I will tell you something this morning about some work that is not directly my own work
but in which I have a little bit participated and that’s work that is going on in many places over the world in the United States
especially at Stanford, at CERN in Geneva, in Russia Novosibirsk, in Japan and various other places.
And this is work that’s trying to find a solution for the problem of making very large linear electron-positron colliders.
Now, where do we want to make those?
As you know with, (this doesn’t seem to work) with old-fashioned accelerators one accelerates a particle and
Okay you accelerate the particle and shoot it against this fixed particle and now you want to look at the interaction.
But you have to conserve the momentum and since this particle has a momentum to start with
your final product must have the same momentum.
And therefore a lot of this energy is going to sit in the kinetic energy of the product, of the interaction
and what you have left for instance producing new particles or changing states or so is the energy in the centre of mass.
And that is much smaller than this energy you’ve put in, it only increases with the square root.
Now in classical physics this energy in centre of mass is just one half of this,
but if you take into account special relativity you’ll find that it works like this and especially for electrons
which have a low mass this is very small.
If you accelerate an electron to 1,000 GeV and you shoot it on a fixed electron the energy in the centre of mass is only 1 GeV.
So that’s why modern accelerators work as colliders where you shoot two particles against each other
and you get twice the energy of each particle in the centre of mass, which is very much more interesting.
Now, why electrons and positrons?
You can also accelerate and collide protons and protons or antiprotons.
The point is that you only want to study not proton-proton collisions
but you want to study quark-quark collisions, at very high energy.
Of course these protons consist of quarks and gluons keeping them together and if you have a quark-quark collision
with a certain energy you need at least ten times as much energy in your proton-proton system
to get the comparable quark-quark collision energy as you would get here.
So if you build a hadron collider you must have about ten times more energy to get comparable physics.
Also hadron colliders give much more background
because the actual quark-quark interactions at high energy you want to study have a very low cross-section.
That goes in with the energy squared, whereas all kinds of other peripheral processes in this collision have a cross-section
that is maybe ten orders of magnitude bigger.
And that gives you a lot of background.
Now, you might say why doesn’t everyone build electron-positron colliders
and that is because it’s very much more difficult than to build hadron colliders.
The reason it is more difficult is of course that you are used to building these circular machines
with protons and protons colliding against each other.
And you can bend them in the circle which means that they meet each other many, many times
whereas in a linear collider they can only meet once.
And you cannot use electrons in circular colliders because they radiate when you deflect them
and especially at a high energy they radiate very much.
It depends very strongly on energy.
So we are building an electron-positron collider that is circular at CERN and that will have 50 or 100 GeV energy.
And that’s about the highest that we can ever build in electron-positron collider for because it just gets,
you get too much radiation if you make higher energy.
So if you use higher energy you have to make linear colliders
and the only example we have at present is this machine at Stanford, so called SLC.
And it works as follows.
You have an electron gun, you accelerate electrons and accelerate them in this linac,
and shoot them on a target and make positrons here, you make a shower.
You collect the positrons put them back and accelerate them again.
And put them in a little dumping ring here.
And this dumping ring is to make the beam more intense, to dump the oscillations and the energy spread.
So it circulates here for some time and then you make other electrons and accelerate them
and also put them in a little dumping ring.
And when both electrons and positrons have been dumped sufficiently, you eject them from these rings and accelerate them together,
they are very near together in this common ring or accelerator and then electrons go one way
and the positrons the other way and there they interact.
Now this trick of using only one accelerator too accelerate both the electrons and positron you can use
because here we have 50 GeV and you can still bend them around.
But if you want to go to higher energies like we would like 1 GeV then you cannot do this trick at all.
They would radiate far too much.
So you have to make two linear colliders that are really co-linear or maybe at a very, very small angle.
What we would like would be 1 GeV twenty times more, and since the interesting cross-sections go with 1/e^2,
we also need a very much higher luminosity.
And that is really what the problem is, it’s not difficult to make a linac that gives a very high energy
but what makes the difficulty is this high luminosity.
Of course these machines are very much bigger than what Giaever told us about in his lecture.
But they are very much less big than the machines that Blumberg had told us about.
So that is the constellation.
Now, there is the luminosity of these machines which you can very simply describe by this equation,
it is the square of number of Pi that goes per bunch, times the frequency
at which you collate these bunches divided by, well, the cross section area.
This is for long beams.
Now if you want higher luminosity you can increase N or F but that also increase the powers in the beam
and the power in the beams is what limits these machines.
It gets very high, and it’s very difficult to make.
So what you want to do is make a very small cross-section at the interaction point.
You focus your beams to very small points.
For instance in a SLAC machine the design value for the focuses about the micron what they have actually achieved
I think is four or five microns but they are still busy running it in, it’s not yet finished.
What we want to do in our new machines of 1 GeV is something in the order of 50 nanometres or something like that.
It’s very much smaller.
Now the limits on making very small spot sizes, technological limits, it’s difficult to make strong enough focusing lenses,
it’s difficult to have a chromatic aberration that’s small enough and so on.
And then there are two other limits which are disruption and what is called,
not a very beautiful word, beamstrahlung and what's that?
That's if you have a bunch of electrons and positrons
and you shoot a particle in the opposite direction this green thing is a bunch, that is a particle.
It’s deflected by the field from this bunch and it pinches,
the other one is also deflected by the field from this bunch and it also pinches.
Now you might think that is nice, because the blue cross-section got smaller,
you got higher luminosity and in fact up to a certain point it’s nice.
But as its effect gets stronger and stronger the focusing gets so strong that the beam more or less explodes
before it has had any chance to interact.
Well I will not go into this because I haven’t got much time.
But that is the beam disruption and what also happens during this process is that as the particles are being deflected
they radiate and that’s called beamstrahlung as analogy to bremsstrahlung.
And that depends in a different way from the parameters of the beam, like number of particles and the cross-section and so on.
And therefore these two things together limit the parameters very strongly.
And in fact if you specify what luminosity you want to have and what beam power you allow and what disruption factor you allow
and what beamstrahlung factor you allow, then most of the parameters are pretty well fixed.
There are a few that you can still choose like the frequency of your accelerator, but there isn’t very much choice.
Now one of the tricks you can do is to make not round beams but to make flat beams in the collision point.
Because if you keep the same area you will have the same luminosity.
But obviously in this case, well you can see the magnetic lines of force would be longer than here so you will have less field
and less disruption, less beamstrahlung.
But the problem with that is of course that if you want to keep the same area and still make a flat beam it means
that the beam heights will have to be smaller and even smaller than it would already be.
And that makes it even more difficult.
Now to make a very small beam spot of course one thing you can do is to start out with a very small beam,
to have a very low emittance beam, very dense.
And that’s what these dumping rings are for.
Particle still round in this dumping ring and being deflected, they radiate.
Particles with higher energy radiate more than particles with lower energy.
And that reduces the energy spread.
Of course they are kept at the same energy by a radio frequency accelerating system.
And also when a particle makes oscillations like this and it radiates while its going up
then some of the transverse momentum is also reduced and therefore it also gives dumping of betatron oscillations
if you arrange the focusing properly.
These dumping rings are quite an art in themselves you construct, usually the radiation is intensified
by using wigglers like you do in free electron lasers.
By all the bending you increase the radiation.
But I cannot go into any detail in this talk.
Now, how does a linear accelerator work like the one in Stanford for instance?
It’s built up out of accelerating sections which are kind of radio frequency structures.
They are tubes divided by level irises which are plates with a hole in the middle and you fill this structure with RF energy
made in transmitting tubes, glass ones, which give a short pulse, typically a microsecond or few microseconds.
And this RF frequency is in the gigahertz region, that fills these, these are like little cavities that are all coupled.
So the cavities are filled one by one, it propagates slowly here with good velocity, which was lower than the light velocity.
And by the time the structure has filled that’s what the length of both corresponds to, you shoot through a particle
which goes of course much faster, because light velocity.
And then you shoot through a bunch of particles and they take part of the energy out of the structure and are accelerated.
Now it would be very nice for the sake of efficiency to take all of the energy out of this structure with your particles
but that you cannot do because if you do that then the last particle will see no field at all
and the front particle will see the full field.
So you have a very large energy spread.
And to reduce the energy spread is very necessary because a large energy spread makes it very difficult
to make your final focusing, you get chromatic aberration.
So you can at most take out something like 5% of the energy of the structures
and the rest is going into the termination, it’s lost.
But you have to post these accelerators, if you would do this, you’d see the powers you need here it would be terrific,
it would heat very much, too much.
Now, so the problem is that if we want twenty times more energy than SLC
and this thing is 3 kilometres long we would then get two linacs of 60 kilometres and that’s far too expensive, far too long.
So we want to have a higher accelerating gradient.
That of course that increases again the power we need.
And the power is increased because we need higher energy and the power is increased because we need a higher luminosity.
So we really are limited by power very much.
Now one way to solve this would of course be to use a superconducting linac which you could operate the same,
you could have a very high bunch frequency.
No problem with efficiency, it would be very efficient apart from the cryogenic losses.
Then the problem is that with the superconducting cavities you can only make very low gradients.
This is about the highest it has been made for practically operating cavities.
And what we need is at least three or four times more than that, otherwise these accelerators get too long.
Now the problem here is not a fundamental one, but the problem is that these superconducting cavities are limited
by field emission effects, by little impurities on the surfaces, they have to be cleaned very carefully.
Then there are always some hotspots that you have to detect and to clean again.
And to do that for a 10 kilometre length accelerator is unthinkable at the moment.
So this is completely out.
Maybe the higher temperature superconductivity will give a solution but we are still very, very far from the parameters we need,
we need high current densities and very high cues.
And that is still not solved.
Now I propose to tell you various ways that have been thought of to improve the construction of these accelerators,
various new methods that have been thought of.
Most of which are at present as far as we can see not immediately useful
but I wanted to tell you about this because it’s fun – it’s nice physics.
Now one of the things that have been proposed is a switched-power linac which is like this, you have a lot of discs,
parallel discs with hole in the middle and around there are rings here that go around like this
and this is a blown-up image of this.
This is a ring which you charge at say 100 kilovolt or so and this is a photocathode surface on which the laser force is erected.
It discharges your ring and there’s an electrical pulse running to the centre.
And because here of course the radius gets smaller the field strength gets bigger.
You get very high fields here in the centre and you use that to accelerate your beam.
Now this is a very nice idea and it has been worked on very hard, mainly on paper but also some models have been built.
One of the big problems with early photocathode is to make them reliable
and it’s much too early yet to be sure that that will work.
Also the efficiency of these things it looks at first site as if it may be better than radio frequency
because the force gets in only once and not for a microsecond, and it should be more efficient in principle.
But it hasn’t yet been proved that this is so.
Now, one other class of accelerators uses or proposes to use wakefields.
What is a wakefield?
If you send a bunch of particles through one of these accelerating structures,
suppose you have no voltage in the structure to start with.
Then these particles will have lines of force associated with them.
I’ve tried to draw the electrical lines of force here.
And they will fill these cavities with energy and they will stay behind because these particles go at light velocity
and this field can never overtake it anymore.
Now it looks as if this is a small technical problem but it is very fundamental
because this is the way the particles are accelerated.
After all they have to take energy out of the electromagnetic field and to do that the electromagnetic field has to be reduced
and that’s the wakefield that does that.
Wakefield is very important.
Now you can also think of using that, you take an empty structure and you shoot a bunch through it
but with wakefields behind it and you use these wakefields to accelerate other bunches.
Now the problem is of course that these other bunches are accelerated but once you shoot in first these are decelerated
and you would like to have a large transformation ratio to accelerate the bunches that come behind much more
than you decelerate your first bunch.
Now that is not so easy, there is a theorem about that which I will skip,
which says that you cannot do that very easily unless you use special tricks.
And one of the tricks has been tried out in Hamburg at DESY and it is like this,
you again have these discs with holes and now this primary beam, this driving beam is a ring here.
A ring-shaped beam and it makes wakefields that go outside and are reflected here and this is what represents the wakefield.
It goes inward and it is amplified, the voltage is amplified because here the characteristic impedance gets higher and higher.
And here is then the ring that is accelerated and which sees a very high gradient.
Now this is of course very nice.
It’s a bit complicated because we have to make these ring-shaped beams.
You have to be very careful that there are no transfer field components here that would spoil your … (inaudible, 17.02) beam.
And this is still being studied in great detail and maybe it will lead to some solution.
It is however rather complicated and it does not solve the problem of efficiency that is there like in all other accelerators.
Now, one other way of using wakefields is by using plasma.
You use plasma oscillations.
Now what happens in a plasma, you have electrons and you have ions and these electrons can oscillate,
they have mass and they repel each other.
It’s a little bit like an elastic medium.
But it is different if you have an acoustic wave in the air the particles collide and that’s when they fill each other.
But electrons fill each other from a distance because of their electromagnetic fields.
So if you write down the equations, maximal equations and the equations of movement
you find that there is a good velocity corresponding to these oscillations that this happens to be zero in the plasma.
That’s very nice, because it means that if you now shoot a bunch of particles through the plasma, this grey thing here.
In the wake of that you have these oscillations, this is trying to represent density of fluctuations
and so this is kind of wave that follows this bunch.
So you have a face velocity that is the same as the bunch velocity but you have a good velocity zero
which means that this modulation of the density doesn’t spread out.
It remains confined to the wake of this bunch.
Of course the fields, the electric fields which is supposed to be these lines here go a little bit outside but not very much.
Now there’s a plasma wavelength which is a characteristic of the plasma,
it only depends on the density of the gas and on some fundamental constants.
It can be very small, it can be in the order of tens of millimetres.
And the maximum fields you can make are easy to calculate and they are in the order of GeV per meter which is extremely high.
However that hasn’t yet been done, that works very nicely on paper but nobody has yet made fields of GeV per meter.
The idea then is to use a driving bunch and to let it be followed by a smaller bunch that gets accelerated by the wakefield.
Now again this wakefield you want to have a high transformation ratio.
Now one of the tricks you can do is to have, this is the bunch direction of movement, this is the density of the driving bunch
and you see it’s like a sore tooth, it’s like a motor boat that goes through water
and it has a shape like a triangle and it softly pushes the water away.
And behind it, it suddenly ends and the water makes enormous waves.
You see these waves here, this is the wakefield and you can accelerate this bunch of particles
if you put it here at the maximum of that wave.
And that is much higher than this and in fact the ratio of the two is 2 Pi N, where N is the number of wave length,
of plasma wave length, this length extends over.
Of course the driving bunch must be much more intense than that for conservation of energy.
Now this all looks very nice, and a lot of work has been done on that on paper,
but the problem is that apart from accelerating fields there are also focusing fields.
And you might think that’s very nice because it focuses your beam but the focusing field tends to be very strong.
It is 90 degrees out of phase with the accelerating field so it if you put your particles here they are not focused in principle.
If you could put them slightly in front then they would be focused.
But if you calculate it you find that for practical solutions you can only tolerate bunches
that are of the order of angstroms long.
That is too short.
And this focusing is much too strong unless you make this driving beam very wide
and if you make it very wide then the efficiency gets very bad.
Because then the wakefield extends over wider region, whereas your driven beam has a very low emittance, it’s very, very narrow.
So this focusing problem is really the big problem to be solved, also the focusing of the driving beam is much too strong.
Because the driving beam of course has low energy.
And that is still not solved.
There is one other way to make waves in plasma that do very similar things, which the plasma beat wave principle.
Here you use two light waves from lasers which beat with each other
and if you have a single wave then the electrons of the plasma will move like this in figures of eight.
Because the electric field is without angles and because the magnetic fields do this and it will not be accelerated.
But if you have a beat like this it tends to go down the slope, these figures of eight deform
and particles move in towards here and you get density fluctuations of your electrons that again move in this direction
with a phase velocity and they can then accelerate other particles.
Now, this principle even has more problems than the plasma wakefield accelerator and although people are still working on it,
it doesn’t promise very good results very soon.
Now, other possibilities, we stored energy in one of these radio frequency structures of linacs,
it’s inversely proportional to the square of the frequency.
Because if you increase your frequency you can reduce the size and for the same field you have less energy.
So the solution is to use very high frequencies.
In fact people have proposed to use laser frequencies but then you have to have your accelerated beam very,
very near to the accelerator structure and in fact it turns out that this is not practical.
But what you can do is increase the presently used frequencies of say 3 gigahertz to ten times that value
where you have a wave length of a centimetre and you may just be able to make suitable structures.
So that is one approach that is at present looks the most likely thing that we could possibly use.
The problem is that high frequency sources are not available at this wavelength at least not of sufficient power.
So one idea is to instead of using klystrons, which we don’t have at these frequencies,
to use a single beam that runs parallel to the beam you want to accelerate.
So in fact you combine all the klystrons which have their own electron beams into one single beam.
And one of the ways to do that is what they have been doing at Berkeley and Livermore, you take a low energy beam,
you accelerate it from time to time by so-called induction accelerator gaps and in between you have wigglers
where the electrons are made to wiggle and they then emit photons and you get a frequency
that depends on the wiggler frequency and on the energy of these particles.
And you make for instance 30, I think they use 35 gigahertz and use that for your main linac.
Now they have made actually of the order of one gigawatt per meter or so which is more or less in the order of magnitude you want.
And this may well be the way to make high energy accelerators although there are serious problems with this approach.
One of the problems is that these electrons are not really very relativistic, there are a few MeV
and that’s because otherwise you don’t get the right frequency.
And if these electrons are not quite relativistic their speed varies, here they are decelerated and accelerated and so on.
And this frequency will also, the phase of the signal will also vary a little bit and it is extremely difficult
to keep the phase of all these generators constant over the whole ten kilometre length of the accelerator.
And that is one of the big problems, there are some other problems.
Now, one of the approaches is this one, that is what we are studying at CERN, now we have again two beams.
The drive linac is accelerated from time to time at distances by superconducting cavities at the lowest frequency
and it is then bunched at this frequency.
But there are also little bunchlets, the bunches of 350 megahertz are subdivided in little bunches of 30 gigahertz
and they pass through accelerating structures here where the wakefield produces a wave that fills these structures
and then you can get a very high gradient here whereas the gradient here is very low.
It turns out that the ratio of gradients here and there scales with the ratio of these frequencies.
So you can use very low frequency here, like we do here, compared with this one.
And that is just what you want, because these superconducting cavities at these frequencies exist,
being built for the lab machine.
So this is the approach which on paper seems at least to give a good solution from the RF point of view,
a point of view that all seems to work very nicely.
We have made some models but it is getting a bit too late so I’ll skip that.
I would like to say something about one of the other problems in these accelerators.
That problem is the transverse wakefields.
I told you about the longitudinal wakefields but the particle that is not exactly in the centre,
on the centre axis of the accelerator will also cause transverse wakefields, transverse electric fields
which will deflect particles coming after these particles.
Now if you have a particle that’s offset it will make oscillations because with the focusing structure
and these wakefields will also oscillate in the same way.
And the particles at the tail of the bunch will then be deflected by these wakefields also in an oscillatory way.
And if they have the same frequency as the particles in front of the bunch then there will be resonance
and these bunches will break up and that is in fact one of the things that limits Stanford linac.
This problem has been really a plague for people who designed this high energy machines.
But we think that at CERN we have now found a solution to that.
One of the solutions that people propose is to have very, very strong focusing and then you can reduce this effect.
But it’s very expensive and it makes the alignment of the machine very, very critical.
The other possibility is to have slightly different focusing frequency between the front and the tail of the bunch.
And one way to do that which we have resurrected you might say at CERN is to use in these accelerating structures
instead of little round holes to use slits which cause radio frequency focusing.
And the focusing then depends on the place of the particle in the bunch and you make quite a big difference
between the focusing of the front of the bunch and the end of the bunch.
And if you adjust the sign properly in fact these wakefields may even dump the offsets that you have initially.
So the result will then be that initial beam offsets will be reduced by these wakefields
and they will make the alignment of the whole machine much easier.
Now this is something I cannot go into much detail about but I think it is one of the big advances
that we have made in the last year at CERN.
Now one of the problems is of course the final focus but I see that I'm nearly running out of time.
So I am only going to mention that the problem is to focus the beam to a very small point for all different energies in the beam.
So a chromatic aberration is the big problem.
We somehow have to compensate that.
And that is done with very complicated systems where you deflect the beams a little bit and you don’t have a dispersion
and particles of different energy are at different places and you use nonlinear lenses to give them different focusing.
That problem is not yet quite solved on paper, we have, at CERN we have designed the machine with certain parameters.
But we have not yet completely obtained a focusing system on paper that fits these parameters.
It is fair to say that nobody anywhere has yet made a completely coherent design so that even if we would get the money today
we would not know how to build such a machine.
But we are getting near, there is quite clear progress visible and that is a thing I would like to end with.
The problems to be solved are these, to make a very intense bunch for the driving beams, to design a proper final focus,
to work out how we can get sufficiently small tolerance in alignment and you see the transverse wakefield there I’ve crossed out
because since I gave this talk last time I think this has been solved.
Now I wouldn't like to leave you with the impression that this is all very, very difficult,
it is true that it is very, very difficult but there are many interesting problems for young physicists to work on.
And I can all recommend you, if you have some time to think about these problems and to help us solve these propositions.
Thank you very much.