Physics 226 (Fall 2001) Lecture #2
Accelerators
High Energies
Scattering Experiemnt :
The space resolution limited by the wavelength: lambda = 2pi / P, where P is the momentum transfer.
Large momentum transfers correspond to small distances, and vice versa.
To probe the short-distance behavior requires high energy beam.
Rutherford et al. revealed the presence of a nucleus within the atom.
lambda < 10^-8 cm --> atomic structure
SLAC inelastic scattering experiment revealed the presence of quarks within the proton.
lambda < 10^-13 cm --> p, n structure
Proton (quark/gluon) scattering experiment
lambda < 10^-17 cm --> quark structure ?
Creating Massive Particles :
Most of the elementary particles are unstabe because they have large masses.
To study them requires high energy beam
c-quark
b-quark
W, Z bosons (80, 90 GeV) : ~300 GeV on ~300 GeV p-bar
t-quark (175 GeV) : ~1 TeV p on ~1 TeV p-bar
Fixed Target vs. Collider
Fixed Target
Ecm = sqrt(m1^2 + m2^2 + 2 E1m2) = sqrt(2 E1m2)
Collider (colliding beams, head-on collisions between two beams)
Ecm = sqrt(m1^2 + m2^2 + 2 E1E2 + 2 p1p2) = sqrt(4 E1E2)
Colliders will have much higher energy available for particle production. Thus critical for massive particle searches.
The need for antiparticles
S and T channel diagrams
S is "annihilation",
But can only happen for particle - antiparticle collisions.
e+ e- colliders : LEP, SLC (beam energy = 45 - 100 GeV)
p p-bar collider : Tevatron (beam energy = 1 TeV)
At very high energy hadron (p or p-bar) colliders,
gluons dominate
little difference between p p collider and p p-bar collider.
easy to make / accumulate protons than antiprotons
LHC : p p collider (beam energy = 7 TeV)
Event Rate (Luminosity)
Instantaneous Luminosity = the interaction rate per unit cross section.
Total Luminosity = time integral of Instantaneous luminosity
Total number of interactions (events) = Total Luminosity x physics cross section.
Bunch to bunch collision
A bunch of particles (uniformly distributed in a cylinder, circle area A)
N particles in the cylinder.
A particle in a bunch sees a fraction of the area of the other bunch.
N x (sigma_int / A)
Number of interactions per passage
N x N x (sigma_int / A) = N^2 x (sigma_int / A)
Frequency of bunch collisions = f
interaction rate
R = f x (N^2 / A) x sigma_int.
Liminosity
L = f x N^2 / A
Figure of merit for a collider
Realistic beam profile : round Gaussian
L = f x N^2 / (4 pi sigma^2)
sigma = 1 standard deviation of particle density
e.g. Tevatron
L = 10^31 - 10^32 cm-2sec-1
total cross section ~ 100 mb = 10^-25 cm^2 (barn = 10^-24 cm^2)
Interaction rate ~ 10^7 / sec
Total number of events for a year
= 10^32 cm^-2sec^-1 x 10^7 seconds/year x 10^-25 cm^2
= 10^14 events
Top quark events : cross section ~ 7 pb
= 10^32 cm^-2sec^-1 x 10^7 seconds/year x (7 x 10^-36 cm^2) = 7,000 events.
Improving luminosity
increase f : bunch frequency (collision frequency)
difficulties : multi-bunch instabilities
increase N : # of particles in bunch (bunch intensity)
difficulties : collective single-bunch stability
decrease sigma^2 : beam size (beam cross sectional area)
more demands on beam sources, focusing systems.
Accelerator History
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Last updated by Young-Kee Kim (ykkim@lbl.gov)