Theory of accelerators. I. Electrostatic Machines II. Cyclotrons III. Linacs IV. Synchrotrons V. Colliders VII. Synchrotron Radiation Sources VIII. Other Applications. →. →. →. →. Centripetal Force. Lorentz force.
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I. Electrostatic Machines
VII. Synchrotron Radiation Sources
VIII. Other Applications
Fixes the relation between magnetic field and particle’s energy
LHC: ρ = 2.8 km given by LEP tunnel!Basic concepts
Charged particles are accelerated, guided and confined by electromagnetic fields.
- Bending: Dipole magnets - Focusing: Quadrupole magnets - Acceleration: RF cavities
In synchrotrons, they are ramped together synchronously to match beam energy.
- Chromatic aberration: Sextupole magnets
Two-in-one magnet design
LHC: B = 8.33 T ⇒ E = 7 TeV
Transverse focusing is achieved with quadrupolemagnets, which act on the beam like an optical lens.
Linear increase of the magnetic field along the axes (no effect on particles on axis).
Focusing in one plane, de-focusing in the other!
xAlternating gradient lattice
An illustrative scheme
(LHC: 2x3 dipoles per cell)
One can find an arrangement of quadrupole magnets that provides net focusing in both planes (“strong focusing”).
Dipole magnets keep the particles on the circular orbit.
Quadrupole magnets focus alternatively in both planes.
K(s) describes the distribution of focusing strength along the lattice.
G. Hill, 1838-1914Transverse equation of motion
Magnetic field [T] :
Field gradient [T m-1] :
Normalized grad. [m-2] :
and its solution
Eight arcs and eight straight sessions:
Point 1: Atlas, LHCf
Point 2: Alice, injection
Point 3: Momentum cleaning
Point 4: RF
Point 5: CMS, TOTEM
Point 6: Beam Dumps
Point 7: Betatron cleaning
Point 8: LHCb, injection
- These are the key parameters of a collider – the LHC
- Why are they important for physics?
- What is the basic theory which limits each one of them?
Imagine a blue particle colliding with a beam of cross section area - A
Probability of collision for an interaction is
For N particles in both beams
Suppose they meet f times per second at the revolution frequency
Event rateLuminosity (single bunches)
s section area -Acceleration
Acceleration is performed with electric fields fed into Radio-Frequency (RF) cavities. RF cavities are basically resonators tuned to a selected frequency.
In circular accelerators, the acceleration is done with small steps at each turn.
LHC: 8 RF cavities per beam (400 MHz), located in point 4
At the LHC, the acceleration from 450 GeV to 7 TeV lasts ~ 20 minutes (nominal!), with an average energy gain of ~ 0.5 MeV on each turn. [Today, we ramp at a factor 4 less energy gain per turn than nominal!]
ΔE section area -
LHC bunch spacing = 25 ns = 10 buckets ⇔ 7.5 m
450 GeV 7 TeV
RMS bunch length 11.2 cm 7.6 cm
RMS energy spread 0.031% 0.011%Buckets and bunches
The particles oscillate back and forth in time/energy
The particles are trapped in the RF voltage:
this gives the bunch structure
When the electron speed gets close to the speed of light,
e radiation comes out only in a narrow forward cone;
a laser-like concentrated stream
This 300 MeV electron section area - synchroton at the General Electric Co. at Schenectady, built in the late 1940s. The photograph shows a beam of synchrotron radiation emerging.
Spring 8, a synchrotron light source located in Japan. section area -
This intricate structure of a complex protein molecule structure
has been determined by reconstructing scattered synchrotron radiation
Engines of Discovery section area -Linac Coherent Light Source and the European Union X-Ray Free Electron Laser(Fourth Generation)
FELs, invented in the late 1970’s at Stanford are now becoming the basis of major facilities in the USA (SLAC) and Europe (DESY) .They promise intense coherent radiation. The present projects expect to reach radiation of 1 Angstrom (0.1 nano-meters, 10kilo-volt radiation)
Spallation Neutron Sources (SNS) section area -
mean current 1 mA
= 1.4 MW of power
0.7 microsecuond burst
Cost is about 1.5 B$
An overview of the Spallation Neutron Source (SNS) site at Oak Ridge National Laboratory.
Unstable Isotopes and their Ions section area -
The Rare Isotope Accelerator (RIA) scheme. The heart of the facility is composed of a driver accelerator capable of accelerating every element of the periodic table up to at least 400 MeV/nucleon. Rare isotopes will be produced in a number of dedicated production targets and will be used at rest for experiments, or they can be accelerated to energies below or near the Coulomb barrier.
Proton Drivers for Power Reactors section area -
A linac scheme for driving a reactor. These devices can turn thorium into a reactor fuel, power a reactor safely, and burn up long-lived fission products.
Art and archaeology