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Simulation of Magnetic Field Guided Plasma Expansion Frans H. - - PowerPoint PPT Presentation

Jan 04, 2023 284 likes •651 views

Simulation of Magnetic Field Guided Plasma Expansion Frans H. Ebersohn, J.P. Sheehan, Alec D. Gallimore, and John V. Shebalin This research is funded by a NASA Space Technology Research Fellowship and DARPA contract number NNA15BA42C. Magnetic

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Simulation of Magnetic Field Guided Plasma Expansion

Frans H. Ebersohn, J.P. Sheehan, Alec D. Gallimore, and John V. Shebalin

This research is funded by a NASA Space Technology Research Fellowship and DARPA contract number NNA15BA42C.

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SLIDE 2

Magnetic field guided plasma expansions show up in the laboratory and in nature.

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  • Plasma thrusters (electrode-

less, magnetic nozzle)

  • Solar phenomena
  • Astrophysical plasma jets
  • Aurora Borealis

Aurora borealis CubeSat Ambipolar Thruster

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SLIDE 3

Ions can be accelerated during the expansion.

How are ions accelerated in these magnetic field expansions?

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SLIDE 4

Ions can be accelerated by the electric field created by fast expanding electrons.

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Quasi-neutral plasma Vacuum

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SLIDE 5

The magnetic dipole force can accelerate ions along magnetic field lines.

  • Particles accelerated by magnetic dipole force. (𝜈 = magnetic

moment) 𝑮𝑒 = 𝛼(𝝂 ⋅ 𝑪)

  • Quantity (𝝂 ⋅ 𝑪) acts like a magnetic potential

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SLIDE 6

The Quasi-1D PIC code incorporates 2D effects to a 1D electrostatic PIC code without 2D costs.

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  • Ion and electron particles
  • Constant background neutral

density

  • Ion and electron collisions

with neutral background

  • Constant magnetic field in

source region (1D)

  • Decreasing magnetic field in

expansion region

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SLIDE 7

The plasma is heated by an oscillating electric field. Heated electrons collide with neutral background.

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𝐾𝑧,𝑢𝑝𝑢 = 𝜗0 𝜖𝐹𝑧 𝜖𝑢 + 𝐾𝑑𝑝𝑜𝑤 𝐾𝑧,𝑢𝑝𝑢 = J0sin(2𝜌 × 𝑔 × 𝑢) 𝑔 = 10 𝑁ℎ𝑨

Based on Meige (2005)

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SLIDE 8

The cross-sectional area variation is found by assuming particles follow field lines.

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𝜖𝑤⊥ 𝜖𝑢 = 1 2𝐶 𝜖𝐶 𝜖𝑡 𝑤∥𝑤⊥ 𝜖𝑤∥ 𝜖𝑢 = − 1 2𝐶 𝜖𝐶 𝜖𝑡 𝑤⊥

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Cross-section variation Magnetic field forces

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SLIDE 9

Simulation parameters are chosen to compare with previous simulations.

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Similar to parameters used by Meige (2005) and Baalrud (2013)

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SLIDE 10

Incorporation of two-dimensional effects leads to capturing ion acceleration.

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SLIDE 11

Incorporation of two-dimensional effects leads to capturing ion acceleration.

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SLIDE 12

Incorporation of two-dimensional effects leads to capturing ion acceleration.

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Ions develop into a beam with some lower energy particles.

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Magnetic field effects on electrons leads to the acceleration of the ions.

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The light electrons are heated in the heating region

𝑤⊥,𝑓 ↑

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Magnetic field effects on electrons leads to the acceleration of the ions.

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𝜖𝑤∥,𝑓 𝜖𝑢 = − 1 2𝐶 𝜖𝐶 𝜖𝑡 𝑤⊥,𝑓

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The light electrons are heated in the heating region

𝑤⊥,𝑓 ↑

High perpendicular velocities leads to rapid acceleration of electrons

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SLIDE 16

Magnetic field effects on electrons leads to the acceleration of the ions.

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𝜖𝑤∥,𝑓 𝜖𝑢 = − 1 2𝐶 𝜖𝐶 𝜖𝑡 𝑤⊥,𝑓

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The light electrons are heated in the heating region

𝑤⊥,𝑓 ↑

High perpendicular velocities leads to rapid acceleration of electrons Charge imbalance leads to the formation of an electric field which accelerates the ions out with the electrons

𝜖𝑤∥,𝑗𝑝𝑜 𝜖𝑢 = q m Einduced

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SLIDE 17

Magnetic field effects on electrons leads to the acceleration of the ions.

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𝜖𝑤∥,𝑓 𝜖𝑢 = − 1 2𝐶 𝜖𝐶 𝜖𝑡 𝑤⊥,𝑓

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The light electrons are heated in the heating region

𝑤⊥,𝑓 ↑

High perpendicular velocities leads to rapid acceleration of electrons Charge imbalance leads to the formation of an electric field which accelerates the ions out with the electrons

𝜖𝑤∥,𝑗𝑝𝑜 𝜖𝑢 = q m Einduced

Ion beam formation

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SLIDE 18

Conclusions and future work.

  • Electrons driven by magnetic field forces create

potential drops which result in ion acceleration.

  • Future simulations will investigate HDLT, CAT, and

VASIMR ion acceleration mechanisms.

  • Perform further parametric study with this test
  • problem. (Additional magnetic field topologies,

heating currents, etc)

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SLIDE 19

Acknowledgements

Thank you for your time!

Questions?

This research is funded by a NASA Office of the Chief Technologist Space Technology Research Fellowship and the DARPA contract number NNA15BA42C. Simulations were performed on the NASA Pleiades and University of Michigan ARC FLUX supercomputers. Thank you to the members of PEPL and NGPDL for their discussions about this research.

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SLIDE 20

BACKUP SLIDES

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SLIDE 21

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Rapid expansion leads to rapid potential drop and more ion acceleration.

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Kinetic simulations are necessary to capture important ion acceleration physics.

  • Evolution of the ion and electron energy distribution functions
  • Instabilities in the plasma
  • Potential structures which form in the plasma plume
  • Capture most fundamental physics for ion acceleration

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SLIDE 23

Electron temperatures are around 4-5 eV

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Electron distribution only varies slightly spatially.

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Electron temperatures vary greatly through domain when including two-dimensional effects

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Electron distribution shows significant variation through the domain.

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Cross-sectional area variation changes density, but no major ion acceleration is seen.

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Magnetic field forces result in ion acceleration.

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SLIDE 29

Full simulations shows characteristics of both effects.

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Magnetic mirror simulation setup Physics:

  • Charged particles moving from

weak magnetic field to strong magnetic field region are confined for certain conditions.

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Setup:

  • One-dimensional domain
  • Particles loaded Maxwellian

velocity distribution at center of domain.

  • Ignore electric field forces,

uncoupled particle motion. Goal:

  • Validate magnetic field forces

Z

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SLIDE 31

Code correctly reproduces analytical loss cone

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Magnetic mirror velocity distribution and loss cone (blue)

𝑤⊥

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𝑤∥

2 + 𝑤⊥ 2 > 𝐶𝑛𝑗𝑜

𝐶𝑛𝑏𝑦 Conditions for trapped particles:

𝑤∥,0 𝑤⊥,0 = 𝐶𝑛𝑏𝑦 𝐶𝑛𝑗𝑜 − 1 = 1.0

Loss Cone:

𝐶𝑛𝑏𝑦 𝐶𝑛𝑗𝑜 = 2.0

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SLIDE 32

The fraction of particles trapped agrees well with theory

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𝛿 = 1 −

𝐶𝑛𝑗𝑜 𝐶𝑛𝑏𝑦 = 2 2

𝐽𝑜𝑗𝑢𝑗𝑏𝑚 𝑄𝑏𝑠𝑢𝑗𝑑𝑚𝑓𝑡: 105 𝑄𝑏𝑠𝑢𝑗𝑑𝑚𝑓𝑡 𝑄𝑠𝑓𝑒𝑗𝑑𝑢𝑓𝑒: 7.0710 ⋅ 104 𝑄𝑏𝑠𝑢𝑗𝑑𝑚𝑓𝑡 𝑇𝑗𝑛𝑣𝑚𝑏𝑢𝑗𝑝𝑜: 7.0733 ⋅ 104 𝑄𝑏𝑠𝑢𝑗𝑑𝑚𝑓𝑡 𝐹𝑠𝑠𝑝𝑠: 0.033%

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SLIDE 33

Quasi-neutral plasma expansion simulation setup

Physics:

  • A quasi-neutral plasma beam expansion is controlled by a strong

magnetic field.

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Setup:

  • Hydrogen ions and electrons are injected into a domain with a

diverging applied magnetic field.

  • Simulations are compared between a 2D r-z simulation (OOPIC) and

QPIC. Goal:

  • Validate cross-sectional area variation
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SLIDE 34

OOPIC simulation of quasi-neutral jet expansion following magnetic field lines

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SLIDE 35

Results from QPIC agree well with the centerline number density from OOPIC

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