Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Investigation of electron beam emittance and acceleration in interaction of an energetic proton beam with plasma

Document Type : Research Paper

Author

A. Kargarian

Plasma and Nuclear Fusion Research School, Nuclear Science and Technology Research Institute, P.O.Box: 14399-51113, Tehran - Iran

https://doi.org/10.24200/nst.2024.1599
Abstract
Plasma accelerators are using high-energy proton beams as driven beams to produce plasma waves. In this approach, the proton beam energy is transferred through the formed plasma wave to the witness electron beam for achieving high energies. In this paper, using two-dimensional particle simulation, the interaction of a Gaussian high-energy ion beam with plasma containing linear density with a density gradient of 0.03% along the beam propagation direction has been investigated in order to produce a high energy electron beam with excellent quality. To investigate electron acceleration, an 18 MeV witness electron beam is sent to the plasma at the back of the ion beam. The simulation results show that, due to the interaction of the energetic proton beam with plasma, the strong plasma wave field with amplitude 400 MeV/m is created. This field accelerates the trapped electrons of witness beam to high energy gradients of several hundred MeV. Moreover, the evolution of the electron beam emittance as an important parameter in the investigation of the accelerated beam quality, indicates that by considering the appropriate parameters for the plasma, proton and electron beams, the emittance of the witness electron beam grows less than 50% compared to its initial value.

Highlights

  1. Kurz T, Heinemann T, Gilljohann M.F, Chang Y.Y, Couperus Cabadağ J.P, Debus A, Kononenko O, Pausch R, Schöbel S, Assmann R.W, Bussmann M, Ding H, Götzfried J, Köhler A, Raj G, Schindler S, Steiniger K, Zarini O, Corde S, Döpp A, Hidding B, Karsch S, Schramm U, Martinez de la Ossa A, Irman A. Demonstration of a compact plasma accelerator powered by laser-accelerated electron beams. Nat. commun. 2021;12:2895.

 

  1. Tajima T, Dawson J.M. Laser electron accelerator. Phys. Rev. Lett. 1979;43:267.

 

  1. Leemans W.P, Nagler B, Gonsalves A.J, Tóth C, Nakamura K, Geddes C.G.R, Esarey E, Schroeder C.B, Hooker S.M. GeV electron beams from a centimeter-scale accelerator. Nat. Phys. 2006;2:696.

 

  1. Blumenfeld I, Clayton C.E, Decker F.J, MJ Hogan M.J, Huang C, Ischebeck R, Iverson R, Joshi C, Katsouleas Th, Kirby N, Lu W, Marsh K.A, Mori W.B, Muggli P, Oz E, SiemannR.H, Walz D, Zhou M. Energy doubling of 42 GeV electrons in a meter-scale plasma wakefield accelerator. Nature. 2007;445:741.

 

  1. Caldwell A, Lotov K, Pukhov A, Simon F. Proton-driven plasma-wakefield acceleration. Nat. Phys. 2009;5:363-367.

 

  1. Assmann R, Bingham R, Bohl T, Bracco C, Buttenschön B, Butterworth A, Caldwell A, Chattopadhyay S, Cipiccia S, Feldbaumer E, Fonseca R.A, Goddard B, Gross M, Grulke O, Gschwendtner E, Holloway J, Huang C, Jaroszynski D, Jolly S, Kempkes P, Lopes N, Lotov K, Machacek J, Mandry S.R, McKenzie J.W, Meddahi M, Militsyn B.L, Moschuering N, Muggli P, Najmudin Z, Noakes T.C.Q, Norreys P.A, Öz E, Pardons A, Petrenko A, Pukhov A, Rieger K, Reimann O, Ruhl H, Shaposhnikova E, Silva L.O, Sosedkin A, Tarkeshian R, Trines R.M.G.N, Tückmantel T, Vieira J, Vincke H, Wing M, Xia G. Proton-driven plasma wakefield acceleration: a path to the future of high-energy particle physics. Plasma Phys. Control. Fusion. 2014;56:084013.

 

  1. Lotov K.V, Sosedkin A.P, Petrenko A.V, Amorim L.D, Vieira J, Fonseca R.A, Silva L.O, Gschwendtner E, Muggli P. Electron trapping and acceleration by the plasma wakefield of a self-modulating proton beam. Phys. Plasmas. 2014;21: 123116.

 

  1. Pukhov A, Meyer-ter-Vehn J. Laser wake field acceleration: the highly non-linear broken-wave regime. Appl. Phys. B. 2002;74:355-361.

 

  1. Joshi C, Adli E, An W, Clayton C.E, Corde S, Gessner S, Hogan M.J, Litos M, Lu W, Marsh K.A, Mori W.B, Vafaei-Najafabadi N, O'shea B, Xu X, White G, Yakimenko V. Plasma wakefield acceleration experiments at FACET II. Plasma Phys. Control. Fusion. 2018;60:034001.

 

  1. Lu W, Huang C, Zhou M.M, Mori W.B, Katsouleas T. Limits of linear plasma wakefield theory for electron or positron beams. Phys. Plasmas. 2005;12:063101.

 

  1. Allen B, Yakimenko V, Babzien M, Fedurin M, Kusche K, Muggli P. Experimental study of current filamentation instability. Phys. Rev. Lett. 2012;109:185007.

 

  1. Huschauer A, Bartosik H, Cave S.C, Coly M, Cotte D, Damerau H, Di Giovanni G.P, Gilardoni S, Giovannozzi M, Kain V, Koukovini-Platia E, Mikulec B, Sterbini G, Tecker F. Advancing the CERN proton synchrotron multiturn extraction towards the high-intensity proton beams frontier. Phys. Rev. Accel. Beams. 2019;22:104002.

 

13.Plyushchev G, Kersevan R, Petrenko A, Muggli P. A rubidium vapor source for a plasma source for AWAKE. J. Phys. D: Appl. Phys. 2017;5:025203.

 

  1. Adli E, Ahuja A, Apsimon O, Apsimon R, Bachmann A.-M, Barrientos D, Batsch F, Bauche J, Berglyd Olsen V.K, Bernardini M, Bohl T, Bracco C, Braunmüller F, Burt G, Buttenschön B, Caldwell A, Cascella M, Chappell J, Chevallay E, Chung M, Cooke D, Damerau H, Deacon L, Deubner L.H, Dexter A, Doebert S, Farmer J, Fedosseev V.N, Fiorito R, Fonseca R.A, Friebel F, Garolfi L, Gessner S, Gorgisyan I, Gorn A.A, Granados E, Grulke O, Gschwendtner E, Hansen J, Helm A, Henderson J.R, Hüther M, Ibison M, Jensen L, Jolly S, Keeble F, Kim S.-Y, Kraus F, Li Y, Liu S, Lopes N, Lotov K.V, Maricalva Brun L, Martyanov M, Mazzoni S, Medina Godoy D, Minakov V.A, Mitchell J, Molendijk J.C, Moody J.T, Moreira M, Muggli P, Öz E, Pasquino C, Pardons A, Peña Asmus F, Pepitone K, Perera A, Petrenko A, Pitman S, Pukhov A, Rey S, Rieger K, Ruhl H, Schmidt J.S, Shalimova I.A, Sherwood P, Silva L.O, Soby L, Sosedkin A.P, Speroni R, Spitsyn R.I, Tuev P.V, Turner M, Velotti F, Verra L, Verzilov V.A, Vieira J, Welsch C.P, Williamson B, Wing M, Woolley B, Xia G. Acceleration of electrons in the plasma wakefield of a proton bunch. Nature. 2018;561:363-367.

 

  1. Braunmüller F, Nechaeva T, Adli E, Agnello R, Aladi M, Andrebe Y, Apsimon O, Apsimon R, Bachmann A.-M, Baistrukov M.A, Batsch F, Bergamaschi M, Blanchard P, Burrows P.N, Buttenschön B, Caldwell A, Chappell J, Chevallay E, Chung M, Cooke D.A, Damerau H, Davut C, Demeter G, Deubner L.H, Dexter A, Djotyan G.P, Doebert S, Farmer J, Fasoli A, Fedosseev V.N, Fiorito R, Fonseca R.A, Friebel F, Furno I, Garolfi L, Gessner S, Goddard B, Gorgisyan I, Gorn A.A, Granados E, Granetzny M, Grulke O, Gschwendtner E, Hafych V, Hartin A, Helm A, Henderson J.R, Howling A, Hüther M, Jacquier R, Jolly S, Kargapolov Yu.I, Kedves M.Á, Keeble F, Kelisani M.D, Kim S.-Y, Kraus F, Krupa M, Lefevre T, Li Y, Liang L, Liu S, Lopes N, Lotov K.V, Martyanov M, Mazzoni S, Medina Godoy D, Minakov V.A, Moody J.T, Morales Guzmán P.I, Moreira M, Muggli P, Panuganti H, Pardons A, Peña Asmus F, Perera A, Petrenko A, Pucek J, Pukhov A, Ráczkevi B, Ramjiawan R.L, Rey S, Ruhl H, Saberi H, Schmitz O, Senes E, Sherwood P, Silva L.O, Spitsyn R.I, Tuev P.V, Turner M, Velotti F, Verra L, Verzilov V.A, Vieira J, Welsch C.P, Williamson B, Wing M, Wolfenden J, Woolley B, Xia G, Zepp M, Zevi Della Porta G. Proton bunch self-modulation in plasma with density gradient. Phys. Rev. Lett. 2020;125:264801.

 

  1. Pukhov A, Kumar N, Tückmantel T, Upadhyay A, Lotov K, Muggli P, Khudik V, Siemon C, Shvets G. Phase velocity and particle injection in a self-modulated proton-driven plasma wakefield accelerator. Phys. Rev. Lett. 2011;107:145003.

 

  1. Lotov K.V, Minakov V.A. Proton beam self-modulation seeded by electron bunch in plasma with density ramp. Plasma Phys. Control. Fusion. 2020;62:115025.

 

  1. Gorn A.A, Turner M, Adli E, Agnello R, Aladi M, Andrebe Y, Apsimon O, Apsimon R, Bachmann A-M, Baistrukov M.A, Batsch F, Bergamaschi M, Blanchard P, Burrows P.N, Buttenschön B, Caldwell A, Chappell J, Chevallay E, Chung M, Cooke D.A, Damerau H, Davut C, Demeter G, Deubner L.H, Dexter A, Djotyan G.P, Doebert S, Farmer J, Fasoli A, Fedosseev V.N, Fiorito R, Fonseca R.A, Friebel F, Furno I, Garolfi L, Gessner S, Goddard B, Gorgisyan I, Granados E, Granetzny M, Grulke O, Gschwendtner E, Hafych V, Hartin A, Helm A, Henderson J.R, Howling A, Hüther M, Jacquier R, Kargapolov I.Yu, Kedves M.Á, Keeble F, Kelisani M.D, Kim S-Y, Kraus F, Krupa M, Lefevre T, Liang L, Liu S, Lopes N, Lotov K.V, Martyanov M, Mazzoni S, Medina Godoy D, Minakov V.A, Moody J.T, Morales Guzmán P.I, Moreira M, Nechaeva T, Panuganti H, Pardons A, Peña Asmus F, Perera A, Petrenko A, Pucek J, Pukhov A, Ráczkevi B, Ramjiawan R.L, Rey S, Ruhl H, Saberi H, Schmitz O, Senes E, Sherwood P, Silva L.O, Spitsyn R.I, Tuev P.V, Velotti F, Verra L, Verzilov V.A, Vieira J, Welsch C.P, Williamson B, Wing M, Wolfenden J, Woolley B, Xia G, Zepp M, Zevi Della Porta G. Proton beam defocusing in AWAKE: comparison of simulations and measurements. Plasma Phys. Control. Fusion. 2020;62:125023.

 

  1. Xu X.L, Hua J.F, Wu Y.P, Zhang C.J, Li F, Wan Y, Pai C.-H, Lu W, An W, Yu P, Hogan M.J, Joshi C, Mori W.B. Physics of phase space matching for staging plasma and traditional accelerator components using longitudinally tailored plasma profiles. Phys. Rev. Lett. 2016;116:124801.

 

  1. Ariniello R, Doss C.E, Hunt-Stone K, Cary J.R, Litos M.D. Transverse beam dynamics in a plasma density ramp. Phys. Rev. Accel. Beams. 2019;22:041304.

 

  1. Sharifzadeh Tabrizi J, Khorashadizadeh S.M, Fallah R, Niknam A.R. Amplitude enhancement of plasma wakefield by interaction of relativistic Gaussian electron beam with inhomogeneous magnetized plasma. AIP Adv. 2020;10:015330.

 

  1. Kuznetsov S.V. Trapping of electrons and acceleration of the electron bunch in a wake wave. Plasma Phys. Rep. 2014;40:611-622.

 

  1. Lehe R, Kirchen M, Jalas S, Peters K, Dornmair I. Fourier-Bessel Particle-In-Cell (FBPIC) v0. 1.0. No. FBPIC. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA, United States. 2017.

 

  1. Kirchen M, Jalas S, Mahncke S, Maier A.R. FBPIC: A spectral, quasi-3D, multi-GPU Particle-In-Cell code for plasma accelerators. Verhandlungen der Deutschen Physikalischen Gesellschaft. 2018;50:1.

 

  1. https://anaconda.org/petrenko/fbpic_awake_ru N_inj/notebook.

Keywords

Beam emittance
Driven proton beam
Witness electron beam acceleration
  1. Kurz T, Heinemann T, Gilljohann M.F, Chang Y.Y, Couperus Cabadağ J.P, Debus A, Kononenko O, Pausch R, Schöbel S, Assmann R.W, Bussmann M, Ding H, Götzfried J, Köhler A, Raj G, Schindler S, Steiniger K, Zarini O, Corde S, Döpp A, Hidding B, Karsch S, Schramm U, Martinez de la Ossa A, Irman A. Demonstration of a compact plasma accelerator powered by laser-accelerated electron beams. Nat. commun. 2021;12:2895.

 

  1. Tajima T, Dawson J.M. Laser electron accelerator. Phys. Rev. Lett. 1979;43:267.

 

  1. Leemans W.P, Nagler B, Gonsalves A.J, Tóth C, Nakamura K, Geddes C.G.R, Esarey E, Schroeder C.B, Hooker S.M. GeV electron beams from a centimeter-scale accelerator. Nat. Phys. 2006;2:696.

 

  1. Blumenfeld I, Clayton C.E, Decker F.J, MJ Hogan M.J, Huang C, Ischebeck R, Iverson R, Joshi C, Katsouleas Th, Kirby N, Lu W, Marsh K.A, Mori W.B, Muggli P, Oz E, SiemannR.H, Walz D, Zhou M. Energy doubling of 42 GeV electrons in a meter-scale plasma wakefield accelerator. Nature. 2007;445:741.

 

  1. Caldwell A, Lotov K, Pukhov A, Simon F. Proton-driven plasma-wakefield acceleration. Nat. Phys. 2009;5:363-367.

 

  1. Assmann R, Bingham R, Bohl T, Bracco C, Buttenschön B, Butterworth A, Caldwell A, Chattopadhyay S, Cipiccia S, Feldbaumer E, Fonseca R.A, Goddard B, Gross M, Grulke O, Gschwendtner E, Holloway J, Huang C, Jaroszynski D, Jolly S, Kempkes P, Lopes N, Lotov K, Machacek J, Mandry S.R, McKenzie J.W, Meddahi M, Militsyn B.L, Moschuering N, Muggli P, Najmudin Z, Noakes T.C.Q, Norreys P.A, Öz E, Pardons A, Petrenko A, Pukhov A, Rieger K, Reimann O, Ruhl H, Shaposhnikova E, Silva L.O, Sosedkin A, Tarkeshian R, Trines R.M.G.N, Tückmantel T, Vieira J, Vincke H, Wing M, Xia G. Proton-driven plasma wakefield acceleration: a path to the future of high-energy particle physics. Plasma Phys. Control. Fusion. 2014;56:084013.

 

  1. Lotov K.V, Sosedkin A.P, Petrenko A.V, Amorim L.D, Vieira J, Fonseca R.A, Silva L.O, Gschwendtner E, Muggli P. Electron trapping and acceleration by the plasma wakefield of a self-modulating proton beam. Phys. Plasmas. 2014;21: 123116.

 

  1. Pukhov A, Meyer-ter-Vehn J. Laser wake field acceleration: the highly non-linear broken-wave regime. Appl. Phys. B. 2002;74:355-361.

 

  1. Joshi C, Adli E, An W, Clayton C.E, Corde S, Gessner S, Hogan M.J, Litos M, Lu W, Marsh K.A, Mori W.B, Vafaei-Najafabadi N, O'shea B, Xu X, White G, Yakimenko V. Plasma wakefield acceleration experiments at FACET II. Plasma Phys. Control. Fusion. 2018;60:034001.

 

  1. Lu W, Huang C, Zhou M.M, Mori W.B, Katsouleas T. Limits of linear plasma wakefield theory for electron or positron beams. Phys. Plasmas. 2005;12:063101.

 

  1. Allen B, Yakimenko V, Babzien M, Fedurin M, Kusche K, Muggli P. Experimental study of current filamentation instability. Phys. Rev. Lett. 2012;109:185007.

 

  1. Huschauer A, Bartosik H, Cave S.C, Coly M, Cotte D, Damerau H, Di Giovanni G.P, Gilardoni S, Giovannozzi M, Kain V, Koukovini-Platia E, Mikulec B, Sterbini G, Tecker F. Advancing the CERN proton synchrotron multiturn extraction towards the high-intensity proton beams frontier. Phys. Rev. Accel. Beams. 2019;22:104002.

 

13.Plyushchev G, Kersevan R, Petrenko A, Muggli P. A rubidium vapor source for a plasma source for AWAKE. J. Phys. D: Appl. Phys. 2017;5:025203.

 

  1. Adli E, Ahuja A, Apsimon O, Apsimon R, Bachmann A.-M, Barrientos D, Batsch F, Bauche J, Berglyd Olsen V.K, Bernardini M, Bohl T, Bracco C, Braunmüller F, Burt G, Buttenschön B, Caldwell A, Cascella M, Chappell J, Chevallay E, Chung M, Cooke D, Damerau H, Deacon L, Deubner L.H, Dexter A, Doebert S, Farmer J, Fedosseev V.N, Fiorito R, Fonseca R.A, Friebel F, Garolfi L, Gessner S, Gorgisyan I, Gorn A.A, Granados E, Grulke O, Gschwendtner E, Hansen J, Helm A, Henderson J.R, Hüther M, Ibison M, Jensen L, Jolly S, Keeble F, Kim S.-Y, Kraus F, Li Y, Liu S, Lopes N, Lotov K.V, Maricalva Brun L, Martyanov M, Mazzoni S, Medina Godoy D, Minakov V.A, Mitchell J, Molendijk J.C, Moody J.T, Moreira M, Muggli P, Öz E, Pasquino C, Pardons A, Peña Asmus F, Pepitone K, Perera A, Petrenko A, Pitman S, Pukhov A, Rey S, Rieger K, Ruhl H, Schmidt J.S, Shalimova I.A, Sherwood P, Silva L.O, Soby L, Sosedkin A.P, Speroni R, Spitsyn R.I, Tuev P.V, Turner M, Velotti F, Verra L, Verzilov V.A, Vieira J, Welsch C.P, Williamson B, Wing M, Woolley B, Xia G. Acceleration of electrons in the plasma wakefield of a proton bunch. Nature. 2018;561:363-367.

 

  1. Braunmüller F, Nechaeva T, Adli E, Agnello R, Aladi M, Andrebe Y, Apsimon O, Apsimon R, Bachmann A.-M, Baistrukov M.A, Batsch F, Bergamaschi M, Blanchard P, Burrows P.N, Buttenschön B, Caldwell A, Chappell J, Chevallay E, Chung M, Cooke D.A, Damerau H, Davut C, Demeter G, Deubner L.H, Dexter A, Djotyan G.P, Doebert S, Farmer J, Fasoli A, Fedosseev V.N, Fiorito R, Fonseca R.A, Friebel F, Furno I, Garolfi L, Gessner S, Goddard B, Gorgisyan I, Gorn A.A, Granados E, Granetzny M, Grulke O, Gschwendtner E, Hafych V, Hartin A, Helm A, Henderson J.R, Howling A, Hüther M, Jacquier R, Jolly S, Kargapolov Yu.I, Kedves M.Á, Keeble F, Kelisani M.D, Kim S.-Y, Kraus F, Krupa M, Lefevre T, Li Y, Liang L, Liu S, Lopes N, Lotov K.V, Martyanov M, Mazzoni S, Medina Godoy D, Minakov V.A, Moody J.T, Morales Guzmán P.I, Moreira M, Muggli P, Panuganti H, Pardons A, Peña Asmus F, Perera A, Petrenko A, Pucek J, Pukhov A, Ráczkevi B, Ramjiawan R.L, Rey S, Ruhl H, Saberi H, Schmitz O, Senes E, Sherwood P, Silva L.O, Spitsyn R.I, Tuev P.V, Turner M, Velotti F, Verra L, Verzilov V.A, Vieira J, Welsch C.P, Williamson B, Wing M, Wolfenden J, Woolley B, Xia G, Zepp M, Zevi Della Porta G. Proton bunch self-modulation in plasma with density gradient. Phys. Rev. Lett. 2020;125:264801.

 

  1. Pukhov A, Kumar N, Tückmantel T, Upadhyay A, Lotov K, Muggli P, Khudik V, Siemon C, Shvets G. Phase velocity and particle injection in a self-modulated proton-driven plasma wakefield accelerator. Phys. Rev. Lett. 2011;107:145003.

 

  1. Lotov K.V, Minakov V.A. Proton beam self-modulation seeded by electron bunch in plasma with density ramp. Plasma Phys. Control. Fusion. 2020;62:115025.

 

  1. Gorn A.A, Turner M, Adli E, Agnello R, Aladi M, Andrebe Y, Apsimon O, Apsimon R, Bachmann A-M, Baistrukov M.A, Batsch F, Bergamaschi M, Blanchard P, Burrows P.N, Buttenschön B, Caldwell A, Chappell J, Chevallay E, Chung M, Cooke D.A, Damerau H, Davut C, Demeter G, Deubner L.H, Dexter A, Djotyan G.P, Doebert S, Farmer J, Fasoli A, Fedosseev V.N, Fiorito R, Fonseca R.A, Friebel F, Furno I, Garolfi L, Gessner S, Goddard B, Gorgisyan I, Granados E, Granetzny M, Grulke O, Gschwendtner E, Hafych V, Hartin A, Helm A, Henderson J.R, Howling A, Hüther M, Jacquier R, Kargapolov I.Yu, Kedves M.Á, Keeble F, Kelisani M.D, Kim S-Y, Kraus F, Krupa M, Lefevre T, Liang L, Liu S, Lopes N, Lotov K.V, Martyanov M, Mazzoni S, Medina Godoy D, Minakov V.A, Moody J.T, Morales Guzmán P.I, Moreira M, Nechaeva T, Panuganti H, Pardons A, Peña Asmus F, Perera A, Petrenko A, Pucek J, Pukhov A, Ráczkevi B, Ramjiawan R.L, Rey S, Ruhl H, Saberi H, Schmitz O, Senes E, Sherwood P, Silva L.O, Spitsyn R.I, Tuev P.V, Velotti F, Verra L, Verzilov V.A, Vieira J, Welsch C.P, Williamson B, Wing M, Wolfenden J, Woolley B, Xia G, Zepp M, Zevi Della Porta G. Proton beam defocusing in AWAKE: comparison of simulations and measurements. Plasma Phys. Control. Fusion. 2020;62:125023.

 

  1. Xu X.L, Hua J.F, Wu Y.P, Zhang C.J, Li F, Wan Y, Pai C.-H, Lu W, An W, Yu P, Hogan M.J, Joshi C, Mori W.B. Physics of phase space matching for staging plasma and traditional accelerator components using longitudinally tailored plasma profiles. Phys. Rev. Lett. 2016;116:124801.

 

  1. Ariniello R, Doss C.E, Hunt-Stone K, Cary J.R, Litos M.D. Transverse beam dynamics in a plasma density ramp. Phys. Rev. Accel. Beams. 2019;22:041304.

 

  1. Sharifzadeh Tabrizi J, Khorashadizadeh S.M, Fallah R, Niknam A.R. Amplitude enhancement of plasma wakefield by interaction of relativistic Gaussian electron beam with inhomogeneous magnetized plasma. AIP Adv. 2020;10:015330.

 

  1. Kuznetsov S.V. Trapping of electrons and acceleration of the electron bunch in a wake wave. Plasma Phys. Rep. 2014;40:611-622.

 

  1. Lehe R, Kirchen M, Jalas S, Peters K, Dornmair I. Fourier-Bessel Particle-In-Cell (FBPIC) v0. 1.0. No. FBPIC. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA, United States. 2017.

 

  1. Kirchen M, Jalas S, Mahncke S, Maier A.R. FBPIC: A spectral, quasi-3D, multi-GPU Particle-In-Cell code for plasma accelerators. Verhandlungen der Deutschen Physikalischen Gesellschaft. 2018;50:1.

 

  1. https://anaconda.org/petrenko/fbpic_awake_ru N_inj/notebook.

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