Beams and magnetized plasmas 1 Jean-Pierre BOEUF LAboratoire PLAsma et Conversion d Energie LAPLACE/ CNRS, Université Paul SABATIER, TOULOUSE
Beams and magnetized plasmas 2 Outline 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
Beams and magnetized plasmas 3 Outline 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
anode Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier 4 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 plasma ions electrons EXB drift must be closed (azimuthal symmetry) Hall thrusters, ion sources for processing E cathode (electron emission)
Electric Field (10 4 V/m) Magnetic Field (Gauss) Potential (V) Ionization (10 23 m -3 s -1 ) Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier 5 Hall Thruster EXB B 300 200 V S exhaust plane 15 10 E 100 acceleration 5 x 0 0 0.00 0.02 0.04 0.06 3 ionization Position (cm) exhaust plane 200 150 Electron drift in the azimutal direction: Hall current // EXB 2 1 E x B r 100 50 Magnetic barrier is efficient because of closed drift in azimutal direction 0 0 0.00 0.02 0.04 0.06 Position (cm)
Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier 6 20 kw Hall Thruster PPS 20k ML, SNECMA CNRS CNES, Euopean project HiPER
Azimutal Position Rq (mm) Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier 7 2D PIC simulations predict azimuthal instability 5 E q (V/cm) Amplitude of the azimutal field ~ 0.2-0.4 axial field 4 3-200 -100 Wavelength ~ larmor radius 2 0 y=rq x 1 0 0 1 2 3 Axial Position X (cm) 100 200 B r E x J.C. Adam et al., Physics of Plasmas 11, 295 (2004) EPS 2008 Hersonissos
Beams and magnetized plasmas Principle of positive ion acceleration through a magnetic barrier 8 Azimuthal drift instability - theory 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 V x V z 1. 0. 1. 1. 0. 1. x10 7 m/s 0 1 2 3 Axial Position (cm) Quasi linear theory gives resonances at kvd Large azimutal drift velocity in the exhaust region instability plasma turbulence Short wavelength close to electron gyroradius kvd n n A Ducroq et al. Physics of Plasmas, 13, 102111 (2006) EPS 2008 Hersonissos
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier 9 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? EPS 2008 Hersonissos
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier 10 1D PIC MCC model (azimuthal, EXB direction) z (radial) B EXB direction periodic boundary conditions E x y (azimuthal) x (axial) - 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
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier 11 1D PIC MCC model (azimuthal, EXB direction) B turbulence in azimuthal direction L=0.5 cm E x EXB y 70 V/cm n i n e E y E x =100 V/cm B=100 Gauss n=10 16 m -3 p=0.01 torr
Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier 12 1D PIC MCC model (azimuthal, EXB direction) B turbulence in azimuthal direction E x EXB y L=1 cm L=2 cm n i n e n i n e y y E E E x =100 V/cm B=100 Gauss n=5x10 16 m -3 p=0.02 torr
Mobility (m 2 /V/s) Beams and magnetized plasmas Collisional & turbulent EXB electron transport in a magnetic barrier 13 1D PIC MCC model (azimuthal, EXB direction) e n Classical mobility e 2 2 m n Electron mobility can be deduced from PIC model and compared with classical mobility 10 E=10 4 V/m; B=10 mt - 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 10 12 10 13 m -3 ) 1 0.01 0.1 1 Pressure (torr) classical PIC, n=10 17 m -3 PIC, n=10 16 m -3 Question: can we define a mobility in the conditions of a Hall thruster if we include wall losses (momentum and energy) thruster
Beams and magnetized plasmas 14 Outline 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
Principles of NIS for NBI 15 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
Principles of NIS for NBI 16 EC, IC, and H-NB heating systems, i.e. 73 MW, all required for the 1st phase of ITER EC IC Electron Cyclotron 20 MW/CW, 170 GHz, 24 gyrotrons Ion Cyclotron 20 MW/CW, 35-65 MHz H-NB Heating-Neutral Beam 2 x 16.5 MW, 1 MeV, Deuterium 200 A/m 2, 3600 s The Neutral Beam Injection system is essential for the ITER program
Principles of NIS for NBI 17 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/m 2 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
Principles of NIS for NBI E. Speth et al, Nucl. Fusion 46 S220 (2006) 18 Requirements 1 MeV negative ions, 40 A, 200 A/m 2, 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 H 2 N S grids H - Driver Expansion Region Extraction Region
Plasma transport across the magnetic filter 19 2D PIC MCC model of negative ion source Source geometry and Magnetic Filter driver expansion filter extraction B bias 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)
Plasma transport across the magnetic filter 20 2D PIC MCC model of negative ion source Plasma density and plasma potential Electron Density Plasma Potential 10 18 m -3 5 10 17 42 V 36 V Biased plasma grid 20 V bias 2 10 17 31 V Plasma not uniform along extracting grid due to diamagnetic currents P=80 kw/m
Plasma transport across the magnetic filter 21 2D PIC MCC model of negative ion source 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 Electron Current Density Distribution no negative ions
Plasma transport across the magnetic filter 22 2D PIC MCC model of negative ion source Positive Ion Current Density from PIC MCC simulations v Ions are only weakly magnetized v Positive Ion Current Density Distribution no negative ions
Plasma transport across the magnetic filter 23 2D PIC MCC model of negative ion source Understanding Electron Current Density Distribution n kt e Electron Pressure: P e =n e kt e e n kt e e B B Large electron pressure gradient at the entrance of the filter e e n 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
Plasma transport across the magnetic filter 24 2D PIC MCC model of negative ion source 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 Electron Current Density Distribution
Plasma rotation in an e-beam sustained magnetized plasma column 25 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
1 m Negative Ion Source for Neutral Beam Injection Plasma rotation in an e-beam sustained magnetized plasma column 26 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 filaments ICP or helicons B grids B grids 20 cm Simonin et al., Nucl. Fusion 52 (2012) 063003
Plasma rotation in an e-beam sustained magnetized plasma column 27 Simonin et al., Nucl. Fusion 52 (2012) 063003
Plasma rotation in an e-beam sustained magnetized plasma column 28 New source under investigation Similarities with magnetized plasma columns studied in different labs bias limiter e.g. magnetized plasma column MISTRAL at the PIIM lab in Marseille, france
Plasma rotation in an e-beam sustained magnetized plasma column 29 New source under investigation Similarities with magnetized plasma columns studied in different labs e.g. magnetized plasma column MIRABELLE at IJL, Nancy, France
Plasma rotation in an e-beam sustained magnetized plasma column 30 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 S. Jaeger, N. Claire, C. Rebont, Phys. Plasmas 16, 022304 (2009)
Plasma rotation in an e-beam sustained magnetized plasma column 31 Magnetized plasma column studied in Marseille PIIM Lab m=2 mode, LIF measurements of ion velocity and electric field Measured plasma density (probes) Measured Ion velocity (LIF) C. Rebont, N. Claire, Th. Pierre, and F. Doveil, PRL 106, 225006 (2011)
Plasma rotation in an e-beam sustained magnetized plasma column 32 2D PIC MCC model of magnetized plasma column X 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: 2U B /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
Plasma rotation in an e-beam sustained magnetized plasma column 33 2D PIC MCC model of magnetized plasma column Time averaged potential distribution 1 f 0
Plasma rotation in an e-beam sustained magnetized plasma column 34 2D PIC MCC model of magnetized plasma column Time averaged plasma density distribution 1 0
Plasma rotation in an e-beam sustained magnetized plasma column 35 2D PIC MCC model of magnetized plasma column Time averaged electron temperature distribution 1 0
Plasma rotation in an e-beam sustained magnetized plasma column 36 2D PIC MCC model of magnetized plasma column No steady state solution Rotating Instability Rotation in about 200 s 1 f 0 n (10 14 m -3 ) o Plasma density o Electric Potential
Plasma rotation in an e-beam sustained magnetized plasma column 37 2D PIC MCC model of magnetized plasma column No steady state solution Rotating Instability o Plasma density o Distribution of ion velocity o Electric Potential 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
Plasma rotation in an e-beam sustained magnetized plasma column 38 2D PIC MCC model of magnetized plasma column 1 n (10 14 m -3 ) f (2.5 V) 0 o Plasma density t = s o Electric Potential
Plasma rotation in an e-beam sustained magnetized plasma column 39 2D PIC MCC model of magnetized plasma column 1 n (10 14 m -3 ) f (2.5 V) 0 o Plasma density o Electric Potential t = s
Plasma rotation in an e-beam sustained magnetized plasma column 40 2D PIC MCC model of magnetized plasma column 1 n (log, 10 14 m -3 ) f (2.5 V) 0 o Plasma density o Electric Potential t = s
Beams and magnetized plasmas 41 Conclusions 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
Plasma rotation in an e-beam sustained magnetized plasma column 42 n (10 14 m -3 ) f (2.5 V) 1 n (log, 10 14 m -3 ) T e (5 ev) 0
Plasma rotation in an e-beam sustained magnetized plasma column 43 1 n e (log, 10 14 m -3 ) n i (log, 10 14 m -3 ) 0 Electron and ion densities (log)