Particle-in-cell (PIC) codes are used since the early 1960s for calculating self-consistently the motion of charged particles in plasmas, taking into account external electric and magnetic fields as well as the fields created by the particles itself. Due to the used very small time steps (in the order of the inverse plasma frequency) and mesh size, the computational requirements can be very high and they drastically increase with increasing plasma density and size of the calculation domain. Thus, usually small computational domains and/or reduced dimensionality are used. In the last years, the available central processing unit (CPU) power strongly increased. Together with a massive parallelization of the codes, it is now possible to describe in 3D the extraction of charged particles from a plasma, using calculation domains with an edge length of several centimeters, consisting of one extraction aperture, the plasma in direct vicinity of the aperture, and a part of the extraction system. Large negative hydrogen or deuterium ion sources are essential parts of the neutral beam injection (NBI) system in future fusion devices like the international fusion experiment ITER and the demonstration reactor (DEMO). For ITER NBI RF driven sources with a source area of 0.9 × 1.9 m2 and 1280 extraction apertures will be used. The extraction of negative ions is accompanied by the co-extraction of electrons which are deflected onto an electron dump. Typically, the maximum negative extracted ion current is limited by the amount and the temporal instability of the co-extracted electrons, especially for operation in deuterium. Different PIC codes are available for the extraction region of large driven negative ion sources for fusion. Additionally, some effort is ongoing in developing codes that describe in a simplified manner (coarser mesh or reduced dimensionality) the plasma of the whole ion source. The presentation first gives a brief overview of the current status of the ion source development for ITER NBI and of the PIC method. Different PIC codes for the extraction region are introduced as well as the coupling to codes describing the whole source (PIC codes or fluid codes). Presented and discussed are different physical and numerical aspects of applying PIC codes to negative hydrogen ion sources for fusion as well as selected code results. The main focus of future calculations will be the meniscus formation and identifying measures for reducing the co-extracted electrons, in particular for deuterium operation. The recent results of the 3D PIC code ONIX (calculation domain: one extraction aperture and its vicinity) for the ITER prototype source (1/8 size of the ITER NBI source) are presented.
REFERENCES
1.
Y.
Takeiri
, O.
Kaneko
, K.
Tsumori
, Y.
Oka
, K.
Ikeda
, M.
Osakabe
, K.
Nagaoka
, E.
Asano
, T.
Kondo
, M.
Sato
et al., “High-power and long-pulse injection with negative-ion-based neutral beam injectors in the large helical device
,” Nucl. Fusion
46
, S199
(2006
).2.
Y.
Ikeda
, N.
Umeda
, N.
Akino
, N.
Ebisawa
, L.
Grisham
, M.
Hanada
, A.
Honda
, T.
Inoue
, M.
Kawai
, M.
Kazawa
et al., “Present status of the negative ion based NBI system for long pulse operation on JT-60U
,” Nucl. Fusion
46
, S211
(2006
).3.
A.
Kojima
, M.
Hanada
, Y.
Tanaka
, T.
Inoue
, K.
Watanabe
, M.
Taniguchi
, M.
Kashiwagi
, N.
Umeda
, H.
Tobari
, and L. R.
Grisham
, “Achievement and improvement of the JT-60U negative ion source for JT-60 super advanced (invited)
,” Rev. Sci. Instrum.
81
, 02B112
(2010
).4.
R.
Hemsworth
, A.
Tanga
, and V.
Antoni
, “Status of the ITER neutral beam injection system (invited)
,” Rev. Sci. Instrum.
79
, 02C109
(2008
).5.
R.
Hemsworth
, H.
Decamps
, J.
Graceffa
, B.
Schunke
, M.
Tanaka
, M.
Dremel
, A.
Tanga
, H. P. L.
De Esch
, F.
Geli
, J.
Milnes
et al., “Status of the ITER heating neutral beam system
,” Nucl. Fusion
49
, 045006
(2009
).6.
A.
Masiello
, G.
Agarici
, T.
Bonicelli
, M.
Simon
, V.
Antoni
, H. P. L.
De Esch
, A.
De Lorenzi
, M.
Dremel
, P.
Franzen
, R.
Hemsworth
et al., “European programme towards the 1 MeV ITER NB injector
,” Fusion Eng. Des.
84
, 1276
(2009
).7.
A.
Masiello
, G.
Agarici
, T.
Bonicelli
, F.
Fantini
, M.
Gagliardi
, M.
Paolucci
, M.
Simon
, P.
Wikus
, P.
Agostinetti
, M.
Bigi
et al., in Proceedings of the 24th IAEA Fusion Energy Conference
, San Diego, USA
, 2012
.8.
E.
Speth
, H. D.
Falter
, P.
Franzen
, U.
Fantz
, M.
Bandyopadhyay
, S.
Christ
, A.
Encheva
, M.
Fröschle
, D.
Holtum
, B.
Heinemann
et al., “Overview of the RF source development programme at IPP Garching
,” Nucl. Fusion
46
, S220
(2006
).9.
B.
Heinemann
, U.
Fantz
, W.
Kraus
, L.
Schiesko
, C.
Wimmer
, D.
Wünderlich
, F.
Bonomo
, M.
Fröschle
, R.
Nocentini
, and R.
Riedl
, “Towards large and powerful radio frequency driven negative ion sources for fusion
,” New J. Phys.
19
, 015001
(2017
).10.
B.
Heinemann
, H. D.
Falter
, U.
Fantz
, P.
Franzen
, M.
Fröschle
, R.
Gutser
, W.
Kraus
, R.
Nocentini
, R.
Riedl
, E.
Speth
et al., “Design of the ‘half-size’ ITER neutral beam source for the test facility ELISE
,” Fusion Eng. Des.
84
, 915
(2009
).11.
P.
Franzen
, B.
Heinemann
, U.
Fantz
, D.
Wünderlich
, W.
Kraus
, M.
Fröschle
, C.
Martens
, R.
Riedl
, R.
Nocentini
, A.
Masiello
et al., “Commissioning and first results of the ITER-relevant negative ion beam test facility ELISE
,” Fusion Eng. Des.
88
, 3132
(2013
).12.
P.
Sonato
, P.
Agostinetti
, G.
Anaclerio
, V.
Antoni
, O.
Barana
, M.
Bigi
, M.
Boldrin
, M.
Cavenago
, S.
Dal Bello
, M.
Dalla Palma
et al., “The ITER full size plasma source device design
,” Fusion Eng. Des.
84
, 269
(2009
).13.
V.
Toigo
, R.
Piovan
, S. D.
Bello
, E.
Gaio
, A.
Luchetta
, R.
Pasqualotto
, P.
Zaccaria
, M.
Bigi
, G.
Chitarin
, D.
Marcuzzi
et al., “The PRIMA test facility: SPIDER and MITICA test-beds for ITER neutral beam injectors
,” New J. Phys.
19
, 085004
(2017
).14.
D.
Wünderlich
, L.
Schiesko
, P.
Mcneely
, U.
Fantz
, P.
Franzen
, and NNBI-Team
, “On the proton flux towards the plasma grid in a RF-driven negative hydrogen ion source for ITER NBI
,” Plasma Phys. Controlled Fusion
54
, 125002
(2012
).15.
N.
Takado
, J.
Hanatani
, T.
Mizuno
, K.
Katoh
, A.
Hatayama
, M.
Hanada
, T.
Seki
, and T.
Inoue
, “Numerical analysis of the spatial nonuniformity in a Cs-seeded H− ion source
,” Rev. Sci. Instrum.
77
, 03A533
(2006
).16.
M.
Bacal
and M.
Wada
, “Negative hydrogen ion production mechanisms
,” Appl. Phys. Rev.
2
, 021305
(2015
).17.
C.
Wimmer
, U.
Fantz
, and NNBI-Team
, “Cesium dynamics and H− density in the extended boundary layer of negative hydrogen ion sources for fusion
,” AIP Conf. Proc.
1515
, 246
(2013
).18.
P.
Franzen
, L.
Schiesko
, M.
Fröschle
, D.
Wünderlich
, U.
Fantz
, and NNBI-Team
, “Magnetic filter field dependence of the performance of the RF driven IPP prototype source for negative hydrogen ions
,” Plasma Phys. Controlled Fusion
53
, 115006
(2011
).19.
M.
Fröschle
, U.
Fantz
, P.
Franzen
, W.
Kraus
, R.
Nocentini
, L.
Schiesko
, D.
Wünderlich
, and NNBI-Team
, “Magnetic filter field for ELISE—Concepts and design
,” Fusion Eng. Des.
88
, 1015
(2013
).20.
T.
Inoue
, M.
Kashiwagi
, M.
Taniguchi
, M.
Dairaku
, M.
Hanada
, K.
Watanabe
, and K.
Sakamoto
, “1 MeV, ampere class accelerator R&D for ITER
,” Nucl. Fusion
46
, S379
(2006
).21.
H. P. L.
De Esch
, R. S.
Hemsworth
, and P.
Massmann
, “Updated physics design ITER-SINGAP accelerator
,” Fusion Eng. Des.
73
, 329
(2005
).22.
J. H.
Whealton
and J. C.
Whitson
, “Space-charge ion optics including extraction from a plasma
,” Part. Accel.
10
, 235
(1980
).23.
U.
Fantz
, P.
Franzen
, W.
Kraus
, L.
Schiesko
, C.
Wimmer
, and D.
Wünderlich
, “Size scaling of negative hydrogen ion sources for fusion
,” AIP Conf. Proc.
1655
, 040001
(2015
).24.
U.
Fantz
, P.
Franzen
, and D.
Wünderlich
, “Development of negative hydrogen ion sources for fusion: Experiments and modelling
,” Chem. Phys.
398
, 7
(2012
).25.
J. P.
Boeuf
, J.
Claustre
, B.
Chaudhury
, and G.
Fubiani
, “Physics of a magnetic filter for negative ion sources. II. E × B drift through the filter in a real geometry
,” Phys. Plasmas
19
, 113510
(2012
).26.
S.
Lishev
, L.
Schiesko
, D.
Wünderlich
, and U.
Fantz
, “Spatial distribution of the plasma parameters in the RF negative ion source prototype for fusion
,” AIP Conf. Proc.
1655
, 040010
(2015
).27.
D.
Wünderlich
, U.
Fantz
, B.
Heinemann
, W.
Kraus
, R.
Riedl
, and C.
Wimmer
, “Progress of the ELISE test facility: Towards one hour pulses in hydrogen
,” Nucl. Fusion
56
, 106004
(2016
).28.
D.
Wünderlich
, W.
Kraus
, M.
Fröschle
, R.
Riedl
, U.
Fantz
, B.
Heinemann
, and NNBI-Team
, “Influence of the magnetic field topology on the performance of the large area negative hydrogen ion source test facility ELISE
,” Plasma Phys. Controlled Fusion
58
, 125005
(2016
).29.
W.
Kraus
, D.
Wünderlich
, U.
Fantz
, B.
Heinemann
, F.
Bonomo
, and R.
Riedl
, “Deuterium results at ELISE
,” Rev. Sci. Instrum.
89
, 052102
(2018
).30.
C. K.
Birdsall
and A. B.
Langdon
, Plasma Physics Via Computer Simulation
(McGraw-Hill
, New York
, 1985
).31.
R. W.
Hockney
and J. W.
Eastwood
, Computer Simulation Using Particles
(Taylor & Francis
, Bristol
, 1988
).32.
D.
Tskhakaya
, “The particle-in-cell method
,” in Computational Many-Particle Physics
, edited by H.
Fehske
, R.
Schneider
, and A.
WeißE
(Springer
, Heidelberg
, 2008
).33.
J. P.
Verboncoeur
, “Particle simulation of plasmas
,” Plasma Phys. Controlled Fusion
47
, A231
(2005
).34.
J. U.
Brackbill
and D. W.
Forslund
, “An implicit method for electromagnetic plasma simulation in two dimensions
,” J. Comput. Phys.
46
, 271
(1982
).35.
G.
Lapenta
, J. U.
Brackbill
, and P.
Ricci
, “Kinetic approach to microscopic-macroscopic coupling in space and laboratory plasmas
,” Phys. Plasmas
13
, 055904
(2006
).36.
H.
Qin
, S.
Zhang
, J.
Xiao
, J.
Liu
, Y.
Sun
, and W. M.
Tang
, “Why is Boris algorithm so good?
,” Phys. Plasmas
20
, 084503
(2013
).37.
T.
Takizuka
and H.
Abe
, “A binary collision model for plasma simulation with a particle code
,” J. Comput. Phys.
25
, 205
(1977
).38.
K.
Nanbu
, “Theory of cumulative small-angle collisions in plasmas
,” Phys. Rev. E
55
(4
), 4642
–4652
(1997
).39.
V.
Vahedi
and M.
Surendra
, “A Monte Carlo collision model for the particle-in-cell method: Applications to argon and oxygen discharges
,” Comput. Phys. Commun.
87
, 179
(1995
).40.
W.
Kawamura
, C. K.
Birdsall
, and V.
Vahedi
, “Physical and numerical methods of speeding up particle codes and paralleling as applied to RF discharges
,” Plasma Sources Sci. Technol.
9
, 413
(2000
).41.
H.
Okuda
, “Nonphysical noises and instabilities in plasma simulation due to a spatial grid
,” J. Comput. Phys.
10
, 475
(1972
).42.
C. K.
Birdsall
, “Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC
,” IEEE Trans. Plasma Sci.
19
, 65
(1991
).43.
S.
Nishioka
, S.
Mochalskyy
, F.
Taccogna
, A.
Hatayama
, U.
Fantz
, and P.
Minelli
, “Code-to-code benchmark tests for 3D simulation models dedicated to the extraction region in negative ion sources
,” AIP Conf. Proc.
1869
, 050006
(2017
).44.
R.
Courant
, K.
Friedrichs
, and H.
Lewy
, “Über die partiellen differenzengleichungen der mathematischen physik
,” Math. Ann.
100
, 32
(1928
).45.
F.
Taccogna
, S.
Longo
, M.
Capitelli
, and R.
Schneider
, “Negative-ion-source modeling: From expansion to extraction region
,” IEEE Trans. Plasma Sci.
36
, 1589
(2008
).46.
D.
Wünderlich
, R.
Gutser
, and U.
Fantz
, “PIC code for the plasma sheath in large caesiated RF sources for negative hydrogen ions
,” Plasma Sources Sci. Technol.
18
, 045031
(2009
).47.
T.
Sakurabayashi
, A.
Hatayama
, and M.
Bacal
, “Effects of a weak transverse magnetic field on negative ion transport in negative ion sources
,” J. Appl. Phys.
95
, 3937
(2004
).48.
T.
Sakurabayashi
, A.
Hatayama
, and M.
Bacal
, “Effects of the weak magnetic field and electron diffusion on the spatial potential and negative ion transport in the negative ion source
,” Rev. Sci. Instrum.
75
, 1770
(2004
).49.
M.
Turek
, J.
Sielanko
, P.
Franzen
, and E.
Speth
, “Influence of transversal magnetic field on negative ion extraction process in 3D computer simulation of the multi-aperture ion source
,” AIP Conf. Proc.
812
, 153
(2006
).50.
M.
Turek
and J.
Sielanko
, “Simulations of negative ion extraction from a multi-aperture ion source in the presence of the magnetic filter
,” Vacuum
83
, S256
(2009
).51.
K.
Miyamoto
, S.
Okuda
, and A.
Hatayama
, “Meniscus and beam halo formation in a tandem-type negative ion source with surface production
,” Appl. Phys. Lett.
100
, 233507
(2012
).52.
K.
Miyamoto
, S.
Okuda
, A.
Hatayama
, M.
Hanada
, and A.
Kojima
, “Study of beam optics and beam halo by integrated modeling of negative ion beams from plasma meniscus formation to beam acceleration
,” Appl. Phys. Lett.
102
, 023512
(2013
).53.
F.
Taccogna
and P.
Minelli
, “PIC modeling of negative ion sources for fusion
,” New J. Phys.
19
, 015012
(2017
).54.
J. P.
Boeuf
, G.
Fubiani
, and L.
Garrigues
, “Issues in the understanding of negative ion extraction for fusion
,” Plasma Sources Sci. Technol.
25
, 045010
(2016
).55.
G.
Fubiani
, L.
Garrigues
, G.
Hagelaar
, N.
Kohen
, and J. P.
Boeuf
, “Modeling of plasma transport and negative ion extraction in a magnetized radio-frequency plasma source
,” New J. Phys.
19
, 015002
(2017
).56.
S.
Nishioka
, I.
Goto
, K.
Miyamoto
, A.
Hatayama
, and A.
Fukano
, “Study of ion-ion plasma formation in negative ion sources by a three-dimensional in real space and three-dimensional in velocity space particle in cell model
,” J. Appl. Phys.
119
, 023302
(2016
).57.
S.
Nishioka
, K.
Miyamoto
, S.
Okuda
, I.
Goto
, A.
Hatayama
, and A.
Fukano
, “Study of plasma meniscus and beam halo in negative ion sources using three dimension in real space and three dimension in velocity space particle in cell model
,” Rev. Sci. Instrum.
85
, 02A737
(2014
).58.
K.
Miyamoto
, S.
Nishioka
, I.
Goto
, A.
Hatayama
, M.
Hanada
, A.
Kojima
, and J.
Hiratsuka
, “Analysis of the beam halo in negative ion sources by using 3D3V PIC code
,” Rev. Sci. Instrum.
87
, 02B124
(2016
).59.
F.
Taccogna
, P.
Minelli
, M.
Cavenago
, P.
Veltri
, and N.
Ippolito
, “The characterization and optimization of NIO1 ion source extraction aperture using a 3D particle-in-cell code
,” Rev. Sci. Instrum.
87
, 02B145
(2016
).60.
M.
Cavenago
, T.
Kulevoy
, S.
Petrenko
, G.
Serianni
, V.
Antoni
, M.
Bigi
, F.
Fellin
, M.
Recchia
, and P.
Veltri
, “Development of a versatile multiaperture negative ion source
,” Rev. Sci. Instrum.
83
, 02A707
(2012
).61.
M.
Cavenago
, G.
Serianni
, M.
Muri
, P.
Agostinetti
, V.
Antoni
, C.
Baltador
, M.
Barbisan
, L.
Baseggio
, M.
Bigi
, V.
Cervaro
et al., “First experiments with the negative ion source NIO1
,” Rev. Sci. Instrum.
87
, 02B320
(2016
).62.
S.
Mochalskyy
, U.
Fantz
, D.
Wünderlich
, and T.
Minea
, “Comparison of ONIX simulation results with experimental data from the BATMAN testbed for the study of negative ion extraction
,” Nucl. Fusion
56
, 106025
(2016
).63.
A.
Revel
, S.
Mochalskyy
, I. M.
Montellano
, D.
Wünderlich
, U.
Fantz
, and T.
Minea
, “Massive parallel 3D PIC simulation of negative ion extraction
,” J. Appl. Phys.
122
, 103302
(2017
).64.
P. C.
Stangeby
, “Plasma sheath transmission factors for tokamak edge plasmas
,” Phys. Fluids
27
, 682
(1984
).65.
S. A.
Self
, “Exact solution of the collisionless plasma-sheath equation
,” Phys. Fluids
6
, 1762
(1963
).66.
G. D.
Hobbs
and J. A.
Wesson
, “Heat flow through a Langmuir sheath in the presence of electron emission
,” Plasma Phys.
9
, 85
(1967
).67.
I. M.
Montellano
, “3D-PIC modelling of a low temperature plasma sheath with wall emission of negative particles and its application to NBI sources
” (unpublished).68.
L. A.
Schwager
, “Effects of secondary and thermionic electron emission on the collector and source sheaths of a finite ion temperature plasma using kinetic theory and numerical simulation
,” Phys. Fluids B
5
, 631
(1993
).69.
G. A.
Emmert
, R. M.
Wieland
, A. T.
Mense
, and J. N.
Davidson
, “Electric sheath and presheath in a collisionless, finite ion temperature plasma
,” Phys. Fluids
23
, 803
(1980
).70.
M.
Ichikawa
, A.
Kojima
, G.
Chitarin
, P.
Agostinetti
, D.
Aprile
, C.
Baltador
, M.
Barbisan
, R.
Delogu
, J.
Hiratsuka
, N.
Marconato
et al., “Determination of the meniscus shape of a negative ion beam from an experimentally obtained beam profile
,” AIP Conf. Proc.
1869
, 030024
(2017
).71.
T.
Kalvas
, O.
Tarvainen
, T.
Ropponen
, O.
Steczkiewicz
, J.
Ärje
, and H.
Clark
, “IBSIMU: A three-dimensional simulation software for charged particle optics
,” Rev. Sci. Instrum.
81
, 02B703
(2010
).72.
P.
Spädtke
and C.
Mühle
, “Simulation of ion extraction and beam transport
,” Rev. Sci. Instrum.
71
, 820
(2000
).73.
J.
Lettry
, D.
Aguglia
, P.
Andersson
, S.
Bertolo
, A.
Butterworth
, Y.
Coutron
, A.
Dallocchio
, E.
Chaudet
, J.
Gil-Flores
, R.
Guida
et al., “Status and operation of the Linac4 ion source prototypes
,” Rev. Sci. Instrum.
85
, 02B122
(2014
).74.
J.
Lettry
, D.
Aguglia
, J.
Alessi
, P.
Andersson
, S.
Bertolo
, S.
Briefi
, A.
Butterworth
, Y.
Coutron
, A.
Dallocchio
, N.
David
et al., “Linac4 H− ion sources
,” Rev. Sci. Instrum.
87
, 02B139
(2016
).75.
J.
Lettry
, private communication (2017
).76.
K.
Tsumori
and M.
Wada
, “Diagnostics tools and methods for negative ion source plasmas, a review
,” New J. Phys.
19
, 045002
(2017
).77.
R. J.
Procassini
, C. K.
Birdsall
, and E. C.
Morse
, “A fully kinetic, self-consistent particle simulation model of the collisionless plasma–sheath region
,” Phys. Fluids B
2
, 3191
(1990
).78.
G.
Gozadinos
, D.
Vender
, and M. M.
Turner
, “Boundary conditions and particle loading for the modeling of a semi-infinite plasma
,” J. Comput. Phys.
172
, 348
(2001
).79.
L.
Garrigues
, G.
Fubiani
, and J. P.
Boeuf
, “Appropriate use of the particle-in-cell method in low temperature plasmas: Application to the simulation of negative ion extraction
,” J. Appl. Phys.
120
, 213303
(2016
).80.
G. J. M.
Hagelaar
, G.
Fubiani
, and J.-P.
Boeuf
, “Model of an inductively coupled negative ion source: I. General model description
,” Plasma Sources Sci. Technol.
20
, 015001
(2011
).81.
J. P.
Boeuf
, G. J. M.
Hagelaar
, P.
Sarrailh
, G.
Fubiani
, and N.
Kohen
, “Model of an inductively coupled negative ion source: II. Application to an ITER type source
,” Plasma Sources Sci. Technol.
20
, 015002
(2011
).82.
S.
Lishev
, L.
Schiesko
, D.
Wünderlich
, and U.
Fantz
, “Influence of the configuration of the magnetic filter field on the discharge structure in the RF driven negative ion source prototype for fusion
,” AIP Conf. Proc.
1869
, 030042
(2017
).83.
U.
Fantz
, C.
Hopf
, D.
Wünderlich
, R.
Friedl
, M.
Fröschle
, B.
Heinemann
, W.
Kraus
, U.
Kurutz
, R.
Riedl
, R.
Nocentini
et al., “Towards powerful negative ion beams at the test facility ELISE for the ITER and DEMO NBI systems
,” Nucl. Fusion
57
, 116007
(2017
).84.
U.
Fantz
, P.
Franzen
, W.
Kraus
, M.
Berger
, S.
Christ-Koch
, H. D.
Falter
, M.
Fröschle
, R.
Gutser
, B.
Heinemann
, C.
Martens
et al., “Physical performance analysis and progress of the development of the negative ion RF source for the ITER NBI system
,” Nucl. Fusion
49
, 125007
(2009
).85.
W.
Eckstein
and J. P.
Biersack
, “Reflection of low-energy hydrogen from solids
,” Appl. Phys. A
38
, 123
(1985
).86.
H.
Nakano
, K.
Tsumori
, K.
Nagaoka
, M.
Shibuya
, U.
Fantz
, M.
Kisaki
, K.
Ikeda
, M.
Osakabe
, O.
Kaneko
, E.
Asano
et al., “Cavity ring-down system for density measurement of negative hydrogen ion on negative ion source
,” AIP Conf. Proc.
1390
, 359
(2100
).87.
S.
Christ-Koch
, U.
Fantz
, and M.
Berger
, “Laser photodetachment on a high power, low pressure RF-driven negative hydrogen ion source
,” Plasma Sources Sci. Technol.
18
, 025003
(2009
).88.
F.
Taccogna
, P.
Minelli
, S.
Longo
, M.
Capitelli
, and R.
Schneider
, “Modeling of a negative ion source. III. Two-dimensional structure of the extraction region
,” Phys. Plasmas
17
, 063502
(2010
).89.
S.
Mochalskyy
, A. F.
Lifschitz
, and T.
Minea
, “Extracted current saturation in negative ion sources
,” J. Appl. Phys.
111
, 113303
(2012
).90.
R.
Mcadams
and M.
Bacal
, “The negative ion flux across a double sheath at the formation of a virtual cathode
,” Plasma Sources Sci. Technol.
19
, 042001
(2010
).91.
F.
Taccogna
, P.
Minelli
, and S.
Longo
, “Three-dimensional structure of the extraction region of a hybrid negative ion source
,” Plasma Sources Sci. Technol.
22
, 045019
(2013
).92.
U.
Fantz
, H. D.
Falter
, P.
Franzen
, M.
Bandyopadhyay
, B.
Heinemann
, W.
Kraus
, P.
Mcneely
, R.
Riedl
, E.
Speth
, A.
Tanga
et al., “Diagnostics of the cesium amount in an RF negative ion source and the correlation with the extracted current density
,” Fusion Eng. Des.
74
, 299
(2005
).93.
94.
A.
Simon
, “Ambipolar diffusion in a magnetic field
,” Phys. Rev.
98
, 317
(1955
).95.
A. J. T.
Holmes
, “Electron flow through transverse magnetic fields in magnetic multipole arc discharges
,” Rev. Sci. Instrum.
53
, 1517
(1982
).96.
F. A.
Haas
, E.
Surrey
, and A. J. T.
Holmes
, “Investigation of the electron fluid equations in a hydrodynamic model of the negative ion source
,” Rev. Sci. Instrum.
63
, 2720
(1992
).97.
A. J. T. A.
Holmes
, “one-dimensional model of a negative ion source
,” Plasma Sources Sci. Technol.
5
, 453
(1996
).98.
D.
Wünderlich
, R.
Gutser
, U.
Fantz
, and NNBI-Team
, in Proceedings of the XX ESCAMPIG
, Novi Sad, Serbia
, 2010
.99.
100.
J. P.
Boeuf
, B.
Chaudhury
, and L.
Garrigues
, “Physics of a magnetic filter for negative ion sources. I. Collisional transport across the filter in an ideal, 1D filter
,” Phys. Plasmas
19
, 113509
(2012
).101.
A.
Hatayama
, S.
Nishioka
, K.
Nishida
, S.
Mattei
, J.
Lettry
, K.
Miyamoto
, T.
Shibata
, M.
Onai
, S.
Abe
, S.
Fujita
et al., “Present status of numerical modeling of hydrogen negative ion sources
,” New J. Phys.
(submitted).102.
K.
Miyamoto
, S.
Okuda
, S.
Nishioka
, and A.
Hatayama
, “Effect of basic physical parameters to control plasma meniscus and beam halo formation in negative ion sources
,” J. Appl. Phys.
114
, 103302
(2013
).103.
S.
Kuppel
, D.
Matsushita
, A.
Hatayama
, and M.
Bacal
, “Numerical analysis of electronegative plasma in the extraction region of negative hydrogen ion sources
,” J. Appl. Phys.
109
, 013305
(2011
).104.
T.
Fukuyama
, S.
Okuda
, A.
Fukano
, K.
Tsumori
, H.
Nakano
, and A.
Hatayama
, “Analysis of the double-ion plasma in the extraction region in hydrogen negative ion sources
,” AIP Conf. Proc.
1515
, 74
(2013
).105.
O.
Fukumasa
and R.
Nishida
, “Modelling of negative ion transport in caesium-seeded volume negative ion sources
,” Nucl. Fusion
46
, S275
(2006
).106.
D.
Wünderlich
, R.
Gutser
, and U.
Fantz
, “Influence of magnetic fields and biasing on the plasma of a RF driven negative ion source
,” AIP Conf. Proc.
925
, 46
(2007
).107.
R.
Gutser
, D.
Wünderlich
, U.
Fantz
, and NNBI-Team
, “Negative hydrogen ion transport in RF-driven ion sources for ITER NBI
,” Plasma Phys. Controlled Fusion
51
, 045005
(2009
).108.
109.
R. S.
Hemsworth
, H. P. L.
Esch
, M.
Kovari
, L.
Svensson
, and F.
Villecroze
, “Status of the development of the SINGAP accelerator for ITER
,” AIP Conf. Proc.
925
, 290
(2007
).110.
H. P. L.
De Esch
and L.
Svensson
, “Negative ion beam halo mitigation at the 1MV testbed at IRFM
,” Fusion Eng. Des.
86
, 363
(2011
).111.
S.
Mochalskyy
, D.
Wünderlich
, B.
Ruf
, P.
Franzen
, U.
Fantz
, and T.
Minea
, “3D numerical simulations of negative hydrogen ion extraction using realistic plasma parameters, geometry of the extraction aperture and full 3D magnetic field map
,” Rev. Sci. Instrum.
85
, 02B301
(2014
).112.
A.
Hatayama
, private communication (2017
).113.
K.
Makino
, T.
Sakurabayashi
, A.
Hatayama
, K.
Miyamoto
, and M.
Ogasawara
, “Analysis of negative ion velocity distribution at the extraction holes in a negative ion source
,” Rev. Sci. Instrum.
73
, 1051
(2002
).© 2018 EURATOM.
2018
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