European Spallation Source (ESS): EM Fields & SC Cavities...

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European Spallation Source (ESS): EM Fields & SC Cavities in Particle Accelerators 11 th Jan 2011 Steve Molloy, Royal Holloway, University of London

Transcript of European Spallation Source (ESS): EM Fields & SC Cavities...

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European Spallation Source (ESS):EM Fields & SC Cavities

in Particle Accelerators

11th Jan 2011

Steve Molloy, Royal Holloway, University of London

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Outline

�European Spallation Source (ESS)� Intro, main features

�Quick intro to resonant fields in accelerators• Maxwell’s equations.....

�Acceleration & parasitic fields

�Parasitic resonances�Higher Order Modes (HOMs)

� Problems� Uses

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European Spallation Source

�A joint European Project• Similar in organisation to CERN

�Construct world’s most intense neutron source

�5 MW protons on target� Compare with:

�Spallation Neutron Source (SNS), Oakridge, USA• Goal = 1.4 MW (achieved 1 MW)

� ISIS, RAL, UK• 160 kW

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Spallation

�Bombard with 5 MW protons� 2 ms bunch train pulsed at 20 Hz

�Bunches spaced at 352 MHz� 2.5 GeV protons

�Liquid metal target• Probably Hg

� Easier to disperse the heat generated�Neutron flux:

�Average = 1014 cm-2.s-1

�Peak = 1017 cm-2.s-1

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European Spallation Source

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European Spallation Source

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Environmental impact of accelerators

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A carbon neutral accelerator?

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Machine layout

High current (60-90 mA)Low emittance (0.2 m� m.rad)

2 ms pulse @ 20 Hz100 ns rise-time

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Beam intensity leads to problems

�5 MW proton beam (at end of linac)�Spec calls for <1 W/m of losses!

�Uncontrolled fields may exacerbate losses�Limiting peak machine performance

� Where might these fields come from?� How can they be controlled?� Can they be made useful?

�To answer these questions, we need to think about the basics of acceleration....

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Basics of acceleration

Static fields

RF fields

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“Pill box” cavity

��E���

��B�0

��E�B t

��B��0 J��0�0E t

Cylindrical waveguide, with plane,perpendicular, end-caps.Infinitely conductive walls.

Filled with lossless dielectric.

��E�0

��B�0

��E�i B

��B�i�� E

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Simplify using boundary conditions

Boundary ConditionsNo tangential E field

No normal B field

Two classes of solutionTM – No long. B fieldTE – No long. E field

E �� ,� , z , t ��E �� ,��exp ��ikzi t �Cylindrical boundaries – cylindrical coords

End-caps lead to standing waves

A sin �kz ��B cos �kz� , k�p �d

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Mode indices – TEmnp

TMmnp

�m, n, and p, count nodes in each of the degrees of freedom

������������

� ������������ �������������������� ������������

�� ��������������������������• ��������� � ����������

� � ����� �� �

������� ��������������������������• ���� ��������������������������

� ������������

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Monopole solutions

EzTM-02p

EzTM-03p

EzTM-01p

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Dipole solutions

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Quadrupole solutions

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Real cavities aren’t pill-boxes!

�Multiple, coupled cells�Behave like masses on springs

� There are multiple ways for single “mnp” oscillation to occur

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Coupled oscillators

� Eigenmodes of coupled oscillators split according to the phase difference

� “0-mode”, “�-mode”, etc.

� For N+1 coupled oscillators� i /N radians phase advance (i=0,1,...N)

� Frequency also splits� Dependent on the coupling strength� Each new mode may be plotted on a Brillouin curve

• For N<∞ the modes are equally spaced along the curve

2� ��22 �1� cos ����

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Coupling to the beam� The beam may also be indicated

on the dispersion plot� Crossing points indicate equal

phase velocity� i.e., the beam will always “see” the same RF phase

� Energy transfer is maximised� Unequal phase velocities implies

relative phase rotation� Energy transfer experiences

cancellations

V� �L �2

�L �2

�E �� � z � ,� � z � , z ��ei z� c dz U��0��E � r ��2dr3

�W��V�2

Uq2�kq2

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Typical Cavity

• So-called “elliptical cavity”• Parameters chosen to maximise energy transfer

•Minimising chance of “break down”• Power coupler to resonantly excite TM010• “Standing wave” design

•No output coupler• High Q to maximise efficiency

•Implies long “filling time”

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Example modesAccelerating mode

(TM010-�)

R/Q is a measurement ofthe coupling.RQ�

k�

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Show the animations......

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Beam-pipe cut-off

�Most modes are below the natural cut-off frequency of the beam pipe

• Fundamental = 704 MHz

� Localised within one cavity?�People tend to forget about the evanescent field...

kc�pnm

a�2.40480.04

�60 �c�2�kc�0.105

f c�c�c�2.871GHz

ei �k2kc

2 z�ei 2�c � f 2

f c2 z

Mode propagation in the beam pipe:

f� f c implies i2�c � f 2 f c

2 z� Real

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Cavity-to-cavity coupling

�Modes modelled as complex oscillator� Imaginary in cavity, real (therefore not oscillatory) in beam pipe

� Decaying field allows coupling of modes• Therefore, coupling happens through “forbidden” region

�Mathematically identical to QM tunnelling!Mathematically identical to QM tunnelling!

�Describe the cavity as a finite well in 1D• Choose mass & length to obtain desired frequency• Couple to an additional cavity

� Choose wall height to match wavenumber of cutoff mode

• Observe frequency splitting & calculate coupling� 2 cavities � 0-mode & �-mode

�A work in progress....

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Cryomodule modes

�Cavities strung together in series• ESS � 8 cavities/cryomodule

� Evanescent coupling breaks mode degeneracy�Accelerating mode TM010�

� N cell cavity• N resonances i /(N-1) phase advance� �

� M cavity cryomodule• NxM resonances

�Important when designing the cryomodule

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Why Higher Order Modes (HOMs) are bad

�Efficiency of acceleration � High Q�Strongly excited modes are weakly damped

• May live to couple with subsequent bunches

� Monopole modes interfere with acceleration� Dipoles give position dependent kicks

• Longitudinal kicks (acceleration) for TM modes• Transverse kicks for TE

�Emittance blow-up, jitter amplifications, etc.� The energy has to go somewhere!

• Propagate down the beam-pipe?• Heat up the cryogenics?

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Are they useful?

�Mode excitation depends on beam�Coupling defined by trajectory (for dipole and higher)�Phase of excitation depends on beam arrival time

� Each mode carries information�Can this be extracted?

�Vacuum/cryo infrastructure already exists• Bandstop filtered coupler extracts power

� Replace resistive load with monitoring electronics�Very cheap hardware installation!

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Dipole modes are polarised

Two polarisations, rotated �/2 in � Not necessarily coincident with xy plane Alignment may depend on cell number

Four degrees of freedom Phase & amplitude in each polarisation

Horizontal and vertical position: Only 2 trajectory dofs?

What info is carried by the other dofs?

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“Beam” degrees of freedom

�Position and angle in each plane

Cannot separate these two

Analyse bunch with finite length, �z, as two

“macro particles”.Head and tail particles excite equal but

opposite signals, separated by �z/c.

Vector sum is really a time-delayed subtraction – much like a differential.

Thus, the “tilt” signal is equivalent to “offset” signal, but phase rotated by �/2.

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Our experiment

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Measurement electronics

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Raw data

Calibration tone

Exponentially decaying sinusoids.Polarisation degeneracy broken, so twofrequencies beating against each other.Beat frequency indicates ∆f is very small

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Analysis

�“Standard analysis”�Determine complex amplitude of signal�Correlate real & imaginary components with position &

angle• Matrix transformation – rotation & scaling

�Problem......

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Idea?

�Data from each pulse is a vector� Actually, two vectors (1 from each coupler), but these may be concatenated into one.

• 1600 points per coupler per aquisition

� This could be considered as 1 point in a hugely dimensional space (3200 dimensions)�A dataset will be a “fuzz” of points plotted in 3200-D!

�The data produced by a “pure” move in 1 dof (x, x’, y, y’) is also a vector

• New coord system defined by aligning with each of these� How do we do this?� What about the other 3196 dims?

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Matrix decompositionX � data matrix (~100x3200)

X�X T�U�S�V T�V�S�UT�U�!�UT

X T�X�V�S�UT�U�S�VT�V�!�VT

Singular Value Decomposition: X�U�S�VT

U & V are unitary UT�U1 VT�V1

S is diagonal. Contains the “singular values”.

Each of these is an eigenvalue equation, and U and V are matrices containing the

respective eigenvectors

�V contains “time dependent” eigenvectors�Unitary, so (by definition) also orthonormal

• New basis for 3200-D data?• X may be represented by U.S in “V space”

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How to use this new vector basis?

�For each incoming pulse:�Determine location in 3200-D space

� Dot product with V vectors

�Correlate this with trajectory info from other devices� SVD calculates and orders V to maximise each

subsequent singular value�Only four beam dofs, so we can discard 3196 vectors!

� Maybe choose 6 to be safe!

�Correlate these with the trajectory

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Identical to JPEG compression!

�Break image into blocks�8x8 pixels

�Dot product each with 2D basis function� Converts 64 pixel image to 64

amplitudes�Compress by discarding

information� Remove high frequency

blocks

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Eigenmodes and singular values

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Results

~0.3 mm

~0.3 mm

Resolution ~4 m

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4 um resolution – is that good?

�No!� Compare:

�The power in the mode• with

�The thermal noise in the electronics*� Find the beam position at which these are equal

� Since R/Q is position dependent

�130 nm!!!� Problem in the electronics

• Signal jitter mixes position and angle�Updates should fix this.....

* Yes Stew, I know thermal noise is rarely the real problem, but it is a useful lower limit

Um�RQ� 2�q

2

U th�12�kBT

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What about multi-bunch?

�Decay time >> bunch separation• Can bunches be separated?

� Subtracting bunch by bunch leads to large errors� Work with single bunch modes

�Measure the mode amplitudes in one bunch window�Then again in the second window

• No bunch in this region!�Calculate the transformation matrix

� Calculate mode amps for each bunch subtracting the previous bunch

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Multibunch data

Multibunch residual is equivalent toa position noise of ~1-2 um.

Added in quadrature to 4 um,this increase is negligible.

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Stability

�In real world:�Diagnostics must be stable as well as high res.

� Can’t constantly interrupt machine time to calibrate HOM BPMs!

�Questions:�Why does the calibration change?

� Temperature drifts, cable changes, etc. cause phase rotations and gain changes

�Can we prevent it changing?

�Solution?�Measure gain/phase of cal. Tone.�Remove gain/phase deltas

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Convert to “pure” modes

�Construct pure modes from cal data�Monitor phase/gain of cal tone�Alter incoming data appropriately�Determine amplitude of pure modes

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Summary

�Impossible to completely eradicate HOMs�Dealt with by appropriate accelerator design

� This infrastructure can be designed to allow HOMs to be useful

�4D trajectory monitoring�Many machines are dominated by their linac, so such

measurements give lots of information

�Other measurements possible�Bunch timing wrt accelerating phase� Internal alignment of cryomodules & cavities