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LINEAR ACCELERATORS
General introduction
F. Gerigk (CERN/BE/RF)
OVERVIEW
• Historical
developments,
• Fundamental
concepts,
• Characteristics
of accelerating cavities,
• Electron/hadron
accelerators
COCKROFT - WALTON (1932)
voltage multiplier + proton accelerator (< 1 MeV)
typically used up to
750 kV
crucial technology: voltage multiplier
the original machine
(200 keV)
CERN Linac2 pre-injector
until 1993 (750 keV)
VAN DER GRAAFF GENERATOR
(1931)
• a DC voltage is connected to
the lower electrode (7),
• charges
are transported (4)
to the dome (1), where they
are collected by the upper
electrode (2)
• until
a spark equalises the
potentials
•1
MV for 90 $!
(< 25 MV, tandem operation)
crucial technology: charge
separation and accumulation
20 MeV accelerator in
1981 (NSF, Daresbury, UK)
5 MV generator in 1933
(MIT, Round Hill, USA)
• one
sphere contains an ion
source, the other one a target,
• beam
through the air or later
through vacuum,
From DC to RF acceleration
THE WIDERÖE LINAC (1927)
energy gain:
period length
increases with
velocity:
E-field
particles
crucial technology: RF
oscillators & synchronism
the RF phase changes by 180 deg, while the particles
travel from one tube to the next
The use of RF enables to have
ground potential on both sides of
the accelerator. This allows a limitless
cascade of accelerating gaps!!
BUT:
•
the Wideröe linac was only efficient for low-energy heavy ions,
•
higher frequencies (> 10 MHz) were not practical, because then the drift
tubes would act more like antennas,
•
when using low frequencies, the length of the drift tubes becomes
prohibitive for high-energy protons:
3.5
e.g. 10 MHz proton
acceleration
length of drift tubes [m]
3
2.5
2
1.5
1
0.5
0
0
5
10
proton energy [MeV]
15
20
THE ALVAREZ LINAC
(1946)
after WW2 high-power high-frequency RF
sources became available (radar technology):
most old linacs operate at 200 MHz!
the RF field was enclosed
in a box: RF resonator
While the electric
fields point in the
“wrong direction” the
crucial technology: high-freq. particles are shielded
by the drift tubes.
RF sources & RF resonators
inside a drift tube linac
Linac2 at CERN, 50 MeV
DIFFERENCES BETWEEN
HADRON AND ELECTRON
ACCELERATION
Einstein:
Newton:
relativistic factor:
1.6
v/c - electrons (Einstein)
v/c - protons (Einstein)
v/c - protons (Newton)
1.4
1.2
v/c
1
0.8
0.6
rest energy:
0.4
0.2
0
0
200
400
600
energy [MeV]
800
1000
total energy:
PROTON VS. ELECTRON
ACCELERATION
• protons
change their velocity up to the GeV range (β=0.95 at
W=2 GeV),
➡accelerating structures (distance between gaps) need to be
adapted to the changing velocity,
• electrons
are almost immediately relativistic (β=0.95 at W=1.1
MeV),
➡basically from the source onwards one can use the same
accelerating structure (optimised for β=1.0) for the rest of
the linac,
Example of a 2/3 π-mode travelling wave structure for
electrons
synchronism condition:
- explanations on 2/3 π-mode in appendix
FUNDAMENTAL CAVITY
CHARACTERISTICS
BASICS OF RF ACCELERATION I
energy gain of a particle with charge q:
RF phase
passing a gap with the electric field E:
gap
-L/2
synchronous
phase
this can be written as:
average electric transit time
field on axis
factor
-L/2
cavity or
cell length
BASICS OF RF ACCELERATION I
energy gain of a particle with charge q:
RF phase
passing a gap with the electric field E:
gap
-L/2
synchronous
phase
this can be written as:
average electric transit time
field on axis
factor
-L/2
cavity or
cell length
BASICS OF RF ACCELERATION I
energy gain of a particle with charge q:
RF phase
passing a gap with the electric field E:
gap
-L/2
synchronous
phase
this can be written as:
average electric transit time
field on axis
factor
-L/2
cavity or
cell length
BASICS OF RF ACCELERATION II
average electric field:
transit time factor:
ignoring the velocity change in the cavity and assuming
a constant field between -g/2 and g/2, T simplifies to:
assuming:
FUNDAMENTAL CAVITY
CHARACTERISTICS: SHUNT IMPEDANCE
shunt impedance (linac definition):
maximising ZT2: maximising energy gain per length for a given
power loss
be careful: shunt impedance (synchrotron definition):
FUNDAMENTAL CAVITY
CHARACTERISTICS: (R/Q)
quality factor of a resonator:
Q= f(surface resistance, geometry)
acceleration efficiency per
unit stored energy:
(r/Q)= f(geometry)
(independent of surface losses!)
surface losses
DESIGNERS OF NORMAL CONDUCTING
CAVITIES ARE OPTIMISING FOR:
• maximum
effective shunt impedance ZT2(high electric efficiency),
different structures are efficient for different particle velocities,
• peak
fields below a certain threshold (avoid sparking and
breakdowns),
• maintain
• choose
synchronism between the cells and the particles,
a number of coupled cells so that: i) structure can still have
a flat field (stabilisation), ii) power consumption is compatible with
existing power sources, iii) there is enough space for transverse
focusing (quadrupoles between multi-cell cavities)
SUPERCONDUCTIVITY
• In
1965 the High-Energy Physics Lab (HEPL) at Stanford
University accelerated electrons in a lead plated cavity.
• In
1977 HEPL operated the first superconducting linac (with
niobium cavities), providing 50 MeV with a 27 m long linac.
• In
1996, 246 metres of SC (Nb sputtered on Cu) cavities are used
in LEP with an installed voltage (per turn) of 1320 MV (electrons).
• In
2005 SNS commissions a SC proton linac providing 950 MeV in
230 m (incl. transverse focusing).
• 2010
DESY is constructing XFEL (electrons), which will provide 20
GeV of acceleration (electrons) within 1.6 km.
• European
Spallation Source (ESS) is funded and will be
constructed in Lund (Sweden).
SPALLATION NEUTRON SOURCE,
OAKRIDGE
1 GeV, 1-1.4 MW on target, 60 Hz, linac pulse length 1 ms
WHEN ARE SC CAVITIES
ATTRACTIVE?
Instead of Q values in the range of ~104, we can now reach
109 - 1010, which drastically reduces the surface losses (basically
down to ~0) ➜ high gradients with low surface losses
However, due to the large stored energy, also the filling time
for the cavity increases (often into the range of the beam
pulse length):
(only valid for SC cavities)
PULSED OPERATION & DUTY CYCLES
FOR RF, CRYO, BEAM DYNAMICS
1.8
Vg
1.6
cavity voltage
1.4
1.2
Vsteady state
•
beam duty cycle: covers only the
beam-on time,
•
RF duty cycle: RF system is on and
needs power (modulators, klystrons)
•
cryo-duty cycle: cryo-system needs
to provide cooling (cryo-plant, cryomodules, RF coupler, RF loads)
1
0.8
Vdecay
0.6
0.4
0.2
0
0
1
2
3
4
5
ol
beam duty cycle
RF duty cycle
cryogenics duty cycle
6
7
Depending on the electric gradient, beam current,
particle velocity, and pulse rate, SC cavities can actually
be less cost efficient than NC cavities!
Nevertheless, one can generally get higher gradients (for
high beta) than with NC standing-wave cavities! (E.g.
XFEL cavities: ~23.6 MeV/m in a 9-cell 1300 MHz cavity,
vs 3-4 MeV/m in traditional NC standing wave cavities.)
LEP Nb on Cu cavity
XFEL 9-cell cavity
ANL triple spoke cavity
THANK YOU!!
MATERIAL USED FROM:
•
M. Vretenar: Introduction to RF Linear Accelerators (CAS lecture 2008)
•
T. Wangler: Principles of RF Linear Accelerators (Wiley & Sons)
•
H. Braun: Particle Beams, Tools for Modern Science (5th PP Workshop,
Islamabad)
•
D.J. Warner: Fundamentals of Electron Linacs (CAS lecture 1994, Belgium, CERN
96-02)
•
Padamsee, Knobloch, Hays: RF Superconductivity for Accelerators (Wiley-VCH).
•
F. Gerigk: Formulae to Calculate the Power Consumption of the SPL SC Cavities,
CERN-AB-2005-055.
APPENDIX:
Basics of Accelerating Cavities
WAVE PROPAGATION IN A
CYLINDRICAL PIPE
Maxwells equations
propagation constant:
cut-off wave number:
solved in cylindrical coordinates for
the simplest mode with E-field on axis:
TM01
wave number:
+ boundary conditions on a metallic cylindrical pipe: Etangential=0
cut-off wavelength in a
cylindrical wave-guide
(TM01 mode)
a
TM01 waves propagate for:
the phase velocity is:
TM01 field configuration
λp
E-field
B-field
dispersion
relation
Brioullin diagram (dispersion relation)
no waves propagate below the
cut-off frequency, which depends
on the radius of the cylinder,
each frequency corresponds to a
certain phase velocity,
the phase velocity is always larger
than c! (at ω=ωc: kz=0 and
vph=∞),
group velocity:
energy (and therefore information)
travels at the group velocity vgr<c,
synchronism with RF (necessary
for acceleration) is impossible
because a particle would have to
travel at v=vph>c!
We need to slow down the phase velocity!
put some obstacles into the wave-guide: e.g: discs
h
2a
2b
L
Dispersion relation for disc loaded travelling wave structures:
Brioullin diagram
disc loaded structure:
damping:
structure with: vph=c at kz= 2π/3 (SLAC/LEP injector)
Example of a 2/3 travelling wave structure
synchronism condition:
TRAVELLING WAVE
STRUCTURES
•
The wave is damped along the structure and can be designed as
“constant-impedance” structure or as “constant-gradient” structure.
•
Travelling wave structures are very efficient for very short (us) pulses, and
can reach high efficiencies (close to 100% for CLIC), and high accelerating
gradients (up to 100 MeV/m, CLIC).
•
are used for electrons at β≈1,
•
cannot be used for ions with β<1: i) constant cell length does not allow
for synchronism, ii) long structures do not allow for sufficient transverse
focusing,
STANDING WAVE CAVITIES
•
Closing of the walls on both sides
of the waveguide or disc-loaded
structure yields multiple
reflections of the waves.
•
After a certain time (the filling
time of the cavity) a standing
wave pattern is established.
•
Due to the boundary conditions
only certain modes with distinct
frequencies are possible in this
resonator:
dispersion relation
Brioullin diagram
STANDING WAVE CAVITIES
• for
n cells the fundamental
pass-band has n modes
from 0 to (n-1)π/(n-1),
• the frequency difference
between 0 and π-mode is
given by the cell-to-cell
coupling k,
the 0, π/2, or πmode is used for
acceleration,
• cell length can be matched
to any particle velocity!
• usually
• the
mode names correspond to
the phase difference from one cell
to the next,
0-MODE CAVITIES: ALVAREZ DTL
• most
common structure
for protons and ions with
β<0.3-0.4 (< 50 - 100
Quadrupoles
MeV for protons),
Drift Tubes
Power coupler
gap per βλ,
• optimum for gap/cell
length ≈0.2 - 0.3,
• at higher energies the drift
tubes become very long
Pumping port and increase the losses,
• one
Electrical efficiency depends on the electric field (P∼E2) and beam
current (50 MeV DTL with 3.2 MV/m,
Pbeam ≈ Pcopper ≈ 4.7 MW ηDTL ≈ 50%)