Upload
others
View
0
Download
0
Embed Size (px)
Citation preview
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
University of Illinois Optical and Discharge Physics
• 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
University of Illinois Optical and Discharge Physics
• 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
__________________University of Illinois
Optical and Discharge PhysicsGEC01_KAPIL_ 05
• 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
University of Illinois Optical and Discharge Physics
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)
__________________University of Illinois
Optical and Discharge PhysicsGEC01_KAPIL_ 07
• 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
__________________University of Illinois
Optical and Discharge PhysicsGEC01_KAPIL_ 08
• 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
__________________University of Illinois
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
University of Illinois Optical and Discharge Physics
• 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
University of Illinois Optical and Discharge Physics
• 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
University of Illinois Optical and Discharge Physics
• 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
University of Illinois Optical and Discharge Physics
• 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
University of Illinois Optical and Discharge Physics
• 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
University of Illinois Optical and Discharge Physics
• 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
University of Illinois Optical and Discharge Physics
• 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
University of Illinois Optical and Discharge Physics
• 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.