Accelerator basics

Particle Accelerators:
Erik Adli, University of Oslo, August 2014, [email protected] , v2.01
Video: the LHC accelerator
youtube: the LHC Accelerator
Experimental High-Energy Particle Physics
Event rate in ATLAS :
N = L x  (pp)  109 interactions/s
Mostly soft ( low pT ) events
Interesting hard (high-pT ) events are rare
Particle accelerators for HEP
•LHC: the world largest accelerator,
both in energy and size)
• First collisions end 2009
• Gradual commissioning with steadily
increased luminosity and CM energy
• 27 fb-1 integrated luminosity
delivered to the ATLAS up to 2014
• lead to the Higgs Boson discovery
Future colliders for HEP
The next big thing? After LHC, a high
energy, high luminosity Linear Collider
of several 10 km length, may be
needed – why?
Particle collider Livingstone plot
Way forward?
Others accelerators
• The driving force of accelerator development was highenergy physics experiments
• Today there are estimated to be more than 30'000
particle accelerators in the world, and only a fraction
is used in HEP
• Over half of them used in medicine
• Accelerator physics: a scientific discipline in itself,
and growing field
• Some examples of particle accelerators for various
applications on the following pages
Medical applications
• Therapy
– The last decades: electron
accelerators (converted to X-ray via
a target) used successfully for
cancer radiation therapy
– Increasing popularity : particle
therapy/hadron therapy - direct
use of proton/ion beams - provide an
improved alternative for various
types of cancer. Energy deposition
can be controlled better, however,
significant accelerator physics
• Imaging
– Isotope production for PET scanners
Advantages of hadron therapy
From U. Amaldi
Hadron therapy accelerators
Beam transport lines
Beam delivery
25 m
(gantry size)
Heidelberg Ion-Beam Therapy Center (HIT)
State of the art of commercial hadron therapy
centers. Can particle accelerator R&D drive size
and cost down?
Synchrotron Light Sources
Synchrotron radiation emitted from accelerated charged particles can
produce very intense radiation at X-ray frequencies
The last decades, vast increase in the use of synchrony radiation for photon
science. Some uses: material sciences; life sciences; earth sciences.
Synchrotron radiation
covered later in the course.
Radiation from ultra-relativistic
electrons: forward direction.
Soleil, France
Neutron spallation sources (ESS)
Neutron spallation sources: intense flux of protons at high energies.
Lund, Sweden: building Europe’s first neutron spallation source, the European
Spallation Source, using superconducting technology.
Thorium - Accelerator Driven Systems
Advanced acceleration research
Cutting edge accelerator physics research. The target is to overcome the limitations in conventional rf based
accelerator technology.
Plasma wakefield acceleration
Ideas of ~100 GV/m electric fields in plasma, using 1018 W/cm2 lasers: 1979
T.Tajima and J.M.Dawson (UCLA), Laser Electron Accelertor, Phys. Rev. Lett. 43, 267–
270 (1979)
PWFA: plasma wakefield acceleration
Drive a wake in plasma by the space
charge field of an intense charged
particle beam (beam-driven) or by
the radiation pressure of an intense
laser beam (laser-driven).
* Typical plasma densities: 1014-18/cm3
* Length scales: lp~10-1000 um
* Plasma usually modeled as
We will treat this topic in separate lectures in October
Accelerator Physics
Accelerator physics deals with the dynamics of charged particle beams, under the effect of
collective electromagnetic forces in an accelerator. Extensive research in accelerator physics
is in order to advance the high-energy particle physics. Proud Norwegian tradition :
Bjørn Wiik
Rolf Wideröe
Pioneer både for
betatronprinsippet og for
lineære akseleratorer
Odd Dahl
Leder av CERN PS prosjektet
(en viktig del av LHCkomplekset den dag i dag)
Professor og direktør ved
Europas nest største
akseleratorsenter (DESY i
Kjell Johnsen
Leder av CERN ISR, og leder av
CERN's gruppe for
Basic description of charged
particle beams
Single particle coordinates
• We usually describe particle movement in a particle
accelerator in a frame co-moving with a reference position at
the beam center
• The state of a particle is characterized by the deviation from
the reference position along the three spatial dimensions,
– (x, y, z)
• and their complementary dimensions, for example
– (x’ ≈ dx/ds, y’ ≈ dy/ds, E).
• The choices are not unique.
• The coordinates are usually given in the laboratory frame
s: co-ordinate
along accelerator
It’s about a beam, in 6D
y(x, y, z)
Any charged particle beams, taken at a given point in time, can be characterized as a
distribution in 6D phase space.
Description in terms of moments
Discrete distributions
We may also use representations where each particles have different weight, in
case the weight of each particle enters the above formulas.
Gaussian distributions
Example distribution
The following example 6D distribution is from a simulation of an electron photo-injector line :
y(x, y, z)
Some questions one may ask:
What are the rms beam sizes?
What are the correlations?
y(x’, y’, E)
Example distribution
y(x, y)
y(x, y, z)
Gaussian fit beam sizes
x = 9.4 um, y = 5.6 um
<x y> ≈ 0
Example distribution
The two transverse planes are often to a large degree uncoupled <x y> = 0.
However, evidently the position and the angle of particles in a given plane are
dynamically coupled, and the correlation <x x’>, <y y’> will change as the beam
evolves in time. Below: the effect of letting the beam propagate in free space,
from a time t1 to a time t2 :
y phase space at t=t1. <y y’> ≈ 0
y phase space at t=t2 . <y y’> > 0
Beam dynamics: beta function and emittance
Evolution of the beam (y,y’) when propagating in free space along beamline, s :
y= √(eyby (s))
Two key concepts that defines a
charged particle beam:
Beta function, b(s): quantifies how well the beam is focussed. Minimum, b*, at the beam waist.
Emittance, e: phase-space area preserved in the above case; e = √(<y2><y’2> - <y y’>2)
Charged particle propagation
versus laser beam propagation
Beam propagates in s direction
Charged particle beams :
- b* represents focus depth and strength
- Emittance, e, is conserved (when?)
- At waist: e = √(<y2><y’2>) = *y ’y
- Evolution along beamline, s, given by :
Gaussian laser beams :
- Rayleigh length ZR <-> b*
- Wavelength l <-> 4pe
- e =  ’ ~ w0 q
- Evolution along beam path, s, given by :
In the “transverse optics” part of the course we will treat this topic in detail.
Beam Parameters
Main parameters to characterize
a charged particle beam
Particle type
Energy spectrum
Time structure
Requirements from a High-Energy Physics point of view
Main parameters: particle type
Hadron collisions: compound particles
– Mix of quarks, anti-quarks and gluons: variety of processes
– Parton energy spread
– Hadron collisions  large discovery range
Lepton collisions: elementary particles
– Collision process known
– Well defined energy
– Lepton collisions  precision measurement
“If you know what to look for, collide leptons, if not collide hadrons”
Parameters: particle energy
New physics can be found at larger unprobed energies
Energy for particle creation: centre-of-mass energy, ECM
Assume particles in beams with parameters m, E, E >> mc2
– Particle beam on fixed target:
ECM  mE
– Colliding particle beams:
ECM  2E
 Much more efficient to collide beam
Collision energy is affected by beam-beam interactions;
an initial small energy spread maybe converted into a spectrum :
Right: example spectrum
from a 3 TeV CLIC design
Parameters: luminosity
High energy is not enough, high event rate is as important in HEP
Cross-sections, , for interesting processes are very small. E.g. Higgs
production in e+e- colliders are ~ 100 fb = 10−37 cm²
R  L
– Depending on the process we want to study we need L >> 1030 cm-2s-1 in order
to observe a significant amount of interesting processes (1 year ~ p x 107)
L [cm-2s-1] for “bunched colliding beams” depends on
– number of particles per bunch (n1, n2)
– bunch transverse size at the interaction point (x, y )
– bunch collision rate ( f)
L f
4p x y
Parameters: time structure
The collider time structure is driven by both accelerator design constraints and detector / data
analysis constraints.
Circular collider time structure : constant collision rate
Example for LHC, nominal parameters
charge delivered in bunches at 25 ns spacing
16 nC charge in each bunch
2800 bunches in
each beam,
colliding at 40
Linear collider time structure : charge delivered in micro-bunched pulses
Example for the International Linear Collider (500 GeV high lum.)
- charge delivered in pulses of 1 ms, at 5 Hz
- 3 nC charge in each micro-bunch
Parameters: LEP, LHC and CLIC
CERN-based colliders, nominal parameters :
Particle type
e+ and e-
p, ions (Pb, Au)
e+ and e-
Max. collision
209 GeV
p: 14 TeV
(~ 2-3 TeV mass
reach, depending
on physics)
3 TeV
Time structure
4 bunches
circulating, 50
MHz collsion rate
2800 bunches
circulating, 40
GHz collision rate
312 microbunches, colliding
at 50 Hz repeition
Peak: 1032 cm-2s-
1034 cm-2s-1
(IP1 / IP5)
Integrated L up to
now : ~ 27 fb-1
(per experiment)
1034 cm-2s-1
Integrated L in
total : ~ 1000 pb-1
(per experiment)
Accelerator lectures for FYS4550
Accelerator types, main parameters, basic Concepts
Acceleration and Longitudinal Dynamics
Basic Transverse Dynamics (single particle)
Advanced Transverse Dynamics (multiple particles)
Synchrotron radiation and collective effects
Linear colliders and CLIC
Advanced Accelerator Research with focus on plasma wakefield acceleration
Visit to the CERN accelerator complex, LHC injectors and linear collider test
Focus: accelerators for high-energy physics, with thus emphasize highenergy accelerators, especially synchrotrons and linear colliders
Goal: understand the basics of why and how we accelerate particles,
plus the challenges and the limitations

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