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Jim Rohlf | USLHC | USA

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The Ponderator: a one-trick pony

The annual US LHC Users Organization (USLUO) meeting took place at Argonne National Lab yesterday and today. It is a time when colleagues from competing LHC experiments get together and discuss a variety of common issues. It is also a time to meet informally with representatives from the funding agencies. John Huth told me he was going to blog about the meeting so I will leave all the wonderful physics which was discussed to him. It is also a time to meet new people. I met Eva Holtzer early on Friday morning when to her surprise her car was iced over and I lent her my scraper, “breaking the ice” so to speak. A short time later, she was to deliver a delightfully informative talk on the status and future of the LHC.

Most of us work at the LHC because of the excitement of being on the energy frontier. This has been the case also for many physicists working at the famous accelerators of yesteryear. Let us examine a bit of history. One of the great accelerator builders of the last century was Milton Stanley Livingston who was a student of E. O. Lawrence who won the Nobel Prize in 1939 for development of the cyclotron and the physics that was carried out with this marvelous device.

Livingston and Lawrence with the 27 inch cyclotron which accelerated protons to several MeV, about a million times less kinetic energy than the LHC (see EOL’s Nobel lecture).

Throughout his distinguished career, Livingston was at the center of just about every major development in accelerator technology. As a student he built the first working cyclotron at Berkeley under the direction of Lawrence who was so impressed with his work that he rushed into the lab one day and informed Livingston that he had to stop all work and immediately write his Ph.D. thesis in 2 weeks so he could meet a university deadline and be hired so they could begin work at once on a bigger cyclotron! His most lasting contribution was to that of  strong or “alternating gradient” focusing which greatly reduced the size and cost of magnets and is the operating principle of today’s synchrotrons, including the LHC.

Livingston was the first to point out that the maximum achievable energy was growing exponentially over time since the beginning of particle accelerators. Here is the famous original “Livingston” plot which has been copied and altered many times over since then:


The original plot from M. Stanley Livingston, “High Energy Accelrators” (1954). Livingston famously noted that accelerator energy was doubling every six years (dashed line). Life was good!

Now back to the LHC and the Eva’s talk. Of prime concern to the experimenters is the plan for this coming year in which there will be 20 weeks of proton-proton physics. The key parameters to yet be fixed are bunch spacing (25 or 50 ns, see my previous post on this), beam energy (3.5 or 4 TeV), and the value of β*. This last parameter is a measure of how focused (squeezed) the proton beams are when they collide. It may be thought of as the distance at which the beams are twice as spread out as at the collision point. Smaller is better in this case, corresponding to a better “squeeze”. In 2011 we ran at β*=1.5 m, which may be compared to the LHC design value of 0.5 m. The most likely scenario for 2012 would seem to be 4 TeV per beam, 50 ns bunch spacing, and β=0.7 m.

In 2013-14 there will be a long shutdown to prepare the LHC for operation at 7 TeV per beam. This will be followed by 3 years of physics from 2015-17. Keep in mind, however, that this is just a plan and the plan can change if something unforeseen happens. The year 2018 will be another shutdown year to prepare the LHC for its “ultimate parameters”. These are 2808 bunches (25 ns), β*=0.5, 7 TeV per beam, and a whopping 2.3 x 10^34 /cm^2/s (or 23/nb/s). See my cross/section luminosity post for what this means and why we care.

Now comes the most interesting part of Eva’s talk. What can we do next? Historically, this question has been asked over and over again and the answers are given in the Livingston plot. Needless to say such scenarios are VERY PRELIMINARY, especially extrapolating out more than 20 years. Anyway, three scenarios were presented: 1) high luminosity LHC (HL-LHC) over the period 2023-2032 which is an approved upgrade project big “bang for the buck” as we like to say, taking the luminosity up to 70/nb/s, 2) a possible electron proton collider (LHeC) which I dare say is not worth doing, and 3) a higher energy LHC (HE-LHC) which is very exciting because it advances the energy frontier! These last two scenarios are in the state of feasibility studies.

The fundamental energy limit of the LHC comes from the size of its ring. Here large is good. Let’s examine the fundamental formula for the magnetic force that makes a proton travel in a circle

p = erB

where p is the momentum, e is the electric charge, and B is the magnetic field. Multiplying each side by the speed of light c, we can write

pc/Berc = e (4200 m) (3e8 m/s) = 1.2 TeV/T

where I have used the units conversion that a m^2 tesla per s equals a volt. This is a very nice and practical way to specify the radius of the LHC tunnel:  it is 1.2 TeV per tesla. That means a tesla of magnet field is needed for each 1.2 TeV of proton energy to keep it in orbit. But wait. In practice, one cannot fill up the entire LHC tunnel with bending magnets. Space is needed for the experiments, focussing magnets, radio frequency acceleration, etc. The LHC is currently designed to give 7 TeV with 8.3 tesla, or 0.84 TeV/T. The feasibility study for the HE-LHC is looking at 20 tesla magnets, This, according to our formula would give (20 T) (0.84 TeV/T) = 17 TeV. That would be a nice energy increase, a bit more than a factor of 2 over LHC original design.
The HE-LHC feasibility study as presented by Eva Holzer. Besides stronger bending magnets, the HE-LHC upgrade would need development of high-gradient quadrupole magnets to focus the beams, and an upgrade of the SPS from 450 to 1300 GeV.
Let’s return to the Livingston plot to see where we are. Livingston retired just about the time the era of colliding proton beams was being ushered in, beginning with the CERN intersecting storage rings (ISR), followed by the CERN proton-antiproton collider, and finally the Fermilab Tevatron. Colliding beams seems to offer a unique technique for exponential growth. This is a kinematic trick. The figure of merit for the energy frontier is center of mass energy, which grows only as the square root of single beam energy hitting a stationary target.  But this is a ONE-TRICK PONY. There is no corresponding technique to make the next step. In 1990 I made my own version of the Livingston plot which I published in my modern physics book. I reproduce it here with the LHC added:
The blue point is where we are today with 3.5 TeV beams, the green point is the 7 TeV beams that are coming “soon”, and the red point is the future projection.  You can see that after 60 years of exponential growth we are now falling short. Painfully short actually. Right  now we are either 20 years behind or 100 TeV short of the prosperity that was enjoyed from 1930 to 1990, take your pick. In the next decades it is going to get worse. Why is the Livingston line important? It is important and interesting because it is a measure of the pace of experimental particle physics on the energy frontier over the last century. Life is now tough.

I just missed getting to know Livingston as he retired from his last project as part of the Fermilab management team during the construction of the main synchrotron as I was beginning my graduate research at Fermilab.  I did encounter him, however, in the form of a bronze plaque next to the elevator at 42 Oxford Street, the site of the Cambridge Electron Accelerator (CEA). I always thought this plaque was really cool, a steely-eyed Livingston checking you out as you entered the lab. Amusingly, Livingston referred to the CEA as a “ponderator” rather than an accelerator because it was imparting energy rather than speed to relativistic particles. I wonder what he would think of our current ponderator, our one-trick pony?


11 Responses to “The Ponderator: a one-trick pony”

  1. LizR says:

    To state the obvious, accelerator power can’t go on increasing exponentially forever. There must be some physical limit that, as it’s approached, turns what looked like an exponential curve into something more S-shaped. This may now be happening to Moore’s Law in computing, and will certainly happen to the Earth’s population in the next century….but in any case, keep up the good work!

  2. Jim Rohlf says:

    Point made, but I am not talking about forever, I am talking about what happened in the last 20 years and what can/may/will/will not happen in the next 20 years. Experimental particle physics has been resource limited in the big-picture view. We could have been on the Livingston line at the turn of the century (yes, there was a plan to get there), already know the physics that we can only hope to know 20 years from now, and today using that information to plan and motivate the next step. Isn’t hindsight wonderfully perfect?

  3. Haryo Sumowidagdo says:

    Hi Jim,

    One thing which sprang to my mind when I read about increasing SPS energy is: Can Tevatron magnets be reused for SPS+ (The 1 TeV SPS). SPS and Tevatron have almost identical dimension (radius approx 1 kilometer). Re-using Tevatron magnets for SPS+ means a significant reduction of cost … and a reborn of Tevatron!

    • Jim Rohlf says:

      Hi Haryo,
      Interesting observation you made. Fermilab does not list any plans for the Tevatron except to use part of the tunnel for educational tours (http://www.fnal.gov/faw/future/accelerators.shtml). The devil, however, is in the details. Each synchrotron needs a minimum injection energy to operate without beam losses. I know the rough rule of thumb is a factor of 10 for the ratio of injection to final energy. The SSC design, for example called for exactly that: a 2 TeV injector to make 20 TeV beams. But each machine is subtly different. Notice that from Eva’s slide, she listed an injection energy of 1.3 TeV to make 16.5 TeV beams. Thus, the Tevatron magnets would come up short by 30%. You could ask the question in reverse, what machine could be built in the LHC tunnel if you had a “free” 1 TeV injector. My guess is that it would come up a little short in energy and/or luminosity to be interesting given the overall huge cost and long time scale.

  4. jfb2252 says:

    1. re third comment: Tevatron magnets were not designed for rapid cycling: they will quench if ramped as fast as SPS+ would need. Much thinner filament SC with much better cooling is needed, Nb3Sn conductor designed for 50/60 Hz use. The HERA ring is the same size as SPS and Tevatron and those magnets are closer and newer – but still not suitable for fast ramping.

    2. Dr. Rohlf, why do you write about an e-p or e-ion collider, LHeC, “which I dare say is not worth doing”? HERA left a lot of QCD parameter space unexplored.

  5. Jim Rohlf says:

    1. Good point about the rapid cycling. They don’t need to run DC, however, so there may be games to be played.
    2. I am not interested in the e-p because the energy would be too low (60 GeV or even 140 GeV electrons). I want to get beyond the reach of the LHC.

  6. jfb2252 says:

    If LHC doesn’t see new physics at 7 on 7 with the luminosity upgrade, implying that the energy scale needed is well above CLIC, I suppose one will have to rebuild LHC as a muon collider. If I scale by mass from LEP-II, 20 TeV on 20 TeV.

    • Jim Rohlf says:

      Yes, the LHC will ultimately have the reach to possibly make CLIC and any other ILC obsolete– we shall see what nature shows us. But CLIC/ILC is painfully low energy unless we get lucky. 20×20 TeV muon collider would be a wonderful “dream machine”, but how do we get there? Maybe someone will figure it out. My guess, however, is another proton machine is a more likely.

  7. okvol says:

    Perhaps one day we will fulfill Niven’s dream of a type of “Ringworld” as a collider. Solar orbit could maintain the alignment of feeders and feeders of feeders. You would also have the benefit of a third dimension for better packing of feeders. We are quickly going to exhaust physical locations on earth.

  8. Stephen Brooks says:

    There’s always the VLHC (233km circumference, 80TeV beams I seem to recall). To be built with tunnel boring machines off the FNAL site – technically feasible but expensive.

    Going beyond that and you’re really talking about laser-plasma or beam-plasma acceleration (higher accelerating gradients to avoid absurd machine size), which oddly didn’t get a mention in the blog.

    Going a LONG WAY beyond that, e.g. if the LHC finds the standard Higgs and nothing else, suggesting an energy desert up to 10^16 GeV, you’re going to have to put all the energy into a single particle (well, two – one in each direction) rather than a beam.

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