Computational Plasma Physics

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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
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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
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Interdiscipline
SoftWArch
Plasma Physics
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Metal Halide Lamp
Gravitation induced Segregation
10 mBar NaI and CeI3 in 10 bar Hg
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The Philips QL lamp

• Buffer argon (33 Pa)
• Light Mercury (1 Pa)
• Inductively coupled
• Power 85 W

Electrodeless lamp ? long life time
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GEC RF discharge
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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

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Microwave Plasma Torch (MPT)
Frequency 2.45 GHz
Power 100W
Argon flushing into The open air
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Booming Plasma Technology
Interest increasing rapidly Material
sciences (sputter) deposition CD, IC, DVD,
nanotubes, solar-cells, Environmental gas-cl
eaning, ozon production, waste destruction
Light Lamps, Lasers, Displays Visible
EUV Propulsion Laser Wake field, Thrusters
Etc. Etc
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Components
Material Particles Neutral Charged Dust
Fields Photons
Note the various interactions
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Particles, Momentum, Energy
Plasma Chemistry Volume Particles
Surface Particles environment
Plasma Propulsion Momentum Plasma Light
Energy
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Ordering
Particles Chemistry m
Momentum Propulsion mv
Energy Conversion 1/2mv2
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Energy Coupling Ordering in frequency
DC Cascaded Arcs Deposition/Lightsources
Pulsed DC pHollowCathodeD EUV gen/switches Cor
ona 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
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Momentum
Via E field Plasma Propulsion Sheath ion
acceleration Ohms law electon current
Via ?p expansion Cascaded Arc
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Chemistry global ordering
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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
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Transport Modes
Fluid mean free paths small mfp ltlt 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
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Particles Plasma Chemistry
Energy Plasma Light
Momentum Plasma Propulsion
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Fluid models a flavor
Continuum approach Differentiation/Integration
possible Not jumping over neighbours garden
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Discretizing a Fluid Control Volumes
Plasma
Particles
Particles
Energy
Energy
Momentum
Momentum
For any transportable quantity ?
Transport via boundaries
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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
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Nodal Point communicating via Boundaries
Transport Fluxes Linking CV (or NPs)
? ? ? -??
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Modularity
Thus The Fluid Eqns Balance of Particles
Momentum Energy
The Momenta of the Boltzmann Transport Eqn.
Treated all as ? -equation
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The ? Variety?
? D? S?
Temperature Heat cond Heat gen
Momentum Viscosity Force
Density Diffusion Creation Molecules atoms i
ons/electrons etc.
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Coupling different ?-equations
Associated with
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Advantages of the ?-approach
The same solution procedure the same base
class Possible to combine all the ?s in one big
Matrix-vector eqn.
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MathNumerics a FlavorSourceless-Diffusion
?T Cst
?T - k?T
-?T /k ?T
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Discretized
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Matrix Representation
1 2 3 4
-Tin 0 0 -Tout
T1 T2 T3 T4
- 2 1 1 -2 1 1 -2 1
1 -2
1 2 3 4

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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
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More general S-less Diffusion/Convection
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Ordering the Sources
???? S?
S? P? - L?
L? ?D
Source combination Production and Loss
Large local ?- value in general leads to large
Loss
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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
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Plasma Artist Impression
Input and Output Intermediated by Vivid
Internal Activity
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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 ???
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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
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Disturbance of BR by an Efflux
?
?
N? ?f
N? ?b
Equilibrium Condition ?t/?b ltlt 1 or ?t ?b ltlt
1 The escape per balance time must be
small
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Equilibrium Departure
?
?
N? ?f
N? ?b
Equilibrium N? eq?f N? eq?b
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The Nature of the Processes PROPER Balances
?1
?
Emission Absorption Planck
Excitation Deexcitation Boltzmann
Ionization Recombin Saha
Kinetic Energy Exchange Maxwell
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Nomenclature induced by dBR
TE, LTE, pLTE ??
Partial Equilibrium
Proper Balances
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Proper versus Improper balances
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Example pLPE
Intense laser irradiates transition
Proper balance Absorption St.Emission
h? ?E
Look for comparable TE situation
T ?? exp-?E/kT1 ?
?(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

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Example pLSE
? s(p) (ne/2) (n/g) h3/(2?mekTe)3/2 exp
(Ip/kTe)
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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)
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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
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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
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Ion Efflux Effecting the ASDF
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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
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Ion Efflux Effecting the EEDF
F(E)
? bulk
? tail
E
E12
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Deviation form pLME
? bulk
Tt /Tb y(?)/ y(?)
? tail
(?t ?b)M C(A) n1/ ne kTe/E122 / ln?c
Competition between bound and bulk
electrons ionization ratio important ne /n1
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Disturbed Bilateral Relation

• To find essential non-equilibrium featuresEfflux
  ??Equilibrium restoring Balance
• Universal Equilibrium Validity Criterion
• Trends and simple formulae
• Nomenclature Proper/Improper
• Guide for diagnostics
• Global Discharge Model

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Global Discharge Model Model
Particle Balance Electrons Energy
Balance Energy Balance Heavies
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The Electron Particle Balance
? ? A ? A e e e
Plasma
Wall
A ? A e
Ion diff ? n1SCR(Te) Da/L2
Thus particle balance ? Te
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The Electron Energy Balance
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Two Channels Heating Creation

• ? ne n1 Sheat (kTe kTh) ne n1 Sion (I
  3/2 kTe)
• elastic ? heat inelastic ? creation
  

? ne n1 Sheat kTe ne Da I L -2
? Creation/Total Creation Efficiency
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dBR single CV compared with PLASIMO
Central T_e and T_h as function of n for Ar
cylinder plasma R 10 mm and power density 106
Wm-3
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Valitidy for dBR
dBR Combination of validity criteria
diagnostic guides and global models
dBR Works for ICPs and CCPs
But does it works for MIP ?
Depends on ...
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The Role of Molecules
Ar
Recall we must compare Forward and
corresponding Backward processes that is along
the same Channel
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Grand models a flavor
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MD2D
?n e, An, An etc.
Various Particle Sources Reactions
?E e solely
No Gas heating No flow
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MD2D-Applications
Low (average) power plasmas
PDP plasma TV CFL ignition DBD Needle Parallel
plate reactors (GEC Cell)
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Plasimo
PhysicoChemistry MathNumerics Software
Architecture
1034 Files 1233 Classes 160.000 Lines
Manuals CVS system CookingBooks

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Modeling Platform
1-? problem SS Heating Rod d/dt Coffee
Cooling
2-? problem SS Water Flow d/dt
3-? problem SS Gas-flow
3-? problem LTE plasma
5-? problem non-LTE
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PLASIMO is
Not just a model
But a Model Platform ? CFD
For a manifold of plasma conditions
SS and d/dt
Object Oriented C
Extendable and reusable
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General Triptych Structure
Configuration Transport Composition
Energy Coupling DC Inductive Capacitively Microwav
e Laser
Gas Mixture
? eqns
Reactions Relations
?? ???? S?
? ? -D? ?? u ??
Transport Coeffs
Ray Tracing
Boundary Conditions
Matrix Eqn Solvers
Grid generation
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PhysicoChemistry
Comes in via Transport Coeffs and Source terms
Collisions providing Rates
Physics Large Variety
Mathematics Similarities
Base Class
Derived Classes
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Runtime Configurability
Functionality abstracted using classes with
virtual methods
Self-registering objects Dynamic loading
Configuration during runtime
Change Flowing/non-Flowing Equilibrium
Departure type Mixture properties
(Chemistry) Discretization methods Algorithm
Matrix solvers
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Particle Models a flavour
Particle behavior The EOM A. No acceleration
Ray Tracing B. Acceleration Field
moves Swarms Swarm changes field Monte
Carlo collisions
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Radiative Transfer
Ray-Trace Discretization spectrum.
Network of lines (rays) Compute I (W/(m2
.sr.Hz) along the lines Start outside
the plasma with I?(?) 0. Entering plasma
I?(?) grows afterwards absorption.
dI?(?)/ds j? - k(?)I?(?)
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Ray Tracing