• 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!

• 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.

• 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!

• 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

• 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.

• 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.

• 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

• 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

• 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.

• 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

• 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?

• 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.