Transcript Chapter 1, Lecture 5 - University of Hawaii at Manoa

History:
After the arms control efforts of both Republican and
Democratic presidents: US and Russia own 93% and
have about 5000 nuclear warheads each.
Today’s plan
Particles are waves: another example
Energy loss for light charged particles
Interactions of photons with matter
Sources of particles: Cosmic rays and
Accelerators
Cherenkov radiation
Quiz in the 2nd half of class on Wednesday.
http://www.phys.hawaii.edu/~teb/phys490/490.html
https://arxiv.org/pdf/1610.08297v1.pdf
QM Particles are waves: a new example
Suppose that dark matter is composed of scalar particles with
mass m~10-22 eV (instead of particles with m~100-200 GeV),
what is the deBroglie wavelength of such entities ?
196 ´10 6 eV ´10 -15 m
15
l~
=
2
´10
m XXX, wrong
-22
10 eV
Takes into account
velocity of dark matter
(4 orders of magnitude)
Ionization loss for “heavy” charged particles
-dE
r Zz 2 ì 2mc 2gb 2
2 ü
=K
ln(
- b )ý
2 í
dx
Ab î
I
þ
where K= 30.7keV m 2 kg -1
Hans Bethe
Figure: PDG
Should be called the Bethe formula.
Felix Bloch had nothing to do with it
Some features to note:
1) energy loss per unit length ~1/β2
2) energy loss grows logarithmically at
large β (relativistic rise)
3) A minimum ionizing particle (“a
mip” ~0.1-0.2 MeV m2 kg-1 ρ)
Question: What
do the colors
mean ?
ALICE heavy ion/nuclear physics
TPC at the LHC.
Question: What
is the d band ?
Why is it so far
to the right ?
Energy loss of electrons
In addition to ionization
loss, there is a second
mechanism for “light”
charged particles called
“bremsstrahlung”
Question: What does the
German word
“bremsstrahlung” mean ?
Ans: braking radiation.
Question: How does the
probability of
bremsstrahlung depend
on the mass of the
particle ?
Ans: ~1/m2 (will protons “brems”
? How about muons ?)
Here P is power, b is the impact parameter
Interactions of photons in matter
What are the three
mechanisms here ?
PDG
Note that this plot is on a log-log scale.
Question: At what energies does Compton scattering dominate for Pb ?
Pair production kinematics
Question: Can a photon (γ) decay to an e+epair in vacuum ? Explain.
s f = 2me2 + 2(E+ E- - p+ p- cosq ) > 2me2 > 0
Do you see why the 2me2 term appears ?
So what about the reaction e+ + e- γ, is that allowed ?
How can pair production occur ?
g + N ® e + e- + N
What about bremsstrahlung, which is the process, e-e- + γ ?
m = (Eg + E + 2Eg Ee ) - ( p + pg + 2 pe pg cosq )
2
e
2
2
e
2
e
2
me2 = mg2 + me2 + 2Eg Ee - 2 pe pg cosq
Do you follow ?
2Eg (Ee - pe cosq ) = 0
but Eg ¹ 0
Ans: Also forbidden in vacuum. Need a nucleon to
conserve energy-momentum
e + N ® e +g + N
±
±
See Bettini
p.11 for a
related
argument
Famous pedagogical
cosmic ray figure
from CERN
Note the
electromagnetic
and hadronic
components of the
cascade from the
primary cosmic ray.
Composition of cosmic rays
Rossi found that
cosmic rays have a
soft component
absorbed by a few
cm’s of lead and a
hard component that
passes through.
Question: What is the
origin of these
components ?
A high energy cosmic ray (proton) may
produce a shower of particles high in
the atmosphere.
Will produce charged pions
(lifetime 26ns)
p ® m nm; p ® m nm
+
+
-
-
The muons have a lifetime of 2.2 μsec (and if
boosted can make it to ground level)
m ® e + n m + n e (and c.c.)
+
+
Other processes:
p 0 ® gg
Bruno Rossi Chicago,
(1905-1993) Cornell, MIT
Question: What does c.c. mean ?
Ans: Charge conjugate
Electromagnetic showers
Some radiation
lengths:
Air X0=300m;
Fe X0~2cm;
Pb X0~5.6 mm
Question: How can we characterize the
energy loss as a function of length for an
electromagnetic shower ?
Ans: Use the concept of
radiation length, denoted X0
dE dx
=
E X0
E(x) = E0 e
What is the
solution for E(x) ?
-
x
X0
The cross-over point between
ionization loss and radiation loss is
the critical energy, Ec.
600MeV
Ec =
Z
Particle Physics started
with cosmic ray physics.
Later with the development of
particle accelerators, it became
more effective to study particles in
accelerator experiments.
Question: Are cosmic rays
still relevant beyond
astrophysics and
understanding violent
phenomena in the universe ?
One answer: (1) Still the source of the highest
energy particles. (2) Understand how to
accelerate particles to such high energies
The first stage of accelerators uses electric field to accelerate charged
particles (electron, protons, heavy ions) to high energies.
F = qE Þ Ed = qV = U
Use DC High Voltage up to about 20 MeV. For higher energies, use high
frequency AC voltage and carefully time each bunch of particles to
obtain a series of accelerating kicks.
In a circular accelerator, use an radio-frequency (RF) voltage source.
Why are the tubes getting longer ?
(in proton accelerators).
Ans: protons get boosted as they travel
down the linac and the effective length
appears shorter as they progress down
the tube. To maintain the correct RF
timing, need the arrangement above.
(Electrons start out relativistic)
A few accelerator basics:
focus on the synchrotron following Bettini.
A synchrotron contains a large number of dipole magnets to
confine the beam and quadrupole magnets to keep the beam
stable.
p(GeV) = 0.3B(T )R(m)
Example: If the radius of curvature of a
synchrotron ring is 1 km and there is a constant
B field of 3.3 T supplied by dipoles, what is the
maximum energy that can be stored ?
pmax = (0.3)(3.3T )10 m = 10 GeV = 1TeV
3
3
For conventional electromagnets, Bmax~1.4 T; For
superconducting magnets Bmax~ 9.0 T FNAL and LHC
and the HERA proton ring used superconducting magnets
There are RF (radio frequency cavities) to maintain the energy.
The beam circulates in a vacuum tube and is grouped into “bunches”.
Question: Why not continuous beams ?
p.34
Bettini
“The particle
accelerator is
unstable;
such an
accelerator
cannot work”
RF cavities
Veksler and
McMillan
Quadrupole
magnets
Courant, Snyder
and Livingston
Probably invented by
N. Christofilos
The first electron-positron collider
ADA at Frascati (courtesy of Archivio Audio-Video, INFN-LNF)
G. K. O’Neil had
conceived and built the
first e- e- “storage ring”
at Stanford in the late
1950’s.
Bruno Touschek built the first
(250 MeV) e+e- storage ring
and collider at Frascati, Italy.
This was followed by
improved machines at BINP
in Novosibirsk, Russia and at
SLAC in Stanford, CA.
Annello Di Accumulazione
The old Fermilab accelerator complex in Batavia, Il.
Old
New
The CERN accelerator complex in Geneva, Switzerland
Old version
Proton and heavy
ion machine
Circumference 27km
Some acronyms:
LHC=Large Hadron Collider
ISR=Intersecting Storage Rings,
SPS =Super Proton Synchrotron
PS=Proton Synchrotron
CMS=Compact Muon Solenoid
ATLAS=A Toroidal LHC Apparatus
LHCb = LHC beauty
ALICE=A Large Ion Collider Experiment
Feb 2016: First Turns at SuperKEKB (4 GeV e+’s and 7 GeV e-’s)
June 28, 2016 (LER beam current at 1000 mA, HER at 870 mA)
Jan 2018: Matter-antiMatter collisions will produce pairs of quantum mechanically
entangled (B-anti B) mesons
First new particle collider since the LHC (intensity frontier rather
than energy frontier; e+ e- rather than p p)
There is a large difference between an electron and proton accelerator:
electrons emit synchrotron radiation (SR) when they bend.
For a 10 GeV/c electron in a 1 km radius ring,
the SR loss is about 1 MeV/turn.
4p e b g
DESR =
(
)
3
r
2
3
4
Question: Can one build a 1 TeV e+e- collider in a km or few
km radius ring ?
Ans: No, in a 1 km ring, since the SR losses go like E4 ;
the SR loss would be 1012 x 1 MeV= 106 TeV/turn.
Question: How can you make a 1 TeV e+emachine ?
Question: Is the SR background useful ?
Ans: ILC (a linear
collider, 30 km long in
Japan)
Cosmic accelerator example
What is the maximum energy of a cosmic ray proton confined
in the solar system ?
Assume R~ 1013m as the radius of the solar system and an
average magnetic field B=1 nT
p(GeV) = 0.3B(T )R(m)
-9
E = p = 0.3(1´10 T )(10 m) = 3000GeV = 3TeV
13
What is the maximum energy of a cosmic ray proton confined
in the galaxy ? (assume R=1021m and B=0.05 nT)
E = p = 0.3(0.05 ´10 -9 T )(10 21 m) = 1.5 ´109GeV = 1.5 ´1018 eV
What can one conclude about a 1019 eV cosmic ray ?