introduction to particle accelerators walter scandale cern - at department roma, marzo 2006
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Introduction to particle accelerators Walter Scandale CERN - AT department Roma, marzo 2006. Lecture III - superconducting devices. topics Limitations of normal conducting dipoles Superconducting material properties Critical temperature Type I and type II superconductors - PowerPoint PPT PresentationTRANSCRIPT
Introduction to particle accelerators
Walter Scandale
CERN - AT department
Roma, marzo 2006
Lecture III - superconducting devices
topics Limitations of normal conducting dipoles Superconducting material properties
Critical temperature Type I and type II superconductors Theoretical approaches
Meissner effect Cooper pairs and BCS theory
MgB2 and HTS SC dipoles
Current density Magnetization Flux jumping Quenches Wires and cables
SC-RF
Dipoles Iron yoke reduces magnetic reluctance (reduced power and ampere-turns) -> small gap height
Field quality -> determined by the pole shape
Field saturation -> 2 Tesla (BEarth = 3 10-5 Tesla)
B > 2 Tesla -> use SC magnets BLHC = 8.4 Tesla
€
B = μμ0H = μ0
N ⋅ Ih
H∫ ds = I ⋅N = h ⋅H0 + l ⋅H iron
Powering a resistive magnet I ≈ 5 kA for 1.8 T I ≈ 3·105 A for 10 T R ≈ 1 m P = R·I2
PLEP = 20 kW/magnet PLHC = 100 MW/magnet (if resistive)
Abolish Ohm’s Law! no power consumption (although do need refrigeration power)
high current density ampere turns are cheap, so we don’t need iron (although often use it for shielding)
Consequences lower power bills higher magnetic fields -> reduced bending radius
smaller rings reduced capital cost new technical possibilities (eg muon
collider) higher quadrupole gradients
higher luminosity
K. Onnes 1911
What is a superconductor
Resistance of Mercury falls suddenly below measurement accuracy at very low temperature
1908 Heinke Kemerlingh Onnes achieves very low temperature producing liquid He (< 4.2 K) 1911 Onnes and Holst observe sudden drop in resistivity to essentially zero SC era starts 1914 Persistent current experiments (Onnes) 1933 Meissner-Ochsenfeld effect observed 1935 Fritz and London theory 1950 Ginsburg - Landau theory 1957 BCS Theory (Bardeen, Coper, Schrieffer) 1962 Josephson effect is observed 1967 Observation of Flux Tubes in Type II superconductors (Abrikosov, Ginzburg, Leggett) 1980 Tevatron: The first accelerator using superconducting magnets 1986 First observation of Ceramic Superconductor at 35 K (Bednorz, Muller) 1987 first ceramic superconductor at 92 K (above liquid Nitrogen at 77 K !) HTS era starts 2003 discovery of a metallic compound the B2Mg superconducting at 39 K (x2 Tc of Nb3Sn)
It took ~70 years to get first accelerator from conventional superconductors. How long will it take for HTS or B2Mg to get to accelerator magnets? Have patience!
Short history of superconductivity
What is a superconductorBelow Tc the B-field lines are expelled out of a superconductor (perfect diamagnetic behaviour)
Type I superconductorsthe superconductivity disappears as T > Tc | B > Bc | J > Jc
Type II superconductorsFor Bc1 < B < Bc2 there is a partial flux penetration through fluxoid vortexes and a mixed phase
Below the critical temperature Tc the resistivity drops
€
ρ T( ) = ρ 0 + cT 5
phonon-e- interaction
Cooper pair appearance Meissner 1933
T < Tc
B < Bc
B = 0
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Meissner effect and magnetization
Inside the SC material one has B = 0 E = 0 (otherwise there is an infinite current flowing !) There is a superficial screening current inducing a diamagnetic polarization M = -H/4 = H The B field penetrate with an exponentially decaying intensity B(s) = B(0)exp(-s/L)
BCS theorySuperconducting state
Tc ~ 1/ √Misotopic -> phonons should play a role in superconductivity
Creation of Cooper pairs (over-screening effect) An e- attracts the surrounding ion creating a region of increased positive charge
The lattice oscillations enhance the attraction of another passing by e- (Cooper pair)
The interaction is strengthened by the surrounding sphere of conduction e- (Pauli principle)
In a superconductor the net effect of e-e- attraction through phonon interaction and the e-e- coulombian repulsion is attractive and the Cooper pair becomes a singlet state with zero momentum and zero spin
To break a pair the excitation energy is ∆E = 2∆
Normal conducting state
Predictions of the BCS theory
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Δ 0K( ) ≈1.76 ⋅kBTc
Δ T( ) ≈1.74 ⋅Δ 0K( ) 1−T
Tc
⎛
⎝ ⎜
⎞
⎠ ⎟
12
Hc T( ) = Hc 0K( ) 1− aT
Tc
⎛
⎝ ⎜
⎞
⎠ ⎟
2 ⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥ with a constant of the SC
€
Δ ≈ hπ ωDe
−1
F ⋅NF
€
h2π ωD ≈ kBTD Debye phonon energy
F effective potential
NF density of Fermi states
BCS theory NOT valid
in the ceramic SC.
Problems with SC type II
Energy bond of a Cooper pair
Size of a Cooper pair 100 nmLattice spacing 0.1 ÷ 0.4 nm
More on type I and II superconductors
Type I: not good for accelerator magnets
Also known as the “soft superconductors”.
Completely exclude the flux lines. Allow only small field (Bc < 0.1 T).
Type II: allow much higher fields Also known as the “hard superconductors”. Completely exclude flux lines up to Bc1
but then part of the flux enters till Bc2
Examples: NbTi, Nb3Sn
In accelerator magnets only Type II Low Temperature Superconductors are used.
NbTi, a ductile material, is the conductor of choice so far to build SC accelerator magnets.
Nb3Sn (higher Bc2) is the only very promising conductor for future higher field magnet. However, Nb3Sn is brittle nature and presents many challenge in building accelerator magnets.
€
Hc T( ) = H0 T( ) 1− aT
Tc
⎛
⎝ ⎜
⎞
⎠ ⎟
2 ⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
Note: of all the metallic superconductors, only NbTi is ductile. All the rest are brittle intermetallic compounds
Physics of type I and II superconductors “London Penetration Depth” L is the e-fold decay length of the magnetic field from the superconductor skin due to the Meissner effect (in the range of 10 to 103 nm)
Ginzburg-Landau Parameter
€
=Lξ ⇒
k < 12
⇔ type I
k > 12
⇔ type II
⎧
⎨ ⎪
⎩ ⎪
“Coherence Length” the average size of Cooper in the superconductor (in the range of 10 to 100 nm, I.e. much larger than the inter-atomic distance typically of 0.1 to 0.3 nm.
More on fluxoids
Fluxoid patter in Nb
Fluxoid motion due to current flow in Nb (SC type II)
a single fluxoid encloses flux
Fluxoids consist of resistive cores with super-currents circulating round them.
spacing between the fluxoids
Weberse
ho
151022
−×==φ
€
d =2
3
φo
B
⎧ ⎨ ⎩
⎫ ⎬ ⎭
1
2= 22nm at 5T
The magnesium diboride MgBDiscovered in January 2001 (Akimitsu)LTS with Tc: ~39 K A low temperature superconductor with high Tc
The Magnesium Diboride MgB2
The basic powder is very cheap, and abundantly available. The champion performance is continuously improving in terms of Jc and Bc.
However, it is still not available in sufficient lengths for making little test coils.
The high temperature SC (HTC)
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100
Critical temperature Tc (K)
Upper critical field Bc2 (T)
NbTi
B2212
many superconductors with critical temperature above 90K - BSCCO and YBCO
operate in liquid nitrogen? 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
metallic
HTS
II
I
B
SC dipole
simplest winding uses racetrack coils
saddle shaped long dipole coils to make more uniform fields
some iron - but field shape is set mainly by the winding
for good uniformity need special winding cross sections
€
B r( ) = μ0
I
2πr•
−sinnφ
cosφ
0
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ for r > a
€
B r( ) = μ0
J ⋅r2
•
−sinnφ
cosφ
0
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ for r < a
€
r1 cosφ1 − r2 cosφ2 = d
r1 sinφ1 − r2 sinφ2 = 0
€
J = 0
Bx = 0
By = μ0Jd
2
d
+J-J
real x-section
Current density
0
100
200
300
400
500
600
0 5 10 15 20 25B Tesla
Je A/mm
2
Nb3Sn at 4.2K
NbTi at 1.9K
NbTi at 4.2K
B2212 at 4.2K
B2212 at 35K
Wire: enough copper to provide stability (Cu/SC ≈ 1.7) against transient heat loads to carry the current in the event superconductor turns normal.
In pure SC filament -> J ~ 3 kA/mm2
In the real world replace J -> Jeng the 'engineering' current density
NbTi
Cu
insulation Cable: the trapezoidal “Rutherford cable” is made of several round wires (filling factor ~ 0.9)
Coil: it consists of many turns. There must be a turn-to turn insulation (filling factor ~ 0.85)
Current density in wires and cables of Nb3Sn
When the B-field raises, large screening current are generated to oppose the changes.
The current densities are initially much larger than Jc which will create Joule heating.
The large current soon dies and attenuates to Jc, which persist. Screening currents are in addition to the transport current, which comes from the power supply.
They are like eddy currents but, because there is no resistance, they don't decay.
Flux jumping
Unstable behaviour is shown by all type II and HT superconductors. The unstable loop is:
reduction in screening currents allows flux to move into the superconductor
flux motion dissipates energy thermal diffusivity in superconductors is low, so energy dissipation causes local temperature rise
critical current density falls with increasing temperatureCure flux jumping by making superconductor in the form of fine filaments
–--> weakens ΔJc ΔT ΔQ
a problem solved using fine SC filaments
Stabilization of flux jumpingcriterion for stability against flux jumpinga = half width of filament
€
a =1
Jc
3γ C θc −θo( )μo
⎧ ⎨ ⎩
⎫ ⎬ ⎭
12
typical figures for NbTi at 4.2 K and 1 T
Jc critical current density = 7.5 x 10 9 Am-2
g density = 6.2 x 10 3 kg·m3
C specific heat = 0.89 J·kg-1K-1
q c critical temperature = 9.0 Kso a = 33 m, ie 66 m diameter filaments
Less stable at low field -> Jc is highest when decreasing T -> Jc up and C down
Magnetization
when fully penetrated, the magnetization per unit volume of filament is
aJM c34
=
where a = filament radius
€
M =I ⋅AVV
∑
€
M =1
aJc ⋅ x ⋅dx
0
a
∫ =Jc ⋅a
2
When viewed from outside the sample, the persistent currents produce a magnetic moment.
Problem for accelerators because it spoils the precise field shape
We can define a magnetization (magnetic moment per unit volume) as:
for a fully penetrated slab
B
up-ramp branch
down-ramp branch
for cylindrical filaments the inner current boundary is roughly elliptical
B
J JJ
synchrotron injects at low field, ramps to high field and then back down again
note how quickly the magnetization changes when we start the ramp up
so better to ramp up a little way, then stop to inject
M
Bmuch better here!
don't inject here!
Synchrotron injection and field errors
Magnetization also produces field error.
The effect is worst at injection because
ΔB/B is greatest magnetization, ie ΔB is greatest at low field
Degraded performance and 'training'
most magnets do not go straight to the expected quench point *, instead they go resistive - quench - at lower currents
at quench, the stored energy 1/2LI2 of the magnet is dissipated in the magnet, raising its temperature way above critical - must wait for it to cool down and then try again
second try usually goes to higher current and so - known as training
8.00
8.20
8.40
8.60
8.80
9.00
9.20
9.40
9.60
9.80
10.00
10.20
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46
Quench Number
St. Steel collars
Aluminum collars
1.98K dI/dt=0
2.07K dI/dt=0
1.90K dI/dt=0
LHC short model dipole training histories: data from Andrzej Siemko
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Causes of training and some cures
Low Specific Heat: at 4.2K the specific heat of all substances is ~2,000 times less than at room temperature – so the smallest energy release can produce a catastrophic temperature rise.
Cure: work at higher temperatures – but HTS materials don’t yet work in magnets
Jc decreases with temperature: so a temperature rise drives the conductor resistive.
Cure: there isn’t one. Conductor motion: JB force makes conductor move, which releases heat by friction - even 10µm movement can raise the temperature by 3K:
Cures: i) make the coils fit together very tightly, pre-compress them
ii) vacuum impregnate with epoxy resin – but……………….
Resin cracks: organic materials become brittle at low temperature, because of differential thermal contraction they are often under tension – cracking releases heat.
Cure: fill the epoxy with low contraction (inorganic) material, eg silica powder or glass fibre.
Point quenching: even if only a very small section of conductor is driven resistive, the resistive zone will grow by Ohmic heating until it has quenched the magnet.
Cure: make the conductor such that a resistive zone will not grow until a large section has been driven resistive.
Causes of training and some cures
make thermal conductivity k large
make resistivity ρ small make heat transfer term hP/A large
NbTi has high ρ and low k copper has low ρ and high k mix copper and NbTi in a filamentary composite wire
NbTi in fine filaments for intimate mixing
make the windings porous to liquid helium --> superfluid is best
twisted filaments
coupledfilament
uncoupledfilament
Superconducting wires & cableso all superconducting accelerators to date still use NbTi (45 years after its discovery)
o performance of superconductors is described by the critical surface in B J T space,
o magnet performance is often degraded and shows ‘training’o SC stability requires making superconductor as fine filaments embedded in a matrix of copper
o magnetic fields induce persistent screening currents in superconductoro flux jumping occurs when screening currents go unstable quenches magnet - avoid by fine filaments - solved problem
o screening currents produce magnetization field errors - reduce by fine filaments
o in changing fields, filaments become coupled increased magnetization - reduce by twisting
o accelerator magnets need high currents cables- cables must be fully transposed ie every wire must change places with every other wire along the length of the cable - Rutherford cable used in all accelerators to date
o can get coupling between strands in cables- causes additional magnetization field error- control coupling by oxide layers on wires or resistive core foils
Rutherfordcable
fully transposed cables
€
ω0 =1
LC
What is an RF cavityA metallic box in which a resonant RF wave generate EM field modes to accelerate charged particles
Acceleration mechanisms
There is a specific resonant frequency of the cavity that one wishes to drive the cavity
The capacitance C and the inductance L of the cavity affect the transfer efficiency of power between the RF amplifying system and the cavity
The most efficient transfer of power would occur when the impedance appears as a simple resistor to the RF amplifying system
The accelerating voltage is V(t) = d·E (t) where d is the effective cavity length
The resonant frequency is
Equivalent circuit
power loss Pc
The high resistance Rskin of the cavity walls is the largest source of power loss.
In a superconducting RF cavity Rskin is 106 times smaller than in a normal conducting cavity
€
Rskin =μω
2σ=
1
σδ
What makes a good RF cavity quality factor Q : it measures the ability of the cavity to store energy
€
Q =ω0
U
Pc
=ω0
L
R=
LC
R
€
U = 12 LI0
2 = 12 CV0
2 =V0
2
2ω0LC
€
Pc = i2 t( ) R =V0
2
2ω0LC
€
Rsh =V 2 t( )
Pc
=V0
2
2Pc
= QL
C=
L
CR
At the resonant frequency: The shunt resistance Rsh is the resistive input impedance
The ratio Rsh/Q measures the acceleration efficiency per unit of stored energy
Shunt resistance
€
Rsh
Q=
V02
2ω0U
Stored energy
Power loss in the cavity wall
€
Pbeam = e V ⋅ Ibeam
€
Pc ∝Eacc ⋅Lacc( )
2
Q
Super/normal conducting RF cavitiesRF power into the beam
RF power into the cavity wall
RF power loss
HOM
Cavity at 700 MHz - ß = 0.65 - 5 cells - Lacc = 5·0.14 m Eacc = 10MV/m - = 0 -> eVacc = eEaccLacc = 7 MeV
Eacc: accelerating fieldLacc: accelerating length : RF-wave phase
5 cell cavity Nb cavity (2 K)real ideal
Cu cavity (300 K)
Rskin 20 n 3.2 n 7 mQ 10 10 6 ·1010 3 ·104
Eacc 10 MV/m 44 M /V m 2 MV/mPbeam (I beam = 10 mA) 60 kW 12 kWPc 16 W @ 2 K 218 kW @ 30 0 KPRF = Pbeam + Pc 60 kW 230 kWPAC fr om the plug 125 kW 400 kWPbeam / PAC 48 % 3 %LACC to reac h 100MeV
30 m 80 m
Plot à la ‘Livingstone’ for SRF cavities
SRF cavity limitations
"Q virus" a recently discovered phenomenon, in which excessive hydrogen in high purity
niobium can condense onto the RF surface of the cavity, forming a niobium hydride with poor superconducting property.
The Q virus is characterized by an anomalously low cavity Q (high surface resistance) at low electric field, followed by a rapid Q decrease with increasing fields.
Cure: a vacuum bake to 900 degrees C is sufficient to remove the hydrogen from the niobium, while not damaging the cavity.
Multipacting or resonant electron emission
Electrons emitted follow a trajectory such that they impact back at the surface of the cavity an integral number of RF cycles after emission, causing an avalanche effect, until all available power goes into this process.
Cure: change the cavity cross section from a rectangular to a spherical or elliptical shape.Thermal breakdown, or quench
Twall > Tc, the cavity becomes normal conducting, rapidly dissipating all stored energy. A small, local "defect" in the RF surface dissipates power more rapidly than the surrounding walls can conduct away.
The quench field depends upon thermal conductivity of the bulk niobium, heat transfer from the niobium to liquid helium bath, and size and resistance of the defect.
Cure: improve the thermal conductivity of the niobium, improving the purity of the metal. Residual Resistivity Ratio (RRR), the ratio of the resistivity at 300 K / 4.2 K is a good indicator.
reminder The main reasons to introduce superconducting devices (magnets and RF cavities) in particle accelerators are power saving and increase of performance.
In a superconductor the resistivity drops below the critical temperature.
Type I SC cannot be penetrated by the B-field,instead, type II SC partially can. The latter are the only useful material for SC devices.
We miss full theoretical explanations for SC. Cooper pairs explains the resistivity drop in type I SC. Dynamics of fluxiods explains properties of type II SC. We have no explanations for HTS.
In SC dipoles we need maximizing the current density, and fighting magnetization, flux jumping and quenches (luckily training helps). This imply optimal design of wires and cables for SC coils. Presently SC improves field and gradient performance by a factor 4 respect to NC.
In SC RF we need high-purity Nb, with thermal treatment to deplete H2 and round or elliptic cavities. Presently SC improves Vacc by a factor 10 and Q by 6 orders of magnitude respect to NC.
Lecture III - superconducting devices