Insertion Devices Lecture 4 Magnet Designs

Jim Clarke ASTeC Daresbury Laboratory Hybrid Insertion Devices – Inclusion of Iron

Simple hybrid example

Top Array

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Bottom Array

2 Lines of Magnetic Flux Including a non-linear material like iron means that simple analytical formulae can no longer be derived – linear superposition no longer works! Accurate predictions for particular designs can only be made using special magnetostatic software in either 2D (fast) or 3D (slow)

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3 Field Levels for Hybrid and PPM Insertion Devices

Assuming Br = 1.1T and gap of 20 mm

When g/u is small the impact of the iron is very significant

4 Introduction

We now have an understanding for how we can use Permanent Magnets to create the sinusoidal fields required by Insertion Devices Next we will look at creating more complex field shapes, such as those required for variable polarisation Later we will look at other technical issues such as the challenge of in-vacuum , dealing with the large magnetic forces involved, correcting field errors, and also how and why we might cool undulators to ~150K Finally, electromagnetic alternatives will be considered

5 Helical (or Elliptical) Undulators for Variable Polarisation

We need to include a finite horizontal field of the same period so the takes an elliptical path when it is viewed head on We want two orthogonal fields of equal period but of different amplitude and phase

3 independent variables

Three independent variables are required for the arbitrary selection of any polarisation state 6 Helical Undulators Pure helical fields are suited to a circular magnet geometry (magnets surrounding the vacuum chamber) but these are not generally practical for a light source A planar geometry is better suited to light sources (all of the magnets in the plane above and below the axis)  This allows the machine to have a narrow vertical gap and a wide horizontal gap – as required for injection or magnet measurements  But, it is not so easy to generate H and V fields  It is not so easy to understand the fields either!  Two degrees of freedom are needed to control the H & V fields independently, ideally three so you can control the phase as well  Hence two (or three) independent motion systems are needed

7 The APPLE-2 Design This undulator consists of four standard PPM arrays Diagonally opposite arrays move longitudinally together All the arrays also move vertically like a conventional undulator The electron beam travels along the central axis of the magnet

Gap is These two altered arrays move also to together tune magnet as usual

Phase shift, D 8 APPLE-2 Fields Denote the bottom left and top right arrays as undulator a Denote the bottom right and top left arrays as undulator b The phase difference between a and b is  The fields on axis from a are b a End View a b And for b are

The horizontal field from b is negative so cancels out when 0 9 APPLE-2 Fields

The total field on axis is just the sum of these contributions (superposition principle)

These simplify to

10 APPLE-2 Phase

From the field equations we can see that the two fields are always /2 out of phase This implies that the polarisation ellipse is always upright The observer will see the electron describe an ellipse with principle axis always on the vertical axis As the phase between the arrays changes from zero (standard PPM – pure vertical field, horizontal linear polarisation) the ellipse will become circular (circular polarisation), finally at   the electron will just oscillate vertically (pure horizontal field, vertical linear polarisation) Moving the phase in the opposite direction will again generate circular polarisation – but of opposite helicity. At it will generate pure vertical polarisation as at  11 Example Trajectories Trajectories viewed head on – as the observer sees them 3 GeV electron beam Undulator period is 50 mm Magnet gap is 20 mm

Fields in circular mode

12 APPLE-2 Examples The typical block shape is square but with cut outs The cut outs are used to mechanically clamp the blocks in place but they are kept well away from the electron beam axis and so they have a very small impact on the fields

SRS HU56 Bottom Arrays

End View (Johannes Bahrdt, HZB)

13 APPLE-2 Examples

SRS HU56 being measured Diamond HU64 14 Engineering Issues for all PM Undulators & Wigglers

Engineering demands are very high: • Very strong forces present during assembly and when complete • Must have high periodicity • Arrays must be parallel to m precision and must stay parallel at all gaps

General design themes: • Blocks are held in individual holders – glued or clamped • Fastened to a backing beam • C shaped support frame • Very long magnets (>5m) are usually split into shorter modules (2 –3m) 15 In-Vacuum Undulators The minimum magnet gap limits the performance of an undulator The magnet gap is determined by the needs of the electron beam In practice this is set by the vacuum chamber For example:  If an electron beam needs 10mm of vertical space  And the vacuum chamber walls are 2mm thick  With an allowance for mechanical tolerances of 1mm  The minimum magnet gap will be 15mm  So 5 mm is effectively wasted One option is to put the undulator inside the vacuum chamber, in this example the magnet gap reduces by ~30% 16 In-Vacuum Undulators Magnet blocks are not very good for use within a vacuum system In-vacuum and out of vacuum concepts They must be coated to prevent outgassing (TiN or Ni) They also should be baked for UHV – this affects the magnet performance and can cause irreversible losses Generally only bake at ~130 C The surface resistance of the blocks is high – need a sheet of copper on top of each array to provide low resistance path for the electron’s image current Magnet measurements are very difficult after full assembly

17 In-Vacuum Examples

Diamond U23 In-vacuum undulator – Before vacuum chamber is fitted 18 In-Vacuum Examples

ALS in-vacuum undulator

19 In-Vacuum Examples

Flexible transition with integrated water cooling between fixed vacuum chamber and variable gap undulator arrays

20 Forces due to the Magnetic Field

A permanent magnet cannot be switched off! Therefore magnetic forces are always present These forces increase rapidly as the gap between the two arrays decreases Mechanical designs must take full account of the forces between individual blocks and also between arrays When two magnets with the same poles are brought together there is a strong repulsion The energy we exert in bringing them together is stored by the magnetic field If opposite poles face each other there will be an attractive force and energy will be removed from the field and do work on the system 21 Example Undulator Forces

Assume a 50 mm period and 20mm gap with a permanent magnet remanent field of 1.1T A typical magnet field width in x is ~60mm

The force between the two arrays is ~3500N per meter of length

Note that this force changes rapidly with gap as the field changes exponentially 22 Cryogenic Undulators These are a relatively new idea that take advantage of the variation of remanent field with temperature If the undulator can operate at ~150K then there will be a significant field increase with NdFeB – a slightly awkward temperature to maintain

The intrinsic coercivity Basically an in- increases also which helps vacuum device with radiation resistance and with cryogenic allows selection of stronger cooling attached grades

H Kitamura, Spring-8 23 Cryogenic Undulators

Other materials are more attractive, especially PrFeB, as it can operate at 77K – an easy temperature to maintain One issue is also wanting to bake the magnets to ~450K to improve the vacuum performance – limits the grades available Unbaked devices have been used successfully on ESRF and DLS

Kitegi et al, IPAC 2012 24 Electromagnetic Devices

Given that virtually all magnets in particle accelerators are electromagnets (dipoles, quadrupoles, sextupoles, …) it seems surprising that relatively few electromagnetic undulators and wigglers are built One niche area where electromagnets are used is when there is a requirement for the fields to be changed quickly This is generally motivated by the need to rapidly change polarisation states – it is much easier to switch the direction of a current quickly than to physically move magnet arrays Superconductors, of course, have always been used in very high field applications

25 Electromagnetic Devices Let’s consider a basic conceptual layout of an electromagnetic

All the coils are connected in series One individual coil is highlighted in red

The magnetic field is varied by changing the current in the coils There is no need to move the arrays Electromagnetic insertion devices generally have a much lower capital cost but a much higher operating cost 26 Simple Electromagnetic Analysis Consider the design concept as a series of dipoles of alternating polarity The (approximate) field produced by a dipole with gap, g, driven by NI Ampere-turns is

So the undulator K parameter will be

Note that to reach K ~ 1 we will require NI ~1000 A-t

If the gap is fixed and we want to reduce u then NI will have to increase to maintain K But, as the period reduces the space for the coil shrinks as well so the current density increases very rapidly At some period the resistive losses will be so high that cooling will not be practical 27 Electromagnet Examples An elliptical is installed on Elettra The period is 212 mm and the peak fields are 0.5 T vertically and 0.1 T horizontally The horizontal field can switch at up to 100Hz The rapid change in polarisation between left and right circular can be utilised by the experiment to increase the signal to noise level

28 Summary So Far

The field limit for a PPM is ~1.5T but if we include iron (hybrid magnet) then >2 T is easily achievable The APPLE-2 is the most popular undulator design for generating variable polarisation states The forces in permanent magnet insertion devices can be very high and increase rapidly as the gap closes In-vacuum solutions allow for smaller magnet gaps at the expense of more complex engineering Cryogenic undulators at ~150K to 77K will generate higher field levels and these are starting to be introduced now Normal conducting electromagnets cannot compete with permanent magnets, especially at short periods but they do allow fast switching of fields

29 Superconducting Magnets

For fields greater than ~3T superconductors are the only real option For intermediate fields (~1 to ~3 T) they can have much shorter periods than Permanent Magnets or Normal Conducting Electromagnets The materials used are only superconducting below ~10K Hence the magnets always sit inside a cryostat In the past they would generally have a closed loop liquid Helium refrigerator permanently connected to them The development of closed cycle cryocoolers has enabled a more ‘stand alone’ approach to be used in some applications – liquid helium is not necessarily required and not always used

30 Superconducting Wavelength Shifter Examples

The highest field has been achieved by the SPring-8 10T wavelength shifter (from BINP)

It uses NbTi and Nb3Sn The stored energy is 400kJ The magnet gap is 42 mm

31 Superconducting Multipole Wigglers

Superconducting MPWs are popular in the intermediate energy light sources (~3GeV) because the high field enhances the flux in the hard X-ray region A key advantage over permanent magnet hybrid wigglers is not just the higher field but also the reduction in period This lowers the K value and so the radiation is emitted over a narrower horizontal width (±K/) – making it easier to manage the cooling arrangement within the facility Note that the majority of the radiation generated by a MPW will not be used by the and so must be absorbed by cooled surfaces

32 Superconducting Multipole Wiggler Examples

Diamond 3.5 T 60 mm period, 45 poles

4.2 T 48 mm period, 45 poles

33 Superconducting Undulators The motivation of using superconductivity is to generate higher fields on axis than are presently available from the best permanent magnet systems They have to have a significantly better performance to make them worthwhile The key region of interest is in short period systems, typically ~15mm The field quality has to be similar to existing undulators

An example specification Magnetic Length: 2 m Period : 15 mm Field on Axis: 1.4 T (K =2.0) Electron Beam Aperture: 5 mm (Vert.) x 40-50 mm (Horiz.)

34 Superconducting Undulators

Comparison of flux output for a 3GeV, 300mA beam Assuming:

K Period (mm) In-Vac 1.7 21

CryoPM 1.8 18

SC 2.0* 15

* Harmonics 1 and 3 will just overlap

35 The Advantage of SC Undulators

ASTeC SCU: period = 15 mm N = 133 (2m long) Magnet pole gap = 7.4 mm

Bo = 1.28 T K = 1.8

SCU/U21 Flux Brightness 25 keV 6.2 7.6 40 keV 15.4 21.5

R Walker, Diamond Undulator Design

The standard solution is very simple – currents flowing perpendicular to the beam axis The challenge is nearly all engineering

Iron yoke

Return paths for currents 37 Superconducting Undulators

A similar scheme has been adopted by several groups

S H Kim, APS 38 Challenges

To achieve the field levels requires the magnets to have a cold beam aperture – no room for an insulating vacuum – any heat transfer from the beam to the wires could trigger a quench The iron poles need to be accurately machined to minimise field errors The on axis field is also dependent upon the accurate positioning of the wires Correction of the field errors is quite tricky – several options have been proposed but they all add an extra level of complication – not as simple as permanent magnets Ideally the magnet should not need error correction but is this practical? What about transition between iron non-saturation and saturation? 39 Wire Position

Wires closest to the electron axis must be positioned very accurately but iron yoke accuracy is even more important

40 Example Superconducting Undulator Installed in ANKA in 2005 The first cold bore undulator ever installed in a storage ring Period is 14mm, 100 periods Magnet gap variable in steps 8 to 16 mm (29 mm for injection) The barrel shape in the field along the axis is due to bending of the two arrays – the gap is 0.25mm larger at the entrance and exit of the magnet S Casalbuoni et al, SRI 06 41 Example Superconducting Undulator Helical Undulator for the ILC Bifilar helix design (DNA-like) 11.5mm period, 2 x 1.75m long 6.35 mm winding bore

42 Example Superconducting Undulator

The quench test results show surprising differences between the two identical magnets Both do actually reach the same final quench current which agreed well with expectations

350

300 ) 250

200

150

100 magnet 1 Quench current (A magnet 2 50 nominal current 0 010203040 43 Quench number Sources of Beam Heating

The electron beam is able to heat the cold bore of the magnet through a variety of methods! radiation from the upstream magnets or even from the undulator itself Wakefield effects – resistive wall, geometric, and surface roughness Secondary electron (or ion) bombardment

The amount of power that the magnet can cope with depends on the specific heat of the materials and this changes significantly with temperature – typically a few W at 4K, 10s of W at 50K, 100s of W at 300K

44 Thermal Screening

Since at 4K the magnet bore can only tolerate a few W intermediate beam screens at ~20K have been used to intercept any beam induced heating These screens are held away from the 4K surface to prevent conduction of heat They have been used in superconducting multipole wigglers, which can tolerate larger magnet gaps, but are not so easy in undulators!

Magnet gap

Vessel at 4.2K Beam Screen at ~20K 45 SC Magnet Summary Wavelength shifters (~5 to 10T) are used to generate the highest energy photons There are several recent MPW examples (3.5 to 7T), used to enhance the flux at high photon energies Superconducting undulators have to be pushed close to their limits to gain a significant advantage over permanent magnet alternatives – on paper SC technology always wins but not true in practice yet! Cold bore increases the risk of quenching due to beam heating – accurate prediction of heating due to wakefields etc is crucial

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