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A Monte Carlo Simulation of Radiation Trapping in Electrodeless Gas Discharges Having Complex Geometries*

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A Monte Carlo Simulation of Radiation Trapping in Electrodeless Gas Discharges Having Complex Geometries* A MONTE CARLO SIMULATION OF RADIATION TRAPPING IN ELECTRODELESS GAS DISCHARGES HAVING COMPLEX GEOMETRIES* 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] *Work supported by Osram-Sylvania and the NSF AGENDA · Radiation transport in low pressure plasmas · Overview of the Hybrid Plasma Equipment Model · Description of Monte Carlo Transport model · Base case plasma properties · Dependence of radiation trapping factor on - Plasma geometry - Pressure - Gas temperature · Emission spectra · Conclusion __________________ University of Illinois Optical and Discharge Physics ICOPS01_2 ELECTRODELESS LAMPS AND TRAPPING · Electrodeless gas discharges are finding increasing use in lighting applications 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 3 from Hg(6 P1) (254 nm) excites phosphors which generate visible light. 1 · Resonance radiation, produced by electron impact excitation of Hg (6 S0) 3 to Hg(6 P1), can be absorbed and reemitted many times prior to striking the phosphor. · The consequence of radiation trapping is to lengthen the effective lifetime of emission as viewed from outside the lamp. · Control of resonance radiation trapping is therefore important to the design of such lamps. __________________ University of Illinois Optical and Discharge Physics ICPOS01_3 PHYSICAL PROCESSES · The excited Hg and Ar levels have been treated as a single state. hv e e Hg e Hg* Hg+ hv e , Ar* , Ar e e Ar Ar* Ar+ e Ar* e · Ar is a buffer gas. Radiation exciting the phosphor is essentially all due to the mercury transition. __________________ University of Illinois Optical and Discharge Physics ICOPS01_4 PAST TREATMENT OF RADIATION TRANSPORT • Characterization of trapping is typically done using Holstein factors • A → A⋅g, where A is the Einstein A-coefficent and g is a geometry-dependent factor. For a cylinder, • = g 1.115 πkpR (impact broadened) • g =1.60 k R π ln(k R) (doppler broadened) 0 0 where k is the lineshape profile. • This method fails for more complex geometries, where the propogator cannot be easily evaluated. __________________ University of Illinois Optical and Discharge Physics ICOPS01_4a MONTE CARLO METHODS FOR RADIATION TRANSPORT · Monte Carlo methods are desirable for complex geometries where it is not easy to evaluate propogator functions. · We have developed a Monte Carlo resonance radiation transport model for the trapping of the 254 nm radiative transition for mercury. · This 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 “drive” the kinetics and to account for evolution of gas densities, temperatures and other plasma parameters. · To address this need, the Monte Carlo resonance radiation transport model is interfaced with the Hybrid Plasma Equipment Model (HPEM) to realistically model the gas discharge. __________________ University of Illinois Optical and Discharge Physics ICOPS01_5 SCHEMATIC OF THE HYBRID PLASMA EQUIPMENT MODEL MONTE CARLO FEATURE PROFILE MODEL IAD(r,z) IED(r,z) CONTINUITY PLASMA S(r,z,f) CHEMISTRY ELECTRON MOMENTUM E (r,z,f) MONTE CARLO MONTE CARLO s SIMULATION SIMULATION ENERGY MAGNETO- B(r,z) STATICS LONG MEAN N(r,z), k MODULE ELECTRON FREE PATH MONTE CARLO BEAM MODULE (MONTE CARLO) RADIATION TRANSPORT ELECTRON SPUTTER MODULE MATCH BOX-COIL k(rad) ENERGY S(r,z,f) MODULE CIRCUIT MODEL EQUATION POISSON T (r,z,f) ELECTRO- e ELECTRO- F(r,z,f) E(r,q,z,f) BOLTZMANN MESO-SCALE MAGNETICS MODULE STATICS FREQUENCY m(r,z,f) MODULE DOMAIN B(r,q,z,f) NON- AMBIPOLAR s(r,z) SURFACE COLLISIONAL ELECTRO- ELECTRO- CHEMISTRY HEATING STATICS MAGNETICS MODULE FDTD SIMPLE ON-THE-FLY CIRCUIT FREQUENCY MODULE F(r,z,f) s(r,z) DOMAIN EXTERNAL SHEATH CIRCUIT J(r,z,f) MODULE MODULE ID(coils) Es(r,z,f) N(r,z) V(rf),V(dc) VPEM: SENSORS, CONTROLLERS, ACTUATORS University of Illinois ICOPS01_6 Optical and Discharge Physics MONTE CARLO RADIATION TRANSPORT MODEL (MCRTM) · Monte Carlo method is used to follow trajectories of photons from initial emission to escape from plasma. · The absorption/emission profile used is a Voigt profile. · MC photons are generated in proportion to the excited atom density at each point in the plasma. · The initial frequency of each photon is not directly sampled from the lineshape profile. Instead, to avoid statistical errors, we choose the frequency uniformly from a chosen bandwidth, and assign to this particle a weighting which accounts for the lineshape profile. · The null collision method is employed for the photon transport. ICOPS01_7 University of Illinois Optical and Discharge Physics TRAPPING FACTOR AND PFR • We define the trapping factor as τ k = res , τnat 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 frequency redistribution is incorporated by randomly choosing a new frequency within a range ν ± ∆∆νν. • The value of ∆∆νν was found by simulating trapping in a cylindrical discharge with a uniform density of Ar and Hg atoms, and comparing the results with those found by Lister. • The results agreed well for ∆∆νν ≈ α ∆∆ννd, where α ranged from 1.75 to 2.0. __________________ University of Illinois Optical and Discharge Physics ICOPS01_8 BASE CASE CONDITIONS · Diameter – 9 cm 8 · Depth – 5 cm · Height – 8 cm Reentrant cavity · Initial pressure – 250 mTorr 6 · Initial temperature – 400 K Outer wall · Operating power – 50 W · Operating frequency – 2.65 Mhz 4 · Initial Ar mole fraction- 0.98 Induction coil · Initial Hg mole fraction – 0.02 Height (cm) Ferrite core · Only 254 nm resonance line has 2 been studied. · The trapping factor for these conditions is »40 0 0 2 4 6 Radius (cm) ICOPS01_9 University of Illinois Optical and Discharge Physics ELECTRON DENSITY AND TEMPERATURE · Peak electron temperature (» 2 eV) surrounds the reentrant coil resulting in a peak plasma density in an annulus around the antenna. 7 7 6 6 5 5 4 4 3 3 Height (cm) Height (cm) 2 2 1 1 0 0 0 1 2 3 4 5 0 1 2 3 4 5 Radius (cm) Radius (cm) n cm-3 Te eV e 11 12 0.11 1.68 2.5 x 10 3.7 x 10 University of Illinois ICOPS01_10 Optical and Discharge Physics Hg GROUND AND EXCITED STATE DENSITIES · Cataphoresis and gas heating produce a maximum Hg density near the walls, which results in the maximum of the Hg* density occurring in the top “dome” and near the walls. 7 7 6 6 5 5 4 4 3 3 Height (cm) Height (cm) 2 2 1 1 0 0 0 1 2 3 4 5 0 1 2 3 4 5 Radius (cm) Radius (cm) Hg cm -3 Hg* cm -3 7.3 x 1012 1.1 x 1014 1.2 x 1011 1.8 x 1012 University of Illinois ICOPS01_11 Optical and Discharge Physics DEPENDENCE ON Ar PRESSURE · The fill buffer gas pressure was increased while keeping other 50 parameters (e.g. Hg density) constant. 40 · The increase in Ar – Hg* collision 30 frequency produces a broader redistribution of re-emission 20 allowing the photons to move into Trapping factor the wings of the lineshape profile. 10 · Owing to a longer mean free path in the wings, the photons can 0 150 250 350 450 escape the plasma more easily, Buffer gas pressure (mTorr) reducing the trapping factor. ICOPS01_12 University of Illinois Optical and Discharge Physics DEPENDENCE ON GAS TEMPERATURE • The initial background gas temperature was varied keeping initial ground state number 70 densities and other parameters 60 constant. 50 • As the temperature is increased, the number of collisions that the 40 gas atoms undergo increases, and 30 this allows for a higher Trapping factor redistribution. 20 10 • Moreover, the increase in temperature affects the Voigt 0 300 400 500 600 profile via the Doppler broadening. Therefore, the Gas Temperature (K) trapping factor decreases. ICOPS01_13 University of Illinois Optical and Discharge Physics DEPENDENCE ON PLASMA GEOMETRY • The plasma volume was increased by increasing the outer radius of the lamp and other parameters are constant. • As the radius increases, the photon has to traverse a larger column of length of Hg before escaping the plasma. • This average column length is less than R, the radius of the 100 discharge, which explains the difference of our results from 80 Holstein factors ( g ~ R ln (R) ). 60 40 Trapping factor 20 Majority of photon 0 emitters 1.5 2.0 2.5 Width of plasma column (cm) University of Illinois Optical and Discharge Physics ICOPS01_14 EMISSION SPECTRA · Due to radiation trapping , line reversal is observed in the UV emission spectra near the center frequency because the photons that leave the plasma are mainly in the wings. 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 Normalized radiation intensity 0.2 Normalized radiation intensity 0.2 0 0 -2.5 0 2.5 -2.5 0 2.5 Normalized frequency ( n-n0/Dnd) Normalized frequency ( n-n0/Dnd) · No trapping · With trapping (base case) __________________ University of Illinois Optical and Discharge Physics ICOPS01_15 EMISSION SPECTRA (contd.) · Emission spectra were also obtained while increasing mole fraction of Hg and the radius of the plasma column. Increased trapping led to greater line reversal. 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 Normalized radiation intensity Normalized radiation intensity 0 0 -2.5 0 2.5 -2.5 0 2.5 Normalized frequency ( n-n0/Dnd) Normalized frequency ( n-n0/Dnd) · Mole fraction of Hg=4% · Radius=4.5 cm __________________ University of Illinois Optical and Discharge Physics ICOPS01_16 SUMMARY AND FUTURE WORK · A self-consistent Monte Carlo radiation transport model has been developed which, in conjunction with a plasma model, can be used to realistically model resonance radiation transport in a gas discharge, for complex geometries.
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