the ions in the accelerator tube?
My guess is unlike the electrons in a klystron the ions are driven by the cavity field if their passing is precisely timed with the peak of the field or something like that ?

thanks alot folks.

ZapperZ
Staff Emeritus