Superconducting magnets for Accelerators Lecture 1 Superconducting Materials

1

Superconducting Accelerators Who needs
superconductivity anyway?

• Abolish Ohms Law!
• no power consumption
• (although do need refrigeration power)
• high current density ? compact windings, high
  gradients
• ampere turns are cheap, so we dont need iron
• (although often use it for shielding)
• Consequences
• lower power bills
• higher magnetic fields mean reduced bend radius
• ? smaller rings
• ? reduced capital cost
• ? new technical possibilities (eg muon
  collider)
• higher quadrupole gradients
• ? higher luminosity
• higher electric fields (dc)

2
Superconducting magnets for AcceleratorsPlan of
the CourseMartin N Wilson (Rutherford Lab ?
Oxford Instruments ? consultant)

• 1 Introduction
• where to find more information
• properties of superconductors, critical field,
  critical temperature critical current density
• high temperature superconductors HTS
• superconducting rf cavities
• magnetic fields and how to create them
• engineering current density
• 2 Controlling training fine filaments
• load lines and quench currents
• degradation and training
• causes of training
• minimum propagating zones MPZ and minimum quench
  energy MQE
• screening currents and the critical state model
• flux jumping
• magnetization and field errors

• 3 Cables quenching
• why cables?
• coupling in cables
• field errors caused by cable magnetization
• the quench process, internal and external
  voltages
• decay times and temperature rise
• propagation of the normal zone,
• quench protection schemes, protection of LHC
• 4 Manufacturing and testing
• conductor and cable manufacture
• magnet manufacture  
• measurement of critical current and magnetization
• current leads and persistent current switching
• some examples of superconducting accelerators

3
Some useful references

• Materials Mechanical
• Materials at Low Temperature Ed RP Reed AF
  Clark, pub Am. Soc. Metals 1983. ISBN
  0-87170-146-4
• Handbook on Materials for Superconducting
  Machinery pub Batelle Columbus Laboratories 1977.
• Nonmetallic materials and composites at low
  temperatures Ed AF Clark, RP Reed, G Hartwig pub
  Plenum
• Nonmetallic materials and composites at low
  temperatures 2, Ed G Hartwig, D Evans, pub Plenum
  1982
• Austenitic Steels at low temperatures Editors
  R.P.Reed and T.Horiuchi, pub Plenum1983
• Superconducting Materials
• Superconductor Science and Technology, published
  monthly by Institute of Physics (UK).
• Superconductivity of metals and Cuprates, JR
  Waldram, Institute of Physics Publishing (1996)
  ISBN 0 85274 337 8
• High Temperature Superconductors Processing and
  Science, A Bourdillon and NX Tan Bourdillon,
  Academic Press, ISBN 0 12 117680 0

• Superconducting Magnets
• Superconducting Accelerator Magnets KH Mess, P
  Schmuser, S Wolf., pub World Scientific, (1996)
  ISBN 981-02-2790-6
• High Field Superconducting Magnets FM Asner,
  pub Oxford University Press (1999) ISBN 0 19
  851764 5
• Case Studies in Superconducting Magnets Y
  Iwasa, pub Plenum Press, New York (1994), ISBN
  0-306-44881-5.
• Superconducting Magnets MN Wilson, pub Oxford
  University Press (1983) ISBN 0-019-854805-2
• Proc Applied Superconductivity Conference pub
  as IEEE Trans Applied Superconductivity, Mar 93
  to 99, and as IEEE Trans Magnetics Mar 75 to 91
• Handbook of Applied Superconductivity ed B
  Seeber, pub UK Institute Physics 1998
• RF Cavities
• Cornell electron storage ring CESR web site
  www.lns.cornell.edu/public/CESR/SRF
• Cryogenics
• Helium Cryogenics Van Sciver SW, pub Plenum 86
  ISBN 0-0306-42335-9
• Cryogenic Engineering, Hands BA, pub Academic
  Press 86 ISBN 0-012-322991-X
• Cryogenics published monthly by Butterworths

4
Materials data web sites

• Cryodata Software Products
• GASPAK
• properties of pure fluids from the triple point
  to high temperatures.
• HEPAK
• properties of helium including superfluid above
  0.8 K, up to 1500 K.
• STEAMPAK
• properties of water from the triple point to
  2000 K and 200 MPa.
• METALPAK, CPPACK, EXPAK
• reference properties of metals and other solids,
  1 - 300 K.
• CRYOCOMP
• properties and thermal design calculations for
  solid materials, 1 - 300 K.
• SUPERMAGNET
• four unique engineering design codes for
  superconducting magnet systems.
• KRYOM
• numerical modelling calculations on
  radiation-shielded cryogenic enclosures.

• Cryogenic properties (1-300 K) of many solids,
  including thermal conductivity, specific heat,
  and thermal expansion, have been empirically
  fitted and the equation parameters are available
  free on the web at www.cryogenics.nist.gov.
• Plots and automated data-look-up using the NIST
  equations are available on the web for a fee from
  www.cpia.jhu.edu.
• Other fee web sites that use their own fitting
  equations for a number of cryogenic material
  properties include www.cryodata.com (cryogenic
  properties of about 100 materials),
• and www.jahm.com (temperature dependent
  properties of about 1000 materials, many at
  cryogenic temperatures).
• Commercially supplied room-temperature data are
  available free online for about 10 to 20
  properties of about 24,000 materials at
  www.matweb.com.
• thanks to Jack Ekin of NIST for this information

5
The critical surface of niobium titanium

• Niobium titanium NbTi is the standard work
  horse of the superconducting magnet business
• it is a ductile alloy
• picture shows the critical surface, which is the
  boundary between superconductivity and normal
  resistivity in 3 dimensional space
• superconductivity prevails everywhere below the
  surface, resistance everywhere above it
• we define an upper critical field Bc2 (at zero
  temperature and current) and critical temperature
  qc (at zero field and current) which are
  characteristic of the alloy composition
• critical current density Jc(B,q) depends on
  processing

6
The critical line at 4.2K

• because magnets usually work in boiling liquid
  helium, the critical surface is often represented
  by a curve of current versus field at 4.2K
• niobium tin Nb3Sn has a much higher performance
  in terms of critical current field and
  temperature than NbTi
• but it is brittle intermetallic compound with
  poor mechanical properties
• note that both the field and current density of
  both superconductors are way above the capability
  of conventional electromagnets

7
Filamentary composite wires

• for reasons that will be described later,
  superconducting materials are always used in
  combination with a good normal conductor such as
  copper
• to ensure intimate mixing between the two, the
  superconductor is made in the form of fine
  filaments embedded in a matrix of copper
• typical dimensions are
• wire diameter 0.3 - 1.0mm
• filament diameter 10 - 60mm
• for electromagnetic reasons, the composite wires
  are twisted so that the filaments look like a
  rope (see Lecture 3 on cables)

8
Critical properties temperature and field 1
It costs energy to keep the field out. Critical
field happens when the condensation energy of the
superconducting state is just equal to the energy
penalty of keeping the field out.
Critical Temperature qc
where kB is Boltzmann's constant and D(0) is
the energy gap (binding energy of Cooper pairs)
of at q 0
where G is the Gibbs Free Energy of the
normal/superconducting state. BCS theory says
Critical Field Bc Type 1 superconductors
show the Meissner effect. Field is expelled when
sample becomes superconducting
where NF is the density of states at the Fermi
surface of metal in normal state - calculate it
from
where g is Sommerfeld coefficient of electronic
specific heat
9
Critical properties temperature and field 2
combining the previous equations
'thermodynamic critical field' Bc so like the
critical temperature, Bc is defined by the
'chemistry' typically for NbTi g 103 J m-3
K-1 so if q 10 K Bc
0.24T Conclusion Type 1 superconductors are
useless for magnets!
Note however Meissner effect is not total, the
magnetic field actually penetrates a small
distance l the London Penetration
Depth. Another characteristic distance is the
coherence length z - the minimum distance over
which the electronic state can change from
superconducting to normal
10
Critical properties type 2 superconductors
Theory of Ginsburg, Landau, Abrikosov and Gorkov
GLAG
defines the ratio k l / x If k gt
1/?2, we have a lower critical field Bc1
above Bc1 the magnetic field can penetrate in the
form of discrete fluxoids - Type 2
superconductivity
a single fluxoid encloses flux
where h Planck's constant, e electronic
charge
in the dirty limit'
upper critical field
where rn is the normal state resistivity - best
superconductors are best resistors!
thus the upper critical field
for NbTi g 900 J m -3 K-2 rn 65
x10 -8 W m qc 9. K hence Bc2
18.5 T
11
Critical properties current density
Fluxoids consist of resistive cores with
super-currents circulating round them.
precipitates of a Ti in Nb Ti
spacing between the fluxoids
a uniform distribution of fluxoids gives no net
current Jc0, but a gradient produces a net
current density
gradients are produced by inhomogeneities in the
material, eg dislocations or precipitates
fluxoid lattice at 5T on the same scale
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Critical properties a summary

• Critical temperature choose the right material
  to have a large energy gap or 'depairing energy'
• Critical field choose a Type 2 superconductor
  with a high critical temperature and a high
  normal state resistivity
• Critical current density mess up the
  microstructure by cold working and precipitation
  heat treatments
• - this is the only one where we have any control

Similar effects in high temperature
superconducting materials fluxoid lattice in
BSCCO
13
Upper critical fields of metallic superconductors

Note of all the metallic superconductors, only
NbTi is ductile. All the rest are brittle
intermetallic compounds
14
High temperature superconductors

• many superconductors with critical temperature
  above 90K - BSCCO and YBCO
• operate in liquid nitrogen?

YBa2Cu3O7 'YBCO'
15
High temperature superconductors
YBCO structure Conduction layers consist of two
CuO2 layers separated by yttrium atoms. The
charge layer consists of copper, barium and
oxygen atoms Note this structure makes the
properties highly anisotropic
16
Irreversibility line - a big disappointment
Unlike the metallic superconductors, HTS do not
have a sharply defined critical current. At
higher temperatures and fields, there is an 'flux
flow' region, where the material is resistive -
although still superconducting The boundary
between flux pinning and flux flow is called the
irreversibility line
17
RF Superconductivity

• moving the fluxoids around is a very dissipative
  process, but below Bc1 currents are only carried
  on the surface and so the ac losses are very low

• for this reason, superconductors can be used in
  low magnetic fields to make rf cavities with
  very low loss
• losses can be described by the two fluid model
  superconducting (paired) electrons and
  non-superconducting (unpaired) electrons

at low frequencies (dc) electric fields are small
(zero) and only the superconducting electrons move

• the proportion of non superconducting electrons
  increases with temperature
• so does the rf resistance

Info from RF Superconductivity 2004 by Hasan
Padamsee to be found at www.lns.cornell.edu/public
/CESR/SRF
18
Superconducting rf cavities

• because of their low losses, superconducting rf
  cavities are being increasingly used in
  accelerators
• the loss is usually expressed in terms of

• for example at 1.3GHz, Q factors as high as 1011
  have been reached, ie a 'ringing time' of 8
  seconds!
• because they have no loss, superconducting rf
  cavities can produce high accelerating voltages -
  up to 35 MV/m

• a copper cavity at 5 MV/m would dissipate several
  MW/m
• however, when pulsed, copper cavities can do
  better 100MV/m
• because there is no need to conserve power, s/c
  cavities can have a better shape - bigger beam
  hole

from RF Superconductivity 2004 by Hasan
Padamsee
19
Superconducting RF 30 years of progress
from RF Superconductivity 2004 by Hasan
Padamsee
20
Cavity performance

• it is usual to measure cavity performance in
  terms of a Q vs E plot
• E for benefit Q for cost
• because the proportion of paired electrons
  increases with decreasing temperature it is best
  to go cold

• the ideal performance is ultimately limited by
  the critical magnetic field of the material -
  usually pure niobium
• additional limitations are imposed by
• - multipacting
• - thermal breakdown
• - field emission
• - grain boundary field enhancement

from RF Superconductivity 2004 by Hasan
Padamsee
21
Performance limitation 1) multipacting

• A resonant process whereby an electron avalanche
  builds up via secondary emission.
• Electrons emitted from the surface are
  accelerated by the electric field and curved by
  the magnetic field to return, in phase, to the
  emission point.
• Here they kick out more secondary electrons
• Process continues with growing intensity until
  total breakdown

• With spherical cavity walls, the electrons travel
  towards the equator where the electric field is
  low
• Here the electrons no longer have enough energy
  to kick out secondaries.
• Problem solved ?

from RF Superconductivity 2004 by Hasan
Padamsee
22
Performance limitation 2) thermal breakdown

• Local rf heating at sub-millimetre sized defects
  can raise the temperature above qc
• Typical defects are foreign metal inclusions,
  pits, burrs, scratches, voids, welding defects
  etc

• Reduce defects by careful control of starting
  material
• Reduce heating by increased thermal conductivity
  of the niobium very pure and annealed

from RF Superconductivity 2004 by Hasan
Padamsee
23
Performance limitation 3) field emission

• Above a certain field, the Qo falls steeply
  because of emission of electrons from high points
• These electrons are accelerated by the field and
  produce losses on impact
• Reduce the incidence of emission points by
  assembly in very clean (class 100) conditions

• Blast off the emission points by high pressure
  water rinsing

• Finally burn off any remaining points by high
  power rf pulses of a few ms duration 'high power
  processing'

24
Performance limitation 4) grain boundary field
enhancement

• Magnetic field is enhanced at surface steps such
  as grain boundaries
• Reduce by electro-polishing

• Steady progress in the accelerating gradient of
  nine cell cavities

from RF Superconductivity 2004 by Hasan
Padamsee
from RF Superconductivity 2004 by Hasan
Padamsee
25
Magnetic Fields and ways to create them (1) Iron

• Conventional electromagnets
• iron yoke reduces magnetic reluctance
• ? reduces ampere turns required
• ? reduces power consumption
• iron guides and shapes the field

Iron electromagnet for accelerator, HEP
experiment transformer, motor, generator, etc
BUT iron saturates at 2T
26
Magnetic Fields and ways to create them (2)
solenoids
B

• no iron field shape is set solely by the
  winding
• cylindrical winding
• azimuthal current flow
• - eg wire wound on bobbin
• axial field

• can also reduce field curvature by making the
  winding thicker at the ends
• this makes the field more uniform

• field lines curve outwards at the ends
• this curvature produces non uniformity of field
• very long solenoids have less curvature and more
  uniform field

• more complicated winding shapes can be used to
  make very uniform fields

27
Superconducting solenoids
small superconducting solenoids for research
applications
a large solenoid in routine commercial operation
for the magnetic separation of Kaolin (china clay)
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(was the) World's largest Delphi superconducting
solenoid
Solenoids are not much used in accelerators. They
are however frequently used in detectors, where
the magnet field provides momentum analysis of
the reaction products. Delphi 1.2T 5.5m
dia 6.8m long 110MJ
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World's largest CMS superconducting solenoid
CMS solenoid 4T at 20,000A 6 m diameter 12.5m
long stored energy 27000MJ
30
Magnetic Fields and ways to create them (3)
transverse uniform fields

• some iron - but field shape is set mainly by the
  winding
• used when the long dimension is transverse to the
  field, eg accelerator magnets
• known as dipole magnets (because the iron version
  has 2 poles)

special winding cross sections for good uniformity
LHC has 'up' 'down' dipoles side by side
31
Dipole Magnets

• made from superconducting cable
• winding must have the right cross section
• also need to shape the end turns

32
Fields and ways to create them (4) transverse
gradient fields

• gradient fields produce focussing
• quadrupole windings

By kx
Bx ky
33
Engineering current density
In designing a magnet, what really matters is the
overall 'engineering' current density Jeng
fill factor in the wire
insulation
where mat matrix superconductor
ratio typically for NbTi mat 1.5 to 3.0 ie
lmetal 0.4 to 0.25 for Nb3Sn mat 3.0
ie lmetal 0.25 for B2212 mat 3.0 to
4.0 ie lmetal 0.25 to 0.2 lwinding takes
account of space occupied by insulation, cooling
channels, mechanical reinforcement etc and is
typically 0.7 to 0.8
NbTi
Cu
So typically Jeng is only 15 to 30 of Jsupercon
34
Importance of (engineering) current density (1)
solenoids

• the field produced by an infinitely long solenoid
  is

• in solenoids of finite length the central field is

• where f is a factor less than 1, typically
  0.8
• so the thickness (volume, cost) of a solenoid to
  produce a given field is inversely proportional
  to the engineering current density Je

35
Importance of (engineering) current density (2)
dipoles
field produced by a perfect dipole is
Je 37.5 Amm-2
LHC dipole
Je 375 Amm-2
120mm
660mm
9.5x105 Amp turns 1.9x106 A.m per m
9.5x106 Amp turns 1.9x107 A.m per m
36
Lecture 1 concluding remarks

• superconductors allow us to build rf cavities and
  magnets which burn no power (except
  refrigeration)
• ampere turns are cheap, so dont need iron
• ? fields higher than iron saturation (but
  still use iron for shielding)
• performance of all superconductors described by
  the critical surface in B J q space,
• three kinds of superconductor
• - type 1 unsuitable for high field
• - type 2 good for high field - but must work
  hard to get current density
• - HTS good for high field temperature - but
  current density still a problem in field
• superconducting rf cavities use type 1
  superconductors or type 2 below Bc1
• for good cavity performance must attend to-
  multipacting, thermal breakdown, field
  emission and grain boundary field enhancement
• all superconducting accelerators to date use NbTi
  (45 years after its discovery)
• different field shapes need different windings -
  simplest is the solenoid,
• - transverse field for accelerators