Non Gaussian transverse distributions in a stochastic model for

ISBN 92-9083-231-2 (Web version)
ISBN 92-9083-232-0 (CD-ROM version)
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Published by the European Physical Society Accelerators Group (EPS-AG) and CERN.
CONFERENCE ORGANIZATION
Organized by
Paul Scherrer Institut (PSI), Villigen
Under the Auspices of
European Physical Society
Supported by
BESSY
CCLRC (ISIS & ASTeC)
CEA DSM
CERN
DESY
ELETTRA
ESRF
FZ Jülich
FZ Karlsruhe
GSI
Chairman Organizing Committee
Chairman Scientific Programme Committee
Chairman Local Organizing Committee
EPAC Conference Coordinator
INFN
MSL
Novartis
PSI
Roche
Synchrotron Soleil
Serono
Swiss International Air Lines
Syngenta
LeonidRivkin, PSI
Christopher Prior, ASTeC CCLRC RAL & Trinity College Oxford
Hans-Arno Synal, ETH & PSI
Christine Petit-Jean-Genaz, CERN
ORGANIZING COMMITTEE
C.Biscari, INFN-LNF, K. Blasche*, GSI, C.Bocchetta*, Sincrotrone Trieste, J. Bordas, LSB-IFAE, R.Brinkmann*,
DESY, H.Danared*, MSL, J.-P.Delahaye*, CERN, J.-M.Lagniel*, CEA, E.Lee*, LBNL, A.Mosnier*, CEA,
S.P.Møller*, ISA, W.Namkung, PAL, C.Pagani*, LASA-INFN, Ch. Petit-Jean-Genaz*, CERN, C. Prior*, ASTeC
CCLRC RAL & Trinity College Oxford, F.Ruggiero*, CERN, Y.Shatunov, BINP, R.Siemann, SLAC, S.Smith*,
ASTeC CLRC DL, H.-A.Synal*, ETH & PSI, U.VanRienen, U. Rostock, T. Weiland, TU-Darmstadt, A.Wrulich,
EPFL & PSI
* Member of the Scientific Programme Committee
LOCAL ORGANIZING COMMITTEE
A.Adelmann, PSI, M.Bugmann, PSI, J.Chrin, PSI, P.Dietrich, PSI, M.Heiniger, PSI, C.Petit-Jean-Genaz, CERN,
J.Poole,CERN L.Rivkin, PSI, G.Schneider, Conventus, D.Vermeulen, PSI, A.Wrulich, EPFL and PSI
SCIENTIFIC ADVISORY BOARD
N. Angert, GSI, R.Assmann, CERN, J.Bergoz, Bergoz Inst., F.Bordry, CERN, P.Burrows, QMUL, J.Byrd, LBNL,
Y.Cho, ANL, L.Dallin, CLS, D.Dinev, INRNE, R.Eichler, PSI, P.Elleaume, ESRF, M.Eriksson, MAX-lab,
J.X.Fang, IHIP, Beijing, G.Fortuna, INFN-LNL, J.Hangst, IPA, Aarhus, H.Henke, TU- Berlin, N.Holtkamp, ORNL,
A.Jackson, ALS, T.Katayama, INS, Tokyo, D.Krämer, BESSY, S.Kulinski, Soltan Inst., S.Y.Lee, IUCF, M.P.Level, Soleil, T.Linnecar, CERN, G. Luijckx, NIKHEF-K, P.Maccioni, CERCA, R.Maier, FZJ, I.Meshkov, JINR,
Y.Mori, KEK, S.Nath, LANL, P.O’Shea, U. Maryland, S.Ozaki, BNL, R. Penco, Ansaldo, F. Perez, FZK-ISS,
L.Picardi, ENEA, N. Pichoff, CEA, M.Poole, ASTeC CLRC DL, P.Raimondi, INFN-LNF, U. Ratzinger, IAP,
T.Raubenheimer, SLAC, D.Reistad, TSL, G.Ryckewaert, U. Louvain, P.Schmüser, DESY, B.Sharkov, ITEP,
Moscow, H.Tanaka, JASRI, S.Tazzari, U. Roma II, M.Tigner, U. Cornell, A.Tkatchenko, IPN, N.Vinokurov, BINP,
R.Walker, Diamond, J. Wei, BNL, T.Weis, U. Dortmund, F.Willeke, DESY, Y. Yamazaki, J-PARC, K.Yokoya,
KEK, C.Zhang, BEPC, F.Zimmermann, CERN
EDITORIAL BOARD
J.Chrin, PSI, Ch.Petit-Jean-Genaz, CERN, J.Poole, CERN, C.Prior, ASTeC CCLRC RAL & Trinity College Oxford,
H.-A.Synal, ETH & PSI
LIST OF PARTICIPANTS
ABO-BAKR, Michael
ABREU, Natalia
ADAMS, Dean
ADELMANN, Andreas
ADOLPHSEN, Chris
AGAPOV, Ilya
AÏT ABDERRAHIM, Hamid
ALEKSANDROV, Vladimir
ALESINI, David
ALEX, Juergen
ALLEN, Curtis
ANDERSON, Oscar
ANDERSSON, Ake
ANDLER, Guillermo
ANGAL-KALININ, Deepa
ANGERT, Norbert
ANTHON, Lars
ARDUINI, Gianluigi
ARKAN, Tug
ARNAUDON, Luca
ARTOOS, Kurt
ASSMANN, Ralph
ATTAL, Maher
AUDITORE, Lucrezia
AUSLENDER, Vadim
AUSSET, Patrick
AYMAR, Robert
BAGLIN, Vincent
BAI, Mei
BALEWSKI, Klaus
BALTATEANU, Nicolae
BANE, Karl
BARON, Eric
BARTH, Winfried
BARTOLINI, Riccardo
BARTOLOME, Maria Sonia
BATHKE, Horst
BAUER, Günter
BAUER, Pierre
BEAUVAIS, Pierre-Yves
BECKER, Reinard
BELLER, Peter
BELLODI, Giulia
BELLOMO, Giovani
BENEDETTO, Elena
BENEDIKT, Michael
BERDEN, Giel
BERG, J. Scott
BERG, Russ
BERGOZ, Julien
BERNAUDIN, Pierre-Emmanuel
BERNHARD, Axel
BERRY, Stéphane
BERTARELLI, Alessandro
BERTONE, Caterina
BERTRAND, Patrick
BESSY
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BETHUYS, Stephane
Thales Electron
BHAT, Chandra
BHATT, Ronak
BIRKEL, Ingrid
BISCARI, Caterina
BIZEN, Teruhiko
BLANDFORD, Roger
BLASCHE, Klaus
BLOKLAND, Willem
BLUEM, Hans
BOCCHETTA, Carlo J
BOGDANOV, Alexander
BOGDANOV, Igor
BÖGE, Michael
BOLSHAKOVA, Inessa
BORISOV, Alexander
BOSLAND, Pierre
BOSOTTI, Angelo
BOUSSON, Sébastien
BOZZINI, Davide
BRAUN, Hans-Heinrich
BRAVIN, Enrico
BREFELD, Werner
BRENNAN, J Michael
BRINKER, Frank
BRINKMANN, Reinhard
BRODBAR, Debbie
BROEMMELSIEK, Daniel
BROOKS, Stephen
BROWN, Kevin
BRUNELLE, Pascale
BRUNI, Christelle
BRUNS, Warner
BUCKLEY, Stephen
BUECHNER, Andree
BULFONE, Daniele
BURROWS, Philip
BYLINSKI, Yuri
CAI, Yunhai
CALAGA, Rama
CALATRONI, Sergio
CAMPMANY, Josep
CAPATINA, Ofelia
CARR, Roger
CARYOTAKIS, George
CASPERS, Fritz
CATALAN LASHERAS, Nuria
CAVENAGO, Marco
CEE, Rainer
CHACON-GOLCHER, Edwin
CHANG, Cheng-Hsiang
CHAO, Yu-Chiu
CHAREYRE, Vincent
CHARNLEY, Graham
CHATTOPADHYAY, Swapan
CHAUTARD, Frederic
CHEL, Stephane
CHEMLI, Samy
FNAL
MIT
Forschungszentrum Karlsruhe
INFN-LNF
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Sincrotrone Trieste
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IHEP
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CHEN, Chiping
CHEN, Sifu
CHOHAN, Vinod
CHUBAR, Oleg
CIANCHI, Alessandro
CIOVATI, Gianluigi
CLARKE, Jim
CLARKE-GAYTHER, Michael
CLAUSER, Tarcisio
CLAYTON, James
COCCOLI, Mirco
CONRADIE, Jl
CORNELL, John
CORSINI, Roberto
COUSINEAU, Sarah
CUFARO PETRONI, Nicola
DALLIN, Les
DALY, Edward
DAMERAU, Heiko
DANARED, Håkan
DANILOV, Viatcheslav
DAVINO, Daniele
DE JONG, Mark
DE MARIA, Riccardo
DE SANTIS, Stefano
DE SIENA, Silvio
DECKER, Franz-Josef
DEHLER, Micha
DEHNING, Bernd
DELAHAYE, Jean-Pierre
DEMMA, Theo
DESMONS, Michel
DEVANZ, Guillaume
DEWA, Hideki
DI GIACOMO, Marco
DIERKER, Steven
DIETRICH, Juergen
DOLINSKYY, Oleksiy
DOUCAS, George
DOVBNYA, Anatoliy
DOWELL, David
DRAGO, Alessandro
DREES, Angelika
DROBA, Martin
DROZHDIN, Alexandr
DRUMM, Paul
DUPERRIER, Romuald
DUTTA, Subhajit
DUVAL, Maurice
DWIVEDI, Jishnu
DYKES, Michael
EICHLER, Ralph
EICKHOFF, Hartmut
EINFELD, Dieter
EKDAHL, Carl
ELLEAUME, Pascal
ELLIS, Malcolm
ELMGREEN-Frederiksen, Henriette
EMMA, Paul
MIT Plasma Sc. & Fusion Center
CAEP
CERN
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INFN-RM2/U. Rome "Tor Vergata"
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Dip. Interateneo di Fisica - Bari
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ENDO, Kuninori
ESPOSITO, Juan
EVTUSHENKO, Pavel
FACCO, Alberto
FAIRCLOTH, Dan
FAN, Tai-Ching
FANG, Zhigao
FARIAS, Ruy
FARTOUKH, Stephane
FAUS-GOLFE, Angeles
FAVALE, Anthony
FEBVRE, Max
FEDURIN, Mikhail
FERDINAND, Robin
FERNANDEZ-HERNANDO, Luis
FERRARIO, Massimo
FILHOL, Jean-Marc
FILIPPINI, Roberto
FINDLAY, David
FISCHER, Wolfram
FISHER, Alan
FLOETTMANN, Klaus
FORCK, Peter
FORKEL-WIRTH, Doris
FOX, John
FRANCHETTI, Giuliano
FRANCHI, Andrea
FRANCO, Jose
FREYBERGER, Arne
FRIIS-NIELSEN, Søren Weber
FUJITA, Kazuhiro
FURUKAWA, Takuji
FUSCO, Valeria
GALAMBOS, John
GALLAGHER, Andrew
GALLO, Alessandro
GALNANDER, Bjorn
GANTER, Romain
GAO, Jie
GEHRING, Michael
GEISLER, Andreas
GENSCH, Ulrich
GEORGSON, Mattias
GHIGO, Andrea
GIBSON, Paul
GIERMAN, Stephen
GILLESPIE, George
GILPATRICK, J. Douglas
GIOVANNOZZI, Massimo
GIOVE, Dario
GJONAJ, Erion
GODDARD, Brennan
GOREV, Vladimir
GOUDKET, Philippe
GOUGH, Christopher
GRANATA, Valeria
GRAU, Silvia
GRAY, James
GREWE, Marc
KEK
INFN-LNL
Forschungszentrum Rossendorf
INFN-LNL
CCLRC RAL
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Advanced Energy Systems, Inc.
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GRIESER, Manfred
GRIFFITHS, Stephen
GRIGORYAN, Bagrat
GRIMM, Oliver
GUBIN, Konstantin
GUENZEL, Thomas
GUIDUCCI, Susanna
GUK, Ivan
GURALIUC, Anda
GUROV, Serge
HAGENBUCK, Frank
HAKULINEN, Timo
HAMDI, Abdallah
HAMPEL, Robert
HAN, Jang Hui
HAN, Sang-Hyo
HANNA, Samy
HARDEKOPF, Robert
HARTEMANN, Fred
HASSE, Rainer W
HAUVILLER, Claude
HAYES, Thomas
HECHT, Dirk
HEINE, Robert
HELMS, Richard
HENDERSON, Stuart
HENDRICKSON, Linda
HENDRIKS, Jimi
HENNING, Walter
HERB, Steve
HERNANDEZ, Michael
HESS, Mark
HILL, Nathan
HITAKA, Yasunobu
HOELZLE, Rainer
HOFFSTAETTER, Georg
HOFLE, Wolfgang
HOFMANN, Albert
HOFMANN, Ingo
HOFSTEE, Mariet
HOLLDACK, Karsten
HOLMES, Jeffrey
HOLMES, Stephen
HOLTKAMP, Norbert
HONKAVAARA, Katja
HUENING, Markus
HÜLSMANN, Dr. Peter
HUTTEL, Erhard
HUTTON, Andrew
IEIRI, Takao
IKEGAMI, Masahiro
INGOLD, Gerhard
INOUE, Kiichiro
IRIE, Yoshiro
ISAWA, Masaaki
IVANOV, Andrey
IVASHCHENKO, Vadim
IWASHITA, Yoshihisa
IWATA, Yoshiyuki
MPI für Kernphysik
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JABLONKA, Marcel
JACKSON, Alan
JAESCHKE, Eberhard
JAGO, Stephen
JANSSEN, Dietmar
JANSSON, Andreas
JENSEN, Jens-Peter
JEON, Dong-O
JOHNSON, Kenneth
JOLY, Jean-Marc
JONES, James
JOST, Edward
KABEL, Andreas
KAIN, Verena
KAKO, Eiji
KALANTARI, Babak
KALANTARYAN, Davit
KALININE, Alexandre
KALTCHEV, Dobrin
KAMPS, Thorsten
KANG, Heung-Sik
KARANTZOULIS, Emanuel
KARATAEV, Pavel
KASHINSKIY, Daniil
KASPAR, Klaus
KAUL, Ortwin
KAWAKUBO, Tadamichi
KAZIMI, Reza
KEIL, Boris
KEIL, Eberhard
KEIL, Joachim
KELLER, Roderich
KEMPKES, Allison
KEMPSON, Vince
KESTER, Oliver
KEWISCH, Jorg
KHAN, Shaukat
KIM, Do Tae
KIM, Dong-Eon
KIM, Eun-San
KIM, Jincheol B
KIM, Suk Hong
KIMBER, Andrew
KISHIRO, Junichi
KITAMURA, Hideo
KITEGI, Charles
KLEIN, Hans-Udo
KLEIN, Horst
KLEIN, Roman
KLOTZ, Wolf-Dieter
KNASTER, Juan
KNOBLOCH, Jens
KOBAYASHI, Toshiaki
KOBETS, Andriy
KOHLER, Claude
KONDRASHEV, Sergei
KORCHUGANOV, Vladimir
KORHONEN, Timo
KOSCHIK, Alexander
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IOP Publishing
SLAC
CERN
KEK
Paul Scherrer Institut
CANDLE
CCLRC DL
TRIUMF
BESSY
PAL,POSTECH
Sincrotrone Trieste
Tokyo Metropolitan University
ITEP
GSI
DESY
KEK
Jefferson Lab
Paul Scherrer Institut
CERN
DESY
LBNL
Diversified Technologies, Inc.
Diamond Light Source
LMU München
BNL
BESSY
PAL POSTECH
PAL POSTECH
PAL POSTECH
PAL POSTECH
ANL
CCLRC RAL
KEK
RIKEN/SPring-8
IAP
ACCEL Instruments GmbH
IAP
PTB
ESRF
CERN
BESSY
SPring-8/JASRI
JINR
Alstom Magnets, Superconductors
ITEP
BINP
Paul Scherrer Institut
CERN
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KOSCIELNIAK, Shane
KOSTKA, Barbara
KOVALENKO, Alexandre
KRÄMER, Dieter
KRASILNIKOV, Mikhail
KREMPASKY, Juraj
KRISCHEL, Detlef
KUBLER, Kristina
KUEHNEL, Kai-Uwe
KUNZE, Marco
KUO, Changhor
KURODA, Ryunosuke
KUROKAWA, Shin-ichi
KUSHNIR, Volodymyr
KUSKE, Peter
KVARDAKOV, Vasily
KWIATKOWSKI, Slawomir
LA CHINA, Marco
LAGNIEL, Jean-Michel
LAMBERT, Guillaume
LAMY, Thierry
LARI, Luisella
LAU, Thomas
LAVERTY, Michael
LAWSON, Wesley
LEBEDEV, Valeri
LEBLANC, Greg
LEBRUN, Paul L. G
LEBRUN, Philippe
LEE, Eunhee
LEE, Seishu
LEE, Tae Yeon
LEIBFRITZ, Jerry
LESREL, Jean
LESSNER, Eliane
LEYH, Greg
LI, Ming
LI, Yanxia
LI, Yongjun
LI, Zenghai
LIDESTRI, Joseph
LILJE, Lutz
LINDROOS, Mats
LLEWELLYN SMITH, Christopher
LOMBARDI, Augusto
LOPES, Mauricio
LOWENSTEIN, Derek
LÜDEKE, Andreas
LUITEN, Jom
LYAKIN, Dmitry
LYLES, John
MACCAFERRI, Remo
MACLEOD, Allan
MAHNER, Edgar
MAIER, Hubert
MANGLUNKI, Django
MANINI, Paolo
MANOLA-POGGIOLI, Elena
MARCELLINI, Fabio
TRIUMF
Forschungszentrum Karlsruhe
JINR
BESSY
DESY
Paul Scherrer Institut
ACCEL Instruments GmbH
SLAC
IAP
TU Darmstadt
NSRRC
Waseda University
KEK
NSC KIPT
BESSY
BINP
LBNL
CERN
CEA
CEA
CNRS-IN2P3
CERN
TU Darmstadt
TRIUMF
University of Maryland
FNAL
ASP
FNAL
CERN
PAL POSTECH
KEK
PAL,POSTECH
FNAL
IPN
ANL
SLAC
CAEP
CPI Inc.
DESY
SLAC
Columbia University
DESY
CERN
UKAEA
INFN-LNL
LAL - IFUSP
BNL
Paul Scherrer Institut
TU Eindhoven
GSI
LANL
CERN
University of Abertay
CERN
Schulz-Electronic GmbH
CERN
Saes Getters Spa
CERN
INFN-LNF
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MARCHAND, Patrick
MARDOR, Israel
MARHAUSER, Frank
MARKS, Neil
MARQUE, Sebastien
MARTI, Zeus
MARTIN, Ian
MARTIN, Siegfried
MASULLO, Maria Rosaria
MATHIAS, Brandin
MAURI, Marco
MCGAHERN, William
MEDDAHI, Malika
MELIKYAN, Robert
MERMINGA, Lia
MERTENS, Volker
MERZ, Wolfhard
MESECK, Atoosa
MESHKOV, Igor
MESHKOV, Oleg
MICHALCZYK, Pierre
MIKHAYLOV, Vladimir
MILARDI, Catia
MINTY, Michiko
MISHIN, Andrey
MITSUHASHI, Toshiyuki
MIURA, Sadao
MOLODOZHENTSEV, Alexendre
MONDELAERS, Wim
MONTAG, Christoph
MORGAN, Alun
MORITZ, Gebhard
MORRIS, William
MOSER, Herbert O
MOSNIER, Alban
MOUAT, Mike
MUELLER, Anke-Susanne
MUELLER, Norbert
MUELLER, Wolfgang
MUÑOZ, Marc
MURATORI, Bruno
MURDOCH, Graeme
MURPHY, James
MUSTAFIN, Edil
MUTO, Toshiya
MYERS, Stephen
MYTSYKOV, Andriy
NADJI, Amor
NAGAITSEV, Sergei
NAGAOKA, Ryutaro
NAKAMURA, Norio
NAKAMURA, Takeshi
NAKAYAMA, Masahiko
NAM, Sang Hoon
NEFF, Stephan
NEMTANU, Monica
NESMIYAN, Inna
NEUMANN, Axel
NEZHEVENKO, Oleg
Synchrotron SOLEIL
Soreq NRC
BESSY
CCLRC DL
CERN
CELLS
Diamond Light Source
Forschungszentrum Jülich
INFN
MAX-Lab, Lund University
INFN-LASA
BNL
CERN
YerPhI
Jefferson Lab
CERN
DESY
BESSY
JINR
BINP
TPC
JINR
INFN-LNF
DESY
American Science and Engineering
KEK
Mitsubichi Heavy Industries, Ltd.
KEK
CEC-JRC-IRMM
BNL
Diamond Light Source
GSI
CCLRC RAL
Singapore SLS
CEA
TRIUMF
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IAP
TU Darmstadt
CELLS
CCLRC RAL
ORNL
BNL
GSI
KEK
CERN
NSC KIPT
Synchrotron SOLEIL
FNAL
Synchrotron SOLEIL
ISSP, University of Tokyo
JASRI
Hitachi Ltd.
PAL, POSTECH
TU Darmstadt
Inst. Lasers, Plasma and Rad. Phys.
GSI
BESSY
Omega-P, Inc.
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NGUYEN, Quyet Huu
NICQUEVERT, Bertrand
NIELSEN, Bjarne Roger
NIELSEN, Jørgen S
NIKITIN, Sergei
NINOMIYA, Shigeshi
NISBET, David
NODA, Akira
NODA, Koji
NOREM, Jim
NORTON, Peter
OHKAWA, Tomohiro
OHMORI, Chihiro
OHSHIMA, Takashi
OHUCHI, Norihito
OLRY, Guillaume
OLSEN, David
ONISHCHENKO, Nikolay
ORTEGA, Jean-Michel
OSTROUMOV, Peter
OVSYANNIKOV, Vladimir
OWEN, Hywel
OZAKI, Satoshi
PAAL, Andreas
PAGANI, Carlo
PAI, Chien-Ih
PALMIERI, Antonio
PALUMBO, Luigi
PAN, Jian
PAPAPHILIPPOU, Ioannis
PAPE MØLLER, Søren
PARALIEV, Martin
PARK, In Soo
PARK, Ki-Hyeon
PASCUAL, Ramon
PASINI, Matteo
PAYET, Jacques
PEACH, Ken
PEDROZZI, Marco
PEGGS, Stephen
PEINIGER, Michael
PELLEGRINO, Luigi
PEREZ, Francisco
PERRON, Thomas
PETIT-JEAN-GENAZ, Christine
PETRENKO, Alexey
PETROSYAN, Marzik
PETTERSSON, Thomas
PHINNEY, Nan
PICARDI, LUIGI
PICHOFF, Nicolas
PICKULIN, Eugene
PIELONI, Tatiana
PIVI, Mauro
PIVIN, Roman
PLOUVIEZ, Eric
PODGORNY, Fedor
PODLECH, Holger
POIRIER, Roger
Univ. Tokyo
CERN
DANFYSIK A/S
ISA, University of Aarhus
BINP
KEK
CERN
ICR, Kyoto University
NIRS
ANL
CCLRC RAL
JAERI
KEK
JASRI/SPring-8
KEK
CNRS/IN2P3
ORNL
NSC KIPT
CNRS
ANL
Leybold Vakuum Dresden GmbH
CCLRC DL
BNL
MSL
INFN & DESY
BNL
INFN-LNL
U. Roma La Sapienza & INFN-LNF
CAEP
ESRF
ISA, University of Aarhus
Paul Scherrer Institut
PAL,POSTECH
PAL,POSTECH
ALBA Synchotron
Sektion Physik LMU
CEA
CCLRC RAL
Paul Scherrer Institut
BNL
ACCEL Instruments GmbH
INFN-LNF
CELLS
ESRF
CERN
BINP
YerPhI
CERN
SLAC
ENEA
CEA
LETI
University of Milan / CERN
SLAC
JINR
ESRF
BINP
IAP
TRIUMF
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POLOZOV, Sergey
PONT, Montserrat
POOLE, John
POOLE, Mike
PÖPLAU, Gisela
POPOV, Eugeni
POPOVIC, Milorad
PORCELLATO, Anna Maria
PRIOR, Christopher
PROCH, Dieter
QUAST, Torsten
QUATTROMINI, Marcello
QUINN, Eamonn
RAGUIN, Jean-Yves
RAIMONDI, Pantaleo
RAMOS, Délio
RATHJEN, Christian
RAUBENHEIMER, Tor
RE, Maurizio
REDAELLI, Stefano
REHM, Guenther
REICHEL, Ina
REICH-SPRENGER, Hartmut
REISTAD, Dag
REMONDINO, Vittorio
REPNOW, Roland
RESENDE, Ximenes
REVA, Vladimir
RIJLLART, Adriaan
RIMJAEM, Sakhorn
RIMMER, Robert
RIVKIN, Leonid
ROBERT-DEMOLAIZE, Guillaume
RODRIGUEZ, Jose Alberto
ROHMIG, Peter
RONSIVALLE, Concetta
ROSER, Thomas
ROSSBACH, Jorg
ROSSI, Lucio
ROSSMANITH, Robert
ROTH, Markus
ROULEAU, Gary
ROUX, Raphaël
RUGGIERO, Alessandro G
RUGGIERO, Francesco
RUMOLO, Giovanni
RUSSO, Thomas
SABJAN, Rok
SAFRANEK, James
SAHOO, Gajendra Kumar
SAITO, Kazuyoshi
SAKAI, Fumio
SAKAI, Hiroshi
SAKAI, Izumi
SAKANAKA, Shogo
SAKAUE, Kazuyuki
SANNIBALE, Fernando
SANTRICH, Alejandro
SATO, Akira
MEPHI
CELLS
CERN
CCLRC DL
Universität Rostock
A.F. Ioffe Physicotechnical Inst.
FNAL
INFN-LNL
CCLRC RAL
DESY
BESSY
ENEA
CCLRC RAL
Paul Scherrer Institut
INFN-LNF
CERN
CERN
SLAC
INFN-LNS
CERN
Diamond Light Source
LBNL
GSI
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MPI for Nuclear Physics
LNLS
BINP
CERN
FNRF
Jefferson Lab
Paul Scherrer Institut
CERN
NSCL
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ENEA
BNL
Universitat Hamburg
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Forschungszentrum Karlsruhe
TU Darmstadt
LANL
LAL
BNL
CERN
GSI
BNL
Josef Stefan Institute / Cosylab
SLAC/SSRL
DESY
Hitachi Ltd.
SHI
ISSP, University of Tokyo
KEK
KEK
Waseda university
LBNL
CERN
Osaka University
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SATOGATA, Todd
SAUER, Andreas
SAVERSKIY, Aleksandr
SAWAMURA, Masaru
SCANDALE, Walter
SCARAMUZZI, Paolo
SCHEMPP, Alwin
SCHILCHER, Thomas
SCHIRMER, Detlev
SCHLOTT, Volker
SCHMIDT, Rudiger
SCHMIDT, Thomas
SCHNEEKLOTH, Uwe
SCHNEPP, Sascha
SCHREIBER, Siegfried
SCHULTZ, David
SCHWICKERT, Marcus
SCIBILE, Luigi
SCOTT, Duncan
SCRIVENS, Richard
SEIDEL, Mike
SEKUTOWICZ, Jacek
SELEZNEV, Igor
SENITCHEV, Yurij
SERMEUS, Luc
SERRIERE, Vincent
SERTORE, Daniele
SESSLER, Andrew
SETTY , Andrew
SHAPOSHNIKOVA, Elena
SHATUNOV, Yuri
SHEA, Thomas
SHELDRAKE, Ron
SHEPHERD, Ben
SHERMAN, Joseph
SHEVTSOV, Vladimir
SHILTSEV, Vladimir
SHIMOSAKI, Yoshito
SHINTO, Katsuhiro
SHIRAI, Toshiyuki
SHIRAKABE, Yoshihisa
SHIRAKATA, Masashi
SHIRKOV, Grigori
SHIROKOV, Valery
SHOJI, Yoshihiko
SIDOROV, Alexei
SILZER, Ricard Mark
SIMONOV, Karl
SIMONSSON, Ansgar
SIMROCK, Stefan
SINYATKIN, Sergey
SKOCZEN , Blazej
SKOV, Henrik
SMALUK, Victor
SMEDLEY, John
SMITH, Kevin S
SMITH, Robert J
SMITH, Susan
SOBENIN, Nickolay
BNL
IAP
American Science and Engineering
JAERI
CERN
Università degli Studi di Milano
Univ. Frankfurt
Paul Scherrer Institut
University of Dortmund
Paul Scherrer Institut
CERN
Paul Scherrer Institut
DESY
TU Darmstadt
DESY
SLAC
GSI
CERN
CCLRC DL
CERN
DESY
DESY
JINR
Forschungszentrum Jülich
CERN
ESRF
INFN-LASA
LBNL
Thales Communications
CERN
BINP
ORNL
e2v technologies Ltd.
CCLRC DL
LANL
JINR
FNAL
KEK
LNS, Tohoku University
ICR, Kyoto University
KEK
KEK
JINR
BINP
LASTI, University of Hyogo
JINR
CLS
FSUE "RPC "Istok"
MSL
DESY
BINP
CERN
DANFYSIK A/S
BINP
BNL
BNL
CCLRC DL
CCLRC DL
MEPHI
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SORTAIS, Pascal
SPANGGAARD, Jens
SPILLER, Peter
SPREHN, Daryl
STANCARI, Giulio
STASSEN, Rolf
STECK, Markus
STEFFEN, Bernd
STEIER, Christoph
STEINER, Bastian
STEINHAGEN, Ralph
STEINMANN, Erik
STOVALL, James
STOWISEK, Jan
STRAIT, James
STREUN, Andreas
SUBERLUCQ, Guy
SUETSUGU, Yusuke
SUH, Hyung Suck
SULLER, Victor
SUZUKI, Shinsuke
SUZUKI, Toshio
SVANDRLIK, Michele
SYNAL, Hans-Arno
SYRESIN, Evgeny
SZELESS, Balazs
TABORELLI, Mauro
TAHIR, Naeem
TAKANO, Junpei
TAKAO, Masaru
TAKEDA, Shigeru
TAKEUCHI, Takeshi
TALANOV, Vadim
TALMAN, Richard
TANAKA, Hitoshi
TANIGAKI, Minoru
TANTAWI, Sami
TARAWNEH, Hamed
TAVARES, Pedro
TEICHERT, Jochen
TENENBAUM, Peter
TEYTELMAN, Dmitry
THEED, Justin
THIBUS, Jan
THOENER, Manfred
THOMAS, Chris
THOMASON, John
THOMPSON, Neil
TILLEY, Kevin
TKACHENKO, Leonid
TKATCHENKO, André
TOCK, Jean-Philippe
TOELLE, Raimund
TONUTTI, Manfred
TORDEUX, Marie-Agnes
TORIKAI, Kota
TORNOE, Bob
TOYAMA, Takeshi
TRIFIRÒ, Antonio
IN2P3
CERN
GSI
SLAC
U. Ferrara and INFN Legnaro
Forschungszentrum Jülich
GSI
DESY
LBNL
TU Darmstadt
CERN
DANFYSIK A/S
ORNL
CERN
FNAL
Paul Scherrer Institut
CERN
KEK
PAL,POSTECH
CAMD
SPring-8/JASRI
KEK
Sincrotrone Trieste
ETH / Paul Scherrer Institut
JINR
CERN
CERN
GSI
Tokyo Institute of Technology
SPring-8/JASRI
KEK
ICR, Kyoto University
IHEP
Cornell University
JASRI
RRI, Kyoto University
SLAC
MAX-Lab, Lund University
LNLS
Forschungszentrum Rossendorf
SLAC
SLAC
CCLRC DL
IAP
EAS
CCLRC RAL
CCLRC RAL
CCLRC DL
CCLRC RAL
IHEP
CNRS/IN2P3/IPNO
CERN
Forschungszentrum Jülich
RWTH Aachen
Synchrotron SOLEIL
KEK
CPI Inc.
KEK
INFN- Gruppo Colleg. di Messina
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Proceedings of EPAC 2004, Lucerne, Switzerland
NON GAUSSIAN TRANSVERSE DISTRIBUTIONS
IN A STOCHASTIC MODEL FOR BEAM HALOS
N. Cufaro Petroni, Bari University, INFN Sez. Bari, Italy
S. De Martino, S. De Siena, and F. Illuminati, Salerno University, INFN Sez. Napoli, Italy
Abstract
We face, in a stochastic framework, the problem of the
halo formation in high intensity beams of charged particles.
We sum up our recent results on this argument, and in the
final part of the paper we introduce non Gaussian distributions as good candidates to account for sensible escape of
particles from the density core.
have adapted our scheme to a preliminary study of the problem of halo formation and control, and we have described
the collective, not deterministically controllable effects by
diffusive (Gaussian) fluctuations. In the present paper we
make the hypothesis that non–Gaussian processes, for example the family of the Student distributions, with longer
tails and non-zero jump probability could provide a better
understanding of the long–distance particle behavior.
INTRODUCTION
STOCHASTIC MODEL FOR HALOS
In high intensity beams of charged particles, proposed in
recent years for a wide variety of accelerator–related applications, it is very important to keep at low level the beam
loss to the wall of the beam pipe, since even small fractional losses in a high–current machine can cause exceedingly high levels of radioactivation. However, numerical
simulations, and a few experiments at high current proton linacs, suggest that an extended, low–density halo is
formed around the beam: it is then necessary to obtain a
more quantitative understanding of the physics of the halo,
in order to control and reduce its undesirable effects. In recent papers [1, 2] we faced this problem in the framework
of a stochastic approach to the collective beam dynamics. Charged particle beams are usually described either
in terms of classical dynamical systems, i. e. by a collisionless plasma with the dynamics of a suitable phase space, or
by a Fokker–Planck equation in the phase–space variables.
In our alternative approach [3] we propose instead to describe the collective dynamics of the particle beams by a
stochastic and time–reversal invariant description in configuration space. This picture is effective in the regime of
stability, where a balance is realized between the energy
dissipation and the external energy pumping. The sample paths of the representative particle are described by a
diffusive stochastic differential equation ruled by the beam
emittance, and the two coupled stochastic–hydrodynamic
equation describing the dynamics of the beam density profile and the motion of its center are derived by a stochastic variational principle [4]. The two coupled equations
are also equivalent to a unique linear equation of the form
of a (mesoscopic) Schrödinger equation, with the universal Planck constant replaced by the emittance of the beam.
Our approach, starting by an apparently different point of
view, formally converges then to the so–called quantum–
like approach to beam dynamics [5]. In the framework of
our scheme is also possible to implement an active control for the beam dynamics [6], an aspect which could be
useful in order to eliminate halos. In references [1, 2] we
The coupled stochastic–hydrodynamic equations derived by the stochastic variational principle [4] and describing the particle beam dynamics in the stability regime [3]
take the form , respectively, of a continuity equation:
∂t ρ = −∇ · (ρv) ,
(1)
and of an evolution (Madelung) equation for the conservative dynamics
√
∇2 ρ
m
+ V (r, t) = 0 ,
(2)
∂t S + v2 − 2mD2 √
2
ρ
where , if m is the mass of a particle, the drift velocity
and the (Jacobi-Madelung) function S are connected by the
gradient form mv = ∇S, and the diffusion coefficient is
proportional to the beam emittance α: α = 2mD. Eqns.
(1) and (2) describe the collective behavior of the beam at
each instant of time through the evolution of both its particle density and its velocity field. Introducing the repre√
sentation ψ = ρ eiS/α , the two coupled real equations
(1) and (2) are equivalent to a single complex Schrödinger
equation for the function ψ, with the Planck action constant
h̄ replaced by the unit of action α:
iα∂t ψ = −
α2 2
∇ ψ+Vψ.
2m
(3)
In this “Schrödinger-like” (Sl) formulation the phenomenological “wave function” ψ carries the information on the
dynamics of both the beam density and the beam velocity
field, since the velocity field is determined via the gradient
relation by the phase function S.
Space–charge effects
Among the various possible sources of halos, in [1] we
have taken into account the spreading effects due to the
presence of a space–charge distribution in the framework
of our approach. We have implemented the Sl-equation (3)
2056
Proceedings of EPAC 2004, Lucerne, Switzerland
1
associated potential and of the associated velocity fields.
The potential exhibits an extra relative maximum if compared with the harmonic one, while in correspondence the
velocity field exhibits a “bump” with respect to the straight
(linear) behavior.
0.8
0.6
0.4
s w2 +s/
Dynamical control of the halo
0.2
s
1
2
3
4
5
Figure 1: The radial distribution s w2 (s) compared with
the distribution in absence of space charge (dashed line)
for a strong space-charge strength . All quantities are dimensionless.
in a cylindrically symmetric configuration and coupled it
with the Maxwell equations for the electromagnetic field
generated by the charge distribution. We have thus obtained two nonlinear coupled equations. Considering the
stationary distribution of the particle density, we have obtained that the density profile associated to the presence of
space–charge is sensibly spread with respect to the Gaussian profile obtained if space–charge is absent (see Fig. 1).
The distribution exhibits a larger dispersion, and we have
shown that, for sufficiently intense charge density, we can
find up to 105 particles per meter beyond a distance of 10σ
(with σ denoting the width of the Gaussian core), at variance with the zero particles in absence of charge effects.
Stationary halo distributions
The solutions discussed in the previous subsection have
been obtained through a numerical approach, because the
nonlinearly coupled equations do not allow for exact analytical solutions. In the same reference [1] we have then
also employed a variational technique to obtain an approximate analytical version of the numerical solution for the
density profile. In fact, an analytic expression for the density profile leads to analytical forms for the drift velocity
and the generating potential, which in turn are needed if
one wish to engineer a controlling mechanism to eliminate
the halo. We have then optimized a reasonable test form
for the density profile, and we have found that the variational solutions show the presence of a node in the density
profile, and a corresponding singularity in the potential. A
node can be the signature for the presence of a ring–shaped
halo, well separated by the core; in fact, it is completely
open the question if halo is due to long tails in the density distribution, or if a true halo must be separated from
the core. On the other hand, we have obtained a tail by
space–charge effects, which however are not the only possible source of halo. Then, in the spirit of a preliminary inquiry about both the interpretations, we have reversed our
point of view; we have in fact explicitly introduced a realistic ring distribution, and we have used the dynamical
equations to obtain information on the characteristics of the
In reference [2] we have extended our analysis to the
problem of the halo dynamics, considering both the the
halo elimination and its reformation. This last problem
cannot be accounted for in a pure Quantum–like (Ql) description since, because of the stochastic extremal principle, a change in the distribution produces a change in the
dynamics. On the other hand the Ql dynamics leads to
distributions which are stable attractors; thus, the halo, if
scraped away, will be restored in characteristic times, but
through a not extremal Fokker–Planck evolution. We have
then accordingly modified our scheme: the velocity field
changes slowly on the relaxation time scales, while the evolutions are ruled only by a Fokker–Planck equation until the
balance has been restored. We got an estimate of the time
τ needed by a non stationary, halo–free distribution to relax toward the stationary distribution with a halo when the
dynamics is supposed frozen in the configuration that produces this halo: we have obtained τ ≈ 10−8 ÷10−7 sec [2].
Since this relaxation time depends on the parameters of our
beam, a comparison with possibly measured phenomenological times could constitute a good check on the soundness of the model. We have also begun to analyze possible
transitions from a beam with halo toward a halo–free one,
putting an emphasis on the possible dynamics which allows
this halo elimination.
NON GAUSSIAN DISTRIBUTIONS
Non gaussian stationary states
Values of the maximum-to-RMS ratio as large as 10 or
12 have been observed in simulations and it is generally
agreed that this is called halo (see [8] p. 286). Hence there
are good reasons to try non gaussian transverse distributions with longer tails so that the probability of finding particles far away from the beam axis becomes larger. Generalized Student distributions Σ(ν; a2 )
Γ ν+1
aν
2 f (x) = √
ν > 0.
(4)
ν+1 ,
π Γ ν2 (a2 + x2 ) 2
are good candidates. They have finite variance σ2 only for
ν > 2 and a2 = (ν − 2)σ 2 . Moreover Σ(ν, (ν − 2)σ 2 )
converges in distribution to N (0, σ 2 ) for ν → +∞. The
radial control potential for a stationary cylindrical beam:
2
2
r
σ
α2 2
ν−2 + (ν + 10) 4
r
(ν
+
2)
Vν (r) =
2
2mσ 2
[r2 + (ν − 2)σ 2 ]
tends to be harmonic for ν → +∞, and is constant beyond
a certain radius. This possibly points to some effect due to
the presence of the conducting walls.
2057
Proceedings of EPAC 2004, Lucerne, Switzerland
Lévy driven processes
The trajectories of a process with a stationary Student
Σ(ν, (ν − 2)σ 2 ) ground state can be simulated from the
Gaussian driven SDE
√
dX(t) = vν (X(t))dt + 2D dW (t)
-100
-200
-300
with suitable velocity field. On the other hand a different kind of process can be generated by independent increments with Student law (4) through a SDE
Figure 2: Student process with ν = 2.0
dX(t) = β(X(t))dt + γ dS(t)
125
where dS(t) is distributed according to Σ(ν; a2 ), and β(x)
is a suitable velocity field. No complete theory is available
for a Lévy driven stochastic mechanics.
The Student distributions Σ(ν; a2 ) are infinitely divisible (Lévy distributions) [9]. Hence they are possible limit
distributions of row-sums of r.v.’s, but different from the
gaussian. As every infinitely divisible law, the Σ(ν; a2 )
are possible distributions of the increments of a Markov
process with independent increments (Lévy process) [10].
Non-gaussian Lévy processes have moving discontinuities:
only gaussian Lévy processes have almost every trajectory everywhere continuous [11]. The standard example
of a non-gaussian Lévy process is the compound Poisson
process. The rate of occurrence, and the height of the
moving discontinuities are regulated by the Lévy function
Lt (x) characteristic of a given process with independent
increments [11]. However the Lévy function of a Student
Σ(ν; a2 ) process is not explicitly known.
Discontinuities in these processes can be used to describe the occasional escape of particles out from an otherwise well collimated beam in an accelerator. Moreover, by
suitably tuning the parameters (a and ν) we can also keep
the transverse distribution of the beam reasonably close to a
gaussian. We can contrast the trajectories for both a Gauss
and a Student process with comparable dispersions. In the
Figures 2, 3 a few examples of the Student trajectories are
produced. Since for fixed a the Student variance (which
diverges for 0 < ν ≤ 2) is a decreasing function of ν, it is
apparent that also the jump probability and their length will
generally decrease with ν. The Figures for ν > 2 (finite,
decreasing variance) are selected among the possible cases
by excluding all the trajectories showing an almost gaussian behavior. For ν > 2 several trials are needed before
getting a trajectory definitely drifting away from the beam
core.
In this model we suppose that a Student-Lévy noise
will be active only inside the beam, while beyond a given
distance from the core the process will be driven by a
Gauss noise; moreover the velocity field attracts the trajectory back toward the core only in its neighborhood, while
beyond a given distance the process is just a free diffusion. Remark that in this example the Gaussian trajectories
would be essentially that of an Ornstein–Uhlenbeck process.
100
75
50
25
Figure 3: Student process with ν = 3.0
We conclude by remarking that in our opinion for a halo
model the possibility of rare, long jumps in the trajectories is more relevant than just the modest increase in the
variance produced by the Student noise with respect to the
Gauss (almost everywhere continuous) noise.
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[3] N. Cufaro Petroni, S. De Martino, S. De Siena, and F. Illuminati, Phys. Rev. E 63, 016501 (2001)
[4] F. Guerra and L. M. Morato, Phys. Rev. D 27, 1774 (1983);
E. Nelson, Quantum Fluctuations (Princeton University
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[5] R. Fedele, G. Miele and L. Palumbo, Phys. Lett. A 194, 113
(1994), and references therein; S. I. Tzenov, Phys. Lett. A
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[6] N. Cufaro Petroni, S. De Martino, S. De Siena, and F. Illuminati, J. Phys. A 32, 7489 (1999).
[7] N. Cufaro Petroni, S. De Martino, and S. De Siena, Phys.
Lett. A 245, 1 (1998).
[8] T. Wangler, RF Linear accelerators (Wiley, New York
1998).
[9] L. Bondesson, Generalized gamma distributions and related
classes of distributions and densities (Springer, New York
1992).
[10] W. Feller, An introduction to probability theory and its applications - vol. II 2nd edition (Wiley, New York 1971).
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