WP3: HOM wakefields simulations,

WP3: HOM wakefields simulations,
beam dynamics and beam diagnostics at FLASH/XFEL LC-ABD Birmingham University 17/04/08 Dr Ian Shinton The University of Manchester; Cockcroft Institute, Daresbury, UK

Roger Jones’s group RF cavity electromagnetic simulations for linacs
Dr R.M. Jones Dr I.R.R.Shinton C.Glasman N.Juntong V.Khan Dr F.Roncarolo N.Chanlek S-matirx cascading Linac simulation DESY HOM measurements HOM high gradient Cavity simulation. Cavity instability effects/tracking Coupler kicks Circuit models RF cavity electromagnetic simulations for linacs Interested in the Higher order modes (HOM’s) within RF cavities Calculation of wakefields and the effects of other instabilities within the cavity structures Trapped modes, HOM’s and “kicks” in various parts of the structure. Beam break up (BBU) and severe emittance dilution can readily occur if attention is not paid to the modal properties of these structures. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Alignment errors and trapped modes...
A trapped mode is a resonant mode (HOM) which is non- propagating and is strongly localised in part of the accelerating structure. Simulated trapped mode in new Ichiro cavity in the third dipole band at GHz Alignment and machining errors are simply a departure away from the idealised geometry, cause by incorrect alignment or manufacture of a series of cells. Experimental measurement of cavity electrical centres illustrating signifigant offsets I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Simulations of large RF accelerating structures using a globalised scattering matrix approach
I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

A quick summary of Cascading Advantages of Cascading
Calculation involves cascading two RF junctions using S matrices to obtian the S matrix data of the combined structure The generalised scattering matrix technique is a well established mature RF technique. Can be used to describe any RF structure Advantages of Cascading Provided the correct physics of the problem have been considered the method is highly accurate The method requires little in the way of computational resources and is exceedingly fast (once the unit cell calculations have been made) Perturbations and cell miss-alignments can easily be implemented into the scheme without the necessity to remesh the entire structure as would be the case in a full numerical simulation. Large scale simulations (of multi-module structures) is beyond the computational resources of a purely numerical approach such as FEM,FD….. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

How accurate is Cascading?
Average percentage error between cascaded and fully simulated structure was 0.014%. Note errors below 2.5GHz are the result of meshing; however because of the later inclusion of beam pipes this aspect is a mute one. The cascading calculation took 1.3 seconds while the full numerical HFSS equivalent simulation took about 1 day GSM compilation error across a hypothetical symmetric 100m structure – the error obtained from cascading from any cell is less that 0.005% I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

FLASH 6 module Cascaded scattering matrix S21 of mode 1 TE11 as a function of mode 1
The resonant frequencies (eigenmodes) of any accelerating RF structure can be quickly and efficiently calculated using our recently developed GSM code Here all 6 modules of the FLASH Linac have been simulated – with the presently available computational resources this calculation can only be done with GSM!! The structure is too large for traditional (FEM, FD) numerical techniques as these methods rapidly become overwhelmed with unnecessary eigenmodes!! I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Initial dented structure simulations
An initial investigation was made into adding machining errors into the cascading scheme using a symmetrical dented perturbation During the construction of large scale RF accelerating cavities potentially harmful misalignments and perturbations may be introduced Beam break up (BBU) and severe emittance dilution can readily occur if attention is not paid to the modal properties of these structures – Tolerances need to be determined before such structures are built. Certain types perturbations could be used to shift potentially harmful trapped modes Slater's theorem is an excellent benchmarking technique, provided the perturbation itself does not significantly alter the modal structure. Benchmarked the symmetrical perturbation against Slater's theorem for a series of “Slices” for the three cavity designs of the TESLA, Cornell re-entrant and the Ichiro cavity. Dents greater than 5mm perturb the modes and Slaters theorem can no longer be used I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Cascaded dented simulations
Use of GSM allows rapid perturbation studies with maximum efficiency to be made without the need for time consuming re-meshing as in FEM or FD techniques. 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 S21 Tesla 9cell Sliced Tesla 9cell GSM of S21 matrix for a 9cell TESLA structure with randomly assigned dents compared to an idealised structure. Note the 3rd and 8th dipole bands are signifigantly modified. The area under the peaks gives an indication of modal kicks. Redesigning the HOM damping may be required as a consequence of the redistribution of the modes I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Obtaining the electromagnetic fields, kicks, R/Q's and wakefields from a cascading simulation
By itself the GSM gives us the eigenvalues (resonant frequencies) The derivation of the electromagnetic fields from the GSM is required for kicks, R/Q's, Wakefields etc There are a number of possibilities that could be used to calculate the electromagnetic field from the GSM: Mode matching – computationally inexpensive; however care with the physics must be used. Use the GSM as boundary conditions in a reworked driven modal solution – note this method would be computationally very expensive and time consuming. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

A mode matching approach using the GSM
A mode matching technique has been developed along the lines of: J.Shmoys, R.M.Jones, B.R.Cheo, CEBAF-Report , pg K.Rothemund, D.Hecht, U. van Rienen, Proceedings of LINAC 2004, pg Derive a formula in terms of an infinite series Using mode matching the formula can be condensed into the following form: and are special S matrices describing the infinite series in terms of regions 1 and 2, “T” is a diagonal matrix containing the exponential of propagation constant for the modes and “e” is the analytical field for a waveguide for a particular mode Finally consider there to be a 0 gap length. I. Shinton Wakefest07 12/12/07

Application of the initial mode matching technique
Consider the junctions between each of the unit cells in the structure and derive a GSM on each side of the junction i.e. cascade left and right of the junction Obtain and (these are special S matrices that describe each side of the GSM junction – derived from the infinite series) Use mode matching in terms of and , the normalised field at the junction for any chosen mode can then be obtained. This initial technique, used in conjunction with the overall GSM, can be used to give a rapid indication of the electromagnetic field across a structure. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

A benchmarking example using a mode matching approach and the GSM
Initial benchmark of mode matching scheme for a 3 cell structure against full simulation of HFSS The results in the table below show the typical error being between approximately 4% and 13% In its current form this mode matching technique could be simply extended by taking a series of slices to get a fuller picture of the field across the structure – care needs to be taken in doing this. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

A quick look at the normalised fields at the junctions across a band of frequencies
First dipole band Second dipole band I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

The use of HOM’s for diagnostic purposes

FLASH FLASH is a user free electron laser facility at DESY, Hamburg Germany The Linac of “currently” 6 TESLA modules FLASH produces wavelength in the range of 80nm to 120nm and is a pilot facility for XFEL and the ILC The FLASH produces pulse trains with up to 800s length at a repetition rate of up to 10Hz. The pulse spacing is usually 1s (1MHz) Major participation in the new measurement program at FLASH on the 3.9GHz bunch-shaping cavities and HOM BPM studies in 2009/2010 I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

HOM’s used as BPM’s There has been an ongoing studies at DESY in which the HOM from the HOM couplers are used as BPM’s Traditionally used BPM’s provide limited information about the position of the beam within the accelerating cavities. HOM’s can provide additional information regarding cavity (and sub-cavity) and beam alignment. The transverse HOM’s frequencies have a distinct relationship with the beam position. There exist two orthogonal polarizations of these modes. An observed resolution better than 6μm has been obtained in the vertical polarization using HOM’s as BPM’s The beam position using a HOM can be extracted by considering the amplitudes of the peak frequencies of the two polarizations and relating this to the known frequencies – can be difficult to curve fit so SVD is often used: Phys. Rev. ST Accel. Beams 9, (2006) The TE111-6 mode (1.7GHz) was chosen as the mode used for diagnositic purposes as it has a strong coupling to the beam (i.e. a high R/Q although other modes will be investigated in the near future). All the downmixing electronics have been designed to filterout everything except this mode. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Down-mixing electronics, narrowband and broadband measurements
The downmixing electronics are tuned to filter out all other modes except the TE111-6 mode – this gives Narrowband data and allows fast real time anaysis Broadband data is obtained is obtained directly from the HOM couplers (after appropriate attenuation). I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

The DOOCS system The DOOCS control system that allows a single user to fully operate and control all aspects of the accelerator – MATLAB subroutines. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

BPM readouts at FLASH taken as the beam was bumped across module 5
The HOM readouts At FLASH in DESY HOM's have be implemented as a primary beam positioning system in the “DOOCS” system. Real time alignment of the beam and entire modules BPM readouts at FLASH taken as the beam was bumped across module 5 HOM readouts across module 5 at FLASH taken as the beam was bumped across module 5 I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Determining cavity misalignments
The geometrical centre of a cavity is what we reference as the centre of a cavity; however this is not where the centres of the modes actually lie. Each mode has a unique electrical centre in which the minimum power is coupled into that mode. By offsetting the beam by a known amount, calculating the power from the data obtained from the HOM couplers the electrical centre of a mode may be determined from the minima obtained from a plot of power as a function of offset. This method was successfully developed at SLAC (R.M.Jones: SLAC-PUB 7539) The electrical centre obtained from narrowband data (i.e. a single filtered mode) will give an indication of the misalignments of this mode from cavity to cavity. The electrical centre obtained from broadband data (i.e. several modes) will give an indication of the misalignments of cells within a cavity across a module. We are in the process of developing this method for L-band cavities (using numerous principles originally employed for the X-band cavity). I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Determining cavity misalignments/perturbations using HOM’s – Previous studies
Each mode has a unique electrical centre in which the minimum power is coupled into that mode. Determination of the experimental electrical centres will give an indication of the misalignments between cavities. Initial cavity misalignment study at FLASH Initial investigation into cavity misalignment at DESY using HOM's narrow band data, in which the electrical centre of the TE111-6 mode is considered on a cavity by cavity base only. Here we can see that the electrical centres of this mode vary greatly from cavity to cavity. Stephen Molloy, Josef Frisch, Nicoleta Baboi, Nathan Eddy et al. PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 9, (2006) More advanced cavity misalignment study at ELBE HOM investigation using broadband data at ELBE. The investigation confirmed/showed that each and every mode has a unique electrical centre. Using the broadband data the electrical centre of each cell in a cavity was determined experimentally. The picture just left shows how the electrical centres were determined from a plot of power variation as a function of offset In the picture on the far left the electrical centres for the three most dominant modes in the first two passbands (averaged over five measurements) is displayed ERL-related HOM measurements at ELBE: G.Burt et al, ERL07 workshop I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

New FP7 cavity misalignments/perturbations method
The information from the HOM couplers may be used to determine the beam position and cell misalignment. Misalignments and cavity perturbations are introduced during the construction of a large RF accelerator which will cause it’s operation to depart from the idealised design. These must be within the design tolerance otherwise, information from broadband data taken from the HOM couplers may be the only feasible way of experimentally determining/identifying problem areas New proposed method by which perturbations and individual cell miss-alignments could be identified Simulate an ideal structure in which the motion of the beam is simulated with a small wire – comparison of this to the experimentally determined electrical centres will give the misalignment of a mode with regard to the geometrical centre As all modes have a unique electrical centre, consideration of a sufficient number of modes within a band will allow identification of the localised area of misalignment/perturbation. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Coupler kicks and circuit modelling of large accelerating structures

Progress in coupler kicks and a new circuit model
In the ILC design the HOM coupler RF kick and wakefield dominate the alignment of cavities Recent studies have illustrated that careful rotation of the couplers can reduce the effect of the Coupler kick by a factor of 10. Development of a highly accurate circuit model for dipole models will allow fast, large scale accurate simulations in which the effect of the couplers can be investigated. Comparison of calculated kick factors from a full numerical simulation of a 9cell TESLA cavity and those obtained from the newly developed double chain circuit model, which is in good agreement with the full simulations. Field plot of the dominant TE11 mode for the new TESLA TTF3 power coupler. Calculated with HFSSv11 using a driven modal scheme. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Alternative design higher gradient RF cavities for Linacs and beam dynamic studies

Re-entrant Cornel design
Cavity designs There exist higher gradient alternative designs for Superconducting RF accelerating cavities. The higher the gradient of a cavity the shorter the Linac; hence less cost. Cornell Reentrant and KEK “Ichiro” single cells have gradients in excess of 50MV/m. (TESLA aiming at 35MV/m) Higher Order Mode trapping and wakefield effects need to be investigated. Tesla type Re-entrant type Ichiro type Re-entrant Cornel design Ichiro design Preliminary Beam dynamic studies using LIAR have been made for both the alternative designs of the Re-entrant Cornel and the Ichiro design. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

New HOM analysis in the latest Ichiro design
It is important in any new cavity design to locate potentially harmful trapped modes and to damp modes that could contribute large kick’s to the beam. Beam break up (BBU) and severe emittance dilution can readily occur if attention is not paid to the modal properties of these structures. Conducted code comparisons between commercial software GDFIDL, MAFIA, HFSS and ANALYST: Simulations of transverse higher order deflecting modes in the main linacs of ILC, SRF07, C.J.Glasman, R.M.Jones, I.Shinton, G.Burt. Analysis of the new ICHIRO design, using ANALYST, showing a hitherto unobserved trapped mode at GHz and a multi-cavity mode at GHz both in the third dipole band Dispersion curves of first 8 dipole and 5 sextupole bands Comparison of Loss factors calculated with GdfidL (red) and MAFIA 2D (blue) Envelope of long-range wake-field I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Beam dynamic studies of an ILC machine built with Ichiro cavities using LIAR
Emittance dilution due to long-range wake-fields damped with a Q of 106 in Ichiro cavity. The beam is offset with 1y (~12.4 m). The mean dilution is approximately 17% (with a standard error of .25 %) machines are indicated together with the mean and the 95% confidence level. Y-Y’ phase space at end of linac I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Beam dynamic studies of an ILC machine built with Re-entrant cavities using LIAR
Emittance dilution due to long-range wake-fields damped with a Q of 106 in Ichiro cavity. The beam is offset with 1y (~12.4 m). The mean dilution is approximately 23% (with a standard error of .25 %) machines are indicated together with the mean and the 95% confidence level. Y-Y’ phase space at end of linac I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Future Work GSM Studies at FLASH Coupler kicks and circuit models
Develop a mode matching scheme to describe the fields in their entirety across any cavity Calculate Kicks, R/Q’s and wakefield effects from the re-derived fields Incorporate these effects into the newly developed Cascading code so that any large scale RF accelerating structure can be modelled. This code will be freely available to the scientific community. Studies at FLASH Major participation measurement and simulation of the new 3.9GHz bunchshaping cavities and HOM BPM international collaboration studies in 2009/2010 Investigate the new FP7 proposed broadband method for determining actual cavity misalignments and perturbations Coupler kicks and circuit models Investigate coupler kicks in the new TTF3 design and develop a circuit model to describe large accelerating structures including coupler modelling. Large scale beam dynamic studies Perform in-depth large scale beam dynamic studies Detailed beam dynamic studies with LIAR, PLACET and LUCRETIA (some benchmarking studies). I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Summary I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Summary of HOM's used as a beam diagnostic tool and the possibility of determining cavity misalignment International collaboration between DESY (Dr N.Baboi et al), SLAC (Dr S.Molloy et al), FERMILAB (Dr N.Eddy et al), The University of Rostock (Dr U.Van.Rienen and H.W.Glock) and The Cockcroft Institute (Dr R.M.Jones et al, Leader EU-FP7 HOM/BPM studies ) HOM's have been shown to be a highly accurate diagnostic tool for beam alignment, with a higher degree of precision than traditional BPM’s with an observed resolution better than 6μm. The information from the HOM couplers may be used to determine the beam position and cell misalignment and may be the only feasible way of experimentally determining/identifying problem areas. Major participation in the new 3.9GHz bunchshaping cavities and HOM BPM studies in 2009/2010 New FP7 proposed broadband method Determination of actual misalignment by comparison of electrical centre experimental results to simulation. Consideration of enough modes could allow identification of the localised area of misalignment/perturbation. Initial narrowband investigation into cavity misalignment Only the electrical centre over an entire cavity was determined. Stephen Molloy, Josef Frisch, Nicoleta Baboi, Nathan Eddy et al. More advanced broadband investigation into cavity misalignment Using the broadband data the electrical centre of each cell in a cavity was determined experimentally. G.Burt et al. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Summary of using a globalised cascading scheme to model large RF accelerators
GSM is a proven RF technique that can be used to accurately model the electromagnetics of large (kilometres long) RF accelerating structures. GSM gives the results as accurately as those obtained by large scale parallel numerical means (FEM,FD) It requires little in the way of computational resources or time and is capable of solving problems that cannot be solved by any other method. For multi-module simulations this method is the only one capable of accurately determining the resonant frequencies. GSM compilation error across a hypothetical symmetric 100m structure – showing that the error obtained from cascading from any cell is less that 5x10-3% Cascaded simulation over an entire TESLA module GSM does not require the time consuming re-meshing of other schemes for perturbation studies GSM enables the resonant frequencies and fields to be determined accurately with maximum efficiency . We are developing a mode match tracking scheme to rederive the electromagnetic fields. Presently we have a prototype scheme which can be used to quickly view the field distribution at the iris’s as a function of junction position. I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

Re-entrant Cornel design
Summary of large scale beam dynamic studies, alternative high gradient designs In the construction of any large accelerating structure only one machine can be built we must aim for the best possible machine (within tolerance) that can be built; careful analysis of alternative designs is required. Beam break up (BBU) and severe emittance dilution can readily occur if attention is not paid to the modal properties of these structures. Re-entrant Cornel design Ichiro design RE-ENTRANT LINAC The mean dilution is approximately 23%. ICHIRO LINAC The mean dilution is approximately 17% Analysis of the new ICHIRO design, using ANALYST, showing a hitherto unobserved trapped mode at GHz and a multi-cavity mode at GHz both in the third dipole band Emittance dilution due to long-range wake-fields damped with a Q of 106 in Ichiro cavity. The beam is offset with 1y (~12.4 m). 200 machines with random seeds have been simulated using LIAR Recent invited talks Globalised scattering matrix simulation in ILC cavities and modules, Wakefest07 SLAC: I.Shinton Wakefields and beamdynamics, WakeFest07 SLAC: R.M.Jones Beam dynamics simulations and wakefield in Main Linacs, LET08 SLAC: R.M.Jones Prospects for weakly damping HOMs in CLIC Accelerator, The CLIC X-Band Accelerating Structure and design Workshop, CERN, Geneva, 18/6/2007:R.M.Jones High precision SC cavity alignment/diagnostics/BPM with HOM measurements, ESGARD OMIA/SRF-AS FP7, CERN, 11/9/2007: R.MJones I. Shinton , WP3, LC-ABD, Birmingham 17/04/08

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