### Superconducting RF Cavities for Particle Accelerators: An

```Superconducting RF Cavities for
Particle Accelerators: An
Introduction
Ilan Ben-Zvi
Brookhaven National Laboratory
In a word:
• Superconducting RF (SRF) provides efficient,
• SRF accelerator cavities are a success story.
• Large variety of SRF cavities, depending on:
– Type of accelerator
– Particle velocity
– Current and Duty factor
– Acceleration or deflecting mode
What is a resonant cavity and how
do we accelerate beams?
• A resonant cavity is the highfrequency analog of a LCR
resonant circuit.
• RF power at resonance builds
up high electric fields used to
accelerate charged particles.
• Energy is stored in the electric
& magnetic fields.
f
Q
f
Q  
Pill-box cavity
  2.61a

2
U  da2 J1 (2.405) E02
2
Q=G/Rs
G=257
Rs is the surface resistivity.
Some important figures of merit
• U=PQ/
V2=P·Q·R/Q
• A cavity is characterized
For a pillbox cavity R/Q=196
by its quality factor Q
and the geometric
Per cavity: P = V2 · Rs · 1/G · Q/R
factors R/Q and G
• Dissipated power per Other quantities of interest for a pillbox cavity:
cavity depends on
Epeak /Eacceleration =1.6 (~2 in elliptical)
voltage, surface
resistivity and geometry
Hpeak /Eacceleration = 30.5 Gauss / MV/m
factors.
(~40 in elliptical cavities)
RF Superconductivity
• Superconducting
electrons are paired in a
coherent quantum state,
for DC resistivity
disappears bellow the
critical field.
• In RF, there is the BCS
resistivity, arising from
the unpaired electrons.
For superconducting niobium
Rs = RBCS + Rresidul
Hc(T)=Hc(0)·[1-(T/Tc)2]
For copper
 = 5.8·107 -1 m-1 so at
1.5 GHz, Rs = 10 m
RBCS
f
Rs 

2 104  f

  17.67 
~
exp




T  1.5GHz 
T


2
and at 1.8K, 1.5 GHz, RBCS = 6 n Rresidual ~ 1 to 10 n
Various SRF materials – only one
practical and commonly used
Material
Tc (K)
Hc1 (kGauss)
H c2(kGauss)
7.7
0.8
0.8
Niobium
9.2
1.7
4
Nb3Sn
18
0.5
300
MgB2
40
0.3
35
“Superheating” field for niobium at 0 K is 2.4 kGauss
Design Considerations
• Residual resistivity: RactualRBCS+Rresidual
• Dependence on field – shape, material, preparation
– “Q slope” Electropolishing, baking
– Field emission- cleanliness, chemical processing
– Thermal conductivity, thermal breakdown – High RRR
• Multipacting – cavity shape, cleanliness, processing
• Higher Order Modes – loss factor, couplers
• Mechanical modes– stiffening, isolation, feedback
Measure of performance:
The Q vs. accelerating field plot
Magnetic fields of 1.7 kGauss (multi-cell) to 1.9 kGauss (single cell)
Can be achieved, and recently 2.09 kGauss achieved at Cornell.
Limit on fields
• Field emission – clean
assembly
• Magnetic field
breakdown (ultimate
limit) - good welds,
reduce surface fields
• Thermal conductivity –
high RRR material
• Local heating due to
defects
Fields of 20 to 25 MV/m
at Q of over 1010 is
routine
Choice of material and preparation
• High “RRR” material (300 and above)
• Large grain material is an old – new approach
• Buffered Chemical Polishing (BCP) (HF – HNO3 –
H2PO4 , say 1:1:2)
• Electropolishing (HF – H2SO4)
• UHV baking (~800C)
• Low temperature (~120C).
• High pressure rinsing
• Clean room assembly
Multipacting
• Multipacting is a
resonant, low field
conduction in
vacuum due to
secondary emission
• Easily avoided in
elliptical cavities
with clean surfaces
• May show up in
couplers!
Multipacting in Stanford SCA cavity,
1973 PAC
Higher Order Modes (HOM)
• Energy is transferred
from beam to cavity
modes
• The power can be
very high and must
Energy lost by charge q to cavity modes:
be dumped safely
Longitudinal
2
• Transverse modes
U  kq
and Transverse
can cause beam
Solution: Strong damping of all HOM,
Remove power from all HOM to loads
breakup
Isolated from liquid helium environment.
Electromechanical issues
• Lorentz detuning
• Pondermotive instabilities
• Pressure and acoustic noise
Solutions include
curve
– feedback control
– good mechanical design
of cavity and cryostat
Miscellaneous hardware
•
•
•
•
Fundamental mode couplers
Pick-up couplers
Higher-Order Mode couplers
Cryostats (including magnetic
shields, thermal shields)
• Helium refrigerators (1 watt at
2 K is ~900 watt from plug)
• RF power amplifiers (very large
for non energy recovered
elements
Some Examples
•
•
•
•
•
•
Low velocity
Particle deflection
High current / Storage rings
High current / Energy Recovery Linac
RF electron gun
Low  Resonators
Split Loop Resonator
Spoke cavity
Multi-spoke
Quarter Wave
Resonator
Elliptical
Critical applications:
Heavy ion accelerators, e.g. RIA
High power protons, e.g. SNS, Project-X
Critical applications:
Linear colliders e.g. ILC
X-ray FELs e.g. DESY XFEL
Deflecting Cavities
Critical applications:
Crab crossing (luminosity) e.g. KEK-B, LHC
Short X-ray pulses from light sources
Energy Recovery Linac:
A transform to a boosted frame
• Energy needed for
acceleration is
“borrowed” then
returned to cavity.
• Little power for field.
Energy taken from cavity
JLab ERL Demo
Energy returned to cavity
High current ERL cavities
• Multi-ampere current
possible in ERL
E_2
E_4
E_5
E_6
E_7
E_8
E_9
Critical applications:
High average power FELs (e.g. Jlab)
High brightness light sources (e.g. Cornell)
High luminosity e-P colliders (e.g. eRHIC)
E_13
High current SRF photo-injector
• Low emittance at high
average current is required
for FEL.
• The high fields (over 20
MV/m) and large
acceleration (2 MV) provide
good emittance.
• High current (0.5 ampere) is
possible thanks to 1 MW
power delivered to the
beam.
• Starting point for ERL’s
beam.
Summary
• SRF cavities serve in a large variety of
purposes with many shapes.
• The future of particle accelerators is in SRF
acceleration elements – light sources,
colliders, linacs, ERLs and more.
• While there is a lot of confidence in the
technology, there is still a lot of science to be
done.
```