sc wigglers and undulators · 2019. 2. 28. · 19.04.2011 1 superconducting wigglers and undulators...

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Superconducting wigglers and undulators :

technical aspects

Mezentsev Nikolay

Budker institute of Nuclear Physics,Novosibirsk, Russia

Joint US-CERN-Japan-Russia Accelerator School, 6-16 April 2011 1

Contents

•Introduction•History•Superconducting materials•SC coil design types for multipole wigglers and undulators•SC ID field calculations•Transition of superconductor to normal state. (Quench)•Quench detection and quench protection •Influence of SC ID field on beam dynamics•SC ID cryogenic systems•Current feeding of SC ID•SC ID magnetic measurements systems


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Superconductivity phenomena -100 years

The phenomenon of superconductivity wasdiscovered in 1911 by the Dutch physicist H.Kamerlingh Onnes and his assistant Gilles Holstin Leiden. They found that dc resistivity ofmercury suddenly drops to zero below 4.2 K.

In 1933, W. Meissner and R. Ochsenfeld discoveredin Berlin one of the most fundamental properties ofsuperconductors: perfect diamagnetism.

The first microscopic theory ofsuperconductivity in metals was formulated byJ. Bardeen, L. Cooper and R. Schrieffer in 1957,which is now known as theBCS theory.

Introduction

]T[]cm[934.0 00 BK λ⋅=K~1 - undulator.K>>1 - wiggler

There is no any basic difference between wiggler and undulator. Phase errors in a magnetic field are more important for undulators as spectrum-angular properties of radiation are formed by all undulator length.

The main parameter of alternating-sign magnetic field which defines radiation property is K-value:

Superconducting (SC) wigglers (SCWs) and undulators (SCUs) arehigh performance IDs suitable for extending the spectral range of SRstorage rings towards shorter wavelengths and harder x-rays, increasebrightness of photon sources. The SCWs can be either wave lengthshifters (WLS) with a few magnet poles with very high magnetic fieldor multipole wigglers (MPW) with a large number of poles with highmagnetic field. The maximum magnetic field in SCWs and SCUs isdefined by the critical curve of the SC wire. SC MPWs fabricatedwith use of Nb-Ti/Cu wire provide magnetic fields that are 2-3 timeshigher than what can be obtained using permanent magnets for thesame pole gap and period length. SCWs and SCUs, as a rule, havezero first and second magnetic field integrals along electron orbit andtheir operation does not affect the working reliability of the storagering.


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History

The history of SC IDs used for generation ofSR started more than 30 years ago in BudkerINP where the first SC MPW was designed andfabricated in 1979. The first SC MPW wasinstalled on the 2 GeV storage ring VEPP-3 toincrease photon flux density with higher energy.The cross section of the vacuum chamber ofthe SCW was like a keyhole where a widevertical area was used for injection (30 mm),and narrow area (8 mm) was used for creationof magnetic field by the wiggler. These twoareas were connected by narrow 5.5 mm slit forelectron beam moving from injection area toarea with high magnetic field. In order to movethe electron orbit from the injection area to theworking area, 4 steering magnets were used.

Cross section of the magnet with vacuum chamber


First superconducting multipole wiggler, BINP, Russia

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Pole number 20Pole gap, mm 15Period, mm 90Magnetic field amplitude, T 3.5Vertical beam aperture, mm 7.8

A) The wiggler cryostat with magnetB)Undulator radiation from the wiggler

Sketch of the wiggler cryostat

The wiggler cryostat was built in the traditional scheme of those times with use of liquid nitrogen and liquid helium with a consumption of approximately 4 l/hr. Main benefit of the wiggler installation on VEPP-3 storage ring was a 200 times increase of the photon flux in the photon energy range 15–20 keV.

Photo of the wiggler magnet

Abstract. A superconducting undulator has been fixed onthe ACO storage ring. It has been observed that theelectron beam is stable in the small gap of the vacuumchamber and unperturbed by the magnetic field of theundulator. Light emission has been observed at 140 and240 MeV in the visible and ultra-violet. First results indicatethat its geometrical as well as spectral distribution agreewith theoretical predictions; small disagreementsvery probably arise from the fact that the electrons are nottravelling exactly on the axis of the undulator.

First superconducting undulator, ACO, Orsay, France


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Period 40 mmNumber of periods 23Effective length 0.96 mMaximum field Bo 0.45 T (K = 1.68).


Superconducting materials

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History of critical temperature of SC materials The critical surface of niobium titanium:superconductivity prevails everywhere below thesurface and normal resistivity everywhere above it.

The greatest interest from the point of view of creation of superconducting magnets represents such propertiesof superconductors, as critical temperature Tс, density of current Jс and field Вс. These parameters defineposition of critical surface in space with coordinates T, J and B and, hence, limiting characteristics of amagnet. Therefore it is desirable, that the specified critical parameters had higher values.


Main properties of SC materials

B-J diagrame of Nb3Sn and NbTi superconductorsfor 4.2K temperature

B-T critical curves of most popular SC materials for current in superconductors J=0A

B-T (critical field-critical temperature) and B-J (critical field – critical current) diagrams are shown in the figures belowfor best low temperature superconductors. Most of them exceed superconductors NbTi and Nb3Sn by maximal magneticfield. However they, as a rule, essentially are more complex in manufacturing, and only two materials V3Ga and Nb3Alare possible to receive in the comprehensible form and the sufficient length for winding.


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Nb-Ti/Cu SC wire

BC2 ~ 14.5 Tesla at T=0K, TC0 ~9.2К at B=0T.

C0, α, β и γ – empirical parametersTypical values:C0=30Т, α=0.6, β=1 и γ=2

Bottura’s formula

NbTi/Cu superconductor began one of the first to be used as a material suitable for magnet manufacturing. Owingto reliability and simplicity of windings manufacturing it still is the basic superconducting material for variousmagnets with field up to 8Т.

NbTi/Cu wire cross sectionJoint US-CERN-Japan-Russia

Accelerator School, 6-16 April 2011 13


Nb-Ti/Cu SC wire

There are two basic processes for Nb-Ti/Cu which are used for manufacturing of windings:

•Wet winding – epoxy coating is used during winding with special fillers for alignment of contraction coefficients between superconducting wire and epoxy coating, for increasing of heat capacity (Al2O3, Gd2O2S etc)

•Dry winding - vacuum impregnation or impregnation under pressure with hot (1200C) hardening epoxy coating with corresponding fillers.

There is a technology of dry winding at which each coil layer is covering by the glass tape impregnated by silicon-organic varnish which hardens at low temperature, but at room temperature again becomes viscous.

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Nb3Sn/Cu SC wire

−⋅

⋅−⋅

−=

)(ln77.11

)(31.01

)(1

)(),(

0

2

0

2

020

2

εεεεε

CCCC

C

TT

TT

TT

BTB

TBC 3020 = critical field at T=0K

KTC 180 = critical temperature at B=0T

( )317.100 1)( εε ⋅−⋅= aTT mCCε – deformation

а =900 for compressive deformation a=1250 for tensile deformation

Magnet manufacturing with use of superconductors on base ofNb3Sn/Cu demands much more complex technology connectedwith baking out of a ready magnet at high temperature invacuum or inert gas.

Three main processes of fabricating Nb3Sn wires:•Bronze process •Internal Sn process•Powder in tube (PIT) process


Comparison of NbTi and Nb3Sn


Nb3Sn/Cu SC wire

The Nb3Sn wire will have superconducting properties at low temperature after baking out invacuum or in inert gas at temperature 600-7500С. But after this process the wire becomes veryfragile as glass and there are technological restrictions at manufacturing windings with use suchwire during bend.

Most technically comprehensible process of manufacturing of superconducting windings fromNb3Sn is “Wind and react”. At this process the winding is made of a "crude" wire which hascomprehensible properties for winding, and then the winding is baked out and as a result the wirepossesses superconducting properties at low temperature.

Process of baking out of Nb3Sn/Cu coilNb3Sn/Cu coil after baking out

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High Temperature SuperConductors (HTSC)

1G BSCCO-2223 Tape (AMSC)

2G YBCO Wire (SuperPower, Inc.)

20µm Cu

20µm Cu

YBCO (~1 µm)

YSZ Buffer (~1.5 µm)

SS-Substrate (100 µm), non-magnetic

CeO2 Buffer (~0.05 µm)

Au Protective/stabilizing layer (~0.2 µm)

Cu Shunt layer (~20 µm)

YBCO (~1 µm)






YBCO (~1 µm)






Bruker EHTS



High Temperature Super Conductors (HTSC)

Critical current versus magnetic field for different orientation of tape and for various temperature.

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SC coil design types for multipole wigglers and undulators


Nb3Sn wire may increase field by another 1.5 times

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Planar coils:

•Vertical racetrack coils•Horizontal racetrack coils


Horizontal racetrack Vertical racetrack

Short SC wire is required Long SC wire is required

Large number of splices for large number of poles.

Less number of splices.

Total SC wire length is minimal Total SC wire length is 3-4 time more.

There is a possibility to make multi sections coils

There is no possibility to make multi section coils

The coils are stressed by bronze rods to compensate magnetic pressure in coils.

There is no possibility to stress coils by external compression

Minimal stored magnetic energy and inductance

Stored energy and inductance is more by 3 times

The coils have good thermo contacts with iron yoke after cooling down due to external compression

The thermo contacts became worth after cooling down. This is important disadvantage for indirect cooling magnets

Comparison of horizontal and vertical racetrack coils

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Horizontal racetrack type (SC wigglers)

Budker Institute of Nuclear Physics

Magnet array of horizontal racetrack type poles (example of 30 mm period SC 2.1T wiggler)

Cold welding method of wires connection gives resistance of the connection10-10-10-13 Ohm

Horizontal racetrack coilsassembly allows :•to pre-stress all coils togetherfor compensation of magneticpressure•to use 2 or more sections coils,which gives a possibility toobtain higher field for the sameSC wire.

Drawing and photo of racetrack type poles (example of 2-sections coil of 48 mm period 4.2T wiggler


42 pole undulator APS prototype, period -16 mm

Vertical racetrack coils (SC undulators)


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Period length, mm 15Number of full periods - 100.5Max field on axis with 8 mm magnetic gap, T 0.77Max field in the coils,T 2.4Minimum magnetic gap, mm 5.4Operating magnetic gap, mm 8Gap at beam injection, mm 16K value at 5 mm gap - >2Design beam heat load, W 4

Under development in collaboration with ANKA



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Vertical racetrack coils (SC undulators)Jim ClarkeASTeC, STFC Daresbury Laboratory


Vertical racetrack coils (SC wigglers)LBNL

NbTi coils

Nb 3Sn coils

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SCU Helical constructed from NbTi (0.86T @ 11.5mm)Nb3Sn short prototypes will be constructed soon (1.5T @ 11.5mm?)

Daresbury and Rutherford Appleton Laboratories

Helical coils (SC helical Undulators)


Double helical coils


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SC ID field calculations

1-section coils (example, SC wiggler)

Wire diameter with/without insulation, mm 0.55/0.5NbTi/Cu ration 1.4Number of filaments 312Diameter of filament, micron 37Critical current at 7 Tesla, A 236

Wire parameters:

Period, mm 30Pole gap, mm 12.6Pole number 119Nominal field ,T 2.1

Magnetic field distribution at the inner radius ofthe coil along vertical coordinate (B, kGs; z, cm).

Critical current curve of used superconducting Nb-Tiand field-current critical points inside coil correspondto magnetic field in median plane. Temperaturedecreasing gives a possibility to increase field.


Maximal field in the coil

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 80

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

0.5 -230-7T 4.2Kmaximum field in coilload line (one section coil)external sectioninternal sectionmaximum field in coil

Critical current curve

Magnetic field, Tesla

Curr

ent,

A

3.2

Critical curve of SC wire

One section coil load line

Two sections coil load line –external section

Two sections coil load line –internal section

Maximal field inside coils

Figure shows a comparison of one andtwo section coils with identical layernumbers in the coils. The one-sectioncoil reaches a critical current at 450Aand field of 4.5Т at internal layer. Thetwo-section coil has different currentsin sections which simultaneouslyreach critical values. The externalsection reaches a current of 649А andfield of 3.2T at internal layer of thesection. The internal section reaches acurrent of 380А and field of 5.2T atinternal layer of the section. Due tosplitting the coil into two sections withequal layer numbers and feedingsection with different currents thefield value increases by 15 % (5.2Tand 4.5T) in comparison with an one-section coil. Maximal field may beincreased by 30% in comparison withone section coil with use ofindependent current feedings of eachcoil layer. This approach requires a lotof independent power supplies and itis technical complication. Two-sectioncoil is a reasonable compromise.

Comparison of one and two sections coils

Magnetic field distribution at theinner radius of the coil 1-st sectionalong vertical coordinate (B, kGs; z,cm).

Magnetic field distribution at the inner radius of the coil 2-nd section along vertical coordinate (B, kGs; z, cm)

Period, mm 48Pole gap, mm 14.4Pole number 49Nominal field, T 4.1

2-sections coils (example, SC wiggler)

Two-sections coil gives up to 15% higher field for the same SC wire.

Wire parameters:

Wire diameter with/without insulation, mm 0.91/0.85NbTi/Cu ration 1.4Number of filaments 312Diameter of filament, micron 37Critical current at 7 Tesla, A 700

Critical current curve of usedsuperconducting Nb-Ti wire (red line)and field-current critical points insidecoil correspond to magnetic field inmedian plane

Load lines for 4-section magnet with separate feeding


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Magnetic field distribution in high field wigglers (Example of 7.5 T SC wiggler)


Iron yoke Iron yoke

Iron yoke Iron yoke

Median plane Median plane

Iron core

Iron core

The magnetic flux inside of a pole in multipole wigglers and undulators is closing through the neighbor poles. Incase of 2-dimensional field distribution (infinitely wide poles) the longitudinal field integral in median plane isautomatically equal to zero. It follows from Maxwell’s equations. At a high field in a wiggler iron cores arecompletely saturated and represent permanent magnets which give to the field some small contribution. Thiscontribution may be increased with use some materials like Dy or Ho which are saturated at higher field. Themaximal field inside the coils is on a wire layer which is nearest to an iron pole and approximately on half of heightof the pole. This fact should be taken into account at field calculation as this part of the wire is most close to a criticalcurve on the diagram a field-current. External iron yoke is in use mainly as support system for poles and closes astray field.

Vertical component of magnetic field distribution Horizontal component of magnetic field distribution

Lorentz forces in high field SC wigglers (Example of 7.5 T SC wiggler)

Distribution of horizontal component of Lorentz forces acting on windingsJoint US-CERN-Japan-Russia

Accelerator School, 6-16 April 2011 36

Horizontal component of Lorentz forces acting on windings along a horizontal line passing through middles of coils

The forces acting on windings in horizontal direction, aspire to tear off the winding from the iron core. If there is nocounteracting force a winding may move and as a result a heat will be extracted, temperature of a superconductingwire will rise up and the wire may transit to normal state (quench). Usually in such situations the further quenchtraining of the magnet does not lead to field increasing. Presence of counteracting force may create a high pressureinside of windings (several hundreds bar) at which epoxy starts to crack with heat extraction. This also may be areason of a quench. But here there is a hope, that quench training increase the field.

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0 2 4 6 8 104− 103×

3− 103×

2− 103×

1− 103×

0

1 103×

2 103×

force acting on internal sectionforce acting on external sectiontotal Lorentz force acting on coil

Magnetic field in median plane, Tesla

Lore

ntz

forc

e, k

G

0 2 4 6 8 103− 104×

2− 104×

1− 104×

0

force acting on internal sectionforce acting on external sectiontotal Lorentz force acting on coil

Magnetic field in median plane, Tesla

Lore

ntz f

orce

, kG

Lorentz forces (vertical component ) acting on windings in vertical direction

Lorentz forces (vertical component ) acting on windings in vertical direction along a vertical line passing through a coil mid. A)- wiggler with iron yoke, B)- wiggler without iron yoke

A B

A BIntegral forces acting on coil sections versusfield level . A) wiggler with iron yoke. B)wiggler without iron yoke.

The forces acting on windings, lead to theircompression. Presence of iron yoke decreaseintegral force acting on windings.

Lorentz forces in high field SC wigglers (Example of 7.5 T SC wiggler)

Main parameters of a superconducting multipole IDare:λ0- period,B0- magnetic field in median plane,g- pole gap.These parameters are linked by means of the formula:

Bp - parameter is defined by magnet design and used superconducting materials.

Main parameters of multipole SC ID

0p

0

p0

cosh

λπ

λπ

g

eBg

BB

−

≈

=

Ratio p0 / BB versus 0/ λg


Correlation of Bp parameter with magnetic field for various SC wires

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Transition of superconductor to normal state.(Quench)

Quench is transition of a magnet in normal state occurs at occurrence in its winding of zones with normal resistance.As the superconductor in a normal state possesses high specific electroresistance, at presence in the winding of themagnet with high density current the superconductor in these zones is warmed up to the temperatures considerablyexceeding its critical temperature, and the sizes of normal zones are increasing with time. This irreversible processleads to transformation of all energy reserved in the magnet into heat.

The energy necessary for translation of a winding in a normal state is rather small owing to low thermalcapacities of materials at low temperatures: typical values of a thermal capacity at temperature of liquid heliumapproximately in 1000 times less than at room temperature.The reason of a quench in a winding can be jumps of magnetic flux at ramp field, movement of badly fixedsuperconducting wire, epoxy crack, bad electric contact in a junction of wires, external heat in-leak.

Appearance of a normal zone underaction of local perturbation in asuperconducting wire with current

( ) 2/12

02

−=

c

c

Jl

ρθθκ

Jс– critical currentl – minimal propagation zone (MPZ)ρ- specific electroresistanceΘ0, θс – temperatures


Normal zone propagation

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Threshold density of energy of volumetric perturbations for quenchappearance in " a typical winding » at Т=4.2К

Quench initiation

Reasons:• mechanical movement of SC wire• crack of epoxy resin in coil• heating of coil due to eddy current• heating of coil due to bad electrical junction• magnetic flux jump

Coil heating during quench

During propagation of normal zone inside magnetwinding there is a non-uniform non-stationarytemperature distribution changing within the limits offrom 4.2K up to some maximal temperature θm inpoint the quench happened.

)()()()(

0

20

2

0

md UdCtJdttJ

m

θθθρθγθ

θ

===∫ ∫∞

θθγθρ dCdttJ )()()(2 =

Thermal balance for normal zone:

Function U(θ) for various conductors and typical magnet windings of small sizes.1- copper RRR=150, 2-copper RRR=30, 3-aluminium ρ0=5*10-11 Ohm*m, 4- winding (23 % NbTi, 47%Cu, 30 % epoxy.

Universal function U (θm) depends only on physicalproperties of the materials used in a winding, and allowsto define the maximal temperature on initial currentdensity in the winding and to characteristic time tdattenuations of the current.

C- specific heat capacity,γ – average winding density


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2/1

0

0

2/1

0

−

=

−

=θθ

θγθθ

ρκγ s

s

s

LCJ

CJv

Normal zone propagation velocityL0 =2.45*10-8 W*Ohm/K2 – Lorentz constant

20 40 60 80 1000

2 103×

4 103×

6 103

×

8 103×

RRR=50RRR=100RRR=150RRR=300RRR=500

Temperature, KH

eat c

ondu

ctio

n, W

/m*K

20 40 60 80 1001 10

11−×

1 10 10−×

1 109−

×

1 10 8−×

RRR 50RRR 100RRR 150RRR 300RRR 500

Temperature, K

Res

istiv

ity,O

hm/m

Copper heat conductionCopper electrical resistivity

TL0=σκ

Wiedemann-Franz-Lorentz law

TRRR ⋅

≈

76κ

Useful relation between κ and RRR for copper

W/cm/К (RRR=σ4.2K/σ300K )



Quench detection and quench protection

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Quench detectionThe high potential develops inside of a winding whereexists resistive voltage component directed towards toinductive. The small voltage difference between feedingwires is caused by small internal resistance of powersupply which is usually automatically disconnected atquench. But even if it will not occur, the voltage on thepower supply is only some volt in comparison withhundreds and, probably, thousand volt in a normalzone. Therefore the voltage of the power supply can beneglected, but it should be disconnected quicklywhenever possible to not admit a long heating windinginside a cryostat.

Electric potential distribution in a winding during quench

dttdILtRtItV QQQ)()()()( ⋅+⋅=

0)()()( =⋅+⋅dt

tdILtRtI Q

−⋅⋅=

LL

tRtItV QQQ 1)()()(

L – total inductance of a magnet,LQ- effective inductance of quenched magnetpart.Resistance of normal zone RQ(t) and its effectiveinductance LQ grow with time, and current I(t) isdamping. Voltage VQ in normal zone all over againgrows up to the maximal value, and then decreases.

I1 = 203 A, I2 = 203 A, B = 2.1 Tesla

-0.05 0 0.05 0.1 0.15 0.2 0.25Time, s

-5

0

5

10

15

20

25

30

35

40

U, V

Pole 41upper coil bottom coil Quench

Time dependence of taps voltage of one section quenched coil


Quench detection

Bridge scheme of quench detecting

The scheme of quench detecting by means of a compensating winding

On bridge scheme the potentiometer is set in position at which gauge D does not react to current change in a magnet dI/dT. It is supposed, that gauge D registers voltage difference between top and bottom magnet sections caused by occurrence of a normal zone in a winding.

Compensating winding scheme is a registrator of transformer type in which the secondary winding is set on one of current leads and registers a signal dI/dT in magnet circuit. This signal amplifies, and then by the electronic detector is subtracted from the voltage of certain part of the winding.

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Quench protection

Passive quench protection scheme Active quench protection scheme

ee TTLTR eIeII /0/

0−− ==

)(22 2

20

02

202

me

e

UATI

RALIdTJ θ===∫

∞

Active quench protection scheme a magnet with inductanceL, consists of external resistance Rg and switch S. Duringmagnet feeding or operating conditions switch S is closedand the current practically does not flow through resistanceRg. As soon as quench detector will register the beginning ofquench, switch S is disconnected and current flows throughresistance Rg. If Rg is big enough in comparison with theresistance arising in the magnet the constant of time T0 ofcircuits is defined by external resistance Rg.

Cold Si diods are used as passive quenchprotection system in combination with dumpresistor Rb. The cold Si diod is closed in bothdirections for voltage less than several volts. Athigher volt the diod becomes normal diod.This property of the diod gives a possibility toramp up and down field in a magnet withoutcurrent branch, but if quench happened the diodopening and current flows through dumpresistor.

Quench protection

0.3 Ohm

0.3 Ohm

I2

3 Ohm

0.3 Ohm

0.3 Ohm

0.3 Ohm

0.3 Ohm

0.3 Ohm

0.3 Ohm

I1

3 Ohm

Quenchdetector

The electric scheme of protection of the partitioned superconducting magnet with use of "cold" diodes and external resistors

Cold diods

Dump resistors

SC wiggler


Significant part of stored energy in a magnet may be extracted toexternal resistance as an element of magnet quench protection. Itallows to reduce losses of liquid helium on evaporation at aquench and, besides to eliminate the usual danger connected withoccurrence is excessive a high pressure inside cryostat as a resultof boiling liquid helium. However reliability of such activemethod of protection entirely depends on non-failure operation ofsystems of registration and the breaker of a current. Therefore inmany cases preference give passive ways of protection withoutapplication of any mechanical devices.

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Quench training effect

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80Quench number

3.55

3.6

3.65

3.7

3.75

3.8

3.85

3.9

3.95

4

4.05

4.1

4.15

4.2

4.25

4.3

4.35

B, T

esla

Quench hystory dataBath cryostatFactory acceptance testSite acceptance test


Example of SC wiggler for DLS training effect


Influence of SC ID field on beam dynamics

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Field integrals

Field integrals along ID magnet

First field integral (angle deviation of beam orbit inside ID with Bρbeam rigidity). Bz(s) – vertical component of ID magnetic field, s-longitudinal coordinate, L> ID length.If Bz(-s)= -Bz(s) –asymmetric system ф=0 For symmetrical system Bz(-s)= Bz(s) to provide ф=0 currents in side poles should be adjusted.

∫∫∫ ∫−⋅

+⋅

−⋅=′′′′

′=−

′

−

2/

0

2/

0

2/

2/ 2/

)()()( L zL

zL

L

s

L

z dsB

sBsdsB

sBsLsdB

sBsdρρ

φρ

δ

∫⋅

−=2/

0

)(2L

z

BdssBs

ρδ

End poles are using for compensation of field integrals.Odd number of pole

SC multipole wigglers and undulators represents sign-variable magnetic structure with many poles and with magnetic field definedby critical curve of a SC wire. Generally these devices are symmetrical or asymmetrical relative a mid point of magnetic structure.Main requirement for field feature is equality of first and second field integrals to zero. To provide this requirement two powersupplies are used for feeding main and side coils.

∫∫∫ −+==−

2/

0

2/

0

2/

2/

)(1)(1)(1L

z

L

z

L

Lz dssBB

dssBB

dssBB ρρρ

φ

The second field integral (orbit distortion inside L-interval:

If Bz(-s)= -Bz(s) asymmetric system and ф=0, is twice more than the orbit distortion at the ID mid point.

For cases а) and б) in the figure the integral is not zero but forsymmetrical case Bz(-s)= Bz(s) the integral is zero.For case в) for both cases the integral may be set to zero using twopower supplies.400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 18005

4

3

2

1

0

1

2

3

4

5Magnetic field, Tesla

Longitudinal coordinate, mm

MA

gnet

ic fi

eld,

Tes

la

.

Field distribution in SC 4.2T wiggler with odd pole number


Orbit inside ID

400 600 800 1000 1200 1400 1600 18004

2

0

2

4Orbit angle deviation


Ang

le, m

rad

400 600 800 1000 1200 1400 1600 18000.06

0.04

0.02

0

0.02


Orb

it, m

m

Angle orbit deviation inside 49-pole wiggler at field setting 4.2 Tesla, E=3 GeV

Orbit distortion inside 49-pole wiggler at field setting 4.2 Tesla, E=3 GeV

)(1)(2/

0 sBsdBsx z

s

L

′′=′ ∫−ρ

)(1)(2/2/

0 sBsdsdBsx z

s

L

s

L

′′′′′= ∫∫′

−−ρ


First field integral Second field integral

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0.08− 0.06− 0.04− 0.02− 0 0.02 0.046−

4−

2−

0

2

4

6

Electron beam orbit horizontal coordinate, mm

Orb

it an

gle,

mra

d

2.5− 2− 1.5− 1− 0.5− 0 0.5 1 1.5 2 2.56−

4−

2−

0

2

4

6

Photon beam horizontal coordinate, mm

Phot

on b

eam

ang

le, m

rad

Electron beam orbit phase space Photon beam phase space reduced to the wiggler center

Phase space of electron orbit and photon beam


Focusing property of SC ID

0=⋅+′′ xKx x0=⋅+′′ zKz z

−′+=

xB

sBx

BBBK zzzx ∂

∂∂

∂ρρ1

)( 22

−′−=

xB

sBx

BK zzz ∂

∂∂

∂ρ1

∫∫−− ∂

∂−=

2/

2/

2/

2/

L

L

zL

Lx B

dsBx

dsKρ

∫ ∫∫− −−

−=2/

2/

2/

2/2

22/

2/

L

L

L

Lx

zL

Lz dsKdsB

BdsKρ

Vertical and horizontal betatron tune shifts forBESSY SC 7 T WLS versus magnetic fieldlevel.

Betatron motion equations

Local and integral focusing rigidity


19.04.2011

28


Beating beta-functions

−−=

∆2

,

2

,

,,

,

,

121

)sin(2 zxzxzxzx

zx

zx LLKβµ

βββ

Betatron β-functions beating

Effect of 3.5 Tesla SC wiggler installed on MAX-II ring,

Radiation (structural) integrals:

dsB

sBsxI

L

zx∫−

=∆ρ

η )())(( 01

∫=∆L

z dsB

sBI 22

2)(

ρ

∫=∆L

z dsB

sBI 3

3

3)(

ρ

∫ −

−

⋅=∆

Lx

xz dssxBK

BsBI ))((2)( 03

3

4 ηρρ

( )∫ ′−′+′−′−+−=∆L

xxxxxxxz dssxsxsxsxB

sBI 2000

203

3

5 ))(())())(((2))(()(

ηβηηαηγρ

xxx γβα ,, are Twiss parameters

02

4203

31

04

022

4221

03

312

I

I

I

I

II

III

I

EE ∆−

∆+≈

+

∆+∆+

∆+

=

′

σ

σ

02

205

51

04

02

421

05

51

I

I

I

I

II

III

I

xx ∆−

∆+≈

−

∆−∆+

∆+

=′

ε

ε

Horizontal emittance BESSY storage ringversus magnetic field level in SC 7 TWLS.

Energy spread in BESSY storage ring versus magnetic field level in SC 7 T WLS.


Energy spread change

Emittance change

19.04.2011

29

SC ID field expansion into multipole components

Magnetic field measurements of an ID are usually carrying out in Cartesian coordinates which will havedesignations χ, z, σ, thus the axis σ coincides with a longitudinal axis of an ID, χ and z are horizontal andvertical directions correspondingly. Planes z = 0, χ = 0, σ = 0 are corresponding planes of symmetry of WLSmagnetic systems; therefore, the basic members of magnetic field expansion into multipole components inCartesian coordinates, following K. Steffen (1965), may be written down in the forms:

...36

)3

22(

2

...36

)33(6

...424

412

224

)42264(24

22

)22(2

+⋅′′′

−−⋅′

+⋅′=

+⋅′′

−−⋅+⋅=

+′′′′

+′′

+⋅′′

−+−⋅+⋅′′

−−⋅+=

zaz

zb

zaB

zb

zzc

zbB

za

zb

zb

zzc

za

zb

az

B

χσ

χχχχχ

χχχχ



2000

00

20

2

2

xaxxbbSaxxbG

xbaBz

′′′+′′−=

′′−⋅=

⋅+=

If magnetic system is homogeneous enough so that orbit deviation is much less than characteristic sizeof field decrease, the formulas may be simplified:

)(0 σx

...23

22

...)242

(6

...242

20

20

200

3000

20

40

200

300

40

20

+′′′

+′′′+′′

−′′−+=

+′

+′

+′′−⋅+⋅=

+⋅+⋅+=

xxbxaxxcxxbxcbS

xcxbaxxcxbG

xcxbaBz

The primes in formulas mean a derivative on longitudinal coordinate σ. We shall designate ascoordinate and angle of beam orbit deviation to a ID axis accordingly. In displaced on coordinate androtated on angle the basic field multipole components (field, gradient, and sextupole) may be expressedas:

)(),( 00 σσ xx ′)(0 σx

)(0 σx′

19.04.2011

30

( )( )...))()(2)(sin(...))()(cos()(

...))()(sin(...))()(cos()(

...))(211)(cos()(

0002

0200

20

200

00002

00

2200 0

+′−++′−−=

+′++−=

+−=

σσσσσσ

σσσσσ

σσσ

xxkkkxkkkBSkxkxkkBG

xkkBB

xx

x

xz

Where , , ; are wiggler characteristics magnetic field periods in σ,χ, z-directions and are following from Maxwell equations

SC ID field expansion into multipole componentsMagnetic field of multipole ID with periodic magnetic field may be approximated by formulas:

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )zkkkBkkB

zkkkBkkB

zkkkBB

zxz

zxz

x

zxz

sinhcossin

sinhsincos

coshcoscos

000

00

00

χσ

χσ

χσ

σ

χ

−=

−=

=

00 /2 λπ=k xxk λπ /2= zzk λπ /2= zx λλλ ,,020

22 kkk xz +=

10

19.04.2011

31

The basic cryostat function is maintenance of SC wiggler magnets at temperature of liquid helium of 4.2 K. Thewiggler magnet is placed into a bath with liquid helium and all heat emission inside the magnet and heat in-leakoutside lead to liquid helium evaporation process. The cryostat consists of external vacuum housing, 60 K and 20 Kshield screens, liquid helium vessel with a SC multipole magnet inside, throat, vacuum chamber (beam duct) withcopper liner inside, upper flange, filling tube, two 2-stage coolers with stage temperature 4.2 K/50 K, and two 2-stagecryocoolers with stages temperature 20 K/50 K for shield screen cooling.

Bath cryostat systems

Pattern of a cryostat cross section.

Photo of SC wiggler installed on CLS storage ring.


Bath cryostat systems (shield screens)The inner liquid helium vessel is

surrounded by two shield screens toreduce the irradiation heat flux fromoutside. The temperature on theoutside shield screen is about 60 K,and on the inner one the temperatureis about 20 K.

Shield screens are made ofcopper by thickness of 3 mm. The60K and 20K copper screens areassembled to common block andinserted into the cryostat housingusing special fiber glass balls. The60 K screen is attached to all of four60 K stages of the coolers by heatsinks. The 20 K stages of the bothbottom coolers are connected tocopper liner and to 20 K screen. The4 K stages of top cryocoolers areattached to HTSC current leads andto liquid helium vessel. The external60 K screen is covered by 30 layersof cryogenic superinsulation.


19.04.2011

32

There is vacuum insulationbetween the helium vessel andexternal warm stainless steel vesselto reduce the residual gas heat flux.The helium vessel is suspendedwith four vertical and fourhorizontal kevlar straps connectedto the external cryostat vessel.These straps pass throughout theboth shield screens and attach tobolts on the external housing wallsand are used for precise alignmentof the vertical magnet position.Superconducting magnet is insertedinto the liquid helium tank which islocated inside of the shield screensand fixed on four vertical and fourhorizontal Kevlar suspensionstraps attached to the externalhousing. The helium vessel is a316LN stainless steel barrel withthe wall thickness of 6 mm. Theaxis of barrel is orientedhorizontally.

Bath cryostat systems (LHe tank)



Cryostat heat load budget

First 60K shield screen, Watt

Second 20K shield screen, Watt

LHe vessel 4.2K, Watt

Radiation 8 0.7 0.0001Central throat bellows 5 0.9 0.03Vacuum chamber bellows 8 0.7 0.02Support system 0.5 0.01 0.01Current leads heat conduction 70 0 0.5Current leads Joule heat 60 0 0.2Measuring wires 5 0.1 0.1Liner 0 10 0.2TOTAL 156.5 12.41 1.0601Cooling machine capacity 210 25 3

Main processes of heat load:

−= ∫

∫

2

1

2

1

)(

)(

1 T

Tx

x

dTT

xAdx

Q κ-heat conduction

4TAQ ⋅⋅⋅= σε-radiation

-image current of electron beam

1 W=1.4 liter/hour of Lhe at 4.2K, or ~2.6kJ=1liter of LHe

19.04.2011

33

Cryocoolers capacity (example)


SRDK 415 D – W71D

Refrigeration CapacityFirst StageSecond Stage

35W/45W@ 50 K (50/60Hz)1.5 W @ 4.2 K Max. (50/60Hz)

Weight 18.5 kG

SRDK 408 S2 – W71DRefrigeration CapacityFirst StageSecond Stage

35W/40W@ 50 K (50/60Hz)5.4/6.3 W @ 10K K Max. (50/60Hz)

Weight 18.5 kG

Liquid helium vessel with vacuum chamberfittings

Beam vacuum chamber system

Copper liner

LHe vessel

Insulating vacuum is separated from UH vacuum of a storage ring and keep at vacuum level 10-6 – 10-7Torr by 300l/s ion pump


19.04.2011

34


Protection of liquid helium vessel from electron beam heating (copper liner)Beam heating effect:• synchrotron radiation from upstream bending magnet• image currents • wake fields• electron clouds

Pole gap and electron beam vertical aperture

Direct cooling magnet with liquid helium (magnet in bath cryostat)

Indirect cooling magnetMagnet in insulating vacuum

Pole gap= V aperture + 4 mmPole gap = V aperture + 1.5 mm

As it was already mentioned above, the formula for multipole IDs forms a bond of key wiggler parameters: field,period, and pole gap. That strongly limits freedom of a choice. Low limit of beam vertical aperture of modern storagerings is about 6–7 mm by requirements of beam dynamics in storage rings.

In the bath cryostat design, it is supposed that inside of pole gap, a vacuum chamber and 20 K shield screen shouldbe installed. The vacuum chamber is a part of liquid helium vessel and has temperature of 4.2 K. Shield screen withtemperature 20 K (copper liner) absorbs heat which is raised by electron beam moving inside the copper liner (SR,heating by image currents, etc.).


19.04.2011

35

Cryogenic System of indirect cooling of magnet


LHe vesselSC magnet He fill/vent turret

20 K radiation shield

60 K radiation shield

Beam chamber

Beam chamberthermal link to cryocooler

LHe piping

Example of cryostat with indirect cooling of undulator magnet in APS


Current feeding of SC ID

19.04.2011

36


I1 I2+

-

I 2 =

250

A

+

-

I 1 =

180A

300K60K4K

brass HTSC

4K60K

300K

brass HTSC

Circuit diagram of ALBA-CELLS 117+2 - pole wiggler F- finish of sectionS- start of section

I1+I2

21

I1

3 60

I1+I2

FS

I1+I2

I1+I2

2

I1

F S

1

I1+I2

F

3

I1+I2

60

4 59

117 118

S

I1+I2

F

I1+I2

119

FS

I1

I1+I2

117

I1+I2

S F

118

61 116 F

I1

119

1T 2T 2T 2T2T 2T 1T

1T 2T 2T 2T 2T 2T 1T

F S F S

F SF S

S

S F

S

4 59 61 116

S F

SF

Side polesCentral poles

Side poles

I 2= 250A

I 2= 250A

I 1= 180A

I 1= 180A

I 1+I2= 430A

Electrical connectionsTwo power supply units are used to feed the central and side coils. Such connection gives a possibility tocontrol the field integral to zero with required accuracy.


Normal conducting current leadsThe primary goal of current leads design is minimizing heat in-leak into cryostat at set current in a magnet. This heatin-leak has two components: one is caused by current leads heat conductivity, and another — Joule heat. Therefore it isnatural, that heat conductivity and current leads electroresistance should be minimal. However, according to lawWiedemann–Franz low these two metal properties are linked:

.

This low is well enough correct for majority of metals and alloys. It means that the minimum heat in-leak intocryostat depends not on current leads material but on their form and dimensions.

0)()(2

=+

AI

dxdA

dxd θρθ

θκ

The equation for temperature distribution along not cooled by gas current leads with a current is as follows:

Not cooled by gas current are used as the first step combined тcurrent leads from normally spending metal in a range of temperatures 300К-70К. The second part of current leads consists of a warm superconductor in a range of temperatures 70К-4К.

For optimal current lead calculated for current I0 made of pure copper the heat in-leak due to heat conduction isequal to W/I0=0.7*10-3 W/A if there is no current, but for electro- technical copper the heat in-leak isW/I0=0.4*10-3 W/A.

Than a current lead material (i.e. the it has smaller heat conductivity) is less pure, it is more suitable for currentleads.

19.04.2011

37


Combined normal and high temperature SC conducting current leadsFeeding current is passing through current lead which consists of normal conducting brass current lead and hightemperature superconducting (HTSC) current lead. The current leads are grouped on two special current leads blockstogether with cryocoolers. The top ends brass current leads are connected to power supplies at room temperature in anatmosphere. The brass current leads feedthrough into insulating vacuum volume and their bottom ends have thermalcontact with first stage of cryocoolers for interception of heat in-leak at temperature 55-60K. In the point of heatinterception the brass current leads are connecting HTSC current leads. The junction is supervised by the temperatureprobes as interlocks for HTSC current leads safety if the temperature of this current leads above 70K.

SC ID magnetic measurements systems


19.04.2011

38


Hall probes measurements

Parameters:•2 Hall probes mutually perpendicular•Temperaure probe•Steps defined by step motor•Ti-tube is warming up to room temperature by DC•Ti-tube horizontal by microcontrol stage translation ± 20 mm•Ti-tube vertical manual translation ±5 mm

400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 18005

4

3

2

1

0

1

2

3

4

5Magnetic field, Tesla


MA

gnet

ic fi

eld,

Tes

la

.

400 600 800 1000 1200 1400 1600 18000.015

0.01

0.005

0

0.005

0.01

0.015

0.02Magnetic field, Tesla

Longitudinal coordinate, mmM

Agn

etic

fiel

d, T

esla

.

Field distribution at zero currents(after normal operation)

Longitudinal field distribution

Field integrals measurements with stretched wire methodMain purposes:• To make a table of currents (main and correctors) to provide field ramping up and down without orbit

distortion• To minimize field ramping time• To estimate field multipole integrals at any field level


Parameters:L1=L2~2-3 mI~0.5-2 AWire- brass 0.3 mm diam.WPM accuracy – 3-5 mkmTension force - ~ 10 N1-st Field integral accuracy - ~4*10-5 T*m2-nd field integral accuracy- ~ 10-4 T*m2

A method of strained wire with a current was used for field measurements and coil currents matching. Themethod is based on a very similar behavior of the wire with dc current in magnetic field and electrons movingalong this magnetic field.

The wire strained by a force P was passed through the vacuum chamber of the wiggler. At the ends of thewiggler, the two Wire Position Probes (WPP) were installed to measure displacements of the wire during theexperiment. The space resolution of WPPs is about 0.005 mm.

19.04.2011

39

Motivation of the method

ρBsB

dsxd )(2

2

=

)(22

4

4

sBIds

xdTds

xdJE ⋅=⋅+⋅⋅

)(22

sBTI

dsxd

⋅=

∫−

′′=s

Lz sdsBsI

2/1 )()(


∫ ∫−

′

−

′′′′′=s

L

s

Lz sdsBsdsI

2/ 2/2 )()(

ρBsI

dssdx )()( 1=

ITB =ρ

ρBsIsx )()( 2=

- beam orbit in magnetic field B(s), ρB - beam rigidity

- bending of stretched wire with current in magnetic field B(s)

IT

- Rigidity of stretched wire with currentFirst term of equation for wire may be neglected for thin wire

The equations for beam and for wire are identical for Beam orbit and wire bends are described by formulas (L-magnet field length) if initial angle and coordinate are equal to 0 at ±L/2:

angle deviation of beam orbit or wire at s-position

X-coordinate of beam orbit or wire at s-position

ρδα

B

LI

= 21

ρδ

B

LIx

= 22

Angle and coordinate at L/2

+==

=

22

11*

21 Lx

Lx

IT

ITLII first

δδδα

)12(22sec

xxIT

ITxLII ond δδδ −=⋅=

=

22

11

Lx

Lx δδδα += Total angle deviation

12 xxx δδδ −= Orbit distortion at condition 0=δα


X

Z

F

z

x

ADC I=0..2A

VME

1.125МГЦ

F

Filter

коммутатор

Wire Position MonitorsStretched wire

DC for beam simulation

AC for WPM

Data readout system

Scheme of measurements and data readout

Wire tension force

19.04.2011

40

Results of measurements

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2B, Tesla

0

40

80

120

160

200

240

280

320

360

400

440

480

I, A

Ramp upIsideIcentral

Field ramping with zero field integrals using two power supplies

0 100 200 300 400 500 600 700 800Time, s

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

B, Tesla

-0.0005

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

1st i

nteg

ral,

Tesl

a*m

0 50 100 150 200 250 300 350 400Time, s

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

B, Tesla

-0.0005

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

1st i

nteg

ral, T

esla

*m

1st Integral1st integral, Tesla*mB, Tesla


The currents Iside and Icentral for zero first field integral versus magnetic field

First field integral behavior during ramping field up and down.


Thanks for your attention

19.04.2011

41

Bibliography1. Fred M. Asner “High Field superconducting magnets”, Clarendon Press, Oxford, 19992. Steffen, K. G. (1965). High Energy Beam Optics . Wiley.3. K.H.Mess,P.Schmϋsser,S.Wolff “Superconducting accelerator magnets”, World Scientific Publishing

Co.,19964. Handbook of cryogenic engineering, Edited by Weisend J.G., 1998, Taylor & Francis5. S. Prestemon,D. Dietderich, S. Marks, R. Schlueter, “NbTiand Nb3Sn Superconducting

UndulatorDesigns”, Workshop on Superconducting Undulatorsand Wigglers, ESRF, July 2003.6. E. Baynham, T. Bradshaw, Steve Carr, Y. Ivanyushenkov, J. Rochford “Superconducting undulator

prototype. Status of work and the plans” , Polarised PositronUndulatorMeeting, Daresbury, 21 April 2004

7. Materials of Workshop on Superconducting Undulators & Wigglers ESRF, Grenoble, France July 1, 2003

8. Materials of The 16thPan-American Synchrotron Radiation Instrumentation Conference September 21-24, 2010 @ Argonne National Laboratory, USA

9. Materials of IDMAX2010 Insertion Devices for Rings and Linacs Workshop, Lund, November 9-10, 2010


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