HybridPIC Modeling of Hall Thrusters

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Hybrid-PIC Modeling of Hall Thrusters

• Fall 1998
• by
• John Michael Fife
• Advisor
• Prof. Manuel Martinez-Sanchez

Sponsored by Air Force HQ, AFOSR, and AFRL
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Outline

• Introduction and Motivation
• Numerical Modeling
• Discussion
• Summary and Recommendations

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Introduction
Typical Hall Thruster Characteristics (SPT-70)
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Motivation

• Hall thrusters are increasingly being selected
  for space missions requiring optimal specific
  impulse of around 1600 s.
• Lifetime of 7000 hrs is limited by erosion from
  ion impact.
• High-amplitude discharge oscillations are
  problematic.
• Understanding of the acceleration process is
  incomplete.

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Related Research

• Bishaev, Kim, 1978 -- measurements inside the
  acceleration channel using electrostatic and
  emissive probes
• Komurasaki et. al., 1991 -- measurements and 1-D
  modeling
• Hirakawa, M., and Y. Arakawa, 1995 -- 2-D PIC
  simulation -- good basic results using
  nonphysical parameters
• Lentz, C., 1993 -- 1-D numerical model with Bohm
  diffusion -- predicted performance of Komurasaki
  thruster

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Objective

• Construct a flexible 2-D numerical model using
  physical parameters which can be used for
• Basic Science
• Engineering
• Performance
• Lifetime
• Spacecraft Interaction

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Numerical Modeling

• Better understanding of the plasma acceleration
  process
• Predict performance and lifetime
• Provide data for spacecraft interaction studies
• Result a flexible tool useful for thruster design

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Numerical Modeling
Hybrid-PIC Method
PIC Method
Te, ?
?t 5e-11 s
nn, un, ni, ui
?t 5e-8 s
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Numerical Modeling
Innovations in PIC Methodology

• Particle follower for non-uniform grids
• Variable particle mass
• Constant ionizations per cell
• Background pressure modeled

r
z
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Numerical Modeling
Electron Equations
Charge Neutrality
Isothermal Along B
Across B
Continuity
Ohms Law
Conservation of Energy
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Numerical Modeling
Electron Cross-Field Mobility
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Numerical Modeling
Particle-Particle Collisionality
Ionization
Electron-Neutral Inelastic Collisions
Cross-sections from Drawin, 1961
Dugan et. al., 1967
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Numerical Modeling
Computational Cost

• 20,000 lines of active C code
• B-field computation takes 6 hrs
• Simulation takes 4 hrs for convergence
• Time shared equally between particle mover and
  electron fluid integrator
• 80 of computing power goes to relating solutions
  on three grids (physical, computational, and
  magnetic field)

Computing times are for an SGI Octane workstation
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Numerical Modeling
Magnetic Field Computation
? T m
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Results from Numerical Modeling
Vp V
Te eV
ne m-3
nn m-3
CASE 2 SPT-70, 300V, 2.34 mg/s, NEAR CATHODE
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Numerical Modeling
Performance Comparison
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Numerical Modeling
Distribution of Ion Energies
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Numerical Modeling
Facility Interaction
Model for measured utilization efficiency
Thrust efficiency comparison
MODEL
NASA LEWIS
Sankovic, et. al., 1994
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Numerical Modeling
Utility of the Model in Design and Spacecraft
Integration
Parameter
Estimated error

• Performance
• Torque
• Wall erosion rate
• Facility interaction

8
0
48
3
using CASE 2
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Numerical Modeling
Ionization Oscillations
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Comparison Between Model and Experiment
Isothermal Assumption Along Lines of Force is Not
Quite Right
Te eV
Isothermal
Adiabatic
Worst-Case Measured
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Comparison Between Model and Experiment
Acceleration Layer Outside the Channel is not
Observed Experimentally
Vp V
Vp V
Numerical Model
Electrostatic Probe Experiment

• Possibilities
• Near-Wall Conductivity
• Electron Loss to the Metallic Body
• Anomalous Diffusion

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Comparison Between Model and Experiment
Losses to Thruster Body
Anomalous Conductivity
e-
Br
e-
e-
e-
z
SPOKE IONIZATION WAVES, TRANSPORT-TIME
INSTABILITY
AZIMUTHAL DRIFT WAVES
Localized enhancement of cross-field electron
mobility possible.
But these values should be independent of (Ia-Ib)!
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Summary and Conclusions

• The numerical model is a powerful
  state-of-the-art tool for basic research of Hall
  thrusters.
• Predictions can be made of real thruster
  performance, lifetime, torque, facility effects,
  and spacecraft interaction.
• Much about the acceleration process is still not
  well understood.

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Recommendations

• Further investigation of the cross-field
  transport of electrons
• Reformulation of quasi-one-dimensional electron
  equations to include an energy balance along
  lines of force
• Refine models for plasma-metal contact
• Consider using a brute-force particle-particle
  approach in anticipation of parallel computing
  developments