Modelling of high-frequency electrodeless lamps. Comparison to experimental data.

Modelling of high-frequency Modelling of high-frequency electrodeless lamps. Comparison electrodeless lamps. Comparison

to experimental data.to experimental data.

N. Denisova, G.Revalde, A. Skudra

Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

Institute of Atomic Physics and Spectroscopy, University of Latvia, Riga, Latvia

12-16 April 2005, Madeira,Portugal


In this work, we present the results of investigations of high-frequency electrodeless discharge lamps (HFEDLs), developed as light sources for atomic absorption spectrometry.

Ganeev A., Gavare Z., Khutorshikov V.I., Khutorshikov S.V., Revalde G., SkudraA., Smirnova G.M., Stankov N.R. 2003 Spectroch Acta B58 879-889.

The light sources based on the principle of electromagnetic induction are receiving increasing attention due to their great promise in lighting technology. For optimization of this kind of light sources, a self-consistent modeling of physical processes in a discharge plasma and electromagnetic field parameters is necessary. Various methods of modeling inductive discharges have been developed. The developed models depend on the discharge pressure. In this work, the inductive discharges with the pressure of the order of 0.5-10 Torr are considered.

Low-pressure inductive coupled plasma (ICP) sources are widely used in practice, which promotes a development of suitable models.



Basic model assumptions:

1.The discharge is presented as a part of an infinitely long cylinder placed inside a solenoid.

2.The plasma is homogeneous along the axis and the discharge parameters depend on the radial coordinate.

3.The electrons are assumed to have a Maxwellian energy distribution function due to the relatively high electron density

The electron energy distribution function is assumed to be isotropic, as the skin layer is thin.

31918 1010 m

31918 1010 m

A self-consistent HFEDL model.


The collision radiative module includes the necessary data base. The calculation of the electromagnetic field profiles is based on the Maxwell equations and is performed self-consistently with the plasma parameters.

1.The collision radiative plasma module1.The collision radiative plasma module

The developed HFEDL model includes three basic blocks:

2.The calculation of the electromagnetic field2.The calculation of the electromagnetic field

3.The calculation of the spectral lines shapes and intensities3.The calculation of the spectral lines shapes and intensities

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HgArHgArHgHgHgHgmkmk

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The electromagnetic field equations.

The excited states balance equations:

The electron density balance equation:The electron density balance equation:

The electron energy balance equation:The electron energy balance equation:


t

H

crotE

1

0)()(2

3

SSqdivkTnt Tee

High-frequency High-frequency electrodeless electrodeless

dischargesdischarges in in argon argon and krypton.and krypton.

Bulyshev AE, Denisova NV, Skudra A 1989 Optical characteristics of a high frequency electrodeless discharge in argon and krypton Optics and Spectr.67 788.

Denisova N V, Preobrazhensky N G 1994 Spectrochimica Acta 49B 2 185-191

High-frequency electrodeless dischargeHigh-frequency electrodeless discharge lamps (HFEDLs) lamps (HFEDLs) in heliumin helium

Usually, one does not use helium for filling HFEDLs, due to the high diffusion of the helium through the walls of the light source. The helium lamps that work for more than 1000 h were produced by Riga’s High Resolution Spectrometry Group at the Institute of Atomic Physics and Spectroscopy by a special technology.


An optimization of such lamps, in the sense of performance for scientific and industrial applications, requires studying of fundamental properties of the high-frequency electrodeless discharge (HFED).

The cylindrical HFEDs samples of 10 mm diameter and 40 mm length were used in experiments. The helium pressure was varied in the range from 0.2 to 7 Torr. An electromagnetic field of approximately 100 MHz frequency was used for the excitation of an inductively coupled discharge in the samples placed into the oscillator coil. The power of the HF discharge was varied by changing the coil current, from about 50 mA to 220 mA.


The typical input HFED operating conditions, considered in this work, are the followings:

1) the gas pressure within the range 0.5 - 10 Torr,

2) the external magnetic field amplitude 0.5-2oe and the frequency of the applied electromagnetic field 100MHz,

3) the gas temperature 400 - 700K,

4) the tube radius ~0.5-1 cm.



The electron temperature versus the gas pressure in the discharge.

Pressure,Torr

T, eV

The electron density versus the gas pressure in discharge for two different values of the external magnetic field amplitude : 1oe and 0.7oe.

Pressure,Torr

ne*10 10

E, (a.u.)

Radius,cm

The electric field profile for two different values of the gas pressure p: (1) p=0.2 Torr, (2) p=1 Torr


Radius,cm

Radius,cm

Ne

Te,eV

1210

Dependence of the electron density and temperature on the discharge tube radius.

NaNe

HPOWER

32

~

Ne

NaHPOWER

2

~

Analytical estimation of the absorbed power

R

Numerical calculation

The absorbed power versus the gas pressure for different values of the external magnetic field amplitude H0: H0=2oe, H0=1oe, H0=0.7oe.


1¹S

2³P

2¹S

2¹P

2³S

¹S ¹P ¹D ³S ³P ³D ³F¹F

5

43

3

4

5

3


He

587.6nm728.1nm 667.8nm

Calculated intensities of the 587.6 nm and 728.1 nm lines versus the gas pressure for two different values of the magnetic field amplitude H0: (1) H0=0.7oe, (2) H0=1.5oe.

1 2 3 4 5Pressure,Torr

20

40

60

80100

Inte

nsi

ty,a

.u.

1

2

1

2

587.6nm

728.1nm

Experimental intensities of the 587.6 nm and 728.1 nm lines versus the gas pressure for two different values of the excitation generator current (1) 100mA, (2) 200mA.


ExperimentNumerical calculation


100 150 200J, mA

10

20

30

40

50

60

70

Inte

nsi

ty,a

.u.

2

3

4

5

1

6

Experiment Numerical calculation

Experimentally measured intensity of the 728.1nm line versus the generator current for different values of the gas pressure p: (1) p=0.35 Torr, (2) p=0.65 Torr, (3) p=1.35Torr, (4) p=2.2Torr, (5) p=3.15Torr, (6) p=5.1Torr.

Calculated intensity of the 728.1nm line versus the external magnetic field amplitude for different values of the gas pressure p: (1) p=0.4 Torr, (2) p=0.6 Torr, (3) p=1Torr, (4 ) p=2 Torr, (5) p=3 Torr, (6) p=5 Torr.

The line intensity profiles versus the radius.

Experimental data:

A.Skudra ‘High-frequency electrodeless helium lamps’,Acta universitatis Latviensis,

573,Riga,1992.

0 0.25 0.5 0.75 1Radius,cm

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Inte

nsi

ty,a

.u.

P=0.5 Torr

1

2

0 0.25 0.5 0.75 1Radius, cm

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Inte

nsi

ty,a

.u.

p=2 Torr

1

2

667.8 nm

1 – H = 0.7 oe, 2 – H = 1.5 oe


An improved self-consistent model of the high-frequency electrodeless discharge lamps in helium is developed. Based on the model, the emission properties of the helium lamps are calculated, being in a good agreement with the experimental data. The developed model is used to obtain optimal operation conditions of high-frequency electrodeless helium lamps.


Conclusion.

High-frequency electrodeless lamps in argon-mercury mixtures.

The intensities of the mercury spectral lines of the wavelengths

and the resonance line are measured at a wide range of mercury pressures varying the HF generator current and argon filling pressure. A stationary self-consistent model of high-frequency electrodeless discharge lamp is developed including kinetics of the excited mercury and argon atomic states. Based on the developed model, the radiation characteristics of the discharge plasma are calculated.

07.546

2,1,03

13 67 PS nm66.404 nm83.435 nm07.546

7.253 01

13 66 SP

Numerical and experimental investigations of high-frequency electrodeless lamps in argon- mercury mixtures are performed.


Calculations of the relative intensities of the visible triplet lines are presented first in this work.

2,1,03

13 67 PS

3.2. Elementary processes.

1. Ionization by electron collisions.

eeHgeHgHgiWI

i

eeHgeHgHgiWI

i eeAreArArkWI

k

0.5 1 1.5 2 2.5electron temperature, eV

10-4

10-3

10-2

10-1

100

101

102

103

ion

iza

tion

rate

coe

ffic

ien

t

2

3

1

The ionization rate coefficients of the ground state (curves 1), the levels - (curves 2) and (curve 3).The circles indicate the calculations in accordance with the semi-empirical formulas [14], diamonds correspond to the data, given in [13] (curve 1) and [5,15] (curves 2,3).

036 P


236 P

Rockwood S.D. 1973 Phys.Rev. A8 2348. Drawin H W, Emard F 1975 Beitr.Plasmaphys.15 273. Vriens M.L., Keijser R.A.J., Lighart F.A.S. 1978 J.Appl.Phys.49 p.3807-3813.

2. Ionization by heavy particles collisions.

eHgHgHgHg HgHgW ** Vriens M.L., Keijser R.A.J., Lighart F.A.S. 1978 J.Appl.Phys.49 p.3807-3813.

3. Penning ionization.

eHgArHgAr ArHgW * Phelps A.V., Molnar J.P. 1953 Phys.Rev. 89 1202.


4. Radiative transitions.

ijjA

i hHgHg ij

kllA

k hArAr kl

The effect of radiation imprisonment was taken into account by using an escape factor.

Radzig A.A., Smirnov B.M. 1980 Reference book on atomic and molecular physics

Moscow Atomizdat p.240. Wiese W L, Smith N W, Glennon B M 1966 Atomic Transition Probabilities NBS Report

NSRDS 4.

Winkler R.B., Wilhelm J., Winkler R. 1983 Annalen der Physik p.90-139.

Vainstein L.A., Sobel’man I.I., Yukov E.A. 1979 Atoms excitation and spectral lines broadening Moscow Nauka p.319.

0.5 1 1.5 2 2.5electron temperature, eV

10-3

10-2

10-1

100

101

102

103

exc

itatio

nra

teco

eff

icie

nt

1

2

3

SP 32

3 76

13

01 66 PS

PS 30

1 66 Curve 1

Curve 2

Curve 3

5. Excitation/de-excitation by electron collisions.

eHgeHg jW

iij

eAreAr lW

kkl



A schematic energy level diagram of the mercury atom

8/14/113 )]105.4/([ eeb TnEI

Biberman L M, Vorob’ev V S, Jakubov I T

1982 Kinetics of non-equilibrium low

temperature plasmas Nauka Moscow.

J.van Dijk, B.Hartgers, J.Jonkers,

J.A.M.van der Mullen 2000 J.Phys.D: Appl.Phys.33 p.2798.

Numerical calculations of plasma parameters and emission properties of HFEDL. Comparison to experiment.


20 30 40 50 60Cold spot temperature, grad C

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Ele

ctro

nte

mp

era

ture

,eV

1

2

3

4


100

200

300

400

500

600

700

800

900

1000

1100

Ele

ctro

nd

en

sity

1

2

3

4

Curves1-P Ar=1Torr, curves2 – P Ar=2Torr, curves 3 – P Ar=3Torr H0=0.7oe

Curves 4 – P Ar=2Torr, H0=0.9oe


103

104

105

106

Ion

iza

tion

rate

s,(a

.u.)

Hg-e

Hg-Hg

total

Ar-e

Ar-Hg

P Ar=1 Torr;

H0=0.7oe

The comparison the partial contributions of the different ionization processes for the two different argon filling pressures: a – 2Torr, b – 1Torr.

a b


20 30 40 50 60 70Cold spot temperature, grad C

100

101

102

Inte

nsi

ty,(

a.u

.)

404.7nm


100

101

102

Inte

nsi

ty,(

a.u

.)

435.8nm


100

101

102

Inte

nsi

ty,(

a.u

.)

546.1nm


The comparison of the measured and calculated emission intensities of the visible triplet lines Solid line – numerical calculation, circles –measured data.Calculated data are normalized to the measured data at . Argon filling pressure .

2,1,03

13 67 PS

CTCS20

TorrPAr 2 oeH 7.00


500

1000

1500

2000

2500

3000

Inte

nsi

ty,a

.u.

253.7nm

The intensity of the resonance line 253.7nm versus the cold spot temperature. Dashed line – numerical calculation, points – experimental data. The numerical and measured results are normalized at the maximum.

The basic physical model and numerical codes of the high-frequency electrodeless discharge lamp (HFEDL) used for spectroscopic applications are developed. The model was tested in our previous works for argon and helium lamps. In the present paper, this model is tested by comparing numerical calculations to the results of experimental data for the argon-mercury lamp.Based on the developed model, the radiation characteristics of the HFEDL are calculated. Numerical simulation of behavior of the line intensities in dependence on the external discharge parameters is performed and is found to be in qualitative agreement with the experimental data.Calculations of the emission intensities corresponding to the visible triplet of mercury atom are presented first in this work.


The basic physical model and numerical codes of the high-frequency electrodeless discharge lamp (HFEDL) used for spectroscopic applications are developed. The model was tested in our previous works for argon and helium lamps. In the present paper, this model is tested by comparing numerical calculations to the results of experimental data for the argon-mercury lamp.Based on the developed model, the radiation characteristics of the HFEDL are calculated. Numerical simulation of behavior of the line intensities in dependence on the external discharge parameters is performed and is found to be in qualitative agreement with the experimental data.Calculations of the emission intensities corresponding to the visible triplet of mercury atom are presented first in this work.

Conclusion.


2,1,03

13 67 PS


Radial properties of high-frequency electrodeless lamps in argon-mercury

mixtures.

Mirror 3 Mirror 2

Mirror 1

Lamp

Registration unit

Lens

Lens

Experimental set-up for the measurement of the radial distribution of the intensities. Mirrors 1, 2, 3 are mounted on the common holder and the moving the mirrors in the necessary direction performs the scanning of the radial emission from the cylindrical spectral lamp. The dotted line shows the place of the mirrors and the rays after displacement of the mirrors.


-1 -0.5 0 0.5 1radius

0

200000

400000

600000

800000

inte

nsi

ty,a

.u.

experiment

404.7nm

1 - HF generator power 74W

2 - 48W

1

2

-1 -0.5 0 0.5 1radius

0

200000

400000

600000

800000

Inte

nsi

ty,a

.u.

calculation

404.7nm

1

2

1 - absorbed power 36W

2 - 19W


Torr2

.Argon pressure:

, mercury pressure:

.


-1 -0.5 0 0.5 1radius

0

200000

400000

600000

800000

inte

nsi

ty,a

.u.

experiment

435.8nm 1

2

-1 -0.5 0 0.5 1radius

0

200000

400000

600000

800000

Inte

nsi

ty,a

.u.

calculation

435.8nm

1

2


-1 -0.5 0 0.5 1radius

0

200000

400000

600000

800000

inte

nsi

ty,a

.u.

1

2

experiment

546.1nm

-1 -0.5 0 0.5 1radius

0

200000

400000

600000

800000

Inte

nsi

ty,a

.u.

calculation

546.1nm

1

2


Numerical calculationExperiment


0 0.25 0.5 0.75 1Radius.cm

0

2

4

6

8

10

12

14

Ele

ctri

cfie

ldst

ren

gth

,V/c

m

1.The basic physical model and numerical codes of the high-frequency electrodeless discharge lamp (HFEDL) used for spectroscopic applications are developed. The model has been tested for argon, krypton, helium and argon-mercury lamps.

2. Numerical simulation of the line intensities behavior in dependence on the external discharge parameters is performed, being in qualitative agreement with the experimental data.

3. Based on the developed model, the radial dependences of radiation characteristics of the HFEDL are calculated.

4.Calculations of the emission intensities corresponding to the visible triplet of mercury atom are presented first in this work.2,1,0

31

3 67 PS


Conclusion.

This work was supported by INTAS grant 01-0200

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Monte Carlo simulation of radiation trapping in Hg-Ar HF EDL.

The line shape in the chosen direction is determined

Using the Biberman equations:

and integral operator:

the solution can be presented in the form of Neumann series:


-50 0 500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Inte

nsi

ty,a

.u.

Experiment Monte Carlo modelling

Computed tomography is a powerful tool for discharge plasma diagnostics. Unfortunately, viewing access in many plasma experiments is strongly limited, which leads to a highly underdetermined ill-posed problem. A Maximum a Posteriori (MAP) reconstruction algorithm is developed which yields the most probable image estimate from limited and noisy data.

Exact model MAP reconstruction ART reconstruction


Computed tomography for discharge plasma diagnostics

Two-view tomography of the plasma optical pulsating discharge in a high-velocity flow of argon

Grachev G.N.,Denisov V.I.,Denisova N.V., Menshikov J.G., Smirnov A.L.



1. Denisova N V 1998 Maximum Entropy based tomography for gas and plasma diagnostics J. Phys. D: Appl. Phys. 31 1888.

2. Denisova N V Two view tomography 2000 J. Phys. D: Appl.Phys. 33 313.

3. Denisova N V A maximum a posteriori reconstruction method for plasma tomography 2004 Plasma Sources Sci.Technol. 14 531.

Modelling of high-frequency electrodeless lamps. Comparison to experimental data.

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