GEC_09_DBD

Plasma Medicine in VorpalTech-X Workshop / ICOPS 2012,Edinburgh, UK 8-12 July, 2012Alexandre LikhanskiiTech-X Corporation

11

Fluid plasma models need artificial seed electrons to launch streamers J. Phys. D: Appl. Phys. 43 (2010)Motivation22 Charged species number density from 1016 m-3 to 1022 m-3 Typical sheath size 10 microns Typical grid size for accurate resolution 1 micronValidity 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?Can fluid model accurately resolve streamers?33 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 processesKinetic effects can be captured using PIC approach:AdvantageMore accurate physicsDisadvantageSlow speed for many particles44 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 simulationsVORPAL has a comprehensive PIC-DSMC plasma model55

Area weighting preserves charge exactly

eeeee

Particles are pushed using standard FDTD algorithm6Exponential growth of number of particles due to avalanche ionization -> significant increase in computational time for PICeeieeieeie1 2 4 8 1000Why are atmospheric pressure discharges so challenging for PIC codes?77eeieeieeieConsider different stages of discharge for one cell Small NDNeed PICModerate NDPIC -> Fluid transitionLarge NDPIC is not feasibleNeed Fluid codeWhy are atmospheric pressure discharges so challenging for PIC codes?88 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?99 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?1010How 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 macroparticleswith W=1 eachHow does it work?1111How 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 macroparticleswith W=1 eachStep 2:Combine pairs of particlesHow does it work?1212Step 1:Have 6 macroparticleswith W=1 eachStep 2:Combine pairs of particlesStep 3:End up with3 macroparticleswith W=2 eachHow 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?1313 Different sorting algorithms Threshold number of macroparticles per cell for the combining Maximum weight of macroparticlesHow 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?1414What 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 with3 macroparticleswith W=2 each1515What 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 with3 macroparticleswith W=2 eachStep 2:Split particles Into pairs1616What 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 with3 macroparticleswith W=2 eachStep 2:Split particles Into pairsStep 3:End up with 6 macroparticleswith W=1 each1717

3.3 ns3.3 nsWe performed studies of surface discharge propagation with different combination parameters and observed no visible difference Does it really work?2D Ex, V/mSet 1Set 21D Ex, V/m1818 Simulation Domain 1cm x 1cm Grid 5000 x 5000 (2m 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

Back to plasma medicine: Simulation parameters1919

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 propagateEvolution 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 tissueEvolution of vertical component of electric field