What is the difference between

Colliding Beams and Fixed Target?

Simple formulas and definitions from SPECIAL RELATIVITY

c = velocity of light in vacuum = 3 x 1010 cm/sec

b = v/c

moc2 = rest mass energy of a particle

E = total energy = moc2 + Kinetic Energy

v is always < c

0 < b < 1

as b approaches 1, g approaches infinity

Relativistic Particles:

v is close to c

b is close to 1

g is very large

E >> moc2

A definition from Special Relativity:

An INVARIANT is a quantity that is the SAME in all frames of reference

The quantity

(total energy)2 - (total momentum)2

is the SAME in all frames of reference

Using E2 - (pc)2 we can move back and forth between our frame (the laboratory) and the

collision frame or center of momentum frame.

In colliding beams these frames are the same (note:  only for the special case when both beams have the same momentum and they collide head-on).

In fixed target mode these frames are very different.

  Center of Momentum frame Laboratory frame
Particle 1 Proton Proton
Particle 2 Proton in nucleus Proton in nucleus
Total Energy Ecm Eb + mpc2
Total Momentum 0 Pb (target not moving)
Invariant Ecm2 (Eb + mpc2)2 - (pbc)2

The "trouble maker" is the Ö

mpc2 is the rest mass energy of a proton @ 1 GeV

Eb is the energy of the Tevatron beam @ 1000 GeV

So this is the relativistic regime and we can simplify

FIXED TARGET COLLISION

Proton-proton collision, Tevatron running at 800 GeV

COLLIDING BEAM COLLISION

Proton-antiproton collision, Tevatron at 900 GeV

Ecm = 900 + 900 = 1800 GeV

accel.gif (11271 bytes)

Fixed Target Experiments have been carried out in the Meson, Proton, and Neutrino areas and more may be carried out in some of those areas in the future.  A fixed target program is being carried out with the Main Injector.   A 120 GeV proton beam is extracted and will create an intense beam of neutrinos.   Learn more about the exciting NuMI project.

Colliding beam physics is carried out primarily at CDF and Dzero.  BTeV, a future colliding beam experiment will be created at Czero, half-way between CDF and Dzero.

Why not always use colliding beams?  Even though the energy in a fixed target collision is much lower, the number of collisions/second is 10,000 to 100,000 larger.  So if the goal of the experiment is to study a process requiring very high statistics, but not requiring enormous energy in each collision then fixed target operation is used.
How fast are the protons traveling in the Accelerator Chain?

Return to "Why High Energy"

Questions?  Ernie Malamud  revised August 28, 2000

 

 

Security, Privacy, Legal