Electron Cloud R&D for Future Linear Colliders

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Presentation transcript:

Electron Cloud R&D for Future Linear Colliders Mauro Pivi (SLAC) CERN Geneva, 20 March, 2008 We acknowledge the support of the European Community-Research Infrastructure Activity under the FP6 "Structuring the European Research Area" programme (CARE, contract number RII3-CT-2003-506395).

The electron-cloud effect (ECE) in a nutshell: Beam residual gas ionization and photons produce primary e- Number of electrons may increases/decreases due to surface secondary electron yield (SEY) Bunch spacing determines the survival of the electrons Especially strong effect and possible consequences: Single- (head-tail) and coupled-bunch instability Transverse beam size increase directly affecting the Luminosity Vacuum pressure and excessive power deposition on the walls (LHC cryogenic system) In summary: the ECE is a consequence of the strong coupling between the beam and its environment: many ingredients: beam energy, bunch charge and spacing, secondary emission yield, chamber size and geometry, chromaticity, photoelectric yield, photon reflectivity, … The electron cloud has been seen PSR, SPS, PEP-II, KEKB, DAFNE..

One of the main limitations to the future Colliders (ILC, LHC CLIC) performances and luminosity reach is the formation of an electron cloud and driven collective instabilities Electron cloud effect occurs mainly in the Damping Ring of the Linear Collider, due to short bunch spacing

Simulation Efforts on LC KEK: PEI and PEHTS codes K. Ohmi LBNL: POSINST M. Furman, WARP J. L. Vay CERN: ECLOUD, F. Zimmermann, D. Shulte, HEAD-TAIL, G. Rumolo, R. Thomas, E. Benedetto, FAKTOR2 codes W. Bruns (Berlin) SLAC: CLOUDLAND L. Wang, POSINST and CMAD codes M. Pivi

Work done for the ILC Reference Design Report (RDR) K. Ohmi KEK Beam size growth from single-bunch instability driven by electron cloud in the 6.7 km positron ring (e- densities in e/m3). Instability threshold set tolerances on maximum allowed SEY.

Work done for the RDR Tune shifts on the order of 0.01 are expected near threshold. Simulations indicate that a peak secondary electron yield of ~1.2 results in a cloud density close to the instability threshold. Based on this, the aim of ongoing experimental studies is to obtain a surface secondary electron yield of 1.1. Simulations also indicate that techniques such as grooves in the chamber walls or clearing electrodes, besides coating, will be effective at suppressing the development of an electron cloud.

Work done for the RDR M. Pivi, SLAC Buildup of the electron cloud and the suppression effect of clearing electrodes in an arc bend of the 6.7 km ring.

Work done for the RDR A clearing electrode bias potential of +100 V is sufficient to suppress the average (and central) cloud density by more than two orders of magnitude. Techniques such as triangular or rectangular fins or clearing electrodes need further R&D studies and a full demonstration before being adopted. Nonetheless, mitigation techniques appear to be sufficient to adopt a single 6.7 km ring as the baseline design for the positron damping ring.

e-cloud expectations in the positron DR Average neutralization levels and single-bunch (SB) instability electron cloud density thresholds for various damping ring options in units of [1012 m-3]. The average density thresholds are for a ring modeled as a dipole region. Circumference 6 km Neutralization e [1012 m-3] 6.0 Simulated e in arcs max=1.4 8.0 SB: e threshold [1012 m-3] 1.0 Sim. e / SB threshold Sections 6 km DR E-cloud SEY threshold arcs dipole expected 1.2 wigglers sections Long straight sections preventable 1.6 - Arcs and wiggler sections: aiming at SEY 1.1 Not an issue in straight sections, a coating (TiN, TZrV NEG) and solenoid or rectangular grooves would lower SEY < 1.6. Large chamber size.

The ECE plan Benchmark sim. Simulations Lab measurements e- trapping mechanism in Quad e- detector meas. in facilities beam dynamics e- cloud generation & equilibrium single and multi-bunch instability self-consistent 3D simulations SEY meas. coatings + treatments Coating durability under vacuum Grooved surface design Path TiN TiZrV increase radius electrodes groove other ? Requirements Demonstration I groove and clearing electrode chambers in PEP-II , KEKB, SPS and CesrTA Demonstration II Installation coated samples in PEPII, SPS and KEKB Meas. SEY ex situ

ILC R&D Ecloud program R&D at KEK. SEY measurements. Installation of dedicated chamber with clearing electrodes, coating and grooves in wigglers. Simulations of build-up and instabilities. Y. Suetsugu, Fukuma, M. Pivi and L. Wang (SLAC), Kato R&D at CERN. Laboratory SEY measurements. SPS tests in magnets with clearing electrodes on enamel substrate, chambers with carbon coatings, TiN and grooves. Simulations of build-up and instabilities. E. Chapochnikova, G. Arduini, M. Jimenez, J.M. Laurent, F. Caspers, Mahner, E. Benedetto, D. Schulte, A. Rossi, G. Rumolo, R. Thomas, P. Chiggiato, T. Kroyer, M. Taborelli, F. Zimmermann, M. Pivi and L. Wang (SLAC), M. Venturini (LBNL)

ILC R&D Ecloud program R&D at LANL. Electron trapping in quadrupole field – R. Macek et al. R&D at Frascati. Characterization electron cloud in Dafne e+ ring – P . Raimondi, R. Cimino, T. Demma R&D at SNS/BNL. Characterization of instability for long bunches. Simulations of build-up and instabilities. S. Cousineau et al. R&D at SLAC. Laboratory SEY measurements. Samples installed in beam line. Installation of grooved chambers. Installation of new chicane and diagnostics in magnets. Simulations of build-up and instabilities. – M. Pivi, J. Ng, L. Wang, B. Smith, B. Kuekan, M. Munro, W. Wittmer, D. Arnett, J. Olszewski, Wallace, D. Kharakh, C. Spencer, T. Raubenheimer, J. Seeman, R. Kirby, F. Cooper, F. King

Secondary Electron Yield Measurements and Surface Analysis at SLAC Secondary Electron Yield (SEY) and Surface characterization R.Kirby, SLAC XPS TiN/Al Electron conditioning TiZrV NEG sample (LBNL) Rectangular groove SEY ~ 0.7! flat surface Rectangular and triangular grooves concept rect. grooves

Why not an aluminum chamber? Al as received Electron conditioning (bombardment) effect on the SEY for aluminum. Laboratory measurements at SLAC and CERN agree very well. The electron conditioning is not completely effective to lowering the aluminum SEY as needed [SLAC-PUB-10894]. Most of the Dafne ring is made of aluminum chambers.

Electron conditioning (scrubbing or processing) of thin films TiN, TiZrV. Laboratory measurements, SLAC. Residual gas recontamination under vacuum Based on laboratory measurements, the required conditioning dose in ILC DR would be achievable in hours of beam operation during commissioning. Concerns about effective e- conditioning time and coatings durability in an accelerator environment …

Electron conditioning: issues Electron conditioning “Asymptotic” behavior: In an accelerator environment, the electron cloud itself is providing the conditioning of the vacuum chamber walls (in laboratory: conditioning is constant by fixed beam) When the SEY decreases, the efficiency of the electron conditioning will decrease as well Recontamination: - Competing effect: residual gas recontamination  e- cloud reappears PICTURE at the SEY threshold: Two effects competing against each other e- (asymptotic) Conditioning SEY threshold recontamination (1) solution (LHC): running at higher current for a period of time (2) key: combined photon/ions conditioning may keep SEY below threshold (?!)

Rectangular Grooves to Reduce SEY Rectangular grooves can reduce the SEY without generating geometric wakefields. The resistive wall impedance is roughly increased by the ratio to tip to floor. Schematic of rectangular grooves Without B field Schematic of rectangular grooves With B field By=0.2T

Effect of triangular grooves on Impedance Impedance enhancement factor for the triangular grooved surface with round tips. Note that this is valid for frequencies ω such that c/ ω >> W; for example, for W~3mm this means n<6e11 Hz. ref. [L. Wang et al. FRPMS079, Proceedings of PAC07.]

Rectangular (!) groove design in field free region: Laboratory measurements, SLAC M.P. and G. Stupakov, SLAC 5mm depth (PEP-II) Same SEY results Artificially increasing surface roughness. 1 mm Special surface profile design, Cu OFHC. EDM wire cutting. Groove: 0.8mm depth, 0.35mm step, 0.05mm thickness. Measured SEY reduction < 0.8. More reduction depending geometry. Triangular groove concept A. Krasnov LHC-Proj-Rep-617

Installed 5 chambers in PEP-II straight, January 2007: R&D work at SLAC on mitigation techniques Installed 5 chambers in PEP-II straight, January 2007: Project “ECLOUD1”: a station with chamber that allows the insertion of samples directly into beam line to monitor the reduction of the SEY due to beam conditioning Project “ECLOUD2”: 4 Grooved and Smooth chambers installed to measure performance in PEP-II beam environment

SLAC test chambers installation layout ECLOUD1 ECLOUD2 SEY TEST STATION GROOVE CHAMBERS EXPERIMENT SEY GROOVE 1 GROOVE 2 FLAT 1 FLAT 2 COLLECTORS ENERGY ANALYZER THERMOCOUPLES ECLOUD1: SEY station can be used to expose samples to PEP-ii beam environment and then measure samples in lab setup (transport in Ultra-High Vacuum load-lock) ECLOUD2: Grooved and Flat chambers installed to measure performance in PEP-ii beam environment

“ECLOUD1” SEY test station in PEP-II 2 samples facing beam pipe are irradiated by SR PEP-II LER e+  Transfer system at 0o Isolation valves Transfer system at 45o ILC tests, M. Pivi et al. – SLAC 20 March, 2008 CERN

SEY TESTS TiN and NEG Expose samples to PEP-II LER synchrotron radiation and electron conditioning. Then, measure Secondary Electron Yield (SEY) in laboratory. Samples transferred under vacuum. PEP-II LER side 20 mm TiN/Al sample exposed to SR Complementary to CERN and KEK studies

Results of Conditioning in PEP-II LER beam line Before installation in beam line After conditioning e- dose > 40mC/mm**2 ILC tests, M. Pivi et al. – SLAC SEY of Tin-samples measured before and after 2-months conditioning in the beam line. 2 samples inserted respectively in the synchrotron radiation fan plane (0o position) and out of this plane (45o). Similar low SEY recently measured in situ in KEKB beam line S. Kato, Y. Suetsugu et al. 20 March, 2008 CERN

Surface analysis: Carbon content decrease X-ray Photon Spectroscopy. XPS Before installation XPS After exposure in PEP-II LER for 2 months (e dose 40mC/mm^2) LER#1 ILC tests, M. Pivi et al. – SLAC Carbon content is strongly reduced after exposition to PEP-II LER  synchrotron radiation + electron + ion conditioning. This is a different result if compared to electron (only) conditioning in laboratory set-up where carbon crystals growth has been observed by many laboratories. 20 March, 2008 CERN

Surface analysis: Carbon content decrease X-ray Photon Spectroscopy. Carbon content is strongly reduced after exposition to PEP-II LER  synchrotron radiation + electron + ion conditioning. This is a different result if compared to electron (only) conditioning in laboratory set-up where carbon crystals growth has been observed by many laboratories. 20 March, 2008 CERN

SEY recontamination after long term exposure in vacuum environment SEY below 1 if sample is left under vacuum following conditioning in PEP-II LER. Measured SEY after 162h and 1074h in laboratory setup. Average pressure 1.0e-9 torr, 10:1 H2:CO.

Results of NEG conditioning in PEP-II e+ beam line NEG as received After NEG heating Attention: sample kept in vacuum ~1e-7 after heating. Also, although we took best precautions, the environment during sample transferring for measurements, may not have been perfectly CO CO2 or contaminants free. After beam conditioning March 2008 ILC tests – SLAC 20 March, 2008 CERN

Installed 5 chambers in PEP-II straight, January 2007: R&D work at SLAC on mitigation techniques Installed 5 chambers in PEP-II straight, January 2007: Project “ECLOUD1”: a station with chamber that allows the insertion of samples directly into beam line to monitor the reduction of the SEY due to beam conditioning Project “ECLOUD2”: 4 Grooved and Smooth chambers installed to measure performance in PEP-II beam environment

“ECLOUD2” groove chambers in PEP-II FAN EVENTUALLY HITS “BOTTOM” OF SLOT FOR FULL SR STRIKE LIGHT PASSES THRU SLOTS BETW FINS BECAUSE FAN IS “THICKER” THAN FIN FIN TIPS= I.D. OF CHAM FAN HITS HERE FIRST VIEW IS ROTATED 90 CCW FROM ACTUAL FAN ORIENTATION Built Rectangular Groove (or “fin”) chambers by Aluminum extrusion, then TiN coated and installed in PEP-II LER straight sections for testing p.30

Installation in PEP-II LER: Groove chambers Flat chamber Electron detectors LER bend magnet upstream

Groove chambers in PEP-II straight Performances in PEP-II beam environment. Straight field free regions. Successfully measured electron signal in Groove chambers much lower than Smooth (or “flat”) chambers. All chambers with TiN coating. CERN

Effect of external solenoid Effect of external solenoid winding on measured electron cloud current in smooth an grooved chambers in PEP-II (10 A  Bz~20 Gauss). CERN

R&D work at SLAC on mitigation techniques New: Installation of an ILC chicane in PEP-II and multiple test chambers, in December 2007: Project “ECLOUD3”: new chicane with ILC DR bend-type field, and test chambers including sections with Aluminum TiN coating Grooves Non-evaporable getter NEG coating Installation plans that we had to stop due to US FY08 budget issues

Mitigations Tests SLAC: New ILC Chicane Installation Verify efficiency of mitigation techniques in dipoles. Installation of a new chicane in PEP-II with ILC DR-type bends, to test chambers with coatings (and chambers with grooves) E-cloud diagnostics PEP-II e+ beam line ILC DR-type bends Layout new chicane installation in PEP-II LER PEP-II chamber with triangular grooves

Vacuum chambers Layout Aluminum TiN coating on Al Groove 2 chambers: 135.3” and 31.2”. 4 analyzer electron cloud detectors, one at each magnet location

Chicane Assembly Layout PEP-II LER HER

Layout of electron cloud tests in PEP-II LER DIRECTION PLAN VIEW AISLE SIDE Last bend of arc 1 ELEVATION VIEW SEY station Grooves/Smooth New chicane

Dec 3, 2007 Chicane

Electron cloud installation studies at SLAC ECLOUD3 INSTALLATION: magnetic field tests PEP-II e+ ring ECLOUD1 and 2 1.5% of the ring ILC tests - SLAC

Electron detector #1 #2 #3 PEP-II positron beam line experimental chamber Magnet iron plates

Latest installation: electron cloud chicane 01-25-08 Chicane magnetic field Off. Electron cloud signal on collectors distributed along the horizontal axis. Aluminum section (above) and TiN coating (below) show a reduction of ~30 in favor of the coating. Internal view of the special electron detectors allow measuring the e- horizontal distribution and electron energy.

Scan Chicane Magnetic field resonances in the electron cloud current ( PEP-II LER e+ beam current Magnetic field scan (0 to 1.1kG - 1Gauss steps) Central collectors electron signals Work in progress LBNL/SLAC to simulate PEP-II case. See C. Celata talk.

Simulations results from C. Celata LBNL

Simulations results from C. Celata LBNL

R&D work plans for the ILC Engineering Design Report (EDR) – e- cloud Working Package 7 Achieving the objective of developing suppression techniques for the electron cloud will involve the following tasks: Study coating techniques, test the conditioning in situ in PEP-II, KEKB, SPS and CesrTA. Test clearing electrode concepts by installing chambers with clearing electrodes in existing machines and in magnetic field regions in KEKB, SPS, CesrTA and HCX (LBNL). Characterize the impedance, the generation of higher order modes, and the power deposited in the electrodes. Test “groove” concepts by installing chambers with grooved or finned surfaces in existing machines, including bend and wiggler sections in PEP-II, KEKB, SPS and CesrTA. Characterize the impedance and HOMs. 20 March, 2008 CERN

Working Package 7 (e-cloud) CERN Fritz Caspers Daniel Schulte Frank Zimmermann Cockcroft Institute Oleg Malyshev Ron Reid Andy Wolski Cornell Jim Crittenden Mark Palmer DESY Rainer Wanzenberg FNAL Panagiotis Spentzouris INFN-LNF David Alesini Roberto Cimino Alberto Clozza Pantaleo Raimondi KEK John Flanagan Hitoshi Fukuma Ken-ichi Kanazawa Kazuhito Ohmi Kyo Shibata Yusuke Suetsugu Shigiri Kato LANL Bob Macek LBNL John Byrd Christine Celata Stefano de Santis Art Molvik Gregg Penn Marco Venturini Miguel Furman Kiran Sonnad Mike Zisman PAL Eun-San Kim Rostock University Aleksander Markovik Gisela Poplau SLAC Karl Bane Bob Kirby Alexander Krasnykh Mauro Pivi Tor Raubenheimer Tom Markiewicz John Seeman Lanfa Wang Potential Investigators 20 March, 2008 CERN

Example: WP 7 (e-cloud) The required input includes: Experimental data from machines including CesrTA, PEP-II, KEKB, SPS and LHC. Data should include detailed comparison of electron cloud density in sections with mitigation techniques compared with the electron cloud density in sections without mitigating techniques. The deliverables will include: Technical specifications for techniques to be used to suppress build-up of electron cloud in the positron damping ring, consistent with aperture and impedance requirements. Guidance for the design of the vacuum chamber material and geometry (Objective 3.1.1.1), and for the technical designs for principal vacuum chamber components (Objective 3.1.1.2). 20 March, 2008 CERN

WP 7 (e-cloud) ILC DR Challenge: 2 pm vertical emittance If the electron cloud density is not reduced below the threshold level for beam instabilities, then the positron damping ring will be unable to provide a beam meeting the specifications for beam quality, stability and intensity; this will have a potentially significant impact on the luminosity of the ILC. 20 March, 2008 CERN

Test Facilities: CesrTA Cesr-c is a wiggler-dominated electron-positron collider. The proposed development of CESR into CesrTA would allow a unique opportunity for electron cloud studies at a dedicated test facility, operating in a parameter regime directly relevant for the ILC damping rings. Requires relocation of wigglers to allow tuning for low natural emittance; upgrade of instrumentation for tuning for low vertical emittance; installation of instrumented test chambers in wigglers. A range of other important studies will also be possible (e.g. low-emittance tuning, development of instrumentation for fast beam-size measurements of ultra-low emittance beams). Presently, funding agencies are supporting CesrTA proposal. 20 March, 2008 CERN

Other Test Facilities KEKB and ATF DANE PEP-II (until April 2008) Electron cloud Fast ion instability DANE electron cloud fast injection/extraction kickers PEP-II (until April 2008) SPS and LHC 20 March, 2008 CERN

R&D work plans for the EDR From “Damping Rings EDPhase Gantt Links” document

Milestones to ILC EDR The goal is to complete the following tasks by early 2010 as input for the Engineering Design Report (EDR) o Test coating techniques and determine conditioning effectiveness in existing accelerator beam lines o Characterize the efficiency of conditioning on TiN coatings with respect to NEG coatings. o Characterize thin-film coating durability after long term exposure in an operating accelerator beam line: analyze PEP-II TiN-chambers after ~10 years operation. o Need to experimentally characterize Photoemission in ILC DR parameters range to estimate initial seed of electrons o Characterize the electron cloud build-up by simulations and measurements in existing accelerators o Characterize the electron cloud in wigglers and quadrupoles 20 March, 2008

Milestones to EDR o Characterize the electron cloud instability by measurements in existing facilities possibly also at CesrTA, KEKB operating at ultra-low emittances o Characterize the ILC DR electron cloud instability by simulations Evaluate the need for Additional Mitigation techniques (besides coating): o Test clearing electrodes in magnetic field regions including wigglers at KEKB and CESR and dipoles at PEP-II and SPS o Test triangular groove or slots in magnetic field regions including wigglers and dipoles PEP-II, KEKB and SPS o Characterize the impedance and HOMs of mitigation techniques o Use of antechambers Recommendation of mitigation techniques to prevent the electron cloud in the ILC damping ring as input for the EDR 20 March, 2008

CesrTA Program I CesrTA Program has been funded jointly by the US NSF and DOE Dedicated DR R&D program starting in mid-2008 CesrTA Configuration: 12 damping wigglers located in zero dispersion regions for ultra low emittance operation (move 6 wigglers from machine arcs to L0) Diagnostic vacuum chambers with EC suppression methods Designated sections available for installation of test devices Precision instrumentation Multi-bunch turn-by-turn BPM system Fast X-ray beam profile monitors 4 ns bunch train operation CESR-c Damping Wiggler Courtesy of Mark Palmer, Cornell Univ.

Current focus is a 2 year program of ILC DR R&D CesrTA Program II Current focus is a 2 year program of ILC DR R&D Reduction in scope from longer (3.5 year) program proposed to NSF/DOE in July Maintain 3 core research areas: Electron cloud studies Low emittance program (revised target of 20 pm vertical emittance) Development of a fast X-ray beam size monitor Target bunch-by-bunch monitor capable of single-pass measurements for ILC DR Integral to CesrTA program a ultra-low emittance measurements

CesrTA Parameters & Capabilities Baseline Configuration Parameters: Baseline optics at 2 GeV for ultra low emittance studies Energy flexibility will allow EC growth studies at 5 GeV as specified for the ILC DR Parameter Value No. of Wigglers 12 Wiggler Field 2.1 T Beam Energy 2.0 GeV Energy Spread (DE/E) 8.6 x 10-4 Target Vertical Emittance <20 pm Horizontal Emittance 2.3 nm Damping Time 47 ms Bunch Spacing 4 ns Bunch Length 9 mm Multi-bunch turn-by-turn BPM EC Measurements 1.2 x 1010 e+/bunch @ 1.9 GeV EC Measurements: Multi-bunch turn-by-turn instrumentation has been commissioned Measured vertical tune shift along a train generating the electron cloud and for witness bunches trailing the train at various intervals

CesrTA Summary CesrTA program presently ramping up R&D Targets: Now through mid-2009 Complete low emittance machine reconfiguration and upgrades Deploy and commission instrumentation needed for low emittance program Study EC growth studies in wigglers, dipoles, quadrupoles and drift regions in CESR Initial EC mitigation studies Mid-2009 through April 1, 2010 Work towards progressively lower emittance operation Complete EC mitigation studies EC beam dynamics studies at the lowest achievable emittances Immediate focus: Engineering preparation for machine reconfiguration Preparation/testing of EC vacuum chambers, vacuum diagnostics, and beam instrumentation Work on Data-Simulation Comparisons Seeing qualitative agreement with shape of EC growth/decay and vertical tune shift data from witness bunch studies ECLOUD Simulation CESR Dipole Region Courtesy of Mark Palmer, Cornell Univ.

R&D program in the SPS CERN Since beam scrubbing in the SPS is limited, the goal is to install a material with low SEY values from the start: not possible to bake vacuum chambers, Laboratory SEY measurements Simulations of electron cloud build-up and instabilities Tests in the PS and SPS in magnets regions and instrumented chambers with: Clearing electrodes on enamel substrate Carbon coatings TiN and coatings Triangular grooves E. Chapochnikova, G. Arduini, M. Jimenez, J.M. Laurent, F. Caspers, Mahner, E. Benedetto, D. Schulte, A. Rossi, G. Rumolo, R. Thomas, P. Chiggiato, T. Kroyer, M. Taborelli, F. Zimmermann, M. Pivi and L. Wang (SLAC), M. Venturini (LBNL)

Summary Measured resonances similar as predicted by simulations: in the DR, the arc magnetic field can be tuned such as to seat at a resonance minimum, to reducing the electron cloud density by a factor ~2-3. Rectangular groove very effective at further decreasing the electron cloud in field free. Conditioning in PEP-II (with photons) decreases the SEY below 1 on TiN coating and very stably in time; SEY of NEG close to 1. Looking forward to future tests at CERN, KEK and at CesrTA operating at ultralow emittancies.

T. Raubenheimer, J. Seeman, Thanks! to F. Zimmermann, G. Arduini, E. Chapochnikova and to: M. Furman, M. Venturini, C. Celata, N. Kurita, G. Stupakov, K. Harkay, B. McKee, G. Collet, K. Jobe, K. Ohmi, A. Wolski, R. Macek, J. Ng, L. Wang, B. Smith, B. Kuekan, M. Munro, W. Wittmer, D. Arnett, J. Olszewski, Wallace, D. Kharakh, C. Spencer, T. Raubenheimer, J. Seeman, R. Kirby, F. Cooper, F. King H. Braun, J. M. Laurent, N. Hilleret, M. Jimenez, F. Caspers, Mahner, E. Benedetto, D. Schulte, A. Rossi, G. Rumolo, R. Thomas, P. Chiggiato, M. Morvillo, M. Taborelli, A. Latina and many other colleagues ..