Transcript Presentatie Lunteren 98

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
TU/e
Structure of the course
Lectures
Joost van der Mullen
Wim Goedheer
Annemie Bogaerts
Ute Ebert
Practicum
Bart Hartgers
Wouter brok
Bart Broks
(Tue)
(FOM Nieuwegein)
(Uni Antwerp)
(CWI)
Has to be organized
Examination: Projects
TU/e
Interdiscipline
MathNum
SoftWArch
Plasma
Physics
TU/e
Metal Halide Lamp
Gravitation induced
Segregation
10 mBar NaI and CeI3 in 10 bar Hg
TU/e
The Philips QL lamp
Electrodeless lamp:
• Buffer argon
(33 Pa)
 long life time
• Light Mercury
(1 Pa)
• Inductively coupled
• Power 85 W
TU/e
GEC RF discharge
TU/e
Spectrochemical Plasma Sources
18 mm i.d.
350 sccm He
central channel (CC)
4 mm i.d.
induction coil
60 mm
active zone (AZ)
15l/min outer flow
transformer
intermediate flow
central flow
CCP
•10- 50 W
•100 kHz;
•Helium
ICP
Open air
•0.3 - 2 kW
•100 MHz
•Argon
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Microwave Plasma Torch (MPT)
Frequency 2.45 GHz
Power 100W
Argon flushing into
The open air
TU/e
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
TU/e
Components
Material Particles
Neutral
Charged
Dust
Continuum or Particle
Fields
Photons
And/Or ??
“Hybrid”
Note the various interactions
TU/e
Particles, Momentum, Energy
Plasma Chemistry
Volume
Particles
Surface
Particles +
environment
Plasma Propulsion
Momentum
Plasma Light
Energy
TU/e
Ordering
Particles
Chemistry
Momentum Propulsion
Energy
Conversion
m
mv
1/2mv2
TU/e
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
TU/e
Momentum
Via E field:
Plasma Propulsion
Sheath: ion acceleration
Ohms law: electon current
Via p :
expansion
Cascaded Arc
TU/e
Chemistry; global ordering
Atomic
Molecular
Low
High pressure
TU/e
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
Final Chemistry
electrons, M-ions A-ions
atoms, molecules; Radicals etc.
TU/e
Transport Modes
Fluid
mean free paths small
mfp << L
mean free paths large
mfp > L
Hybride
Quasi Free Flight
Sampling and tracking
There are many conditions for which
some plasma components behave “fluid-like”
whereas others are more “particle-like”
Hybride models have large application fields
TU/e
Particles
Particles
Energy
Energy
Momentum
Momentum
Particles:
Plasma Chemistry
Energy:
Plasma Light
Momentum: Plasma Propulsion
TU/e
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
Particles
Energy
Energy
Momentum
Momentum
For any transportable
quantity

Source
Transport
via boundaries
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Examples of transportables
Densities
How many species?
Momenta in three directions
How many species?
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 TU/e
Nodal Point communicating via Boundaries
Mean properties  Nodal Points
Transport at boundaries
Transport Fluxes: Linking CV (or NP’s)
 = Source,
t  + = S
Steady State
General structure:
Transient
  = u -D 
Convection

Diffusion
 -
TU/e
Modularity
Thus: The Fluid Eqns: Balance of
Particles
Momentum
Energy
The Momenta of the Boltzmann Transport Eqn.
Other Example: Poisson: .E = /o
E = -V
 = S
  = u -D
Thus no “convection”
Treated all as  -equation
TU/e
The


Variety
D
S
Temperature
Heat cond
Heat gen
Momentum
Viscosity
Force
Density
Diffusion
Molecules
atoms
ions/electrons
etc.
Creation
TU/e
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.
TU/e
MathNumerics: a Flavor
Sourceless-Diffusion
Continuum
Tin
Rod
Tout
t  + = S
0 + T = 0
T = Cst
T = - kT
T
-T /k =T
x
Take k = Cst
TU/e
Discretized
Continuum
Tin
Rod
Tout
Discretized
1
2T2 = T1 + T3
2
3
Intuition;
4
T = Cst
T2 = (T1 + T3)/2
Tin -2T1 + T2
T1 - 2T2 + T3
T2 - 2T3 + T4
T3 - 2T4 + Tout
=0
=0
=0
= 0TU/e
Matrix Representation
1 2
1
2
3
4
-2 1
1 -2 1
T1
-Tin
T2
0
=
3
1 -2 1
T3
0
4
1 -2
T4
-Tout
In matrix:
M T = b
A Sparce Matrix
Many zeros
TU/e
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:
TP 
T
NB
NB
4
TU/e
More general S-less Diffusion/Convection
 c T

 c
NB
If k Cst
TP
NB
TP
NB
NB
 c* T

 c*
NB
Convection
Diffusion
NB
NB
NB
NB
NB
TU/e
Ordering the Sources
 = S
S = P - L
L ~ D
Source combination Production and Loss
Large local - value in general leads
to large Loss
Source of ions
Example ions:  nu+ = P+ - n+D+
RecombinationTU/e
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
TU/e
Particles
Particles
Energy
Momentum
Energy
Momentum
TU/e
Plasma Artist Impression
Input and Output
Intermediated by
Vivid Internal Activity
TU/e
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 ???
TU/e
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
TU/e
Disturbance of BR by an Efflux


N f
t = Nt
N b
Equilibrium Condition: t/b << 1 or t b << 1
The escape per balance time
must be small
TU/e
Equilibrium Departure


N f
N b
y = N/Neq
Non-Equilibrium
Equilibrium
N f
N eqf
= N b +
= N
eq
N t
b
y() = y()[1+ (tb)]
TU/e
The Nature of the Processes; PROPER Balances
=1
=+
Emission = Absorption
Planck
Excitation = Deexcitation
Boltzmann
Ionization = Recombin
Saha
Kinetic Energy Exchange
Maxwell
TU/e
Nomenclature induced by dBR
TE, LTE, pLTE ??
Partial Equilibrium
Equilibrium
Any situation aspects
Non-Equilibrium
Nature
Saha
Boltzmann
Planck
Maxwell
pLSE
pLBE
pLPE
pLME
Proper Balances
TU/e
Proper versus Improper balances
Forward and
corr. Backward
Proper
Improper
MR and Energy Conservation
give standard relations
Backward negligible
Assumption: d/dt = 0
Analytical expressions (!?)
TU/e
Example pLPE
=2
=1
Intense laser irradiates transition:
h= E
Proper balance
Absorption St.Emission
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
TU/e
Example pLSE
Ion
Ground
state
Influx
state
Ionization flow
Outflux
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/(2mekTe)3/2] exp (Ip/kTe)
TU/e
The Saha density: mnemonic
 s(p) = (ne/2) (n+/g+) [h3/(2mekTe)3/2] exp (Ip/kTe)
That is
 s(p) = e  + [V(Te) ] exp (Ip/kTe)
Look at balance Ap  A+ + e
A+ + e
bound  free pair
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)
TU/e
The Corona Balance: an improper balance


Escape of Photons
Restoring: Proper Boltzmann
Tends to
b(2) = b(1) exp { -E12/kTe}
y() = y()[1+ (tb)B ]
with (tb)B = A/ne K(2,1)
The larger ne the smaller departure
TU/e
General: Impact Radiation Leak
 1
2
p
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
N (p)p-9
TU/e
Ion Efflux Effecting the ASDF
Ion
Ground
state
state
Ionization flow
log( elementary occupation )
Influx
Outflux
real
distribution
b = n/ns
b
p
pLSE
pLSE settles
for Ip  0
Saha distribution
since (t/b)S  0
I
1
I
0
p
TU/e
If Ambipolar Diffusion Dominates
1
+
t = n+t = .n+ w+
n+ w+ = -Da .n Diffusion
t = Da/L2
b(1) = (tb)s = t/ (ns(1) Sion)  Cb (A) x 108 Da (neL)-2
For single ionized
ns(1) ~ nen+= ne2
Moderate deviations for large ne, large L and small Da
TU/e
Ion Efflux Effecting the EEDF
F(E)
 = bulk
 = tail
E12
E
TU/e
Deviation form pLME
 = bulk
 = tail
Tt /Tb = y()/ y()
y() = y()(1 + t b)
F(E)
y()/ y() = (1 + t b)-1
E12
E
Tt/Te
(t b)M = C(A) [n1/ ne] {kTe/E12}2 / lnc
Competition between bound and bulk electrons
ionization ratio important ne /n1
TU/e
Disturbed Bilateral Relation
•To find essential non-equilibrium features
Efflux Equilibrium restoring Balance
•Universal Equilibrium Validity Criterion
•Trends and simple formulae
•Nomenclature; Proper/Improper
•Guide for diagnostics
•Global Discharge Model
TU/e
Global Discharge Model Model
Particle Balance Electrons
Energy Balance
Energy Balance Heavies
TU/e
The Electron Particle Balance

Plasma
Wall

A
+
e

A+
+
e
+
e
A

A+
+
e
Ion = diff
Thus particle balance

n1SCR(Te) = Da/L2
 Te
TU/e
The Electron Energy Balance
EM

{e}
ElectroMagnetic
{

{H*} 

{H}
.

wall
Field
={e}
={H}
eff.
nen1Sheat(kTe - kTh) = /L2 Th
Heat branch gives Th
TU/e
Two Channels: Heating & Creation
 =
ne n1 Sheat (kTe – kTh) + ne n1 Sion (I+ 3/2 kTe)
elastic  heat

inelastic  creation
+ ne Da I L -2
ne n1 Sheat kTe
 = Creation/Total
=
ne = ()/(Da L-2)
 Energy Balance gives ne
Creation Efficiency
TU/e
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
TU/e
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 ...
TU/e
The Role of Molecules
Ar2+
Ar+
Recall: we must compare Forward
and corresponding Backward processes
that is: along the same Channel
TU/e
Grand models; a flavor
Grand models
Specific models
“Multi Physics”
Multi 
Mono Physics
Examples
MD2D
PLASIMO
Collisional Radiative M
e.g. to make Look-up Tables
for the grand
TU/e
MD2D
Lean & clean
n
V
{e}, {A+n}, {An*} etc.
Poisson
Potential
E
{e} solely
No
No
Gas heating
flow
40
files
6000 lines
+ Plasimo In/Out
Extravaganza
Various Particle Sources
Reactions
TU/e
MD2D-Applications
Low (average) power plasmas
PDP
plasma TV
CFL
ignition
DBD
Needle
Parallel plate reactors (GEC Cell)
TU/e
Plasimo
PhysicoChemistry
MathNumerics
Software Architecture
1034
1233
160.000
Files
Classes
Lines
+
Manuals
CVS system
CookingBooks
TU/e
Modeling Platform
1- problem
SS
d/dt
Heating Rod
Coffee Cooling
2- problem
SS
d/dt
Water Flow
3- problem
SS
Gas-flow
3- problem
LTE plasma
5- problem
non-LTE
TU/e
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
TU/e
General Triptych Structure
Configuration
Energy
Energy Coupling
DC
Inductive
Capacitively
Microwave
Laser
Boundary
Conditions
Momentum
Transport
 eqns
 + = S
  = -D 
+ u 
Composition
Particles
Gas Mixture
Reactions
Relations
Transport Coeffs
Ray Tracing
Matrix Eqn Solvers
Grid generation
TU/e
PhysicoChemistry
Comes in via Transport Coeffs and Source terms
Collisions providing Rates
Physics: Large Variety
Mathematics: Similarities
Derived Classes
Base Class
TU/e
Runtime Configurability
Functionality abstracted using classes with virtual methods
Self-registering objects
Dynamic loading
Change :
Configuration during runtime
Flowing/non-Flowing
Equilibrium Departure type
Mixture properties (Chemistry)
Discretization methods
Algorithm
Matrix solvers
TU/e
Particle Models; a flavour
Particle behavior
The EOM
A. No acceleration
Ray Tracing
B. Acceleration
Field moves Swarms
Swarm changes field
Monte Carlo collisions
TU/e
Radiative Transfer
Ray-Trace Discretization spectrum.
Network of lines (rays)
Compute I (W/(m2 .sr.Hz) along the lines
dI()/ds = j - k()I()
Start
Entering
outside the plasma with I() = 0.
plasma I() grows afterwards absorption.
TU/e
Ray Tracing
TU/e