tu/e computational plasma physics to “cage” the cosmic medium: plasma get an overview of all the...
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TU/e
Computational Plasma Physics
To “cage” the cosmic medium: plasma
Get an overview of all the various Methods, Models, and Tools
Get controle over its diversity
Introduce young researchers/modellers
Construct a modeling platform for the industry
Aims
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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 HartgersWouter brokBart Broks
Examination: Projects
Has to be organized
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Interdiscipline
MathNumSoftWArch
PlasmaPhysics
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Metal Halide Lamp
10 mBar NaI and CeI3 in 10 bar Hg
Gravitation inducedSegregation
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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
ICP
induction coil
active zone (AZ)
15l/min outer flow
intermediate flow
central channel (CC)
central flow
•100 MHz•100 kHz;
350 sccm He
transformer
60 mm
CCP
4 mm i.d.
18 mm i.d.
Open air
•0.3 - 2 kW•10- 50 W
•Argon•Helium
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Microwave Plasma Torch (MPT)
Frequency 2.45 GHz
Power 100W
Argon flushing intoThe open air
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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
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Components
Material Particles Neutral Charged
Dust
Fields
Photons
Note the various interactions
Continuum or Particle
And/Or ?? “Hybrid”
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Plasma Chemistry Volume Particles
Surface Particles + environment
Plasma Propulsion Momentum
Plasma Light Energy
Particles, Momentum, 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
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
Pulsed DC pHollowCathodeD EUV gen/switchesCorona Disch. Volume cleaning
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Momentum
Via E field: Plasma PropulsionSheath: ion accelerationOhms law: electon current
Via p : expansionCascaded Arc
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Chemistry; global ordering
Atomic Molecular
Low High pressure
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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
Starting gas Xe in HID lamp
Reduction diffusionEnhencing resistance
electrons, M-ions A-ionsatoms, molecules; Radicals etc.
Final Chemistry
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Transport Modes
Fluid mean free paths small mfp << L
Quasi Free Flight mean free paths large mfp > L
Sampling and tracking
Hybride
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
Energy
Particles
Energy
Momentum Momentum
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 neighbour’s garden
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Discretizing a Fluid: Control Volumes
Particles
Energy
Momentum
Particles
Energy
Momentum
For any transportablequantity
Source
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
How many species?
How many species?
As we will see: in many cases energy: 2Tmomentum: Drift DiffusionSpecies depending on equilibrium departure
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Nodal Point communicating via Boundaries
Mean properties Nodal Points
Transport at boundaries
Transport Fluxes: Linking CV (or NP’s)
= u -D General structure:
-
Transient
t + = S = Source,
Steady State
DiffusionConvection
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Modularity
Thus: The Fluid Eqns: Balance of Particles MomentumEnergy
The Momenta of the Boltzmann Transport Eqn.
Treated all as -equation
Other Example: Poisson: .E = /o
E = -V
Thus no “convection”
= S
= u -D
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The Variety
D S
Temperature Heat cond Heat gen
Momentum Viscosity Force
Density Diffusion CreationMoleculesatomsions/electronsetc.
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Coupling different -equations
Source of ions 1
Associated with
Sink in Energy 2
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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
Rod Tin Tout
Continuum
t + = S
0 + T = 0
T = - kT
T = Cst
-T /k =T
T
xTake k = Cst
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Discretized
Rod Tin Tout
Continuum
Discretized
1 2 3 4
Intuition; T = Cst
T2 = (T1 + T3)/2
2T2 = T1 + T3
Tin -2T1 + T2 = 0 T1 - 2T2 + T3 = 0 T2 - 2T3 + T4 = 0
T3 - 2T4 + Tout = 0
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Matrix Representation
- 2 1
1 -2 1
1 -2 1
1 -2
1
2
3
4
1 2 3 4
T1
T2
T3
T4
=
-Tin
0
0
-Tout
M T = bIn matrix:A Sparce MatrixMany zeros
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Sourceless-Diffusion in two dimensions
11 – 4 1 1
T5 = (T2 + T4 + T6 + T8 ) /4
NW P E S
Provided k = Cst !!
In general: 4
NB
NB
P
TT
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More general S-less Diffusion/Convection
NB NB
NBNBNB
P c
Tc
TIf k Cst
NB NB
NBNBNB
P c
Tc
T*
*
ConvectionDiffusion
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Ordering the Sources
S = P - L
L ~ D
Source combination Production and Loss
= S
Large local - value in general leads to large Loss
Source of ionsExample ions: nu+ = P+ - n+D+
Recombination
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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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Particles
Energy
Particles
Energy
Momentum Momentum
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Plasma Artist Impression
Input and Output Intermediated by Vivid Internal Activity
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Global Structure
Inlet Outlet
Internal Activity
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
N f
N b
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Disturbance of BR by an Efflux
t = Nt
N b
N f
Equilibrium Condition: t/b << 1 or t b << 1
The escape per balance time must be small
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N f
N b
Equilibrium Departure
Non-Equilibrium N f = N b + N t
Equilibrium N eqf = N
eqb y() = y()[1+ (tb)]
y = N/Neq
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Emission = Absorption
Planck
The Nature of the Processes; PROPER Balances
Excitation = Deexcitation Boltzmann
Ionization = RecombinSaha
Kinetic Energy ExchangeMaxwell
=1 =+
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Nomenclature induced by dBR
TE, LTE, pLTE ??
Any situation aspectsEquilibrium
Non-Equilibrium
Partial Equilibrium
Nature
Saha Boltzmann
PlanckMaxwell
pLSEpLBEpLPEpLME
Proper Balances
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Proper versus Improper balances
Forward and corr. Backward
MR and Energy Conservationgive standard relations
Proper
ImproperBackward negligible
Assumption: d/dt = 0
Analytical expressions (!?)
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Example pLPE
=1 =2
Intense laser irradiates transition:
Proper balance Absorption St.Emission
Look for comparable TE situation
T : exp-E/kT=1 (1) = (2)
h= E
(p) = n(p)/g(p) number density of a state; n(p) = number density of atoms in level pg(p) = number of states in level p
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Example pLSE
Groundstate
Ion
state
Ionization flowOutfluxInflux
Approaching continuum:
Equi. restoration rates increase
Look for comparable TE situation
Saha equation ruled by electrons from continuum
s(p) = (ne/2) (n+/g+) [h3/(2mekTe)
3/2] exp (Ip/kTe)
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The Saha density: mnemonic
s(p) = (ne/2) (n+/g+) [h3/(2mekTe)
3/2] exp (Ip/kTe)
s(p) = e + [V(Te) ] exp (Ip/kTe) That is
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)
Ap A+ + e Look at balance
A+ + e bound free pair
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The Corona Balance: an improper balance
y() = y()[1+ (tb)B ] with (tb)B
= A/ne K(2,1)
The larger ne the smaller departure
Escape of Photons
Restoring: Proper Boltzmann
b(2) = b(1) exp { -E12/kTe}
Tends to
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General: Impact Radiation Leak
p
y(p) = y(1)[1+ tb]-1
with
tb = A*(p)/ne K(p,1)
Define: N = A(p)/neK(p)
A(p) p-4.5 K(p) p4
N (p)p-9
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I1 0
bp
real
distribution
pLSE
Saha distribution
log(
ele
menta
ry o
ccupatio
n )
Ip
Groundstate
Ion
state
Ionization flowOutfluxInflux
Ion Efflux Effecting the ASDF
pLSE settles for Ip 0
since (t/b)S 0
b = n/ns
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If Ambipolar Diffusion Dominates
t = Da/L2
t = n+t = .n+ w+
n+ w+ = -Da .n Diffusion
b(1) = (tb)s = t/ (n
s(1) Sion) Cb (A) x 108 Da (neL)-2
Moderate deviations for large ne, large L and small Da
For single ionized ns(1) ~ nen+= ne2
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F(E)
E12E
Ion Efflux Effecting the EEDF
= bulk = tail
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Deviation form pLME
F(E)
E12E
= bulk = tail
y() = y()(1 + t b)
y()/ y() = (1 + t b)-1
Tt /Tb = y()/ y()
(t b)M = C(A) [n1/ ne] {kTe/E12}2 / lnc
Competition between bound and bulk electronsionization ratio important ne /n1
Tt/Te
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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
Plasma
Wall
A A+ + e+ +e e
A A+ + e
Ion = diff n1SCR(Te) = Da/L2
Thus particle balance Te
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The Electron Energy Balance
{H*} .
EM {e} ElectroMagnetic {H} Field
{wall
={e} ={H}
eff.
nen1Sheat(kTe - kTh) = /L2 Th Heat branch gives Th
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Two Channels: Heating & Creation
= ne n1 Sheat (kTe – kTh) + ne n1 Sion (I+ 3/2 kTe)
elastic heat inelastic creation
= Creation/Total = Creation Efficiency
ne = ()/(Da L-2) Energy Balance gives ne
ne n1 Sheat kTe + ne Da I L -2
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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
But does it works for MIP ?
dBR: Combination of validity criteria diagnostic guides and global models
dBR: Works for ICPs and CCPs
Depends on ...
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The Role of Molecules
Ar+
Ar2+
Recall: we must compare Forward and corresponding Backward processes that is: along the same Channel
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Grand models; a flavor
Grand models Specific models
MD2D
PLASIMO
Collisional Radiative Me.g. to make Look-up Tablesfor the grand
Examples
“Multi Physics” Mono Physics
Multi
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MD2D
n {e}, {A+n}, {An
*} etc.
E {e} solely
No Gas heatingNo flow
Various Particle SourcesReactions
Lean & clean 40 files6000 lines
+ Plasimo In/OutExtravaganza
V
Poisson Potential
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MD2D-Applications
PDP plasma TVCFL ignitionDBDNeedleParallel plate reactors (GEC Cell)
Low (average) power plasmas
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Plasimo
PhysicoChemistry
MathNumerics
Software Architecture
1034 Files1233 Classes160.000 Lines +
ManualsCVS systemCookingBooks
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Modeling Platform
3- problem LTE plasma
1- problem SS Heating Rod d/dt Coffee Cooling
2- problem SS Water Flowd/dt
3- problem SS Gas-flow
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
Energy CouplingDC
InductiveCapacitivelyMicrowave
Laser
Energy Momentum Particles Configuration Transport Composition
Boundary Conditions
Gas Mixture
ReactionsRelations
Transport Coeffs
Matrix Eqn Solvers
eqns
= -D + u
+ = S
Ray Tracing
Grid generation
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PhysicoChemistry
Comes in via Transport Coeffs and Source terms
Collisions providing Rates
Physics: Large Variety Mathematics: Similarities
Base ClassDerived Classes
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Runtime Configurability
Change : Flowing/non-Flowing Equilibrium Departure type Mixture properties (Chemistry)Discretization methodsAlgorithmMatrix solvers
Functionality abstracted using classes with virtual methods
Self-registering objectsDynamic loading Configuration during runtime
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Particle Models; a flavour
Particle behaviorThe EOM
A. No acceleration Ray Tracing
B. AccelerationField moves SwarmsSwarm 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