monte carlo simulation of radiation trapping in ...gec01_kapil_ 04 • characterization of trapping...

MONTE CARLO SIMULATION OF RADIATION TRAPPINGIN ELECTRODELESS LAMPS:

COMPLEX GEOMETRIES AND ISOTOPE EFFECTS*

Kapil Rajaraman** and Mark J. Kushner*****Department of Physics

***Department of Electrical and Computer EngineeringUniversity of Illinois

Urbana, IL 61801

Graeme G. ListerOsram Sylvania Inc., Beverley, MA

Email : [email protected]@[email protected]

http://uigelz.ece.uiuc.edu

October 2001

* Work supported by Osram Sylvania Inc. and the NSF

AGENDA

GEC01_KAPIL_1

University of Illinois Optical and Discharge Physics

• Radiation transport in low pressure plasmas

• Overview of the Hybrid Plasma Equipment Model

• Description of the Monte Carlo Radiation Transport Model

• Base case plasma properties

• Multi-level transitions and emission spectra

• Isotope effect studies

• Dependence of trapping factor on

• Pressure

• Plasma geometry

• Conclusions

ELECTRODELESS LAMPS AND TRAPPING

GEC01_KAPIL_02


• Electrodeless gas discharges are finding increasing use in the lightingindustry due to their increased lifetime.

• Investigations are underway to increase the efficiency of these lamps, now≅ 25%.

• Typical fluorescent lamps consist of Ar/Hg ≈ 97/3. Resonance radiationfrom Hg (63P1) (254 nm) and Hg (61P1) (185 nm) excites phosphors whichgenerate visible light.

• This resonance radiation can be absorbed and reemitted many times priorto striking the phosphor.

• The consequence of trapping is to lengthen the effective lifetime ofemission as viewed from outside the lamp.

• Control of resonance radiation trapping is therefore important to thedesign of such lamps.

PHYSICAL PROCESSES

GEC01_KAPIL_03


• Detailed level analysis of the radiative transitions as well as isotope effectstudies have been performed.

• The reaction chemistries for the multi-level and the isotope studies aresimilar and are shown here:

Hg Hg* Hg+e e e

e , Ar* , Ar , Ar +

hν

Ar Ar* Ar+e e , Ar*e

e

• Ar is a buffer gas, and radiation exciting the phosphor is all due to themercury transitions.

PAST TREATMENT OF RADIATION TRANSPORT

__________________University of Illinois

Optical and Discharge PhysicsGEC01_KAPIL_ 04

• Characterization of trapping is typically done using Holstein factors

• A→A.g,

where A is the Einstein A-coefficient and g is a geometry-dependentfactor. For a cylinder,

• R0πk1.115g= (impact broadened)

• R)0ln(k πR0k1.60g= (Doppler broadened)

where k0 is the absorption coefficient at line center.

• This method fails for more complex geometries, where the propogatorcannot be easily evaluated.

MONTE CARLO METHODS FOR RADIATION TRANSPORT



• Monte Carlo methods are desirable for complex geometries where it is noteasy to evaluate propogator functions.

• We have developed a Monte Carlo radiation transport model (MCRTM) forthe radiative transitions of mercury.

• This model can be used to study isotope effects as well as multi-leveltransitions.

• The model incorporates the effects of Partial Frequency Redistribution(PFR) and quenching of excitation, using a Voigt profile for emission andabsorption.

• However, one needs a self-consistent plasma model to account forevolution of gas densities, temperatures and other plasma parameters.

• To address this need, the MCRTM is interfaced with the Hybrid PlasmaEquipment model (HPEM) to realistically model the gas discharge.

SCHEMATIC OF THE HYBRID PLASMA EQUIPMENT MODEL

ICOPS01_6


MATCH BOX-COIL CIRCUIT MODEL

ELECTRO- MAGNETICS

FREQUENCY DOMAIN

ELECTRO-MAGNETICS

FDTD

MAGNETO- STATICS MODULE

ELECTRONMONTE CARLO

SIMULATION

ELECTRONBEAM MODULE

ELECTRON ENERGY

EQUATION

BOLTZMANN MODULE

NON-COLLISIONAL

HEATING

ON-THE-FLY FREQUENCY

DOMAIN EXTERNALCIRCUITMODULE

MESO-SCALEMODULE

SURFACECHEMISTRY

MODULE

CONTINUITY

MOMENTUM

ENERGY

SHEATH MODULE

LONG MEANFREE PATH

(MONTE CARLO)

SIMPLE CIRCUIT MODULE

POISSON ELECTRO- STATICS

AMBIPOLAR ELECTRO- STATICS

SPUTTER MODULE

E(r,θ,z,φ)

B(r,θ,z,φ)

B(r,z)

S(r,z,φ)

Te(r,z,φ)

µ(r,z,φ)

Es(r,z,φ) N(r,z)

σ(r,z)

V(rf),V(dc)

Φ(r,z,φ)

Φ(r,z,φ)

s(r,z)

J(r,z,φ)ID(coils)

MONTE CARLO FEATURE PROFILE

MODEL

PLASMACHEMISTRY

MONTE CARLOSIMULATION

Es(r,z,φ)

S(r,z,φ)

IAD(r,z) IED(r,z)

VPEM: SENSORS, CONTROLLERS, ACTUATORS

MONTE CARLO RADIATION

TRANSPORT MODULEk(rad)

N(r,z), k

MONTE CARLO RADIATION TRANSPORT MODEL (MCRTM)



• Monte Carlo method is used to follow trajectories of photons from initialemission to escape from plasma.

• The absorption/emission lineshape function is a Voigt profile.

• MC photons are generated in proportion to the excited atom density ateach point in the plasma.

• To avoid statistical errors, we uniformly choose the frequency of photonsfrom a specified bandwidth and assign a weighting which accounts for thelineshape profile.

• The null collision method is employed for the photon transport.

TRAPPING FACTOR AND PFR



• We define the trapping factor as

natresk ττ= ,

where τres is the average residence time of the photon in the plasma, and τnat is the natural lifetime of the excited state.

• After each absorbing collision at photon frequency ν, the partial frequencyredistribution is incorporated by randomly choosing a new frequencywithin a range ν ± ∆ν.

• The value of ∆ν was found by simulating trapping in a cylindricaldischarge with a uniform density of Ar and Hg atoms and comparing thesimulation results with those found by Lister.

• The results agreed well for ∆ν ≈α ∆νd, where α ranged from 1.5 to 2.0.

BASE CASE CONDITIONS


Optical and Discharge PhysicsGEC01_KAPIL_09

• Diameter – 9 cm• Height – 8 cm• Depth – 5 cm• Initial pressure – 500 mTorr• Initial temperature – 400 K• Operating power – 50 W• Operating frequency – 2.65 Mhz

• Initial Ar mole fraction ≅ 0.98• Initial Hg mole fraction (ground

state) ≅ 0.02

• For the isotope study, the initialconcentrations ≅ 95 : 5 0 2 4 6

0

2

4

6

8

Radius (cm)

Hei

ght (

cm)

Reentrant cavity

Outer wall

Induction coil

Ferrite core

ELECTRON TEMPERATURE AND DENSITY

GEC01_KAPIL_10


• Peak electron temperature (≈ 2 eV) surrounds the reentrant coil resulting ina peak electron density in an annulus around the antenna.

0 2 4

0

1

2

3

4

5

6

7

Radius (cm)

Hei

ght (

cm)

0.1 2eVTe

1 3 5 0 2 4

0

1

2

3

4

5

6

7

Radius (cm)H

eigh

t (cm

)

3 x 1010 2 x 1012cm-3ne

1 3 5

Hg GROUND AND EXCITED STATE DENSITIES

GEC01_KAPIL_11


• Cataphoresis and gas heating produce a maximum Hg density near thewalls, which results in the maximum of Hg* density occurring towards andnear the inner wall.

0 2 41 3 5

0

1

2

3

4

5

6

7

Radius (cm)

Hei

ght (

cm)

Hg cm-3

7 x 1012 1.5 x 10 14

0 2 41 3 5

0

1

2

3

4

5

6

7

Radius (cm)H

eigh

t (cm

)

Hg* cm-3

1 x 1011 2.5 x 10 12

MULTI-LEVEL TRANSITIONS

GEC01_KAPIL_12


• A study was made of the Hg (61P1) → Hg (61S0) transition at 185 nm as wellas the Hg (63P1) → Hg (61S0) transition at 254 nm.

• The states Hg 61S0, 63P0, 63P1, 63P2, 61P1, 63DJ, and 73S1 were treated asseparate species.

• As a result of different vacuumlifetimes, the photons are absorbedand reemitted many more times forthe 185 nm transition before theyleave the plasma, and the trappingfactor goes up by as much as twoorders of magnitude.

• This result agrees well with the Holstein formulation for a Doppler-broadenedline in cylindrical geometry.

• )ln(k k1g≈ , where k=σN, so for the same number density, the trapping factorscales inversely with vacuum lifetime.

6 1S0

6 3P0

6 3P16 3P2

6 1P1

185 nm

254 nm125 ns

1.33 ns

EMISSION SPECTRA FOR MULTI-LEVEL STUDIES

GEC01_KAPIL_13


• The UV profile is line reversed near the center frequency, because most ofthe photons that escape are in the wings of the profile.

• An increase in ground state absorbers due to an increase in cold spottemperaure affects the 185 nm transition more than the 254 nm transition.

0 3-3ν − ν 0 (Ghz)

Inte

nsity

of r

adia

tion

outp

ut (a

rb. u

nits

)

185 nm

254 nm

0 3-3ν − ν 0 (Ghz)

Inte

nsity

of r

adia

tion

outp

ut (a

rb. u

nits

)

185 nm

254 nm

EMISSION SPECTRA FOR ISOTOPE STUDIES

GEC01_KAPIL_14


• At sufficiently large inter-isotope spacing, only self-trapping is seen.

• As the line centers converge, the photons can “spill” easily betweenisotopes, creating asymmetry in the shoulders of the UV profile.

0 5-3

Inte

nsity

of r

adia

tion

outp

ut (a

rb. u

nits

)

ν − ν 0A (Ghz)

Isotope A

Isotope B

0 5-5

Inte

nsity

of r

adia

tion

outp

ut (a

rb. u

nits

)

ν − ν 0A (Ghz)

Isotope A

Isotope B

EFFECT OF PRESSURE ON TRAPPING FACTOR

GEC01_KAPIL_15


• The pressure was increased keeping ground state densities and cold spottemperature constant, leading to a broadening of the line profiles.

• At first, the trapping factor goes up as the lineshapes begin to overlap.

• When pressure is increased further,the trapping factor for an isotopegoes up or down depending onwhether its self-trapping decreasesslower or faster than the otherisotope.

• This is because the photon escapepaths are now limited to the wings ofthe combined profile.

Pressure (Torr)

0

10

20

30

Trap

ping

fact

or

40

50

0 0.4 0.8 1.2 2.0

Isotope A

Isotope B

DEPENDENCE ON PLASMA GEOMETRY

GEC01_KAPIL_16


• The plasma volume was increased keeping other parameters constant.

• As the radius increases, the photons have to traverse a larger column oflength of Hg before escaping the plasma.

1.5 2.0 2.5

Width of plasma column (cm)

0

100

200

300

Tra

ppin

g fa

ctor Holstein analysis

MCRTM

( ~ R ln R)

• The average column length is muchless than R, the radius of the discharge,which explains the difference of theMCRTM results from the Holsteinresult.

Majority of

photon emitters

CONCLUSIONS

GEC01_KAPIL_17


• A self-consistent Monte Carlo radiation transport model has beendeveloped which, in conjunction with a plasma equipment model, can beused to realistically model resonance radiation transport in a gasdischarge, for complex geometries.

• It is seen that for similar number densities, the radiation trapping factorscales inversely with the vacuum radiative lifetime.

• The effect of pressure was investigated on isotopes which were opticallythick. The trend of the trapping factor depends on the relative rate of fall-off of self-trapping for each isotope.

• Finally, we see that cataphoresis causes a non-uniform distribution ofradiative absorbers and emitters, and scaling laws which apply to simplerdensity profiles are not valid in these lamps.

monte carlo simulation of radiation trapping in ...gec01_kapil_ 04 • characterization of trapping...

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