monte carlo simulation of radiation trapping in electrodeless

MONTE CARLO SIMULATION OF RADIATION TRAPPING IN ELECTRODELESS LAMPS:

A STUDY OF COLLISIONAL BROADENERS*

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

***Department of Electrical and Computer Engineering University of Illinois

Urbana, IL 61801

Email : [email protected] [email protected]

http://uigelz.ece.uiuc.edu

May 2002

* Work supported by Osram Sylvania Inc., EPRI and the NSF

AGENDA

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University of Illinois Optical and Discharge Physics

• Radiation transport in low pressure plasmas

• Overview of the Hybrid Plasma Equipment Model

• The Monte Carlo Radiation Transport Model

• Base case

• Variation of plasma parameters and trapping factors with buffer gas • Importance of resonance broadening

• Conclusions

ELECTRODELESS LAMPS AND TRAPPING

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• Electrodeless gas discharges are finding increasing use in the lighting industry 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 radiation

from Hg (63P1) (254 nm) and Hg (61P1) (185 nm) excites phosphors which generate visible light.

• This resonance radiation can be absorbed and

reemitted many times prior to striking the phosphor, increasing the effective lifetime of emission as viewed from outside the lamp.

• Control of radiation trapping is therefore an

important design consideration for these lamps.

MONTE CARLO METHODS FOR RADIATION TRANSPORT

__________________


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• Historically, characterization of trapping has been done by using analytical solutions of the Holstein equation in simplistic geometries.

• However, Monte Carlo methods are desirable for complex geometries

where it is difficult to evaluate propagator functions. • We have developed a Monte Carlo radiation transport model (MCRTM) for

the radiative transitions of mercury. • The model incorporates the effects of Partial Frequency Redistribution

(PFR) and quenching of excitation, using a Voigt profile for emission and absorption.

• However, one needs a self-consistent plasma model to account for

evolution of gas densities, temperatures and other plasma parameters. • To address this need, the MCRTM is interfaced with the Hybrid Plasma

Equipment model (HPEM) to realistically model the gas discharge.

HYBRID PLASMA EQUIPMENT MODEL

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• A modular simulator addressing low temperature, low pressure plasmas.

• EMM: electromagnetic fields and

magneto-static fields • EETM: electron temperature,

electron impact sources, and transport coefficients

• FKM: densities, momenta, and

temperatures of charged and neutral plasma species; and electrostatic potentials

ELECTRO-MAGNETIC MODULE (EMM)

E,B ELECTRON ENERGY TRANSPORT MODULE (EETM)

FLUID KINETICS MODULE (FKM)

V, N

S, T e,

µ

MONTE CARLO RADIATION TRANSPORT

MODEL (MCRTM)

N, T, P, ki krad

MONTE CARLO RADIATION TRANSPORT MODEL (MCRTM)

__________________


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

• The absorption/emission lineshape function is a Voigt profile. • MC photons are generated in proportion to the excited atom density at

each point in the plasma. • 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. • It can be seen that the trapping factor depends on the emitter density and

absorber density profiles as well as parameters defining the Voigt profile (e.g. Tgas, Nbroadeners).

REACTION CHEMISTRY

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Rg + e → Rg* + e Rg + e → Rg+ + 2e Rg* + e → Rg+ + 2e Rg* + e → Rg + e Hg + e → Hg* + e Hg + e → Hg+ + 2e Hg* + e → Hg + e Rg* + Rg* → Rg+ + Rg + e Rg* + Hg → Hg+ + Rg + e Rg* + Hg* → Hg+ + Rg + e Rg+ + Hg → Hg+ + Rg Rg+ + Hg* → Hg+ + Rg Rg+ + Rg → Rg + Rg+ Hg+ + Hg → Hg + Hg+ Hg* + Hg* → Hg+ + Hg + e Rg* → Rg + hν Hg* → Hg + hν

6 1S0

6 3P0

6 3P16 3P2

185 nm

254 nm125 ns

1.33 ns

Hg+

6 1P1

• Ionization potentials: He 24.5 eV Ne 21.5 eV Ar 15.7 eV Xe 12.0 eV

BASE CASE CONDITIONS

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• Diameter – 9 cm • Height – 8 cm • Initial pressure – 500 mTorr • Initial temperature – 400 K • Power – 50 W • Frequency – 2.65 Mhz

• Initial rare gas mole fraction ≅ 0.98 • Initial Hg mole fraction (ground

state) ≅ 0.02 • Only the 185 nm transition has

been studied. 0 2 4 6

0

2

4

6

8

Radius (cm)

Hei

ght (

cm)

Reentrant cavity

Outer wall

Induction coil

Ferrite core

ARGON

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• The power is deposited near the antenna, leading to a maximum electron temperature near the coil, and an electron density in an annulus round the antenna.

1 x 10-5 4.3W cm-3

Power density

1 x 10-2 1.6eV

Te

5 x 1010 9 x 1012cm-3

ne, [Hg+]

ARGON

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• Cataphoresis and gas heating leads to a maximum of [Hg*] near the walls.

3 x 106 1.2 x 108cm-3

[Ar+]

5 x 1012 4 x 1014cm-3

[Hg]

5 x 109 4 x 1012cm-3

[Hg*]

POWER DEPOSITION

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• Due to the large momentum transfer cross-section of Xe, most of the power is deposited near the antenna.

1 x 10-4 3.0W cm-3

Ne

1 x 10-5 4.3W cm-3

Ar

1 x 10-4 7.0W cm-3

Xe

ELECTRON TEMPERATURE

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• Xe and Ar are Ramsauer gases unlike Ne. • Also, the excited state thresholds of the noble gases are different, leading

to different degrees of ionization.

0.1 1.65eV

Ne

1 x 10-2 1.6eV

Ar

0.1 2.5eV

Xe

ELECTRON DENSITY

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• Due to the lower ionization potential for Xe (12.0 eV), the electron density is lowest for the Xe case.

1 x 1011 1.5 x 1012cm-3

Ne

9 x 1010 9 x 1012cm-3

Ar

3 x 1010 1.2 x 1012cm-3

Xe

MERCURY ION DENSITY

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• In the cases of Ne and Ar, [Hg+] maps ne, but the larger mass of Xe does not allow [Hg+] to move to the upper part of the lamp.

1 x 1011 1.5 x 1012cm-3

Ne

5 x 1010 9 x 1012cm-3

Ar

5 x 108 2.5 x 1011cm-3

Xe

MERCURY GROUND STATE DENSITY

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• In the case of Xe, there is more depletion of Hg from the center of the column, because more power is deposited in that region.

8 x 1012 4 x 1014cm-3

Ne

5 x 1012 4 x 1014cm-3

Ar

1.5 x 1013 4.5 x 1014cm-3

Xe

MERCURY EXCITED STATE DENSITY

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• In cases of Ne and Xe, we do not see the peak in [Hg*] near the outer wall because of the smaller [Hg*] density in these cases.

4 x 109 1.8 x 1011cm-3

Ne

5 x 109 4 x 1012cm-3

Ar

1 x 108 7 x 1010cm-3

Xe

VOLUME AVERAGES

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• The volume averages for some plasma parameters of the lamp are shown here.

• Ar has the largest [Hg*] density as

well as the largest [Hg*]/[Hg] ratio.

He Ne Ar Xe1011

1012

n e (

cm-3

)

He Ne Ar Xe

1011

1012

[Hg*

] (c

m-3

)

1010

109

1013

He Ne Ar Xe

10-3

10-2

[Hg*

] / [H

g]

10-4

10-5

TRAPPING FACTORS

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• Even though the Xe case has a lower trapping factor, the lower emitter density in that case results in a lower radiative output.

• At higher pressures of 1 Torr, Ne as a buffer gas has a better radiative

output as well as a lower trapping factor. However, almost all the light is emitted near the inside of the lamp, and may not be all that useful.

TRAP

PIN

G F

ACTO

R

Ne

Ar

Xe

0

50

100

150

200

250

0.5 0.75 1PRESSURE (Torr)

0 2 4-2-4In

tens

ity (a

rb. u

nits

)ν - ν0 (GHz)

Ne

Ar

Xe

EFFECTS OF RESONANCE BROADENING

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• The effects of Hg-Hg resonance broadening was investigated with Ar as the buffer gas, with a foreign gas broadening cross-section of 7 × 10-15 cm2.

• For Hg-Hg broadening cross section ∼10-14 cm2, resonance collisions were

not found to make a significant effect on trapping.

0 2 4-2-4

Inte

nsity

(arb

. uni

ts)

ν - ν0 (GHz) • Hg-Hg crosssection – 1 × 10-14 cm2

Trapping factor w/o collisions ≈ 200 Trapping factor with collisions ≈ 200

0 2 4-2-4

Inte

nsity

(arb

. uni

ts)

ν - ν0 (GHz)

w/o collisions

with collisions

• Hg-Hg crosssection – 1 × 10-12 cm2

Trapping factor w/o collisions ≈ 200 Trapping factor with collisions ≈ 160

SUMMARY

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• A self-consistent Monte Carlo radiation transport model has been developed which, in conjunction with a plasma equipment model, can be used to realistically model resonance radiation transport in a gas discharge, for complex geometries.

• Different buffer gases were investigated, and it is seen that xenon has the

lowest trapping factor for pressures of interest to us. However, the emitter density profile places a restriction on the buffer gas which we can use.

• Ar is the most efficient buffer gas in terms of the number of emitters as

well as the emitter-to-absorber ratio. • Our results indicate that Ne may be a good choice as a buffer gas at

pressures of 1 Torr or more. • Finally, we see that for cross sections of relevance to us, resonance

collisions do not play a significant role in determining exit spectra or trapping factors.

monte carlo simulation of radiation trapping in electrodeless

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