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Plasma Medicine in Vorpal

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 ).

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Plasma Medicine in Vorpal

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  1. Plasma Medicine in Vorpal AlexandreLikhanskii Tech-X Corporation Tech-X Workshop / ICOPS 2012, Edinburgh, UK 8-12 July, 2012

  2. Motivation Fluid plasma modelsneed artificial seed electrons to launch streamers J. Phys. D: Appl. Phys. 43 (2010)

  3. 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?

  4. 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

  5. VORPAL has a comprehensive PIC-DSMC plasma model • Poisson equation is solved using biconjugate gradient method with algebraic multigridpreconditioner (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

  6. Particles are pushed using standard FDTD algorithm e e e e e Area weighting preserves charge exactly

  7. 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 e e i e i e e e i e 1 2 4 8 …… 1000

  8. Why are atmospheric pressure discharges so challenging for PIC codes? e e i Consider different stages of discharge for one cell e i e e e i e Small ND Need PIC Moderate ND PIC -> Fluid transition Large ND PIC is not feasible Need Fluid code

  9. 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

  10. 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?

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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 3: End up with 6 macroparticles with W=1 each Step 1: Start with 3 macroparticles with W=2 each Step 2: Split particles Into pairs

  18. Does it really work? Set 1 Set 2 2D Ex, V/m 1D Ex, V/m 3.3 ns 3.3 ns We performed studies of surface discharge propagation with different combination parameters and observed no visible difference

  19. 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

  20. Evolution of electron number density

  21. 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

  22. Evolution of electric potential

  23. 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

  24. 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

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