Plasma Medicine in Vorpal Tech-X Workshop / ICOPS 2012, Edinburgh, UK 8-12 July, 2012 Alexandre Likhanskii Tech-X Corporation

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

Charged species number density – from m -3 to 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 -> 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? Can fluid model accurately resolve streamers?

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 Kinetic effects can be captured using PIC approach: AdvantageMore accurate physics DisadvantageSlow speed for many particles

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 VORPAL has a comprehensive PIC-DSMC plasma model

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

Exponential growth of number of particles due to avalanche ionization -> significant increase in computational time for PIC e e i e e i e e i e …… 1000 Why are atmospheric pressure discharges so challenging for PIC codes?

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

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 Step 1: Have 6 macroparticles with W=1 each 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 Step 1: Have 6 macroparticles with W=1 each Step 2: Combine pairs of 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 How does it work?

Different sorting algorithms Threshold number of macroparticles per cell for the combining Maximum weight of macroparticles 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?

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

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

Simulation Domain – 1cm x 1cm Grid – 5000 x 5000 (2µm grid size) Time step = 75 fs 1 macroparticle = 4*10 4 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 Back to plasma medicine: Simulation parameters

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 electron number density

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 electric potential

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 Evolution of vertical component of electric field