monte carlo simulation of radiation trapping in electrodeless
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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 : rajaramn@uiuc.edu mjk@uiuc.edu
http://uigelz.ece.uiuc.edu
May 2002
* Work supported by Osram Sylvania Inc., EPRI and the NSF
AGENDA
ICOPS02_KAPIL_01
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
ICOPS02_KAPIL_02
University of Illinois Optical and Discharge Physics
• 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
__________________
University of Illinois Optical and Discharge Physics
ICOPS02_KAPIL_ 03
• 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
ICOPS02_KAPIL_04
University of Illinois Optical and Discharge Physics
• 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)
__________________
University of Illinois Optical and Discharge Physics
ICOPS02_KAPIL_ 05
• 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
ICOPS02_KAPIL_06
University of Illinois Optical and Discharge Physics
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
__________________
University of Illinois Optical and Discharge Physics
ICOPS02_KAPIL_07
• 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
ICOPS02_KAPIL_08
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_09
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_10
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_11
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_12
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_13
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_14
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_15
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_16
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_17
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_18
University of Illinois Optical and Discharge Physics
• 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
ICOPS02_KAPIL_19
University of Illinois Optical and Discharge Physics
• 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.
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