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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

MathNum SoftWArch

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

Continuumt + = 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 4Intuition; 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

TcTIf k Cst

NB NB

NBNBNB

P c

TcT

*

*

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

BoltzmannPlanck

Maxwell

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 flow OutfluxInflux

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

realdistribution

pLSE

Saha distribution

log(

ele

men

tary

occ

upat

ion

)

Ip

Groundstate

Ion

state

Ionization flow OutfluxInflux

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/ (ns(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