Study of a Micro Hollow Cathode Discharge at medium argon gas pressure

Transcription

1 Study of a Micro Hollow Cathode Discharge at medium argon gas pressure Claudia LAZZARONI Antoine ROUSSEAU Pascal CHABERT LPP Ecole Polytechnique, Palaiseau, FRANCE Nader SADEGHI LSP Grenoble, FRANCE

2 I-V characteristic ,6 Torr.cm Voltage (V) ,84 Torr.cm 1 Torr.cm 1,2 Torr.cm confined inside the micro-hole ,0 0,4 0,8 1,2 1,6 2,0 2,4 self-pulsing current (ma) normal: cathode expansion Aubert et al., PSST 16 (2007) 23 32

3 Example of a 2D simulation alumina hundred µm cathode anode 150µm 150µm 250µm DC power supply L. PITCHFORD, K. MAKASHEVA (LAPLACE, Toulouse)

4 Geometry of the system sheath z 150 µ m CATHODE REGION r 250 µ m alumina POSITIVE COLUMN 400 µ m 150 µ m ANODE REGION

5 Geometry of the system sheath z 150 µ m CATHODE REGION r 250 µ m alumina POSITIVE COLUMN 400 µ m 150 µ m ANODE REGION

6 Geometry of the system sheath z 150 µ m CATHODE REGION r 250 µ m alumina POSITIVE COLUMN 400 µ m 150 µ m ANODE REGION

7 Geometry of the system sheath z 150 µ m 250 µ m alumina r CATHODE r E DIELECTRIC 150 µ m 400 µ m ANODE

8 Geometry of the system z 150 µ m sheath e - r 250 µ m alumina E r 400 µ m 150 µ m

9 Setup for spectral measurements cathode anode CCD reflection gating mirrors f =30mm filter monochromator -f =2m -1200g/mm -spatial resolution=2µm

10 Pressure influence Intensity (a.u.) Intensity (arb. u.) line line 30 Torr 0-0,2-0,1 0,0 0,1 0,2 r (mm) Torr line line 0-0,2-0,1 0,0 0,1 0,2 r (mm) Intensity (arb. u.) line line 100Torr 0-0,2-0,1 0,0 0,1 0,2 r (mm) -Ø=400µm -i=1ma Two origins for the light emission: in the centre near the egdes Leads: centre recombination Edge excitation by high energy electron emitted from the cathode

11 Study of the cathodic region sheath z 150 µ m CATHODE REGION r 250 µ m alumina POSITIVE COLUMN 150 µ m 400 µ m ANODE REGION

12 Calculation of the sheath thickness (d) sheath d One-dimensional cylindrical geometry: 0 R r bulk Ions/electrons fluxes: Γ i ( R d ) Γ i (R) Cathode Γ ( R d ) = ξ Γ ( R) i i Γ e ( R d ) Sheath Γ e (R) Γ e ( R) = γγ ( R) r r r Γe = α( r) Γ e i

13 Calculation of the sheath thickness (d) Distance from the cathode (µm) ξ=0 line maximum line maximum P (Torr) Γ ( R d ) = ξ Γ ( R) i i T=470K

14 Calculation of the sheath thickness (d) Distance from the cathode (µm) ξ=0 line maximum ξ=0.3 line maximum P (Torr) T=470K

15 Calculation of the sheath thickness (d) Distance from the cathode (µm) ξ=0 -decrease of the sheath size with the increase of ξ ξ=0.3 ξ=0.5 line maximum line maximum P (Torr) -maxima of both emission lines located after the sheath edge whatever the value of ξ -same trends for the evolution of d that of the maxima of the emission line -the sheath edge coincide with the maxima of the ionic line T=470K

16 1D stationnary model of the cathodic region sheath z 150 µ m CATHODE REGION r 250 µ m alumina POSITIVE COLUMN 150 µ m 400 µ m ANODE REGION

17 1D stationnary model of the cathodic region sheath z 150 µ m CATHODE REGION PLASMA r 250 µ m alumina POSITIVE COLUMN 150 µ m 400 µ m ANODE REGION

18 Model description 3 species : e -,, 2 3 reactions : e 2 2 e * 2e 2 ( K iz ( K ( K 1 ) ) rec ) Numerical tool : MATLAB

19 Governing equations z Set of equations: n Quasi-neutrality: e = n n 2 r Continuity equation: dγi Γi = P L dr r Momentum conservation (drift-diffusion): r Γ i = r n µ E i i r D n i i no energy equation: we need to give us a n e Boundary conditions Integration until the entrance of the sheath (to respect the electroneutrality) Shooting method: ions speed value at the sheath edge T e (r)

20 Ionization rate shape Emission intensity of line α ν iz 1 100Torr Intensity (arb. u.) line ν iz (10 6 s -1 ) Torr 0 0,0 0,1 0,2 Radial position (mm) 0 0,00 0,05 0,10 0,15 0,20 Radial position (mm)

21 Ionization rate shape Emission intensity of line α ν iz 4 30 Torr ν iz (10 6 s -1 ) Torr 100 Torr 200 Torr 150 Torr 0 0,00 0,05 0,10 0,15 0,20 Radial position (mm)

22 Electron temperature ν iz (10 6 s -1 ) Torr 50 Torr 100 Torr 200 Torr 150 Torr 0 0,00 0,05 0,10 0,15 0,20 Radial position (mm) T e (ev) 2,0 1,5 1,0 0,5 50 Torr 100 Torr 150 Torr 30 Torr 0,0 0,00 0,05 0,10 0,15 0,20 Radial position (mm) 200 Torr T E e Ei ( ev ) = ν log( i i0 = ev and 0 0 ν iz ) ν i0 = K iz0 n g = P( Torr)

23 Species density 1,0 200 Torr 0,8 0,6 100 Torr n e /n 0 0,4 30 Torr 0,2 1,0 0,8 30 Torr 50 Torr 150 Torr 0,0 0,00 0,05 0,10 0,15 0,20 Radial position (mm) 1,0 0,8 100 Torr 200 Torr n /n 0 0,6 0,4 50 Torr n 2/n 0 0,6 0,4 50 Torr 0,2 100 Torr 150 Torr 200 Torr 0,0 0,00 0,05 0,10 0,15 0,20 Radial position (mm) 0,2 30 Torr 150 Torr 0,0 0,00 0,05 0,10 0,15 0,20 Radial position (mm)

24 Conclusions of the cathodic region Sheath structure Radial profile of densities: n e (r) has to be confirmed experimentally Lack on a theoretical point of view: Non linear model need of n e power balance Power balance complicated in the cathodic region but not in the positive column easier study of this region sheath negligible Electric field uniform power balance possible Instationnary model

25 Study of the positive column sheath z 150 µ m CATHODE REGION r 250 µ m alumina POSITIVE COLUMN 150 µ m 400 µ m ANODE REGION

26 1D stationnary model of the positive column

27 Model description same species : e -,, 2 same reactions : e 2 2 e * 2e 2 same equations: Quasi-neutrality Continuity equation Momentum conservation Ionization rate constant: ν iz =cte

28 Species density 1,0 0,8 n e 30 Torr n 0 given n/n 0 0,6 0,4 n 0,2 n 2 0,0 0,00 0,05 0,10 0,15 0,20 1,0 0,8 n e 100 Torr Radial position (mm) 1,0 0,8 n e 200 Torr n/n 0 0,6 0,4 n 2 n/n 0 0,6 0,4 n 2 0,2 n 0,0 0,00 0,05 0,10 0,15 0,20 Radial position (mm) 0,2 n 0,0 0,00 0,05 0,10 0,15 0,20 Radial position (mm)

29 Electron temperature 1,7 1,6 T e (ev) 1,5 1,4 1, P (Torr)

30 0D non-stationnary model of the positive column sheath z 150 µ m CATHODE REGION r 250 µ m alumina POSITIVE COLUMN 150 µ m 400 µ m ANODE REGION

31 0D non-stationnary model of the positive column Current (ma) 4 Current (ma) Time(µs) Time(µs)

32 0D non-stationnary model of the positive column Current (ma) 4 Current (ma) Time(µs) Time(µs)

33 Governing equations PARTICLE CONSERVATION Fluid equation n t e 1 r r ( rn e ) =ν n iz e Integration over the space coordinates (between 0 and R) Balance equation with dn dt h R 0 =ν n iz n0 hrub 0 = χ 01 J χ Ru 1( 01) B D a Same equations for the ionic species

34 Edge-to-centre density ratio h r 0,03 0,02 h r 0,01 h r ( ) h r ( 2 ) 0,00 OD non stationnary model Pressure (Torr)

35 Governing equations Energy balance: System of 3 temporal equations with n e, n 2 and T e: dne dt dn dt dte dt = Electric field: E=f(I,n e ) = ν n 2 = iz 2 3 e K n 1 1 en e 2 K n ( P rec abs n e n K P 2 rec loss A χ V ) n e n T n e e 2 01 Γ dn dt e A V e χ 01 Γ 2

36 Temporal evolution of the densities n e /n 0 0,8 0,6 0,4 200 Torr 150 Torr 100 Torr 50 Torr 0,2 30 Torr I=1mA 0, t (µs) Post-discharge: I=0

37 Densities temporal evolution 0,8 0,6 200 Torr 150 Torr 100 Torr n e n e /n 0 0,4 50 Torr 0,2 30 Torr n /n 0 0,3 n 0,2 0,1 50 Torr 100 Torr 150 Torr 200 Torr 30 Torr 0, t (µs) 0, t (µs) n 2/n 0 0,8 200 Torr n 0,6 0,4 0,2 150 Torr 100 Torr 50 Torr 30 Torr 0, t (µs) 2

38 Electron temperature and reduced field temporal evolution 8,00E T e (ev) Torr 200 Torr 50 Torr 100 Torr 150 Torr t (µs) E/N g (V.m 2 ) 6,00E-020 4,00E-020 2,00E Torr 50 Torr 200 Torr 100 Torr 150 Torr 0,00E000 0,0 0,5 1,0 1,5 2,0 2,5 3,0 t (µs)

39 Summary Cathodic region: Experimental results emission: direct excitation by energetic beam electrons emission: direct excitationrecombination argon/e - Theoretical results Ionizing-sheath model sheath structure 1D transport model density and flux profiles BUT n e =input parameter (complexity of the power balance) Positive column Stationnary model: density and flux profiles, Te(P) and h r (P) Non-stationnary model: power balance easy n e =ouput parameter temporal evolution of the differents parameters (n, Te, E/N, ) Next step Experiment: same experimental measurements temporally resolved during the self-pulsing regime Theory: -input parameter of the 0D model=experimental discharge current -power balance in the cathodic region -introduction of the metastables

40 Comparison between the two models 1,7 0,03 0D non-stationnary T e (ev) 1,6 1,5 0D non-stationnary h r 0,02 0,01 1,4 1, , Pressure (Torr) Pressure (Torr) Good agreement between the two models

41 Comparison between the two models 1,7 1D stationnary 0,03 0D non-stationnary T e (ev) 1,6 1,5 0D non-stationnary h r 0,02 0,01 1D stationnary 1,4 1, Pressure (Torr) 0, Pressure (Torr) Good agreement between the two models