The Generation and Properties of Synchrotron Radiation Part 2

1
The Generation and Properties of Synchrotron
RadiationPart 2

• Jim Clarke
• ASTeC
• Daresbury Laboratory

2
Course Syllabus

• Introduction
• Fundamentals of SR Emission
• SR from a dipole
• Introduction to Insertion Devices
• SR from Wigglers
• SR from Undulators
• Generation of Polarised light
• Permanent Magnet Insertion Devices
• Electromagnet Insertion Devices
• Measurement Correction
• Impact of IDs on electron beam
• Special IDs for Free Electron Lasers
• Novel, exotic state of the art IDs

3
Course Book

• The Science and Technology of Undulators and
  Wigglers,
• J. A. Clarke, Oxford University Press

4
Introduction to Part 2

• So far we have discussed at length what the
  properties of SR are and when it is generated
• Especially from bending magnets, wigglers and
  undulators
• But, how do we know what fields are achievable?
• For bending magnets I refer you to earlier
  courses on magnets (Neil Marks)
• In this part we will look at how periodic fields
  are generated and what the limitations are
• Can we have a period of 1 mm and field strength
  of 20 T? Later we will look at the present state
  of the art and some future possibilities

5
What are the possibilities

• To generate the magnetic field we can use
• Current carrying coils (Electromagnets)
• Normal conducting or superconducting
• Permanent Magnets
• Both can be with or without iron

6
Permanent Magnet (PM) Basics

• Brief introduction only
• Magnetic properties of materials is a big topic
• Further reading
• P Campbell, Permanent magnet materials and their
  applications, CUP 1994
• H R Kirchmayr, Permanent magnets and hard
  magnetic materials, J Phys DAppl Phys 292763,
  1996

7
What is a PM?

• Definition
• A magnet is said to be Permanent (or Hard) if it
  will independently support a useful flux in the
  air gap of a device
• A material is magnetically Soft if it can only
  support such a flux with the help of an external
  circuit
• A PM can be considered as a passive device
  analogous to a spring (which stores mechanical
  energy)
• An electron in a microscopic orbit has a magnetic
  dipole moment can be modelled as a current
  flowing in a loop
• In a PM these molecular currents can be
  identified with atoms with unfilled inner shells
• eg 3d metals (Fe, Co, Ni) or 4f rare earths (Ce
  to Yb)

8
Permanent Magnets

• PM materials are manufactured so that their
  magnetic properties are enhanced along a
  preferred axis
• To do this, advantage is taken of crystal
  lattices
• Alignment of the moments in the lattice is called
  magnetocrystalline anisotropy
• The direction of alignment is called the easy
  axis
• When a magnetic field, B, is applied to a
  magnetic material each dipole moment tries to
  align itself with the field direction
• When B is strong enough (at saturation) all of
  the moments are aligned, overcoming other atomic
  forces which resist this
• A PM must be able to maintain this alignment
  after B is removed

9
Permanent Magnets

• Magnetisation, M, is the magnetic dipole moment
  per unit volume
• In the absence of external fields it is related
  to the internal field by
• Amperes law states that B is related to a current
  density J in a conductor by
• If magnetisation is considered to be due to a
  circulating current of density then

10
Permanent Magnets

• If there is an external conductor carrying J and
  a magnet of equivalent current JM then
• So
• A new parameter, H, called the magnetizing force
  is now defined as
• So
• This then gives a more general form of Amperes
  law which allows for real currents and material
  magnetization

11
An ideal PM

• The characteristics of a PM are determined by its
  behaviour under an external magnetization force H

H reducing, moments stay aligned
H large, material saturated, all moments aligned
Intrinsic coercivity
H large and negative, material flips now
aligned with opposite direction
12
Ideal BH Curve

• From can derive BH curve

Gradient m0
Remanent Field
Coercivity
In 2nd quadrant the ideal PM is linear
13
The BH Product

• PMs are operated in the 2nd quadrant no
  external fields present, moments aligned along
  easy axis
• BH represents the energy density of the material
• The peak value for the 2nd quadrant is a way of
  comparing different materials

14
The working point

• The position on the B-H curve at which the PM is
  operated is called the working point
• If the working point is at BHmax then the maximum
  potential energy available is being utilised
• Good practice to design PM systems that work near
  this point
• If PMs are operating well away from this point
  then they are unlikely to be doing anything
  particularly useful
• The line through the origin to the working point
  is called the load line

15
Current Sheet Equivalent Materials

• An ideal PM is uniformly magnetized (homogeneous)
• Equivalent current model is a current sheet on
  the surface with no internal currents
• Relative permeability is 1 so can consider bulk
  material to be vacuum
• This CSEM assumption implies that the
  contributions from different magnets can be added
  linearly
• Analytical calculations fairly simple because of
  this linear superposition

Ideal PM lines of flux
CSEM
16
Real PM Materials

• Not all materials have a linear BH curve in the
  2nd quadrant
• This can be a problem if the working point drops
  into the non-linear region
• eg during assembly or when closing an undulator
  gap

If working point moves from a to b then when B
increases again the magnet will operate at c
instead this is an irreversible effect
17
Temperature Effects

• At higher temperatures the materials become more
  non-linear
• So long as working point stays in linear region
  this is reversible
• Note that remanent field drops with temperature
  reverse is also true, cold magnets have a higher
  remanent field

Day to day temperature variations are important
and must be controlled (minimised)
18
Available Materials

• Two types are generally used Samarium Cobalt
  (SmCo) and Neodymium Iron Boron (NdFeB)

19
How are they made? (courtesy of Vacuumschmelze)

• Melting of alloy under vacuum with inductive
  heating
• Crushing of polycrystalline cast ingots
• Milling of coarse powder
• Alignment in a magnetic field

20
How are they made? (courtesy of Vacuumschmelze)

• Pressing of magnets
• Die pressed parts are sintered in ovens (heating
  a powder below its melting point until its
  particles adhere to each other)
• Result is ceramic like object
• Now final machining can take place possibly
  coating
• Final stage is magnetization usually in strong
  pulsed field

21
Vacodym 633 HR (Vacuumschmelze)

• M-H and B-H curves (2nd quadrant)
• Linear at 20 ?C but non-linear above about 60 ?C
• Irreversible losses for different loadline
  working points as a function of temperature

22
The Future?

• No dramatic improvements in energy density are
  expected/predicted in the future (but who knows
  )
• However, Superconducting permanent magnets do
  exist (persistent currents)
• These perhaps offer the greatest hope for major
  advances
• PMs based on High Tc superconductors do exist
• Remanent fields of 8T and energy density 12 800
  kJ/m3 have been measured
• But, only operate and survive at 77K
• Steps are already being taken for including HTS
  in an undulator development project in Japan

23
Pure Permanent Magnet Undulators

• A magnet which contains no iron or current
  carrying coils is said to be a pure permanent
  magnet (PPM)
• Because of CSEM we can use the principle of
  superposition
• To generate a sinusoidal field an ideal PPM would
  have two arrays of PM with the easy axis rotating
  through 360? per period along the direction of
  the electron beam
• In practice this ideal situation is approximated
  by splitting the system into rectangular magnet
  blocks, M per period

24
Example PPM arrangement, M 4
e-
25
Lines of flux
Electron beam
26
Magnetic Field

• The field strength between the two arrays
  assuming infinite width in the x direction (2D
  approximation) is
• Where and is a packing factor to allow for
  small air gaps between blocks
• The vertical field on axis (y 0) is a number of
  cosine harmonics
• As this reduces to a single cosine
• Longitudinal (and horizontal) field on axis is
  zero

27
A Practical PPM

• The most popular choice is M 4
• Good compromise between on axis field strength
  and quality vs engineering complexity
• Higher harmonics then account for lt 1 of the
  field on axis
• Away from the axis it is definitely not
  cosine-like

Example PPM with 50 mm period, block height of 25
mm, magnet gap of 20 mm and remanent field of 1.1
T Note fields are larger away from the axis
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Peak vertical field vs M
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Ignore other harmonics

• Assume only the first harmonic makes a
  significant contribution
• Equation simplifies greatly on axis to
• Important
• So long as all the block dimensions scale
  together the fields on axis do not change
• This is not true for electromagnets there the
  current densities have to increase to maintain
  the same field levels

30
Effect of different block heights

• Typical selection is half period length loss of
  5
• Quarter period length makes all blocks identical
  but then greater loss

31
Peak Field

• Maximum peak field (ideal) is 2Br
• In practice with M 4 and h lu/2 peak on axis
  field is
• So even with an ambitious gap to period ratio of
  0.1 the peak value is only 1.26Br
• Achieving fields gt 1.5T requires very high Br
  material, small gaps and long periods!
• Higher fields are possible if we include iron in
  the system
• Mixing PM and iron poles is called a hybrid magnet

32
Hybrid Insertion Devices

• Simple example

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Hybrid fields

• Including a non-linear material like iron means
  that simple analytical formulae can no longer be
  derived
• Accurate predictions can only be made using
  special software in either 2D (fast) or 3D (slow)

Electron beam
34
Empirical formulae

• A series of 2D studies were performed in the
  1980s to generate an empirical formula for the
  peak on axis field
• For Br 0.9T
• For Br 1.1T
• Valid over
• Recently these have been updated for Br 1.3T
• Valid over

35
Hybrid vs PPM

• Assumes Br 1.1T and gap of 20 mm

36
End Design

• Want undulators and wigglers to have zero net
  effect on the electron trajectory
• Otherwise, operating one undulator would affect
  all the other users
• Remember
• So, electron exit angle is found from the first
  field integral of the full length of the device
• Such that the exit angle, a is

37
End Design

• The electron position after the undulator is
  found from the second field integral
• Such that
• The requirement is that the first and second
  field integrals should both equal zero at all
  operating points.
• This is achieved (in theory!) by the selection of
  suitable end terminations (entrance and exit) of
  the magnets

38
End Design

• An alternative expression for the final beam
  position is to project it back to the centre of
  the device
• Then

39
Symmetric or antisymmetric

• The position d will be zero when the field is
  symmetric about s 0 (centre of undulator is the
  peak of a pole)
• The ends then need to be set so that the angle is
  also zero
• In the antisymmetric case, the centre of the
  magnet is a zero crossing
• Then the angle will be zero
• The ends then need to be chosen so that the
  position is zero also
• For PPMs the end design is fairly simple because
  of the superposition principle
• For hybrids the non-linear effects mean that the
  integrals are harder to control so active
  compensation is generally used
• In reality the integrals are never zero, due to
  magnet inhomogeneities or engineering tolerances
• A typical target would be to keep the integral to
  below 10-5 Tm (1mrad for a 3 GeV beam)

40
PPM End Design

• Is this design symmetric or antisymmetric?
• There are half length blocks at the ends.
• Why does this give zero first field integral?
• Think about superposition principle

41
Half block end design

• 10 period model
• 3GeV trajectory
• a and d are zero

Small position offset but light emitted parallel
to axis
42
Antisymmetric solution

• First integral zero automatically
• Second integral set to zero by choosing
  appropriate length of end block depends on
  number of poles

43
Antisymmetric solution
Final position and angle of electron both zero
but light will be emitted at an angle
44
Other solutions

• A field strength series of 1/4, -3/4, 1, -1,
  works for both symmetric and antisymmetric cases

45
1/4, -3/4, 1 solution
Electron now oscillates about axis
46
Hybrid end designs

• Hard to passively compensate over a wide range of
  magnet gaps
• Need some active compensation
• Additional coils or movable PM blocks

47
Asymmetric wiggler

• Want field shape something like this
• Simple PPM solution

48
Hybrid Asymmetric Wiggler

• Include iron to enhance fields
• ESRF Example
• 3T and -1.5T at 11mm gap

49
Elliptical Wiggler

• Need horizontal field as well
• Two orthogonal PPMs
• Need to translate horizontal field array so can
  change circular polarisation from R to L
• Horizontal gap much larger so field much lower
  (Japanese example had 1T vertical and 0.2T
  horizontal)

50
Helical Undulators

• Pure helical fields can be made with a circular
  geometry but not generally suitable for a light
  source ok for free electron lasers or other
  linac based machines (eg ILC)
• Rectangular geometry (like the elliptical
  wiggler) can have variable field levels and phase
• Planar geometry better suited to light sources
  (all magnets in plane above or below the axis)
• most common solution
• not so easy to generate H and V fields
• Not so easy to understand fields either!
• Two degrees of freedom needed to control H V
  independently, 3 if want to vary phase as well
• Two (or 3) independent motions needed

51
Helios design

• First planar helical undulator
• Top array generates horizontal, bottom generates
  vertical field (on axis)
• Each array can be adjusted vertically,
  independently, to control field level
• Longitudinal movement of one array gives phase
  control

52
Helical Planar Undulators

• The next designs moved away from two independent
  arrays to a more complex 4 array scheme
• Two above and two below
• Longitudinal and vertical movement of arrays used
  to control field levels
• Most popular design is called APPLE-2
• Many examples are in existence
• Gives high field levels in circular mode
• Complexity not too bad

53
APPLE-2

• Four standard PPM arrays
• Diagonally opposite arrays move longitudinally
• All arrays move vertically like conventional
  undulator
• Electron beam travels through centreline of magnet

54
APPLE-2 Fields

• Bottom left and top right are undulator a
• Bottom right and top left are undulator b
• Phase difference between a and b is f
• Fields on axis from a are
• And for b are
• Horizontal field negative so cancel out when f 0

55
APPLE-2 Fields

• Total field on axis just sum of these
  (superposition)
• These simplify to

56
APPLE-2 Phase

• The two fields are always p/2 out of phase
• Implies polarisation ellipse is always upright
• Observer will see electron on ellipse with
  principle axis always on vertical axis
• As phase changes from zero (standard PPM linear
  H polar) the ellipse will become circular
  (circular polarisation), finally at f p the
  electron will just oscillate vertically (vertical
  polarisation)

57
Example head on trajectories

• 3GeV electron
• Period is 50 mm
• Magnet gap is 20 mm

Fields in circular mode
58
APPLE-2 in opposing mode

• Move longitudinal arrays by equal amounts but in
  opposite directions
• Now fields are in phase at all times
• What polarisation will we see?

59
APPLE-2 in opposing mode

• Linear polarisation is observed
• When array phase changed the angle of the
  polarisation rotates

60
APPLE-2 Fields

• The fields in circular mode are shown (not at the
  same s position)
• Horizontal field changes rapidly
• Small misalignments of electron beam will affect
  output performance
• Impact of helical undulators on the electron beam
  more significant than standard ones

61
APPLE-2 examples

• Typical block shape
• Cut outs are to hold the blocks but are well away
  from the electron beam

SRS HU56 Lower array with magnet blocks
Johannes Barhdt, BESSY
62
APPLE-2 examples
Upper and lower beams
SRS HU56 being measured
63
Other APPLE-2 examples
ALS
Diamond HU64
64
Other helical undulator designs

• APPLE-3 for circular vacuum chambers (FELs)
• Enhances field by 40 in circular mode
• Additional arrays also possible
• Field enhanced by 20
• Six array designs also built

Johannes Barhdt, BESSY
65
Engineering Issues for all PM undulators
wigglers

• Engineering demands very high
• Very strong forces during assembly and when
  complete
• Must have high periodicity
• Arrays must be parallel to mm precision and must
  stay parallel at all gaps
• General design themes
• Blocks held in individual holders glued or
  clamped
• Fastened to backing beam
• C shaped support frame
• Very long magnets (gt5m) split into shorter
  modules (2 3m)

66
In vacuum undulators

• Minimum Magnet gap sets performance of device
• Magnet gap set by needs of electron beam
• In practice set by vacuum chamber
• Example
• electron beam needs 10mm vertical space
• vacuum chamber walls 2mm thick
• allowance for alignment tolerances etc 1mm
• Minimum magnet gap 15mm
• One solution is to put magnets inside the vacuum
  system
• Vacuum pressure must be maintained otherwise
  electrons will be lost affects all users

67
In vacuum undulators

• Magnet blocks not ideal for use within vacuum
  system
• Must be coated to prevent outgassing (TiN or Ni)
• Must be baked to reach good vacuum - affects
  magnet performance (irreversible losses?)
• Only bake at 130 ?C
• Surface resistance of blocks high need sheet of
  copper to provide path for image currents
• Magnet measurements only possible before full
  assembly
• Flexible vacuum chambers are an alternative
  solution

68
In vacuum examples
Diamond U23 Standard planar undulator
69
In vacuum examples
Diamond U23 Standard planar undulator
70
In vacuum examples
71
In vacuum examples
72
Magnet Forces
A PM can not be switched off Forces are always
present They increase rapidly as the magnet gap
decreases Designs must take full account of the
forces between blocks and between arrays When
two magnets with the same poles are brought
together there is a strong repulsion where does
the energy we exert in bringing them together
go? It 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
73
Forces

• To calculate the force we need to know how the
  energy stored by the field changes with unit
  distance
• The energy stored in an inductor, U LI2/2
• Can show that for a solenoid the magnetic energy
  per unit volume is
• This is a general result for the magnetic energy
  density in vacuum and non-magnetic materials

74
Forces

• Since force is work done per unit distance, F
  dE/dy
• The force between two magnets is
• In a region of uniform magnetic field over an
  area of the x-s plane equal to A the force would
  be
• This is a fair approximation to a dipole magnet
  with pole area A

75
Forces

• For an undulator with sinusoidal magnetic field
  then,
• So the force between the two arrays is
• If we assume the peak field is constant in x over
  a width W, and then falls to zero (top hat), the
  force becomes

76
Example forces

• 50 mm period
• 20mm gap
• 1.1T remanent field
• Width of field 60mm
• Force between arrays 3500N/m
• Changes rapidly with gap as field changes
  exponentially

77
Electromagnetic Devices

• Given that virtually all magnets in particle
  accelerators are electromagnets it is surprising
  that relatively few EM undulators and wigglers
  have been built
• We will now look at why that might be
• There has been an increased interest over recent
  years
• This is generally because of need to rapidly
  change polarisation states it is much quicker
  to switch the direction of a current than to
  physically move PMs
• Superconductors have always been used at some
  level for high field applications
• First look at planar EM undulators

78
Electromagnetic Devices

• Basic concept layout
• Field varied by changing current
• No need to move arrays
• Lower capital cost but higher running cost

79
Simple Analysis

• Consider the device as a series of dipoles of
  alternating polarity
• Approximate field produced by a dipole with gap,
  g, driven by NI Ampere turns is
• So the K parameter will be
• For a K 1 will require NI 1000s
• If the gap is fixed and we want to reduce lu then
  NI will have to increase to maintain K
• But, as period reduces space for coil shrinks as
  well so current density increases rapidly
• At some point resistive losses will be so high
  that cooling will not be practical

80
More realistic model

• By examining the fields in a 2D simulation of an
  undulator a better model has been derived

Number of Ampere turns for a given K as a
function of period to gap ratio for the two
models. Simple dipole model holds until period to
gap lt 3, this is when poles no longer act
independently
81
K vs Period

• Assume coil cross section
• And max current density is 10 A/mm2
• Then can plot results for a 20mm gap

K 1 at 55mm period K 10 at 110mm period but
does not include iron saturation effects
82
K vs Period

• Short period EM devices are easily outperformed
  by PM devices

83
Helical Electromagnets

• There are two main families
• the bifilar helix which generates a pure helical
  field
• elliptical wigglers which generate an elliptical
  field
• The bifilar helix was used in the first ever Free
  Electron Laser experiment and is proposed to be
  used in the positron source for the ILC
• Elliptical wigglers have a weak horizontal field
  provided by coils. If the current in the coils is
  switched rapidly (up to 100Hz) then the circular
  polarisation states observed also flips at the
  same rate very useful for increasing the signal
  to noise in some experiments

84
Bifilar Helix

• Two interlocking helical windings separated by
  half a period with current flowing in opposite
  directions
• Same as two loosely wound solenoids of opposite
  field polarity
• Longitudinal fields cancel and are left with a
  helical rotating transverse field
• Electrons travel down central axis of winding

85
Bifilar Helix Example (Superconducting)

• Undulator for ILC positron source
• Period 12mm
• Winding diameter 6.35mm
• K 0.6
• Include iron as well and K 1.1

86
Elliptical Wigglers

• Need strong vertical field and weak horizontal
  field
• Idea is to ensure observer sees the same
  polarisation state from each pole
• If switch polarity of horizontal field then
  observer sees opposite helicity no need to
  change vertical field
• Fast switching of helicity possible if horizontal
  field is electromagnetic
• Vertical field could be from PM or EM

87
Elliptical wiggler example

• NSLS wiggler
• PMs provide 0.8T field
• 160mm period
• Horizontal field 0.22T
• Horizontal poles laminated
• Can switch at 100Hz
• Access for magnet measurements very restricted
• Also no access to vacuum chamber

88
Alternative Elliptical wiggler example

• Vertical field provided by EM
• No vertical gap movement necessary
• Longer period (212mm) but lower fields (0.5 T V
  and 0.1T H)
• Horizontal field can switch at 100Hz
• Much better access for magnet measurements and
  vacuum chamber

Elettra example
89
Elettra EM elliptical wiggler
90
Superconducting Magnets

• Discussed in detail by Martin Wilson

Critical surface of a Type II superconductor Must
stay below the surface to maintain SC state
91
Superconducting Magnets

• To reach high fields (gt 3T) they are the only
  sensible option
• For intermediate fields (1 to 3 T) they can
  have much shorter periods than PM or resistive EM
  devices
• Have to be cold to operate (4K)
• Always sit inside a cryostat
• Traditionally have a liquid Helium refrigerator
  permanently connected to them
• Modern cryocoolers can remove the need for a
  fridge
• Makes for a simpler overall solution

92
Superconducting Magnet Examples

• Diamond
• 3.5T
• 60mm period

93
Superconducting Magnet Examples

• Diamond
• 3.5T
• 60mm period

94
Superconducting Magnet Examples

• Highest field achieved by
• SPring-8 10T wavelength shifter

95
Measuring Magnet Quality Phase Error

• There are various quantitative ways of measuring
  and comparing magnetic field quality
• Here we just consider one which has the largest
  impact on the photon output quality
• Ideally the electron will advance by 2p from pole
  to pole at the first harmonic wavelength to
  maintain the interference condition
• In practice, the magnet will not be perfect, and
  the phase advance from pole to pole will average
  2p but will have some statistical spread about
  that point
• This spread is called the RMS phase error

96
Phase Error

• Example phase error for 20 period device
• In this case is 8?
• Impact of the error is to reduce the output
  intensity the harmonic width broadens
• The error scales with the harmonic number so the
  impact is greater for the higher harmonics

97
Correcting Errors - Shimming

• This is a general term which means making small
  modifications to the magnet so as to optimise the
  magnet performance (minimise phase error, for
  example)
• Magnet block positions may be adjusted by 0.1mm
• Small iron pieces can be placed on top of the
  arrays to slightly modify the field
• The exact dimensions of the iron pieces can be
  selected to have the desired effect upon the
  field level
• Although this can be a time consuming task, it is
  worthwhile in general, since the phase (and
  other) errors can be significantly reduced.

98
The Future

• The field of insertion devices continues to
  evolve
• Higher fields are being proposed by the use of
  cold permanent magnets
• New challenges are presented by the fourth
  generation light sources single pass free
  electron lasers
• Insertion Devices are not just used in light
  sources
• The International Linear Collider needs 400m of
  superconducting wiggler and 200m of
  superconducting undulator
• The LHC uses undulators to generate SR for
  diagnostic purposes

99
Cryo-undulators

• Variation of remanent field with temperature
• If can operate 150K then can gain significantly

In vacuum undulators are being adapted to try out
this novel idea
H Kitamura, Spring-8
100
Undulators for Free Electron Lasers
101
LCLS Undulator Prototype
Full undulator system 130m
102
European X-FEL

• Project based at DESY
• 5 separate undulator systems
• Total undulator length of 652m