topics telecon - dec 18
DESCRIPTION
Topics Telecon - Dec 18. Review Cheryl’s dissertation proposal slides: ignore “Results” section for now (will replace this with more organized results set, primarily based on IEPC 09 run) Need help with slide 6 – relevant Hall thruster simulations Additional comments on slides 5 and 7? - PowerPoint PPT PresentationTRANSCRIPT
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
TopicsTelecon - Dec 18
Review Cheryl’s dissertation proposal slides: ignore “Results” section for now (will replace this with more organized results set, primarily based on IEPC 09 run) Need help with slide 6 – relevant Hall thruster simulations Additional comments on slides 5 and 7?
Wall loss model – review notes sent by Eduardo
Upwind discretization – turned “on/off” in the code?
Research plan: slides 45-52 – seems ambitious, need help with prioritization/goals
IEEE TPS paper edits – Thanks, Eduardo!
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
AXIAL-AZIMUTHAL HYBRID FLUID-PIC SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL
THRUSTER
Cheryl M. Lam
Advisor: Mark A. Cappelli
Stanford Plasma Physics Laboratory
Mechanical Engineering Department
Dissertation Proposal Meeting
December 20, 2013
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Dissertation Outline
I. Introduction
II. Hall Thruster Simulations (Background)
III. Model Description: Hybrid Fluid-PIC z-θ Model
IV. Model Sensitivities
V. Simulation Results
VI. Discussion
VII. Conclusions and Future Work
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Hall Thruster
Electric space propulsion device Demonstrated high thrust efficiencies
Up to 60% (depending on operating power)
Deployed production technology Design Improvements Better physics understanding
Basic Premise:
Accelerate heavy (positive) ions through electric potential to create thrust E x B azimuthal Hall current
Radial B field (r) Axial E field (z)
Ionization zone (high electron density region)
Electrons “trapped” Neutral propellant (e.g., Xe) ionized
via collisions with electrons Plasma
Ions accelerated across imposed axial potential (Ez / Φz) & ejected from thruster
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Motivation
Hall thruster anomalous electron transport Super-classical electron mobility observed in experiments1
Theory: Correlated (azimuthal) fluctuations in ne and uez induce super-classical electron transport
2D r-z models use tuned mobility to account for azimuthal effects2,3
3D model is computationally expensive
First fully-resolved 2D z-θ simulations of entire thruster
** Initial development by E. Fernandez
Predict azimuthal (ExB) fluctuations
Quantify impact on electron transport
Channel Diameter = 9 cm
Channel Length = 8 cm
1Meezan, N. B., Hargus, W.A., Jr., and Cappelli, M. A., Physical Review, Vol. 63, No. 2, 026410, 2001. 2Fife, J. M., Ph.D. Dissertation, Massachusetts Inst. of Technology, Cambridge, MA, 1999. 3Fernandez et al, “2D simulations of Hall thrusters,” CTR Annual Research Briefs, Stanford Univ.,1998.
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Hall Thruster Simulations
2D radial-axial (r-z) simulations Fife Michelle Eunsun? – ongoing
2D axial-azimuthal (z-θ) Aaron Mine French (Garrigues, Bouchoule, Adam, et al.) – not full azimuth Italian (Taccogna, Cappitelli?)
3D Cite recent work – fully-kinetic (PIC) computationally expensive:
smaller geometry (smaller-scale thruster) and/or shorter runs
Review IEPC 2013 papers
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Relevance of Hybrid z-θ Simulations
Thruster geometry Scale (thruster size) Resolve full azimuth
No artificial introduction of periodicity
Time scales of interest Hybrid approach enables longer (~100s μs) simulations Low to mid-frequency waves (~10 kHz – 100 MHz?? More like ~MHz
because inertialess?)
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
2D in z-θ No radial dynamics
E x B + θ
Br: purely radial
(measured from SHT laboratory discharge)
Imposed operating voltage
(based on operating condition)
Geometry
extends 4 cm past channel exitz: 40 points, non-uniform
θ: 50 points, uniform
Channel Diameter = 9 cm
Channel Length = 8 cm
Anode Cathode
G
Anode Exit Plane
G
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Hybrid Fluid-PIC Model
Ions: Particle-In-Cell approach Non-magnetized No particle-particle collisions; Wall collisions modeled in some cases
Neutrals: Collisionless particles (Particle-In-Cell approach) Injected at anode per mass flow rate No particle-particle collisions; Wall collisions modeled in some cases Ionized per local ionization rate
Based on fits to experimentally-measured collision cross-sections, assuming Maxwellian distribution for electrons
Electrons: Fluid continuum Continuity (species & current) Momentum
Drift-diffusion equation Inertial terms neglected
Energy (1D in z) Convective & diffusive fluxes Joule heating, Ionization losses, Effective wall loss
Quasineutrality:ni = ne
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Particle-In-Cell (PIC) Approach Particles: arbitrary positions
Force Particle acceleration
Interpolate: Grid Particle Plasma properties evaluated at grid points
(Coupled to electron fluid solution) Interpolate: Particle Grid
Bilinear Interpolation
Ions subject to electric field:
PIC Ions & Neutrals
rNW
rSE
rNE
rSW
FNW
FSE
FNE
FSW
Interpolation:Particle Grid
Interpolation:Grid Particle
BuqEqamFLorentz
≈ 0
neglect
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Ionization rate Nu_en nedot
Neutral injection Injection velocity: slow vs “normal” (thermalized) Wall collisions
Neutral particles reflected upon collision with anode or inner/outer radial channel walls
Ions recombine (with donor electron) to form neutral upon collision with inner/outer radial channel walls
Particles still otherwise collisionless, i.e., we do not model particle-particle collisions
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Fluid Equations
Species Continuity
Current Continuity
eeee nunt
n
)(
0
Jt
0
ni = ne
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Fluid Equations
Momentum: Drift-Diffusion Neglect inertial terms
ue E Dner
ne
1
1 en
ce
2
Ez
Br 1
1 en
ce
2kTe
eneBr
ne
z 1
1 en
ce
2k
eBr
Te
z
)1( 2
2
en
ceenm
e
Classical Mobility
e
kTD e
uez Ez Dne
ne
z D
Te
Te
z 1
1 en
ce
2
EBr
1
1 en
ce
2
kTe
eneBrrne
Classical Diffusion
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Fluid Equations
Momentum: Drift-Diffusion Neglect inertial terms
ue E Dner
ne
1
1 en
ce
2
Ez
Br 1
1 en
ce
2kTe
eneBr
ne
z 1
1 en
ce
2k
eBr
Te
z
)1( 2
2
en
ceenm
e
Classical Mobility
e
kTD e
uez Ez Dne
ne
z D
Te
Te
z 1
1 en
ce
2
EBr
1
1 en
ce
2
kTe
eneBrrne
θ fluctuations/dynamics
classical E x B diamagnetic
Classical Diffusion
classical E x B diamagnetic
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Fluid Equations
Combine current continuity and electron momentum to get convection-diffusion equation for Φ:
A1
2 2 A2
A3
2z2 A4
z A5 0, where
E
where (φ is electric potential)
A1 ne
r2, A3 ne ,
A2 1r
( ne
r
rne
1
1 en
ce
2
z
ne
Br
ne
Br
z
1
1 en
ce
2 )
A4 1
1 en
ce
2
1rBr
ne
ne
z
ne
z
ne
rBr
1
1 en
ce
2
A5 f (ne ,Te ,, en ,ce ) ne
rui
ui
rne
ne
uiz
z uiz
ne
z
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Fluid Equations
Energy (Temperature) Equation 1D in z
wallionizjouleeeeeeee
e SSSqukTnTut
Tkn
)(23
eeneejoule unmS
eeieiioniz kTnEnS2
3
ewallwallwall kTL
S2
312
where
with ionization cost factor αi = 1 (simplest model)
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Solution Algorithm
Iterative Solve Φ
Time Advance Particle Positions & VelocitiesNeutrals & Ions (subject to F=qE)
Ionize Neutrals
Inject Neutrals
Calculate Plasma Propertiesni-PART, vi-PART, nn-PART, vn-PART ni-GRID, vi-GRID, nn-GRID, vn-GRID
QUASINEUTRALITY: ne = ni = nplamsa
Time Advance Te=Te(ne, ve)
Calculate Φ=Φ(ne, vi-GRID) ↔ EGRID
Calculate ve=ve(Φ, ne, Te)
r = Φ – Φlast-iterationr < ε0
CONVERGED
Calculate vi-GRID-TEST= vi-GRID(EGRID)
EGRID EPART
LEAPFROG
RK4
DIRECT SOLVE 2nd-order F-D
Spline
Boundary Conditions:
• Dirichlet in z (Φ,Te)
• Periodic in θ
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Model Sensitivities
Grid – current non-conservation
ICs and BCs
Numerical stability/sensitivity of energy (Te) equation
Source/Sink terms Ionization cost factor
– Constant factor
– Dugan model Energy loss to wall
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Sample Results
IEPC 2009 runs
Build upon these
More recent – with inclusion of wall collisions?? IEPC2013 – spoke, do not understand Higher voltage – do not understand
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Numerical Grid
40 points non-uniform in z50 points uniform in θ
Previous 100V (IEPC 2009)160V simulation (new)
61 points uniform in z25 points uniform in θ
100V simulation (new)
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Simulation Parameters
Initial Conditions
Neutrals: neutral only run to establish profile
Ions: uniform # particles per cell w/ Maxwellian velocity distribution
Te: based on experiment
Boundary ConditionsTe (z = 0) = 3.2 eV
Te (z = 0.12 m) = 3.0 eV
Operating Voltage 100V (160V)
Neutral Injection 2 mg/s (Xe propellant)
Timestep
Run Length
dt = 1 ns
~187 μs
Computational Performance
~7 days on Intel Xeon 5355 2.66 GHz (64-bit single core)
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Plasma Density
Time-Averaged Plasma PropertiesElectron Temperature
Axial Ion Velocity Electric Potential
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Temperature
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Runaway Ionization
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Axial Ion Velocity
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Fluctuations
Distinct wave behavior observed:
Near exit plane (as before) Tilted: + z, - ExB Higher frequency, faster moving,
shorter wavelength Transition to standing wave
(purely +z) downstream of exit plane (z = 0.1 m)
Mid-channel
Tilted: - z, + E x B Lower frequency, slow moving,
longer wavelength “More tilted” (stronger/faster θ
component) – compared to previous
Near anode Rotating spoke m = 2 (100V)
E x B
Axial Electron Velocity
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Wave Propagation
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Rotating Spoke
Near anode (z ≤ 0.01 m)
Primarily azimuthal m = 2 vph = ~ 1 km/s f = 10-20 kHz
Anode Cathode
E x B
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Correlated ne and uez fluctuations generate axial electron current
Correlated fluctuations generate axial current
Uncorrelated
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Current non-conservationIEPC13 100V run
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Transport
Axial Electron Mobility:ze
ez
Eqn
J
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Transport
Preliminary Simulation:
Spoke does not lead to anomalous transport
Axial Electron Mobility:ze
ez
Eqn
J
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Rotating Spoke – IEPC13 100V case
Near anode (z ≤ 0.01 m)
Primarily azimuthal m = 2 vph = ~ 1 km/s f = 10-20 kHz
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Fluctuations in θ – IEPC09?? Or 13?
Anode Cathode
E x B
E x B
E x B
f = 40 KHzλθ = 5 cmvph = 4000 m/s
f = 700 KHz
λθ = 4 cmvph = 40,000 m/s
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Streak Plots – IEPC09?? Or 13?
E x B
E x B
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
160V SimulationRotating Spoke (m = 1)
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
160V SimulationElectron Transport
Spoke does not lead to anomalous transport
Axial Electron Mobility:ze
ez
Eqn
J
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Electron Fluid Equations
Momentum: Drift-Diffusion Neglect inertial terms
Correlated azimuthal fluctuations induce axial transport:
ue E Dner
ne
1
1 en
ce
2
Ez
Br 1
1 en
ce
2kTe
eneBr
ne
z 1
1 en
ce
2k
eBr
Te
z
)1( 2
2
en
ceenm
e
Classical Mobility
e
kTD e
uez Ez Dne
ne
z D
Te
Te
z 1
1 en
ce
2EBr
1
1 en
ce
2kTe
eneBrrne
Previous modelsunder-predict
Jez=qneuezθ fluctuations/dynamics
eeinducede unJ~~
,
classical E x B diamagnetic
Classical Diffusion
classical E x B diamagnetic
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Azimuthal Fluctuations induce Axial Transport
Consider
Induced Current
r
ce
en
ez B
Eu
xBE
2
1
1
xBExBE ezeez uqnJ
cos2
1
)cos(
1
1)cos(
200
0
020
T
v
En
B
qJ
dttB
EtnqJ
ce
enr
eez
T
tr
ce
en
eez
xBE
xBE
Induced current depends on phase shift ξ
t
ξ
Eθ = E0cos(ωt)
ne = n0cos(ωt + ξ)
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Correlated ne and uez fluctuations generate axial electron current
Correlated fluctuations generate axial current
Uncorrelated
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Fluctuations
Compare to experiments
Linearized dispersion relations?
Future results: include dispersion analysis/maps
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Anomalous current Contributions (from various terms) to electron current Axial variation Relate to shear, other gradients?
Electron transport / anomalous current – trends with operating conditions (e.g., increased voltage)
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Anomalous electron transport
Suggestions for future work FV? Fully kinetic simulations
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Recent Progress & Challenges
Addition of particle collisions with thruster walls Neutral particles reflected upon collision with anode or inner/outer
radial channel walls Ions recombine (with donor electron) to form neutral upon collision with
inner/outer radial channel walls Particles still otherwise collisionless, i.e., we do not model particle-
particle collisions
Finer axial (z) grid resolution near anode
Stability challenges Sensitivity to Initial Conditions and Boundary Conditions Strong fluctuation in Te
Current conservation Finite Difference – present model Finite Volume
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Additional Simulations – 100V
Establish stable long-running simulation (~600 μs – 1 ms) for low voltage (100V) case Start from (continue) IEPC 2009 simulation
Ionization cost factor = 1 No wall collisions; Slow neutral injection velocity Zero-slope BC for Te
Increase number of particles (ionizspc) to enable longer simulation
Grid refinement study Finer grid in z: current non-conservation, structure near anode Finer, varied grid in theta: impact periodicity, azimuthal wavelength?
Initial Conditions Increased neutral density spoke at anode? Shape of neutral density profile (peaked/sloping, by how much) More realistic plasma (electron/ion) density profile and/or magnitude
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Additional Simulations – Higher Voltage
Higher voltage runs Incrementally increase operating voltage Look for trends (in frequency/wavelength/direction of fluctuations,
electron transport, anomalous contribution to transport)
Initial Conditions – Waves Smooth initial profiles (based on prescribed profile or experiment) –
allow fluctuations to evolve (as before) If needed, of interest, “seed” with particular waves/modes
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Development Process
Establish stable low voltage (100 V run)
Increase operating voltage – with all other conditions same as for 100V case Adjustments as needed to establish stable higher voltage run
Changes to 100V case – model improvements, additional physics, etc. Establish stable 100V run Increase operating voltage – with all other conditions same as for 100V
case Adjustments as needed to establish stable higher voltage run
REPEAT
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Model Improvements
Te stability and BC/IC impacts Stability and sensitivity analysis – contribution of source/sink terms,
esp. wall loss and ionization cost Enforcement of (IC/return to) experimental profile and/or experimental-
based limits Prescribed (fixed value) vs. zero-slope condition at domain boundaries Ionization cost factor
Dugan model Tuned constant factor?
Improved/tunable wall loss model Introduction of diffusive damping term? Effect of spline smoothing Implicit solve?
Improve stability – consider more global changes to model “External” power supply circuit model (potential BC) Hyperviscous damping (for potential equation)
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Model Improvements
Incremental changes (additions) to model – additional physics Introduction of wall collisions (w/ higher thermal injection velocity) Revisit ionization rate implementation?
Electron transport/mobility – sustain/generate waves (also help stability) Additive “baseline” mu_perp or nu_en Experimental mobility (in lieu of or in addition to mu_perp) Experimental or additional (or Bohm-like) mobility for electron fluid
equations only
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Analysis
Plasma properties (time-averaged and movies) compared to experiment – axial profiles – give sense of overall simulation performance (how well to we simulate/approximate experimental) Plasma density, axial ion velocity, electron temperature, etc.
Discharge current Axial profile Time evolution
Axial electron mobility – compare to experiment (axial profile)
Characterization of waves By “eye” – velocity, frequency, wavelength, direction Dispersion map/analysis Changes in direction, “Break up” of wave structure Correspond to any known/expected waves?? Experiment or theory?
Anomalous contribution to current Anomalous vs. classical terms Relate to shear, ne/Br gradient, etc.
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Publications
Conference Papers IEPC 2009 GEC 2012? IEPC 2013
Journal Papers IEEE TPS Special Ed. – Submitted
Planned additional publications Journal paper: waves and transport
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Questions?
Dissertation Outline
I. Introduction
II. Background
III. Model Description
IV. Sensitivities
V. Results
VI. Discussion
VII. Conclusions
Research Plan
Timeline
2D SIMULATIONS OF COHERENT FLUCTUATION-DRIVEN ELECTRON TRANSPORT IN A HALL THRUSTER
Stanford UniversityPlasma Physics Lab
Back-up and Throw Away