How Do Particle Accelerators Work?

If you have an older tv, you own an accelerator!

• Acceleration occurs when a charged particle “falls” through a voltage difference.

• So stack up some batteries. A battery is about a buck and provides a 1.5 Volt difference – a buck/ev = a Gigabuck/GeV.

• BNL AGS, Cern PS, and Fermilab original design were a megabuck/GeV – quite a bargain – 1/1000 cost of batteries and does not bump the moon as it goes by!

Brute Force Accelerators:Make a high voltage and drop a

charged particle through it• Van de Graaff – Charge must go to

surface of a conductor. Clever way to use voltage twice.

• Cockroft-Walton – Clever modification of rectifier (AC to DC converter) to get up to 10 or 12 times the voltage.

• Up to a few hundred Mev, more would arc to ground.

• Right energy range for lots of nuclear structure studies.

Cheaters – multiple use

• Trick the particle into falling through the same voltage many (billions) of times, adding to the particle energy each time.

• Usually involves magnets

• Demo – Force on a wire carrying a current – That’s how a motor works!

• Demo --Deflection of bean of electrons by a magnetic field -- That’s how a Tv works!

Circles!

• A charged particle moving in a plane perpendicular to a uniform magnetic field moves in a circle of radius R.

• pc = 0.30 B R where p is momentum (pc is approximately energy in GeV at high energy), B is the magnetic field with max of 2 Tesla for normal magnets.

• Energy Radius• 1 GeV 1.7 m Chicago Syn Cyc• 33 55 Brookhaven AGS, CERN PS• 450 750 Fermilab, CERN SPS

Cyclotron

• Tunafish can cut vertically.• One side +, other –• Protons in neg half near cut attracted into other

half.• Magnetic field bends paths into half circles.• Switch voltages while this is going on• Charges on cans are opposite, so accelerated

on this crossing too.• Repeat many times.

Miracle

• Higher energy, bigger circle, longer path but higher energy is faster and exactly compensates and time for half revolution stays the same.

• Thus continuous bunches of beam come out.• Stronger magnet, or bigger can and should get

to very high energies?• No, at kinetic energies above about half of rest

mass, relativistic corrections invalidate equal time rule. Need different time (period) for faster particles on the outside.

Synchrocyclotron

• Put in a few bunches and change the frequency as they speed up. Beam now comes in bunches (less flux) but higher energy.

• Magnetic field is limited to 2 T, so at 1 GeV the diameter is 3.4 m, and iron is expensive.

• Genius: We have lost on continuous bunches. Save on all that iron in the center by ramping the field so R is constant as energy increases.

• Build Cosmotron (3 GeV) and Bevatron (6 GeV) using RF acceleration instead of halves of cans

Wave Acceleration -- RF cavities

RF cavity

Strong Focusing

• Clever trick: Magnets with 4 poles act like lenses and keep refocusing the beam to keep it small – hold down magnet cost.

• Build AGS, Cern Ps, Fermilab, and CERN SPS

Linacs

• We want an electron beam – particle with no internal structure is a cleaner probe.

• Electrons bent in a circle radiate too much.

• Forget the magnets and just string 2 miles of expensive RF cavities out in a straight line. Expensive, but California is worth it – Build SLAC.

Colliders, why?

• Wasted Energy: At these accelerators the beam hits a piece of metal and the physics was the study of a moving particle hitting a particle at rest. The produced particles had to have the same momentum as the beam, a lot of useless kinetic energy.

• Example: Fermilab 500 GeV proton hits a proton at rest. If all the energy and momentum went into one particle, it’s mass would have to be less than 30 GeV. Proton mass 1 GeV. W mass turns out to be about 90 GeV, cannot be produced at Fermilab or CERN SPS

450 + 1 = 30450 + 450 = 900

• I prefer the second choice, but there is a problem. Particle beams are VERY low density compared with a metal. Will the “colliding” beams just pass through one another with too few proton-proton collisions to be of interest?

Venturesome Souls

• Midwest Research Associates late 1950s• Italian group 1960s electron-positron• CERN 1970s p-p Intersecting Storage Rings• Carlo Rubia, CERN 1980 – proton, antiproton at

450 each. He had only one ring so it did not “intersect”. Alternative – protons going round one way, antiprotons going round the other way in the SAME pipe. TEVATRON at Fermilab.

• Electrons – Spear and BaBar at SLAC, CLEO at Cornell, LEP at CERN, KEK and Belle in Asia

• And now back to pp intersecting rings at LHC.