Two Main Elements of Synchrotrons:
Magnetic fields
guide & focus particles around a closed path
Energy imparted to the beam by RF cavities
Magnets, the
"heart of the matter"
Particle accelerators only accelerate
electrically charged particles. The force on a charged particle is given by the
Lorentz Force. The Lorentz Force on a charged particle is given by the equation
where q is the electric charge,
E and B are the electric and magnetic fields (vectors) and v is the velocity.
Electric forces are small. The protons in the Fermilab synchrotrons are bent in a
circle by magnets and kept focused by quadrupoles, another type of magnet.
The magnetic force is perpendicular to both
the velocity of the particle and the direction of the magnetic field lines. Motion
in a uniform magnetic field is a circle.
Important formula: for q = 1.602
x 10-19 coulomb (charge on one proton or one antiproton)
Radius of circle (meters) = momentum
(in GeV/c) / 0.3B (Tesla)
| Focusing of charged particles
is done with quadrupole magnets. These have two North poles and two South poles and
the magnetic field in the center is zero |
|
 |
These diagrams from the
wonderful World of Beams website at the Lawrence
Berkeley National Laboratory illustrate how the beam is alternately focused in the
horizontal and vertical planes. 
|
| Alternating
focus/defocus/focus/defocus ... in a series of quadrupole magnets is called alternating
gradient or strong focusing. This method of keeping the
beam particles tightly constrained inside a vacuum chamber is used in all the Fermilab
synchrotrons, and also in the many beam lines at Fermilab. The beam lines transport
the beam from one accelerator in the chain to the next. Beam lines also transport
beam to targets in various physics experiments. 
|
Classification of Fermilab Synchrotrons |
| Weak Focussing |
OBSOLETE |
| Strong Focussing |
alternate
focussing & defocusing |
| Combined
Function: bending and focusing combined in the same magnet. |
Booster
Recycler |
| Separated
Function: bending magnets and quadrupoles (focusing) are separate elements. |
Main Ring
(1972-1997)
Main Injector
Tevatron
antiproton Debuncher
antiproton Accumulator |
| Magnets are the
single most costly technical component in synchrotrons and beam lines. A large
variety of magnets are in use at Fermilab. Fermilab is a world leader in
constructing magnets and in designing new and improved types of magnets. |
Accelerator and Beam Line Magnets at Fermilab |
| Conventional |
|
Electromagnets:
copper, water cooled coils |
Booster, Main Injector,
Debuncher, Accumulator |
Permanent
Magnets: pole tips fabricated from Strontium Ferrite, the same material
used in "refrigerator magnets" and in the motors that run the windows up and
down in your car. |
Recycler |
| Superconducting |
|
| Warm Iron:
the iron is outside the cryostat ("thermos bottle") containing the
superconducting coil assembly. |
Tevatron dipoles and quadrupoles |
| Cold Iron:
the entire magnet, coils, and iron is inside the cryostat. |
Low Beta quadrupoles in the Tevatron, special strong lenses to focus the beam to a tiny spot at the collision
points. Low Beta quadrupoles Fermilab is building for CERN's LHC |
| Type of
Superconducting wire used |
Superconductors.org is an excellent site to
learn about Superconductors |
| NbTi (Niobium Titanium) |
All Tevatron
magnets. CERN's LHC. |
| Nb3Sn, Nb3Al,
new High Temperature superconductors (BSSCO, YBCO) |
R&D efforts aimed at
future accelerators use new materials. While more difficult to work with than NbTi
they are able to carry higher current densities in a strong magnetic field than possible
with NbTi. Needed to reach fields in excess of about 9 Tesla. |
RF cavities and Phase Stability
The
principle of phase stability is the underlying basis for all synchrotrons. V. Veksler and E. McMillan were
awarded the Nobel Prize for this discovery. The magnet strength (proportional to
particle momentum) and the RF frequency must be synchronized to keep the particles in the
ring. The links are to the original discovery papers.
Take a charged particle traveling in
a circle. The RF (radio frequency) cavity gives it a "boost" on each turn.
Time =
circumference/velocity
Need
to use special relativity to relate velocity to momentum
This term can be either positive or
negative.
Take two
particles, a red one and a green one on the nth turn. The axes on the graphs can
represent particle energy vs.
time and also RF voltage vs. time.
In the first picture Red is
higher energy and Red and
Green arrive at the RF station at the same time. Both get the same "kick"
In
the 2nd picture Red gets
there first after one revolution because it goes faster. So Red gets a smaller "kick" and Green can catch up.
The particles in the BUNCH oscillate back and forth
(in time and energy) inside the RF BUCKET. At lower energies, the proton velocity
changes with each revolution and the above expression is negative.
At very high energies as the protons get closer and closer to the speed of light, the
velocity hardly changes at all as they are accelerated and the above expression becomes positive
the stable BUCKET moves to the other side of the RF sine wave. When the expression
above is zero (for the Tevatron around 17 GeV), This is called
"transition" and is a tricky place in the acceleration cycle.
