beams and magnetized plasmas jean-pierre boeuf ...bpw anu 30/05-03/06/2013. beams and magnetized...
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1
GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas
Jean-Pierre BOEUF
LAboratoire PLAsma et Conversion d’Energie
LAPLACE/GREPHE
CNRS, Université Paul SABATIER, TOULOUSE
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GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas
Ion acceleration and electron transport through a magnetic barrier Principle of positive ion acceleration through a magnetic barrier
Collisional & turbulent EXB electron transport in a magnetic barrier
Illustration of plasma turbulence with simple 1D PIC
Negative ion sources for neutral beam injection Principles of NIS for NBI
Plasma transport across the magnetic filter in a negative ion source
Plasma rotation in an e-beam sustained magnetized plasma column
Conclusion
Outline
3
GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas
Ion acceleration and electron transport through a magnetic barrier Principle of positive ion acceleration through a magnetic barrier
Collisional & turbulent EXB electron transport in a magnetic barrier
Illustration of plasma turbulence with simple 1D PIC
Negative ion sources for neutral beam injection Principles of NIS for NBI
Plasma transport across the magnetic filter in a negative ion source
Plasma rotation in an e-beam sustained magnetized plasma column
Conclusion
Outline
4
GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier
Ion acceleration through a magnetic field barrier
Magnetic barrier = B field ^ to electron path from cathode to anode
~ 300 V between emissive cathode (no cathode sheath) and anode
Drop of electron conductivity in magnetic field barrier
→ Large electric field Ion extraction and acceleration
B
E
an
od
e
cathode (electron emission)
plasma
ions
electrons
EXB drift must be closed (azimuthal symmetry)
Hall thrusters, ion sources for processing
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GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier
0.00 0.02 0.04 0.06 0
1
2
3
Ele
ctr
ic F
ield
(10
4 V
/m)
Position (cm)
0
50
100
150
200
B r
E x
exhaust plane
Ma
gnetic F
ield
(G
auss)
0.00 0.02 0.04 0.06 0
100
200
300
Pote
ntial (V
)
Position (cm)
0
5
10
15
acceleration
ionization
S
V
exhaust plane
Ioniz
ation (
10
23 m
-3 s
-1)
Electron drift in the azimutal direction:
Hall current // EXB
Magnetic barrier is efficient because of
closed drift in azimutal direction
x
E
B EXB
Hall Thruster
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GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier
PPS 20k ML, SNECMA – CNRS – CNES, Euopean project HiPER
20 kW Hall Thruster
7
GREPHE EPS 2008 Hersonissos
Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier
Br
Ex
x
y=Rq
Amplitude of the azimutal field
~ 0.2-0.4 axial field
Wavelength ~ larmor radius
Eq (V/cm)
-200
-100
0
100
200
0 1 2 3
5 4 3 2 1 0
Azim
uta
l P
ositio
n R
q (
mm
)
Axial Position X (cm)
2D PIC simulations predict
azimuthal instability
J.C. Adam et al., Physics of Plasmas 11, 295 (2004)
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GREPHE EPS 2008 Hersonissos
Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier
Large azimutal drift velocity in the exhaust region instability plasma turbulence
Short wavelength close to electron gyroradius
Velocity spread comparable to EXB drift velocity
Generated by turbulence
Dispersion equation of electrostatic waves in a hot
magnetized electron beam • Cold, non magnetized ions
• Kinetic description of magnetized electrons
• Drift velocity not much smaller than thermal velocity
0 1 2 3
Axial Position (cm)
Vx
Vz
Quasi linear theory gives resonances at dkV n
dkV n
A Ducroq et al. Physics of Plasmas, 13, 102111 (2006)
x107 m/s
1.
0.
–1.
1.
0.
–1.
Azimuthal drift instability - theory
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GREPHE EPS 2008 Hersonissos
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier
Theory + simulation predict that transport across B is enhanced by turbulent azimuthal E field
Realistic (and simpler) models of Hall Thrusters need an estimation of electron mobility
Can we define an electron mobility in the conditions of a Hall thruster ?
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GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier
1D PIC MCC model (azimuthal, EXB direction)
- Given E, B, plasma density, gas density
- Particle-In-Cell Monte Carlo Collisions
- 3D-3V trajectories but Poisson’s equation in ExB direction only
- Collisions included, ionization treated as excitation
B
Ex
x (axial)
periodic boundary conditions EXB direction
y (azimuthal)
z (radial)
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GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier
Ey
ne ni
1D PIC MCC model (azimuthal, EXB direction)
turbulence in azimuthal direction
B
Ex EXB
L=0.5 cm
Ex=100 V/cm – B=100 Gauss – n=1016 m-3 – p=0.01 torr
y
70 V/cm
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GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier
1D PIC MCC model (azimuthal, EXB direction)
turbulence in azimuthal direction
E
ni ne
E
ni ne
B
Ex EXB
Ex =100 V/cm – B=100 Gauss – n=5x1016 m-3 – p=0.02 torr
L=1 cm L=2 cm
y
y y
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GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier
1D PIC MCC model (azimuthal, EXB direction)
0.01 0.1 1
1
10
E=104 V/m; B=10 mT
Mobili
ty (
m2/V
/s)
Pressure (torr)
classical
PIC, n=1017
m-3
PIC, n=1016
m-3
- Turbulence appears around 0.1 torr (/n>~2)
- Turbulent mobility depends on plasma density
- No solutions below ~0.01 torr (depends on n)
- Real operating conditions much below 0.01 torr
(gas density 1012 – 1013 m-3 )
Question: can we define a mobility in the
conditions of a Hall thruster if we include
wall losses (momentum and energy)
thruster
Classical mobility
Electron mobility can be deduced from PIC model and compared with classical mobility
2 2e
e
m
n
n
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GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas
Ion acceleration and electron transport through a magnetic barrier Principle of positive ion acceleration through a magnetic barrier
Collisional & turbulent EXB electron transport in a magnetic barrier
Illustration of plasma turbulence with simple 1D PIC
Negative ion sources for neutral beam injection Principles of NIS for NBI
Plasma transport across the magnetic filter in a negative ion source
Plasma rotation in an e-beam sustained magnetized plasma column
Conclusion
Outline
15
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Principles of NIS for NBI
Magnetic barrier (or filter) is also used in hydrogen negative ion sources
Context of fusion applications
Heating of ITER plasma by high energy deuterium neutral beam (1 MeV)
Negative ions produced in a low temperature ICP plasma source
Ions are accelerated to 1 MeV, then neutralized and injected in ITER plasma
At such high energy negative ions easier to neutralize than positive ions
Magnetic filter used to limit electron energy and electron current extraction
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Principles of NIS for NBI
EC Electron Cyclotron 20 MW/CW, 170 GHz, 24 gyrotrons
IC Ion Cyclotron 20 MW/CW, 35-65 MHz
H-NB Heating-Neutral Beam 2 x 16.5 MW, 1 MeV, Deuterium
200 A/m2 , 3600 s
EC, IC, and H-NB heating systems, i.e. 73 MW, all required for the 1st phase of ITER
The Neutral Beam Injection system is essential for the ITER program
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Principles of NIS for NBI
Negative Ion Source for the ITER NBI System
RF Inductively Coupled Plasma at 1 MHz
Must provide negative ions H-/D-, 40 A, 200 A/m2
Must operate at low pressure ~ 0.3 Pa
Co-extracted electron current < negative ion current
Current uniformity better than ±5%
The negative ion source is developped at IPP Garching
Complete Neutral Beam Injection system built in Padova
Source modeling (+ validation experiments) at LAPLACE in Toulouse
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Principles of NIS for NBI
Requirements
1 MeV negative ions, 40 A, 200 A/m2 , current uniformity better than ±5% , pulse duration 3600 s
pressure ~ 0.3 Pa, ICP 100 kW, 1 MHz
co-extracted electron current < extracted negative ion current
filter field
N
S
Driver Expansion
Region
Extraction
Region
N
S
S
E. S
peth
et al, N
ucl. F
usio
n 4
6 S
220 (
2006)
H- H2
grids
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GREPHE BPW ANU 30/05-03/06/2013
Source geometry and Magnetic Filter
Negative Ion Source for Neutral Beam Injection Plasma transport across the magnetic filter
driver filter expansion
bias
extraction
Given absorbed power in driver
Collisions with neutrals included
(elastic, excitation, ionization)
e-i Coulomb collisions included
Simulations performed at lower densities
(scaling assumed, Debye sheath not resolved)
JP Boeuf, J Claustre, B Chaudhury, G Fubiani, Phys Plasmas 19 ,113510 (2012)
G Fubiani, G J M Hagelaar, St Kolev and J-P Boeuf , Phys. Plasmas 19, 043506 (2012)
B
2D PIC MCC model of negative ion source
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma transport across the magnetic filter
Plasma density and plasma potential
Plasma not uniform along extracting grid due to diamagnetic currents
Electron Density
1018 m-3
P=80 kW/m
5 1017
2 1017
42 V
36 V
31 V
Plasma Potential
20 V bias
Biased
plasma grid
2D PIC MCC model of negative ion source
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma transport across the magnetic filter
Electron Current Density Distribution no negative ions
Electron Current Density from PIC MCC simulations
Chamber walls perpendicular to JXB
Magnetic barrier not as efficient as in
closed drift geometry (e.g. Hall thrusters)
Large electron current through filter
Scales as 1/B
Transport across B is strongly affected
(and controlled) by the presence of walls
2D PIC MCC model of negative ion source
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma transport across the magnetic filter
Positive Ion Current Density Distribution no negative ions
Positive Ion Current Density from PIC MCC simulations
Ions are only weakly magnetized
v
v
2D PIC MCC model of negative ion source
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma transport across the magnetic filter
Understanding Electron Current Density Distribution
Large electron pressure gradient at the
entrance of the filter
e en kT B large in the filter
Diamagnetic electron current large in the filter
Because of walls perpendicular to diamag current,
generation of E field // and opposing diamagnetic current
→ asymmetry of plasma
→ EXB current through filter
Electron Pressure: Pe=nekTe
e en kT
e en kT B
B
2D PIC MCC model of negative ion source
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma transport across the magnetic filter
Electron Current Density Distribution
Electron Current Density from PIC MCC simulations
Chamber walls perpendicular to JXB
Magnetic barrier not as efficient as in
closed drift geometry (e.g. Hall thrusters)
Large electron current through filter
Scales as 1/B
Transport across B is strongly affected
(and controlled) by the presence of walls
2D PIC MCC model of negative ion source
25
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
New source under investigation
New Neutral beam Injection system (for DEMO) based on photo-neutralization of negative ions
Proposed by CEA Cadarache (A. Simonin)
Requires a long and thin source to produce an intense beam sheet
Magnetized plasma column (uniform B field)
Plasma generated by filaments in a first phase, ICP or helicons in a second phase
Better uniformity ? Plasma rotation ?
Simonin et al.
Nucl. Fusion 52 (2012) 063003
26
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
New source under investigation
New Neutral beam Injection system (for DEMO) based on photo-neutralization of negative ions
Proposed by CEA Cadarache (A. Simonin)
Requires a long and thin source to produce an intense beam sheet
1 m
filaments
grids B
ICP or
helicons
grids B
Simonin et al., Nucl. Fusion 52 (2012) 063003
20 cm
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
Simonin et al., Nucl. Fusion 52 (2012) 063003
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
New source under investigation
Similarities with magnetized plasma columns studied in different labs
e.g. magnetized plasma column MISTRAL at the PIIM lab in Marseille, france
limiter bias
29
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
New source under investigation
Similarities with magnetized plasma columns studied in different labs
e.g. magnetized plasma column MIRABELLE at IJL, Nancy, France
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
S. Jaeger, N. Claire, C. Rebont, Phys. Plasmas 16, 022304 (2009)
Observation of EXB rotating instability (~5 KHz), m=1 or m=2 mode
Argon, 0.02 Pa, B=16 mT, 50 eV e-beam, 1 m column length, limiter 8 cm diameter
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
Magnetized plasma column studied in Marseille – PIIM Lab
C. Rebont, N. Claire, Th. Pierre, and F. Doveil, PRL 106, 225006 (2011)
Measured plasma density (probes) Measured Ion velocity (LIF)
m=2 mode, LIF measurements of ion velocity and electric field
32
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
B
2D simulation domain, B^ to simulation domain
3D, 3V trajectories
2D Poisson (assumption of uniform column – flute mode)
Charged particle losses in the B direction included o Bohm losses for ions frequency: 2UB/L
o Electron losses when electron reaches end plates and if
energy in the B direction larger than potential difference
between plasma and end wall
o Grid: negative bias – Limiter and walls grounded
2D PIC MCC model of magnetized plasma column
X
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
f
Time averaged potential distribution
2D PIC MCC model of magnetized plasma column
0
1
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
Time averaged plasma density distribution
2D PIC MCC model of magnetized plasma column
0
1
35
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
Time averaged electron temperature distribution
2D PIC MCC model of magnetized plasma column
0
1
36
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
f
No steady state solution
Rotating Instability – Rotation in about 200 s
o Plasma density o Electric Potential
2D PIC MCC model of magnetized plasma column
0
1
n (1014 m-3 )
37
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
No steady state solution
Rotating Instability
o Distribution of ion velocity o Electric Potential o Plasma density
Ion velocity tangent to limiter edge in plasma arm (as in experiments)
Ion velocity perpendicular to limiter edge ahead of plasma arm (as in experiments)
Ion velocity follows EXB
Rotating Instability (Modified Simon-Hoh ?) + Kelvin Helmhotlz structures
2D PIC MCC model of magnetized plasma column
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
t = s
2D PIC MCC model of magnetized plasma column
0
1 f (2.5 V) n (1014 m-3 )
o Electric Potential o Plasma density
39
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
2D PIC MCC model of magnetized plasma column
o Electric Potential o Plasma density
t = s
f (2.5 V) n (1014 m-3 )
0
1
40
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
2D PIC MCC model of magnetized plasma column
o Electric Potential o Plasma density
t = s
f (2.5 V) n (log, 1014 m-3 )
0
1
41
GREPHE BPW ANU 30/05-03/06/2013
Beams and magnetized plasmas
Ion acceleration and electron transport through a magnetic barrier Very simple and appealing concept
Very complex and non-linear operation
Turbulence and plasma-wall interaction both important
Can we define an electron mobility ?
Negative ion sources for neutral beam injection Magnetic filter with non-closed EXB or XB path induces assymetry and leaks
2D PIC model improve understanding of rotating magnetized plasma column
Conclusions
42
GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
0
1
n (1014 m-3)
n (log, 1014 m-3)
f (2.5 V)
Te (5 eV)
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GREPHE BPW ANU 30/05-03/06/2013
Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column
ne (log, 1014 m-3) ni (log, 1014 m-3)
0
1
Electron and ion densities (log)