Transcript ion extraction and beam optics using the 2D3V and

Negative Ion Modeling Workshop, 16-18, September 2013,
Keio University, Japan
Study of H- ion extraction and beam optics
using the 2D3V and 3D3V PIC method
K. Miyamoto1), S. Nishioka2), S. Okuda3), I. Goto2), A. Hatayama2)
1) Naruto University of Education
2) Faculty of Science and Technology, Keio University
3) Toshiba corporation
Contents
1. Introduction
2. 2D3V PIC model (K. Miyamoto)
1) Negative ion beam optics with integrated model (source plasma,
extraction region, and accelerator)
・Comparison of negative ion trajectories for beam core and beam halo
・Emittance diagrams
2) The dependence of the plasma meniscus formation and beam halo
on the physical parameters
3. 3D3V PIC model (S. Nishioka)
・ Comparison of the plasma meniscus and beam halo fractions
between 2D and 3D models.
Introduction (I)
・A negative ion source which can produce negative ion beams with high power
and long pulse is the key component for the negative ion based NBI system for
plasma heating and current drive of magnetic fusion reactors.
・It is essential for the development of such a negative ion source to suppress heat
loads of the acceleration grids and beamline components.
・The heat loads of acceleration grids are mainly caused by the direct interception
of H- ion beam as well as electrons stripped from negative ions in the accelerator.
・Especially, a beam halo can result in the heat loads even at the optimum
perveance for the beam core.
The beam halo is observed directly as the beam profile, or indirectly as a component
of the heat loads in the accelerator grids.
Beam halo component in the negative ion beam profile
H.P.L. de Esch, L. Svensson, Fusion Engineering and Design
86, 363 (2011)
Beam halo can be clearly observed on the log scale.
Heat load on the acceleration grids due to the interception of negative ion beam
M.Kamada, M.Hanada, Y.Ikeda and L.R. Grisham, AIP Conf. Proc. 1097, 412 (2009).
A1G
A2G
SL
D]
GRG
Introduction (II)
・The purpose of our study is to clarify the physical mechanism of beam halo
formation, especially the relation between the meniscus and beam halo, in order
to suppress the heat load due to the direct interception of negative ion beams.
・We have succeeded in the integrated modeling of negative ion beam from
plasma meniscus formation to the beam acceleration by extending our previous
2D3V PIC model .
・Our extended model makes it possible to simulate not only the source plasma
with surface H- production, but also the H- acceleration self-consistently
without any assumption of plasma meniscus.
・The dependence of the plasma meniscus formation and beam halo on the
following physical parameters are investigated:
- Negative ion current density
- Extraction voltage
- Effective electron confinement time
2D PIC simulation model (I)
e
~
0
electron
+ H+
－ H-
Magnetic filter
All the particles
~
  6350
~
y~
ymax
+
+
－
e
e
e
－
×
source
plasma
B-field for electron
suppression
－
removed
Dirichlet condition
~
y~
y min
PG
EXG ESG
~
x~
xmin
A1G
A2G
GRG
~
x ~
xmax
Physical quantities
Time
First 2D space coordinate
Second 2D space coordinate
Velocity
Electrostatic potential
Magnetic flux density
Current density
density
Cross field electron diffusion
coefficient
Symbol
~
t
~
x
~y
v~
~

~
B
~
J
n~
~
D
Normalization
 pet
x  De
y  De
v vth

e kTe
B me pe e

j ene vth
nN e N x ( N y ) PG
D  De  pe
2
2D PIC simulation model (III)
1. Main physical parameters in the source region
Physical parameters
Symbol
Value
Electron temperature
Te
1 eV
Hydrogen ion temperature
TH 
0.25 eV
0.25 eV (volume production)
1.4 eV (surface production)
TH 
Electron density
ne
1018m-3
Electron Debye length
De
7.4×10-6 m
Electron plasma frequency
 pe
5.6×1010 rad/s
・Initial number of super-particles
electron: Ne = 9.5×105, H+: NH+ = 1×106, volume produced H-: NH- = 5×104
The ratio of NH- to Ne is determined from the experimental result of nH- / ne
in the volume production.
C. Courteille, A. M. Bruneteau, M. Bacal, Rev. Sci. Instrum., vol. 66, 2533-2540 (1995).
・Electrons, H+ ions, and volume produced H- ions are assumed to be launched
with Maxwellian distributions.
2D PIC simulation model (III)
2. Electron Diffusion process across the transverse magnetic field due to
electron-electron and electron-neutral collisions
Magnetic filter
A random-walk process with step lengths
normalized random number
~ ~
~
xd  2Dt   x   //  
D 
kTe
me etot

1

1

 //
 //
e
e

2
 pe  etot

A characteristic time of
electron escape to the
arc chamber
A characteristic time of
electron diffusion across
the magnetic filter
3. Surface produced negative ions on the surface of the PG
PG
H-
y～
HH-
H-H
-
H-
x～
EXG
・Surface produced negative ions are
uniformly launched from the PG
surface with a half-Maxwellian
distribution (TH- = 1.4 eV).
R. McAdams, A. J. T. Holmes, D. B. King, and E. Surrey,
Plasma Sources Sci. Technol. 20, 035023-1 (2011).
Simulation results of negative ion beam trajectory (I)
・The present PIC code can reproduce the beam halo observed in an actual
negative ion beam.
Negative ion beam profile near the
exit of the GRG
Snapshot of electrons and negative ions
electron
EXG
PG
ESG
H- ion
A2G
A1G
GRG
90
JH-
80
～
70
y～
60
50
40
30
20
10
0
0
200
400
600
800
～
x
1000
1200
1400
1600
~
y
Simulation results of negative ion beam trajectory (II)
・Negative ion current density
3 mA / cm2 (only volume production)
17.8 mA / cm2 (volume production + surface production)
・ Fraction of heat loads in the accelerator grids due to the
intercepted negative ion beam are evaluated:
A1G: 0 %, A2G: 0.44 %, GRG: 3.2 %
The heat load due to the intercepted negative ions becomes
larger in the downstream grid. This tendency agrees well with the
experimental result.
Particle density profile around the PG
H+ ion
90
80
70
60
50
40
30
20
10
0
50
y～
y～
electron
n~e
60
70
80
90
～
100
110
120
130
90
80
70
60
50
40
30
20
10
0
50
n~H 
60
70
80
x
・Therefore, the plasma quasi-neutrality is held by
H+ and H- ion, i.e., double ion plasma.
The present calculation result supports
the experimental result.
K. Tsumori et al.,, Rev. Sci. Instrum., 83 02B116-1 (2012).
110
120
130
H- ion
y
・The electron density in the bulk plasma near the
PG is negligible.
100
x
～
・The surface produced H- ion density is high not
only at the location of H- ion extraction aperture,
but also in the bulk plasma away from the PG.
90
～
90
80
70
60
50
40
30
20
10
0
50
n~H 
60
70
80
90
～
x
100
110
120
130
Potential Profile around the PG (I)
Line (a)
~
x  100
～
- A. Hatayama, Rev. Sci. Instrum.79, 02B901/1-7 (2008);
- F. Taccogna, P. Mineli, S. Longo, M. Captitelli, and R. Schneider,
Phys. Plasma, 17, 063502-1 (2010).
Potential distributions
φ
・The potential well, which is formed in order
to accelerate H+ ions and reflect the surface
produced H- ions toward the PG.
・The depth of the potential well is evaluated to
be approximately 0.5 eV.
~
y  40
～
90
80
70
60
50
40
30
20
10
0
50
Line (b)
Line(a)
φ
y～
Line(b)
~
y
n~H 
60
70
80
90
～
x
100
110
120
130
~
x
Potential Profile around the PG (II)
The potential profile with the surface produced negative ions is different from that
without these negative ions:
Without surface produced negative ions
With surface produced negative ions
The electric field for the negative ion
extraction is penetrated into the source
plasma region along the PG surface.
Due to the space charge of these negative
ions, the penetration of the electric field for
the negative ion extraction is suppressed.
PG
PG
y
～
y
～
Side wall
base
edge
～
x
～
x
Beam core trajectories
The surface produced negative ions move into the source plasma region, and are
extracted from the central region of the meniscus.
These negative ions are focused by the electrostatic lens formed around the ESG.
PG
PG
EXG
EXG
ESG
A1G
A2G
GRG
90
80
70
y～
y～
60
50
40
30
20
10
0
～
x
0
200
400
600
～
x
800
1000
1200
1400
1600
Beam halo trajectories
The surface produced negative ions, which are launched from the side wall or the
edge of the PG aperture, are over-focused due to the curvature of the edge of the
meniscus.
Since the electrostatic lens near the beam axis hardly focuses the negative ion
beams, these negative ions have large divergent angles, and become the beam halo.
EXG
PG
ESG
PG
EXG
A2G
A1G
GRG
90
80
70
y～
y～
60
50
40
30
20
10
0
～
x
0
200
400
600
800
1000
～
x
1200
1400
1600
10
Divergence angle (rad)
Divergence angle (rad)
Emittance diagrams
Line (a)
5
0
-5
-10
-15
10
20 30
1
Line (b)
0.5
0
-0.5
-1
10
40 50 60 70 80 90
～
20 30
40 50 60 70 80 90
～
y
PG
y
ESG
90
80
70
y～
60
50
40
30
20
10
Beam halo
Beam core
Divergence angle (rad)
EXG
0.15
Line (c)
0.1
0.05
0
-0.05
-0.1
-0.15
10
20 30
40 50 60 70 80 90
y～
0
60
80
100
120
140 160
～
x
180
200
220
240
Summary
We have developed the integrated 2D PIC code for the analysis of the physics of
the beam halo formation, which can simulate not only the source plasma with
surface H- production, but also the H- acceleration self-consistently without any
assumption of plasma meniscus.
・The simulation code reproduces a beam halo observed in an actual negative ion
beams.
・The following physical mechanism of halo formation is shown:
The negative ions extracted from the periphery of the meniscus are over-focused in
the extractor due to large curvature of the meniscus. Theses ions are not focused by
the electrostatic lenses in the accelerator, and consequently result in the beam halo.
Future Plane
The following optimization of the PIC model will be planed:
・Global 3D PIC model with the parallelization: more precise modeling electron loss
along/across the field line, because the plasma meniscus strongly depends on it.
・Coupling of the PIC code with a Monte Carlo code (PIC-MCC)
- surface production process via H atoms and H+ ions
- H- destruction process, for example, mutual neutralization
The dependence of the plasma meniscus
formation and beam halo on the physical
parameters
Simulation model
H- Ion Source
Extraction region
Number of meshes
X = 170, Y = 94
Size of meshes
DX=DY=0.5
Length of time step
~
1 Time Step = t / 10
Number of particles
H+: 1.0×105
H‐: 1.0×104
e: 9.0×104
I. Effect of negative ion current density on plasma meniscus
Comparison of 2D profiles of H- ion density
3 H- surface production / time step
15 H- surface production / time step
(a)
(b)
~
y
~
x
~
x
The penetration of the plasma meniscus is small under a large amount
of H- surface production.
II. Effect of extraction voltage on plasma meniscus
Comparison of 2D profiles of H- ion density
Normalized EG potential: 120
Normalized EG potential: 180
(a)
(b)
~
y
~
x
~
x
As the extraction voltage is larger, the penetration of the plasma
meniscus becomes larger as and consequently the fraction of the
beam halo increases .
III. Effect of electron confinement on plasma meniscus
 From the comparison without and with the magnetic filter, it is
suggested that the fraction of beam halo depends on the electron
density near the PG aperture.
 The electron density depends on the effective electron
confinement time in the source plasma.
 In the present simulation, the effective electron confinement
time can be varied by changing the parameter of  //   .
 The large value of  //   means that the effective electron
confinement time is long, and thus, the electron density near the
PG aperture becomes high.
Comparison of 2D density profiles
electron density
 //    0.01
 //    0.04
 //    0.01
 //    0.04
negative ion density
 In the case of the short effective electron confinement time, the
penetration of the plasma meniscus into the source plasma
becomes deep since the Debye shielding of the H- extraction
electric field becomes small. Thus, the fraction of the beam halo
increases.
 The electron confinement time depends on the characteristic
time of electron escape along the magnetic field as well as the
characteristic time of electron diffusion across the magnetic
field. Therefore, it is indicated that such parameters as the
strength of the magnetic filter and the size of the arc chamber
are important for the design of the negative ion sources to
reduce the beam halo.
2D PIC simulation model (IV)
・The scale is normalized by the electron Debye length. Since this large different size
between the electron Debye length and the real negative ion source will cause
considerable high computation cost, the simulation model is scaled down.
Lsim = s Lreal (s :scale factor)
・ The strengths of the applied voltages and the magnetic field are modeled followed
by the scale down:
Electric field
(1) Extraction voltage
Magnetic field
The extraction voltage is modeled in order to match
the perveance for the real negative ion source.
 rPG 2sim J H 


.5
Vext 1sim

 rPG 2real J H 


.5
Vext 1real
Vext sim  s 4 / 3 Vext real
(2) Acceleration voltages
The applied voltages in the accelerator are modeled to
satisfy the law of scaling.
The magnetic field in the simulation
is given by the scale down of the
Larmor radii of electrons:
Bsim 
vsim
Breal .
sv real
vsim
Vsim

 s 2 / 3.
vreal
Vreal
V1 sim : V2 sim : V3 sim  V1 real : V2 real : V3 real
V1 : voltage in the first gap (ESG-A1G)
V2 : voltage in the second gap (A1G-A2G)
V3 : voltage in the third gap (A2G-GRG)
Bsim  s 1/ 3 Breal .
Beam optics study
Culham
A. J. T. Holmes and M. P. S. Nightingale, Rev. Sci.
Instrum., 57, 2402 (1986).
JAEA
K. Miyamoto et al., in Proceeding of the joint meeting of the 7th
International Symposium on the Production and Neutralization of
Negative Ions and Beams and 6th European Workshop on the
Production and Application of Light Negative Ions (Upton, New
York, Oct. 23 ~ 27, 1995), AIP CONFERENCE PROCEEDINGS
380 (1996) pp. 390 ~ 396.
Linear scale
Linear scale
Log scale
Log scale