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