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 = 30 450 + 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.