Accelerate This!

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Accelerate This!

• Using the forces of electricity and magnetism
• to make tiny things go really fast
• Daniel Friedman, St. Johns School

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Accelerating a charged particle
Remember opposites attract and likes repel?
Lets call it Coulombs Law!
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Accelerating a charged particle
The force on charged particle q is due to the
charge Q of another nearby particle For two
charges of the samesign
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Another way to look at this uses the idea of an
electric field
If we only know one of the charges (Q), we can
still calculate the force per unit of charge some
unknown q would feel
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Still another way Voltage work/unit charge
To move a charge in the presence of a repulsive
Coulomb force, we have to do some work. But we
can express this in terms of the E field
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Voltage is sometimes called electromotive force
but it is better described in terms of energy
We also use the term potential difference as a
synonym for voltage.
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A charge crossing through a potential difference
gains kinetic energy
The energy measure of particle physics is the
electron volt (eV), defined as the energy of a
single electron across a potential difference of
1 Volt DKE qV
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An eV is tiny!
1 eV 1.6x10-19 Joule keV 103 MeV 106
GeV 109 TeV 1012 Kilo Mega Giga
Terra A billion eV was also known as BeV, which
led to the term Bevatron.
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Want high energy?Youll need a lot of batteries
If you put 600 billion D cell batteries in
series, end to end, youd get 900 billion volts
and each electron would have 900 GeV! But your
circuit would be 23 million miles long!
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Some typical energies
keV103 MeV106 GeV109 TeV1012
Visible light photon 1.5-3.5 eV Ionize atomic
hydrogen (free the proton!) 13.6 eV Your TV
set 20 keV Medical X-Rays 200 keV Natural
radioactivity (a2, b-, g) 2-5 MeV
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Some unusual energies
FermiLab Tevatron 900 GeV CERNs LHC (under
construction) 7 TeV
A Roger Clemens fastball 7 x108 TeV (but
thats spread over a lot of particles!) Highest
energy cosmic ray showers 109 GeV (106 TeV)
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Natural Radioactivity
Ernest Rutherford used naturally occurring alpha
particles with energies of approximately 5 MeV
to discover the nucleus.
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At this energy level, all Rutherford could detect
were the collisions between solid objects
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But to see inside the nucleus, we need higher
energy!
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Welcome to Big Science
FermiLab main accelerator ring over 4 miles
around 900 GeV
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Particle accelerators!
SLAC is 3 km long. Initially 18-20 GeV upgraded
to 50 GeV
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Early Accelerators
Using a very high DC voltage (large E field) to
accelerate an electron across a small gap.
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Cockroft-Walton Accelerators
John Cockroft and Ernest Walton, students of
Rutherford at Cambridge, were leaders in
developing this technology.
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CW accelerators produce very high DC voltages
across a small gap
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The high voltage is obtained by means of a
diode-capacitor ladder
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Popular science fiction liked the look of these
early accelerators
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Robert Van deGraaf uses a moving belt to build
charge by friction
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1931 A giant Van deGraaf in an old dirigible
hanger
Each sphere was at a potential of 750 kV for a
total potential difference of 1.5 MV!
The observation labs were inside the spheres!
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Question Why can the observer sit inside the
sphere without harm?
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A big enough Van de Graaf can produce 10 MeV
the radius of the sphere is the voltage limit
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Linear Accelerators
Copper rings are used as the accelerating field
plates.

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Linear Accelerators
The field polarity is switched by a radio
frequency oscillator. Acceleration occurs due to
the E field across each gap F
Eq ma
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Linear Accelerators
The field polarity is switched by a radio
frequency oscillator. Acceleration occurs due to
the E field across each gap F
Eq ma
-

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Linear Accelerators
The disks act as collimators, blocking any
electrons that are not going in the direction of
the beam.
Interactive linac
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The biggest linacs
use of many thousands of gaps and generate 100s
of MeV requiring a very straight hole in the
ground!
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Some medical devices are small linear
accelerators
You might see one the next time you go to the
dentist!
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Linacs deliver bunches of electrons
Very high-grade vacuumInternal pressure 10-12
torr! (1 atm760 torr)
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Lets introduce the magnetic force
A charged particle with velocity v in the
presence of an external magnetic field of
strength B experiences a force if the mag field
has a component that is perpendicular to the
motion of the charge. Sineopposite/hypoteneuse
B
q v
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The magnetic force is perpendicular to the
velocity of the charge
A perpendicular force can only change the
direction of motion, not the speed.If the
external B field is constant, the particle
moves in a circle.
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The magnetic force is given by
Known as the cross product.
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The direction of the magnetic force is given by
the right hand rule
Fingers along the B field, thumb in the direction
of motion of a positive charge, palm points in
the direction of the force.
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Putting these forces together, the Lorentz
force.
It is vital to note that E and B are always
perpendicular.
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Cyclotrons External B field creates a spiral
path
Relatively low potential difference across the
gap between opposing D s. Acceleration each
time gap is crossed.
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Top view, showing one of the D electrode
cavities
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Cyclotrons particles accelerate around a spiral
path
As particles gain energy, they spiral out.
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Cyclotron Resonance
Radius increases with increasing speed but the
time required to complete ½ circle remains
constant. The frequency of the E field may
therefore be kept constant.
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Cyclotrons
First cyclotron 4 inches in diameter 80
keV 1MeV Lawrence Cyclotron (1932) 11 inches in
diameter
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Cyclotrons
President Eisenhower inspects Columbias 400 MeV
Cyclotron (1950)
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Cyclotrons
Modern 250 MeV Cyclotron might be part of a PET
scan device or cancer treatment facility
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Cyclotrons problem 1
Higher energy requires more turns around the
ring. This means a bigger ring and a bigger,
more expensive magnet.
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Cyclotrons problem 2
Iron core magnets can withstand a maximum of
about 2 Tesla before the iron starts to turn
purple (and burn up). The maximum B field
strength thus limits the energy at the outside
edge.
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The Synchrotron particle racetracks!
Smaller magnets are used only to steer and focus
the particles. Changing the B field strength
to compensate for increasing velocity maintains a
fixed radius.
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Synchrotrons
Pushing the particle at just the right time
increases speed just like pushing a child on a
swing.
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Accelerating protons
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Accelerating anti protons
Oppositely charged particles turn in opposite
directions in the same beamline.
Whats the direction of the B field here?
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A fact that is clearly marked on the road signs
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Synchrotrons
The Cosmotron at BNL First GeV accelerator!
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Go Big Red!
6 GeV under the football field at Cornell. The
192 magnets are each only 3 m long.
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Synchrotrons
6 GeV under a town in Germany
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Synchrotron Radiation
Electrons accelerating in the external magnetic
field give off visible synchrotron radiation.
This lost energy must be supplied by the E
field. Protons do not radiate as much due to
their higher mass.
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Magnets steer the beam
Big B fields require large currents, generating
lots of heat. There are 42500 miles of wire
(8x10-6 m diameter) in each magnet in use at
Fermi.
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Quadrapole Focusing Magnets
A particle near the center of the beam
experiences 0 force. Particles drifting
vertically out of line are forced back to the
center.
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Quadrapole Magnets for Focusing
Paired quad magnets the first focuses the beam
vertically, the second horizontally.
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Particle beams can be extracted for fixed target
experiments
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A focusing magnet can nudge the two beams
together in a collider experiment
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Experiments compared
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The full system at Fermi starts with linear
accelerators
FermiLabs CW accelerator obtains 750 keV by
using a rather large diode-capacitor ladder. For
comparison, your TV is a 20 keV accelerator.
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The 400 MeV 2nd stage linac
E 3 Mega volts/meter 130 m long. If the
linac had to produce the entire 900 GeV, it would
have to be 182 miles long!
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Inside the linac
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The booster synchrotron (940 ft diameter)
produces 8 GeV
Particles in the booster go around 16000 times,
gaining 500 keV per turn.
Booster
Main ring
Injector
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The complete accelerator system at Fermi uses a
combination of synchrotrons
Tevatron ring produces 900 GeV using
superconducting magnets Injector Ring takes in 8
GeV from the booster and outputs 150 GeV
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Injector tunnel
Injector magnets (below) Recycler magnets (above).
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Inside the tunnel
Older Main Ring (above) ran on conventional
magnets. Tevatron ring (below) produces 900 GeV
using superconducting magnets
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Beamline must be a very high quality vacuum (10-6
atm)
Stray particles can degrade the beam. Very
tricky to make flexible joints hold vacuum!
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Super conducting magnets
Who is Jessica?
Built at Fermilabs magnet shop, these bad boys
produce a field of over 4 Tesla theoretically
capable of 15 T!
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Super conducting magnets
At full power, the magnets represent an
inductance of 36 henries, storing 288 megaJoules
of energy in the B field. It can take up to 2
minutes for this field to shut off.
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Super conducting magnets
Since they are superconducting, the cryo system
only requires 13 megawatts of electricity to keep
them cool. Conventional magnets would need over
600 MW just for cooling!
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Need a good reason to study computer science?
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Colliding antiprotons with protons, each at 900
GeVCenter of mass energy 1.8 TeV!
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Trick question Center of mass momentum ?
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Big machines High energy
Who, me?
Protons run around the accelerator in a bunch,
consisting of about 2x1013 particles, with total
mass 4x10-14 kg. At 900 GeV per proton, this
is the same KE as a 1000 kg object moving at 65
m/s!
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The collider that wasnt SSC20 TeV!! 87 km
around!!
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The collider that wasnt SSC Magnets produce
6.5 Tesla!!
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Coming in 2007 the LHC
In Switzerland (CERN)24 km around 14 TeV!
Collision animation
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Collisions produce short-lived new particles
View live events at Fermi
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Such as those that existed in the first
milliseconds of the universe!
Animated collisions
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Sources

• Lederman The God Particle
• http//www.fnal.gov
• http//www.aip.org/history/lawrence/
• http//www.lbl.gov/image-gallery/image-library.htm
  l
• http//www.mos.org/sln/toe/history.html
• http//public.web.cern.ch/public/
• http//www2.slac.stanford.edu/vvc/Default.htm
• http//www.hep.net/ssc/new/repository.html

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When tiny things are going this fast, we need
relativistic momentum
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Relativistic energy-momentum formula
For objects moving really fast, p2c2 gtgt E02, So
E pc
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Relativistic momentum example
An electron with v .95 c m0 0.51 MeV/c2, g
3.2, p g m0v 1.55 MeV/c If we did not use
relativistic momentum, pm0v (0.51 MeV/c2)
(.95c) 0.485MeV/c An error of 68!
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Remember the radius of the cyclotron spiral?
Since we now can deal with relativistic momentum,
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Relativistic energies provide another nice
simplification
E mc2 E0K m0c2K mc2 gm0c2
m0c2K g 1K/m0c2 1K/E0
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Relativistic energies examplesHow fast will
100 MeV move an e- ?
g 1K/m0c2 1K/E0 For e-, E0 .51 MeV.
So g 1100MeV/.51MeV 197
v.99999c Electron-positron colliders were very
popular!
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Relativistic energies examplesHow fast will
100 MeV move a p?
g 1K/m0c2 1K/E0 For p, E0 938 MeV.
So g1100MeV/.51MeV 1.11
v .428c Its lots harder to accelerate protons,
but proton-antiproton colliders are now all the
rage!
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Trick questionHow fast will 100 MeV move an n0?
Its lots,lots,lots harder to accelerate neutrons
theyre not charged!