Table Of ContentLECTURE 1
Circular accelerator
Particle Source
Varieties of accelerators
Particle Sources ,Linear Accelerators,
Circular Accelerators
Linear
Accelerator Technologies
accelerator
Magnets, Radiofrequency Systems,Vacuum
systems
Applications of Accelerators
Research
Other applications
THE GENERIC ACCELERATOR COMPLEX
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Varieties of accelerators: Electron sources
Particle Sources
Ion sources: DC HV guns: 50-500 keV acceleration
Electron production mechanism:
(see N. Augert, “Ion Sources”, Ref. 2, Vol. 2, pp. 619-642)
• thermionic emission (pulse duration controlled by a pulsed grid)
Positive ion sources: the positive ions are formed from electron
• photocathode irradiation by pulsed laser (laser pulse width
bombardment of a gas and extracted from the resulting plasma.
determines the pulse duration)
Species ranging from H to U (multiply charged) are available
Negative ion sources: Principal interest is in H-, for charge-
RF guns: cathode forms one wall of an accelerating RF cavity
exchange injection
Rapid acceleration to above 10 MeV in a few cells->mitigates
Surface sources: In a plasma, H picks up electrons from an
space charge effects, makes for low emittance
activated surface
Electron production mechanism:
Volume sources (magnetron, Penning): electron attachment or
• thermionic emission (pulse duration controlled RF structure)
recombination in H plasma
• photocathode irradiation by pulsed laser (laser pulse width
Polarized ion sources: e.g., optically pumped sources: some
determines the pulse duration)
penalty in intensity, relatively high (>65%) polarization
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Positron sources
(see R. Chehab, “Positron Sources”, Ref. 2, Vol. 2, pp. 643-678)
“Conventional” positron source: Can get from 10-3 :1 up to ~1:1
positron/electron as electron energy rises from 0.2 to 20 GeV Antiproton sources
30-150 GeV antiprotons
0.2-20 GeV Positrons protons to storage rings and
Electrons Target Positrons stochastic cooling systems
RF Linac Target
Lens
Yield of antiprotons/proton is typically 10 –5
Matching Solenoid
solenoid
Positron production by high energy photons
>100 GeV
electrons photons positrons
RF linac
helical Converter
undulator electrons
Sweep magnet
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Linear Accelerators
RF Linacs
Electrostatic Accelerators: (see M. Weiss, “Introduction to RF linear accelerators”, Ref. 2.,
Tandem Van de Graff, Pelletron Vol 2, pp. 913-954)
Ion beam, energy 2qV
Magnetic focusing lens
HV terminal is charged
mechanically
Partcle beam
Stripping foil
..............
HV terminal at potential +V Energies are limited to
10-20 MeV
RF cavity
Lenses are required for transverse stability (the RF cavities are
transversely defocusing)
Negative ion source
charge -q
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RF cavities may be of two forms: “travelling wave” or “standing
wave” For a uniform waveguide, the phase velocity is greater than c, so
the particle gets out of sync with the wave very rapidly. The
Travelling wave cavity: waveguide must be loaded with periodic obstacles (disks) , with
holes (irises) for the beam
RF in LOAD
RF out
LOAD
RF out
RF in
Waveguide
beam particle
Typically operated in a TM mode: longitudinal electric field
provides the acceleration. Beam is bunched, rides at crest of wave Disk-loaded waveguide
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Standing wave cavity: 0 mode: fields are the same in adjacent cavities
Drift-tube (Alvarez) linac: typically used at the first stage in a
RF in proton linac
beam particles RF in
beam particles
Drift tubes
Longitudinal electric field
Longitudinal electric field
π mode: fields alternate in adjacent cavities
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Beam is shielded from the fields when at the wrong phase by using
hollow “drift tubes”
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Induction linac:
Magnetic core (e.g,. metglas)
Beam
Acceleration gap
Radio-frequency quadrupole (“RFQ”):
Pulser Solenoid
A long electric quadrupole, with a sinusoidally varying voltage on
The beam forms the secondary circuit of a high-current pulse
its electrodes. The electrode tips are modulated in the longitudinal
transformer
direction; this modulation results in a longitudinal field, which
Induction linacs have very low rep rates (a few Hz) and
accelerates particles. It is a capable of a few MeV of acceleration.
intermediate voltages (30-50 MeV) but very high peak currents
Typically used between the ion source and the Alvarez linac in
(>10 kA) in short (100 ns-1 µs) pulses
proton RF linacs.
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Circular Accelerators
Cyclotrons To get vertical focusing, field B must decrease with ρ:
(see P. Heikken, “Cyclotrons”, in Ref. 2, Vol. 2, pp. 805-818)
Classical cyclotron: Static B field, DC beam
RF: Voltage V, frequency f Pole tips
Dees
Magnetic field B Magnetic field
Centripetal force=Lorentz
[r r r]
force=e E+v×B ρ
2
mv
ρ =evB
Particle orbit ρ Force
mv p
ρ= =
This fact, and the relativistic mass increase with velocity, limits the
eB eB
maximum energy of the classical cyclotron to about 10% of the
v eB
f = =
rest mass energy.
2πρ 2πm
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Improvements: Synchrotrons
v
e
• Isochronous cyclotron: Vary the B field azimuthally. This gives
vertical focusing (like alternating gradient focusing in a
synchrotron) and the B field can then increase with ρ to keep f
RF Cavity
constant as m increases. ρ
bending fields
focusing fields
• Synchrocyclotron: Increase the RF frequency on the dees as m
increases to maintain synchronism. The beam must then be
bunched, as only a limited region in RF phase is stable, and the
current is reduced.
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p This can be represented as
A ring of magnets at fixed ρ= . As p increases during
eB ρ n
acceleration, B is increased to keep ρ constant. The RF frequency By = B0 ρ0
v
f = is constant for relativistic particles. where n, called the field index, is > 0. However, n cannot be
2πρ
arbitrarily large, since we must also have radial stability:
Focusing: to get vertical stability, we could allow the bending field
x
to decrease with ρ, as in the classical cyclotron.
ρ
evBy mv2
ρ
Magnetic field 0 ρ
ρ
For radial stability, the centrifugal force must be less than the
Force Lorentz force for x>0:
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mv2 mv2 mv2 x Optical analogy:
= ≈ 1−
ρ ρ0 + x ρ0 ρ0 f1 f2
1 1 1 d
≤evB =evB ρ0n =evB ρ0 n ≈evB 1−n x f = f1 + f2 − f1f2 is positive for a large
y 0 ρ 0ρ + x 0 ρ range of focal lengths and d=> net
0 0
focusing both radially and vertically
x x
≥n ⇒1≥n
ρ ρ
0 0 d
If this is done by providing a radially varying field in
Focusing of this kind is called “weak focusing”. In 1952, “strong the bending magnets: the machine is called combined function. If
focusing”, or “alternating gradient focusing”, was invented by this is done by using uniform field dipoles and separate quadrupole
Courant and Snyder. magnets, the machine is called separated function. Much greater
focusing, hence smaller beam sizes, are obtained in a strong
Strong focusing: alternate the focal length of magnetic lenses focusing machine than in a weak focusing one.
around the ring
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The RF cavities in proton synchrotrons are used primarily to Betatron: The circular analog of the induction linac
accelerate the particles.
Magnetic field B
However, in electron synchrotrons of moderate to high
energies, the RF cavities must also provide the energy lost by the
Particle orbit
electrons due to synchrotron radiation. (see R. P. Walker,
“Synchrotron Radiation”, Ref. 2, Vol. 2, pp 437-460)
The energy loss per turn is
ρ
e2 β3γ4
U =
0 3ε ρ
0 Induced electric field
4[ ]
E GeV
In practical units U [MeV]=0.0885 The orbit radius ρ is fixed. The accelerating electric field is
0 ρ[m]
provided by the changing magnetic flux within the orbit. The
The radiation spectrum extends from the infrared to the many keV
required flux change is ∆φ=2πρ2B . Energies up to 300 MeV
region. max
have been obtained.
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Microtron Resonance condition: nλB= 2πVcosφ, n=1,2,… (for relativistic
(see P. Lidbjork, “Microtrons”, Ref. 2, Vol. 2, pp 971-81) c
Racetrack microtron: particles), φ=relative particle-RF phase
Accelerator Technology
Magnetic field B
Magnet Systems
Principal types of magnets used in accelerators:
• Dipoles: provide a “static” transverse uniform field, typically to a
few parts in 104
• Quadrupoles: provide a “static” uniform transverse field
Particle orbits RF Linac: voltage V, gradient, to the same accuracy
Wavelength λ • Sextupoles: provide a “static” quadratic dependence of transverse
field on position
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• Combined function dipoles: provide a mostly uniform transverse “Generation of magnetic fields for accelerators with permanent
field, with a small field gradient magnets”, Ref. 2, Vol. 2, pp 893-998)
• Solenoids: Provide a longitudinal uniform field • Resistive electromagnets-the standard solution: excited with
• The fields are ramped during acceleration in a synchrotron. copper or aluminum coils, dipole field range up to about 2 T (See
N. Marks, “Conventional Magnets”, Ref. 2, Vol. 2, pp 867-912)
Magnet power supplies:
Primarily DC or slowly ramping for ring magnets; currents from • Superconducting magnets-reduced power consumption, higher
10-10,000 A, current regulation required typically 10-100 parts per field range, used in large proton synchrotrons. Dipole fields up to
million. 8 T (with NbTi superconductor), to 15 T (with Nb Sn
3
Principal magnet technologies: superconductor) at 4.2o K. Require extensive cryogenic systems.
(See S. Wolff, “Superconducting Accelerator Magnet Design,
• Permanent magnets-for fixed-energy rings, dipole fields up to Ref. 2, Vol. 2, pp 755-790)
about 1 T. Alnico, ferrite, SmCo , Nd Fe B. Need good • Pulsed magnets: provide rapidly varying fields, for beam
3 2 14
temperature regulation for field stability. (See T. Meinander, injection, extraction, and fast switching in transport lines
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• Superconducting (SC) systems typically use pure Nb cavity
Radiofrequency Systems surfaces (sometimes plated on copper) at 4.2oK. (See H. Lengeler,
“Modern Technologies in RF Superconductivity”, Ref. 2, Vol.2, p
• Traveling wave and standing wave cavities are both possible 791-804)
elements in rf linacs or synchrotrons. The principal performance Higher accelerating fields (at low frequencies) are obtainable with
parameters of a cavity are its electric field (voltage gradient) and SC systems than with NC systems. Power dissipation is much
frequency. Generally, the relation between these is E λ≈constant: reduced in SC systems, although a cryogenic system is required.
a
Higher frequency systems can develop larger voltage gains.
Radiofrequency power sources:
Systems from 20 MHz up to 11 GHz are in operation.
• Triodes and tetrodes:
• Normal conducting (NC) cavities are fabricated from OHFC
high power vacuum tube power generators, useful up to 300 MHz
copper.
and 100 kW
(See M. Puglisi, “Conventional RF System Design”, Ref. 2, Vol.2,
p 677-716)
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• Klystrons: Narrow-band, tuned microwave amplifiers--500 MHz Vacuum Systems
to15 GHz (See A. G. Mathewson, “Vacuum System Design”, Ref. 2, Vol. 2,
pp 717-730)
50-100 kV Electron beam
Catcher
Accelerator vacuum systems are the most challenging for storage
rings: synchrotrons in which the beam is maintained at fixed
Cathode
energy for many hours. Required pressures are typically below 10–9
Torr (about 10–12 atmospheres).
Heater
• Proton storage rings: gas load from thermal outgassing
• Electron storage rings: gas load from thermal outgassing and
Anode
from photodesorption due to synchrotron radiation.
(Very high energy proton storage rings also have photodesorption
Buncher RF signal in High power
Drift region RF out issues)
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Applications of Accelerators: Research
Pumping systems: High Energy and Nuclear Physics
Turbomolecular pumps, sputter ion pumps, non-evaporable getter
pumps, and titanium sublimation pumps.
History: Livingston Plot
The pumping system can be lumped for proton storage rings, but
The collider energy advantage:
must be continuously distributed around the ring for rings with
high photodesorption gas loads.
E
m m
Fixed target (ultrarelativistic): E ≈c 2Em
cm
E E
m m
Collider: E ≈2E
cm
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Luminosity: the other figure of merit (besides energy) of a
high energy collider 1dR dN dN N
Luminosity L = = 1ρl = 1 2
Luminosity (L) = reaction rate per unit cross section q dt dt dt A
Area A
Target:
Colliding beams:
density ρ,
reaction cross
section with beam q
Beam l
N N
N particles 1 2
1
N
Number of target particles N = ρlA L = fN 2
2 1
A
Effective area seen by the beam A = qN = qρlA
eff 2 f is the collision frequency; A is the cross-sectional area of
A
Probability of an interaction P= eff = qρl the beams
A
dR dN dN
Reaction rate = 1P= 1qρl
dt dt dt
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In differential form: Types of high-energy colliders: operating
dL dN dN Type Facility CM Luminosity(1033
= f 1 2
energy(GeV) cm-2 s-1)
dA dA dA
for Gaussian, round beams, of rms size σ: e+-e-, two rings DAFNE (Italy) 1.05 0.01
e+-e-, single ring BEPC (China) 3.1 0.05
e+-e-, single ring CESR (US) 10.4 0.8
dN N r2 e+-e-, two rings SLAC PEP-II (US) 10.4 0.6
= exp− ; then e+-e-, two rings KEK-B (Japan) 10.4 0.3
dA 2πσ2 2σ2
e+-e-, single ring CERN LEP (Europe) 200 0.05
Pbar-p, single Fermilab Tevatron 1,800 0.02
N N ring (US)
L = f 1 2
4πσ2 e-p, two rings DESY HERA 300 0.02
(Germany)
e+-e-, linear SLAC SLC (US) 100 0.002
collider
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