Plasma Medicine in Vorpal
Alexandre Likhanskii
Tech-X Corporation
Tech-X Workshop / ICOPS 2012,
Edinburgh, UK
8-12 July, 2012
Motivation
Fluid plasma models need
artificial seed electrons to
launch streamers
J. Phys. D: Appl.
Phys. 43 (2010)
Can fluid model accurately resolve
streamers?
• Charged species number density – from 1016 m-3 to 1022 m-3
• Typical sheath size – 10 microns
• Typical grid size for accurate resolution – 1 micron
•Validity of Fluid approach – Maxwellian EEDF
• Consider one 3D cell with 1 micron grid size
• One electron per one cell -> 1018 m-3
• Is fluid approach valid for description of
low density plasma phenomena at micron scales?
• Is it possible to resolve 3D structure using fluid code?
Kinetic effects can be captured using PIC
approach:
• Poisson or full Maxwell equations for electric field
• Track motion of macroparticles (groups of charged
particles) instead of considering number densities
• MC collision model for all relevant plasma processes
Advantage
More accurate physics
Disadvantage
Slow speed for many
particles
VORPAL has a comprehensive PIC-DSMC
plasma model
• Poisson equation is solved using biconjugate gradient method with
algebraic multigrid preconditioner (in Trilinos package)
• Plasma model includes kinetic electrons, kinetic nitrogen and oxygen
molecular ions, fluid neutral molecular nitrogen and oxygen
• Several types of collisions: inelastic collisions, ionization, excitation,
charge exchange, recombination, attachment
• Serial/Parallel 2D/3D simulations
Particles are pushed using standard FDTD
algorithm
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Area weighting preserves charge exactly
Why are atmospheric pressure discharges
so challenging for PIC codes?
Exponential growth of number of particles due to avalanche
ionization -> significant increase in computational time for PIC
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8 …… 1000
Why are atmospheric pressure discharges
so challenging for PIC codes?
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Small ND
Need PIC
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Consider different stages of discharge
for one cell
Moderate ND
PIC -> Fluid
transition
Large ND
PIC is not feasible
Need Fluid code
How does VORPAL handle the problem of
exponential particle growth?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
How does VORPAL handle the problem of
exponential particle growth?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
How does it work?
How does VORPAL handle the problem of
exponential particle growth?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
How does it work?
Step 1:
Have 6
macroparticles
with W=1 each
How does VORPAL handle the problem of
exponential particle growth?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
How does it work?
Step 1:
Have 6
macroparticles
with W=1 each
Step 2:
Combine pairs
of particles
How does VORPAL handle the problem of
exponential particle growth?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
How does it work?
Step 1:
Have 6
macroparticles
with W=1 each
Step 2:
Combine pairs
of particles
Step 3:
End up with
3 macroparticles
with W=2 each
How does VORPAL handle the problem of
exponential particle growth?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
What can be assigned?
• Different sorting algorithms
• Threshold number of macroparticles per cell for the combining
• Maximum weight of macroparticles
What happens during plasma decay stage?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
How does it work?
Step 1:
Start with
3 macroparticles
with W=2 each
What happens during plasma decay stage?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
How does it work?
Step 1:
Start with
3 macroparticles
with W=2 each
Step 2:
Split particles
Into pairs
What happens during plasma decay stage?
• PIC code -> particles are represented via macroparticles
• 1 macroparticle = N (nominal number) regular particles
• Introduce weight W of macroparticle ->
one macroparticle contains W*N regular particles
How does it work?
Step 1:
Start with
3 macroparticles
with W=2 each
Step 2:
Split particles
Into pairs
Step 3:
End up with 6
macroparticles
with W=1 each
Does it really work?
1D Ex, V/m 2D Ex, V/m
Set 1
Set 2
3.3 ns
3.3 ns
We performed studies of surface discharge
propagation with different combination parameters
and observed no visible difference
Back to plasma medicine:
Simulation parameters
• Simulation Domain – 1cm x 1cm
• Grid – 5000 x 5000 (2µm grid size)
• Time step = 75 fs
• 1 macroparticle = 4*104 particles/m
• Threshold number of particles in cell for combining is 5
• Gas – atmospheric air (Oxygen/Nitrogen mixture)
• Collisions – ionizations, excitation, elastic
• Boundary conditions – bottom electrode is grounded,
Negative voltage of -30kV (with 0.1ns rise time) is applied to top
electrode
• Relative dielectric permittivity of tissue is 20
• Initial electrons are randomly seeded near top electrode
• Tissue surface acts as an absorber for charged species
Evolution of electron number density
Evolution of electron number density
• Streamers are independently generated, but start to overlap during
propagation
• If streamer is close to the tissue, it propagates faster and tends to
shield/deviate neighboring streamer
• Once one streamer touches the surface, surface discharge starts to
propagate
Evolution of electric potential
Evolution of electric potential
• Electric potential is quasi-uniform within the streamer body
• When plasma touches the tissue, the electric potential of
the tissue is mainly defined by the thickness and permittivity
of top dielectric
Evolution of vertical component of electric field
• Electric field inside streamer body is 1-2 orders of magnitude
lower than outside the streamer
• The is an enhancement of electric field near the tissue when
streamer approaches the tissue
• When streamer touches the tissue surface, strong electric field
penetrates into the tissue