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Computational Plasma Physics

Computational Plasma Physics. Aims. To “cage” the cosmic medium: plasma. Get controle over its diversity. Get an overview of all the various Methods, Models, and Tools. Construct a modeling platform for the industry. Introduce young researchers/modellers. Has to be organized.

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Computational Plasma Physics

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  1. Computational Plasma Physics Aims To “cage” the cosmic medium: plasma Get controle over its diversity Get an overview of all the various Methods, Models, and Tools Construct a modeling platform for the industry Introduce young researchers/modellers

  2. Has to be organized Structure of the course Lectures Joost van der Mullen (Tue) Wim Goedheer (FOM Nieuwegein) Annemie Bogaerts (Uni Antwerp) Ute Ebert (CWI) Practicum Bart Hartgers Wouter brok Bart Broks Examination: Projects

  3. MathNum Interdiscipline SoftWArch Plasma Physics

  4. Metal Halide Lamp Gravitation induced Segregation 10 mBar NaI and CeI3 in 10 bar Hg

  5. The Philips QL lamp • Buffer argon (33 Pa) • Light Mercury (1 Pa) • Inductively coupled • Power 85 W Electrodeless lamp:  long life time

  6. GEC RF discharge

  7. 350 sccm He 4 mm i.d. 60 mm transformer CCP Spectrochemical Plasma Sources 18 mm i.d. central channel (CC) induction coil active zone (AZ) 15l/min outer flow intermediate flow central flow ICP Open air • 10- 50 W • 0.3 - 2 kW • 100 kHz; • 100 MHz • Helium • Argon

  8. Microwave Plasma Torch (MPT) Frequency 2.45 GHz Power 100W Argon flushing into The open air

  9. Booming Plasma Technology Interest increasing rapidly Material sciences (sputter) deposition CD, IC, DVD, nanotubes, solar-cells, Environmental gas-cleaning, ozon production, waste destruction Light Lamps, Lasers, Displays: Visible + EUV Propulsion Laser Wake field, Thrusters Etc. Etc

  10. Continuum or Particle And/Or ?? “Hybrid” Components Material Particles Neutral Charged Dust Fields Photons Note the various interactions

  11. Particles, Momentum, Energy Plasma ChemistryVolumeParticles Surface Particles + environment Plasma PropulsionMomentum Plasma LightEnergy

  12. Ordering Particles Chemistry m Momentum Propulsion mv Energy Conversion 1/2mv2

  13. Energy Coupling; Ordering in frequency DC Cascaded Arcs Deposition/Lightsources Pulsed DC pHollowCathodeD EUV gen/switches Corona Disch. Volume cleaning AC HID/FL lamps Welding/Cutting/light CC GEC cell etc. Etching/Depo/ SpectrChem IC QL lamp Licht/ Spectrochemistry Wave Surfatron Material processing Laser ProPl Ablation Cutting/ EUV generation

  14. Momentum Via E field: Plasma Propulsion Sheath: ion acceleration Ohms law: electon current Via p : expansion Cascaded Arc

  15. Atomic Molecular Low High pressure Chemistry; global ordering

  16. electrons, M-ions A-ions atoms, molecules; Radicals etc. Final Chemistry Chemistry; finer ordering Plasma gas i.e. Hg in a FLamp Buffergas i.e. Hg in a HID lamp; Ar in a FL Reduction diffusion Enhencing resistance Starting gas Xe in HID lamp

  17. Hybride Quasi Free Flight mean free paths large mfp > L Sampling and tracking Transport Modes Fluid mean free paths small mfp << L There are many conditions for which some plasma components behave “fluid-like” whereas others are more “particle-like” Hybride models have large application fields

  18. Particles Plasma Particles Energy Energy Momentum Momentum Particles: Plasma Chemistry Energy: Plasma Light Momentum: Plasma Propulsion

  19. Fluid models; a flavor Continuum approach: Differentiation/Integration possible Not jumping over neighbour’s garden

  20. Source Discretizing a Fluid: Control Volumes Plasma Particles Particles Energy Energy Momentum Momentum For any transportable quantity  Transport via boundaries

  21. How many species? How many species? Examples of transportables Densities Momenta in three directions Mean energy (temperature) of electrons Mean energy (temperature) of heavies As we will see: in many cases energy: 2T momentum: Drift Diffusion Species depending on equilibrium departure

  22. Mean properties  Nodal Points Transport at boundaries  = Source, t  + = S Steady State Transient General structure:   = u -D  Convection Diffusion Nodal Point communicating via Boundaries Transport Fluxes: Linking CV (or NP’s)  -

  23. Other Example: Poisson: .E = /o  = S   = u -D E = -V Thus no “convection” Modularity Thus: The Fluid Eqns: Balance of Particles Momentum Energy The Momenta of the Boltzmann Transport Eqn. Treated all as  -equation

  24. The  Variety  D S Temperature Heat cond Heat gen Momentum Viscosity Force Density Diffusion Creation Molecules atoms ions/electrons etc.

  25. Source of ions 1 Sink in Energy 2 Coupling different -equations Associated with

  26. Advantages of the -approach The same solution procedure: the same base class Possible to combine all the s in one big Matrix-vector eqn.

  27. T Continuum t  + = S Tin Rod Tout x 0 + T = 0 Take k = Cst MathNumerics: a FlavorSourceless-Diffusion T = Cst T = - kT -T /k =T

  28. Continuum Tin Rod Tout Discretized Intuition; T = Cst T2 = (T1 + T3)/2 1 2 3 4 Tin -2T1 + T2= 0 T1 - 2T2 + T3 = 0 T2 - 2T3 + T4 = 0 T3 - 2T4 + Tout = 0 2T2 = T1 + T3 Discretized

  29. In matrix: M T = b A Sparce Matrix Many zeros Matrix Representation 1 2 3 4 -Tin 0 0 -Tout T1 T2 T3 T4 1 2 3 4 - 2 1 1 -2 1 1 -2 1 1 -2 =

  30. Sourceless-Diffusion in two dimensions 1 1 – 4 1 1 N W P E S T5 = (T2 + T4 +T6 + T8 ) /4 Provided k = Cst !! In general:

  31. If k Cst Convection Diffusion More general S-less Diffusion/Convection

  32. Source of ions Example ions:  nu+ = P+ - n+D+ Recombination Ordering the Sources  = S S = P - L L ~ D Source combination Production and Loss Large local - value in general leads to large Loss

  33. The number of -equations How many -equations do we need ?? The number of transportables Depends on the degree of equilibrium departure Method of disturbed Bilateral Relations dBR Insight in equilibrium departure global model ne, Te and Th

  34. Particles Plasma Particles Energy Energy Momentum Momentum

  35. Plasma Artist Impression Input and Output Intermediated by Vivid Internal Activity

  36. Internal Activity Global Structure Inlet Outlet The In/Efflux couple will disturb internal Equilibrium Inlet side will be pushed up; Outlet pushed down But when do we have equilibrium ???

  37.  N f N b TE: Collection of Bilateral Relations TE Equilibrium in (violet) thermal dynamics DB Equilibrium on each level (each ) for any process-couple along the same route

  38. t = Nt Disturbance of BR by an Efflux   N f N b Equilibrium Condition: t/b << 1 or t b << 1 The escape per balance time must be small

  39. y = N/Neq Non-Equilibrium N f = N b + N t y() = y()[1+ (tb)] Equilibrium Departure   N f N b Equilibrium N eqf = N eqb

  40. The Nature of the Processes; PROPER Balances =1 =+ Emission = Absorption Planck Excitation = Deexcitation Boltzmann Ionization = Recombin Saha Kinetic Energy Exchange Maxwell

  41. Equilibrium Any situation aspects Non-Equilibrium Saha Boltzmann Planck Maxwell pLSE pLBE pLPE pLME Nature Nomenclature induced by dBR TE, LTE, pLTE ?? Partial Equilibrium Proper Balances

  42. Forward and corr. Backward Proper MR and Energy Conservation give standard relations Backward negligible Improper Assumption: d/dt = 0 Analytical expressions (!?) Proper versus Improper balances

  43. =2 =1 Example pLPE Intense laser irradiates transition: Proper balance Absorption St.Emission h= E Look for comparable TE situation T : exp-E/kT=1  (1) = (2) • (p) = n(p)/g(p) number density of a state; n(p) = number density of atoms in level p g(p) = number of states in level p

  44. Ion state Ground state Ionization flow Influx Outflux Approaching continuum: Equi. restoration rates increase Look for comparable TE situation Saha equation ruled by electrons from continuum Example pLSE  s(p) = (ne/2) (n+/g+) [h3/(2mekTe)3/2] exp (Ip/kTe)

  45.  s(p) = e + [V(Te) ] exp (Ip/kTe) That is Look at balance Ap A+ + e A+ + e bound  free pair The Saha density: mnemonic  s(p) = (ne/2) (n+/g+) [h3/(2mekTe)3/2] exp (Ip/kTe) Number density of bound {e +} pairs in state p:  s(p) Equals the density of pairs within V(Te) e + [V(Te) ] Weighted with the Boltzmann factor exp (Ip/kTe)

  46. Escape of Photons Restoring: Proper Boltzmann Tends to b(2) = b(1) exp { -E12/kTe} The Corona Balance: an improper balance a b y() = y()[1+ (tb)B] with (tb)B=A/ne K(2,1) The larger ne the smaller departure

  47. p  =1 =2 N (p)p-9 General: Impact Radiation Leak y(p) = y(1)[1+ tb]-1 with tb =A*(p)/ne K(p,1) Define: N= A(p)/neK(p) A(p)  p-4.5 K(p)  p4

  48. Ion state Ground state Ionization flow Influx Outflux b = n/ns pLSE settles for Ip 0 since (t/b)S  0 Ion Efflux Effecting the ASDF

  49. b=+ a=1 t = n+t = .n+w+ n+w+ = -Da.n Diffusion For single ionized ns(1)~ nen+= ne2 If Ambipolar Diffusion Dominates t = Da/L2 b(1) = (tb)s= t/ (ns(1) Sion)  Cb (A) x 108 Da (neL)-2 Moderate deviations for large ne, large L and small Da

  50. Ion Efflux Effecting the EEDF F(E)  = bulk  = tail E E12

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