What happens to ions at the plasma boundary in multiple-ion species plasmas?

Transcription

1 What happens to ions at the plasma boundary in multiple-ion species plasmas? How diode lasers help illumine the problem of sheath formation Greg Severn Plasma Theory and Simulation Group Seminar, University of California-Berkeley gds (USD φysics) ptsg seminar 22 Jun / 22

2 Thanks to my Current Collaborators! University of Wisconsin-Madison (Engineering Physics) Dr. Noah Hershkowitz Dr. Dongsoo Lee Mr. Young-chul Ghim, (now at Oxford University) Suleyman Demirel Universitesi, Isparta, Turkey (Physics) Dr. Lutfi Oksuz Thanks to the NSF/DOE Partnership for Basic Plasma Science which has supported and still supports this work since 03 gds (USD φysics) ptsg seminar 22 Jun / 22

3 Here s what you are in for... (1) Introduction to Sheath Formation, (2) Ideal sheath physics experiments for multiple ion species and (3) Certainties and confusions about these gds (USD φysics) ptsg seminar 22 Jun / 22

4 What is the Bohm criterion, and why do we care? v io c i = kt e /M i ; in order for the sheath to form... gds (USD φysics) ptsg seminar 22 Jun / 22

5 What is the Bohm criterion, and why do we care? v io c i = kt e /M i ; in order for the sheath to form... David Bohm 32, c.1949, Irving Langmuir 49, c. 1930, Single-crystal Si, anisotropic etch: 4 µm /.2µm, aspect ratio 20 gds (USD φysics) ptsg seminar 22 Jun / 22

6 The Bohm criterion is an extremum condition on ion flow near the plasma boundary that allows quasineutrality to break down, i.e., sheath formation Model assumptions: Boltzmann electrons, Γ io = const., E i = const., n i, φ, v i all self consistent. gds (USD φysics) ptsg seminar 22 Jun / 22

7 The Bohm criterion is an extremum condition on ion flow near the plasma boundary that allows quasineutrality to break down, i.e., sheath formation Model assumptions: Boltzmann electrons, Γ io = const., E i = const., n i, φ, v i all self consistent. Poisson s equation(plasma equation) d 2 φ dz 2 = e (n e n i ) = en o e eφ kte ɛ o ɛ o v io v 2 io 2eφ M gds (USD φysics) ptsg seminar 22 Jun / 22

8 The Bohm criterion is an extremum condition on ion flow near the plasma boundary that allows quasineutrality to break down, i.e., sheath formation Model assumptions: Boltzmann electrons, Γ io = const., E i = const., n i, φ, v i all self consistent. Poisson s equation(plasma equation) d 2 φ dz 2 = e (n e n i ) = en o e eφ kte ɛ o ɛ o v io v 2 io 2eφ M Scale the variables; η = eφ/kt e, ξ = z/(ɛ o kt e /n o e 2 ).. gds (USD φysics) ptsg seminar 22 Jun / 22

9 The Minimum ion K.E., consistent with Sheath Formation, is kt e /2, v io > C = kt e /M define one more dimensionless parameter r = kt e 1 2 Mv 2 io, gds (USD φysics) ptsg seminar 22 Jun / 22

10 The Minimum ion K.E., consistent with Sheath Formation, is kt e /2, v io > C = kt e /M define one more dimensionless parameter Plasma equation becomes d 2 η dξ 2 = rη }{{} e η = }{{} n e n i r = kt e 1 2 Mv 2 io, gds (USD φysics) ptsg seminar 22 Jun / 22

11 The Minimum ion K.E., consistent with Sheath Formation, is kt e /2, v io > C = kt e /M define one more dimensionless parameter Plasma equation becomes r = kt e 1 2 Mv 2 io d 2 η dξ 2 = rη }{{} e η = rη (1 η) +... η(1 r 2 ) }{{} n e n i, gds (USD φysics) ptsg seminar 22 Jun / 22

12 The Minimum ion K.E., consistent with Sheath Formation, is kt e /2, v io > C = kt e /M define one more dimensionless parameter Plasma equation becomes r = kt e 1 2 Mv 2 io d 2 η dξ 2 = rη }{{} e η = rη (1 η) +... η(1 r 2 ) }{{} n e n i so the diff.eq is { oscillatory r > 2 exponential r < Mv 2 io > kt e/2, or, v io c i = kt e /M, } gds (USD φysics) ptsg seminar 22 Jun / 22

13 The Minimum ion K.E., consistent with Sheath Formation, is kt e /2, v io > C = kt e /M define one more dimensionless parameter Plasma equation becomes r = kt e 1 2 Mv 2 io d 2 η dξ 2 = rη }{{} e η = rη (1 η) +... η(1 r 2 ) }{{} n e n i so the diff.eq is { oscillatory r > 2 exponential r < Mv 2 io > kt e/2, or, v io c i = kt e /M So What? gds (USD φysics) ptsg seminar 22 Jun / 22, }

14 Kinetic Theory is interested in r, the Bohm Criterion 1 > kt e is 1 2 m v 2 o 2 This is because Kinetic Theory wants (dropping the i subscript...) n(z) = o dv n o 1 ( 2kTe mv 2 o f i (v, z o ) )η gds (USD φysics) ptsg seminar 22 Jun / 22

15 Kinetic Theory is interested in r, the Bohm Criterion 1 > kt e is 1 2 m v 2 o 2 This is because Kinetic Theory wants (dropping the i subscript...) n(z) = o dv n o 1 ( 2kTe mv 2 o f i (v, z o ) n o (1 + 1 )η 2 2kT e m 1 vo 2 η +...) gds (USD φysics) ptsg seminar 22 Jun / 22

16 Kinetic Theory is interested in r, the Bohm Criterion 1 > kt e is 1 2 m v 2 o 2 This is because Kinetic Theory wants (dropping the i subscript...) n(z) = o dv n o 1 ( 2kTe mv 2 o f i (v, z o ) n o (1 + 1 )η 2 2kT e m 1 vo 2 η +...) n o ( r η) and so on, (restoring the i subscript...) 1 vio 2 1/2 c i = kt e /M gds (USD φysics) ptsg seminar 22 Jun / 22

17 Essentially all important plasma systems are Multiple-Ion species Plasmas (MIPs). So finding the Generalized Bohm criterion (GBc) is important! Etching, Fusion, and Auroral Plasmas gds (USD φysics) ptsg seminar 22 Jun / 22

18 GBc for 2 ions is a quadratic curve in 2D velocity space GBc: Generalized Bohm criterion n jo neo arb. # of ions 1 Σ C j 2 j vjo 2 2 ions 1 = n 1o neo C 2 1 v 2 1O + n 2o neo C 2 2 v 2 2O U 1 = v 1O C 1, α 1 = n 1O n eo 1 = α 1 U α 2 U 2 2 gds (USD φysics) ptsg seminar 22 Jun / 22

19 The GBc is marginally satisfied if one species has U 1 > 1 whenever U 2 < 1. Not clear which solution the plasma chooses... gds (USD φysics) ptsg seminar 22 Jun / 22

20 What would be the ideal sheath experiment? gds (USD φysics) ptsg seminar 22 Jun / 22

21 What would be the ideal sheath experiment? gds (USD φysics) ptsg seminar 22 Jun / 22

22 The ideal sheath physics experiment would have (a) plasma potential, (b) space charge, (c) IAW, and (d) ion velocity distribution function (ivdf) diagnostics The emissive probes φ(z) The emissive probe q(z) The ion acoustic wave apparatus Laser-induced fluorescence diagnostics can measure ion velocity distribution functions f (v z, z) gds (USD φysics) ptsg seminar 22 Jun / 22

23 The electropositive plasmas were confined with a multidipole arrangement of permanent magnets.

24 The electropositive plasmas were confined with a multidipole arrangement of permanent magnets. They were hot filament DC discharges.

25 The electropositive plasmas were confined with a multidipole arrangement of permanent magnets. They were hot filament DC discharges. Low temperature, low pressure, and weakly collisional, (T e < 1eV, T i T e, p 0 < 1mTorr)

26 Fluorescence, f LIF (ν), is collected as a function of detuning frequency, and converted to an ivdf, f (v z ) gds (USD φysics) ptsg seminar 22 Jun / 22

27 Fluorescence, f LIF (ν), is collected as a function of detuning frequency, and converted to an ivdf, f (v z ) f (v z ) f (ν), where ν = k v z = 2π λ v z gds (USD φysics) ptsg seminar 22 Jun / 22

28 One still needs a useful LIF scheme in order to see a signal. What s that? gds (USD φysics) ptsg seminar 22 Jun / 22

29 One still needs a useful LIF scheme in order to see a signal. What s that? LIF Scheme = populated metastable state + excited state w. high branching ratio transition in the visible... gds (USD φysics) ptsg seminar 22 Jun / 22

30 One still needs a useful LIF scheme in order to see a signal. What s that? LIF Scheme = populated metastable state + excited state w. high branching ratio transition in the visible... The spectroscopic term scheme CHANGED in 1987! gds (USD φysics) ptsg seminar 22 Jun / 22

31 Typical results for XeII LIF, in the bulk plasma. Here FWHM interpreted as Doppler Broadening yields 400K, about T wall Detuning becomes a velocity through the Doppler relation, ν = k v = 2π λ v, but gds (USD φysics) ptsg seminar 22 Jun / 22

32 Typical results for XeII LIF, in the bulk plasma. Here FWHM interpreted as Doppler Broadening yields 400K, about T wall Detuning becomes a velocity through the Doppler relation, ν = k v = 2π λ v, but one MUST know which frequency corresponds to v = 0 gds (USD φysics) ptsg seminar 22 Jun / 22

33 What do the ivdfs indicate about the validity of the GBc for multiple ion species plasmas? gds (USD φysics) ptsg seminar 22 Jun / 22

34 Moment calculations confirm that the Bohm criterion is satisfied in a single species plasmas Definition 1-D Moments of the distribution function (ivdf) v 2 = 0 vz 2 f (v z )dv z / 0 f (v z)dv z v 2 = 0 v 2 z f (v z )dv z / 0 f (v z)dv z gds (USD φysics) ptsg seminar 22 Jun / 22

35 Moment calculations also confirm that one species reaches the sheath edge traveling way faster than C 1!... PIC code results from en seem to model the sheath velocities well... gds (USD φysics) ptsg seminar 22 Jun / 22

36 In an Ar+Xe plasma, both ions reach the sheath edge close to the ion sound speed of the bulk plasma the big summary result But the big question is why? gds (USD φysics) ptsg seminar 22 Jun / 22

37 In an Ar+Xe plasma, both ions reach the sheath edge close to the ion sound speed of the bulk plasma the big summary result But the big question is why? Does the mean free path matter? gds (USD φysics) ptsg seminar 22 Jun / 22

38 In an Ar+Xe plasma, both ions reach the sheath edge close to the ion sound speed of the bulk plasma the big summary result But the big question is why? Does the mean free path matter? Is it just a matter of mass gds (USD φysics) ptsg seminar 22 Jun / 22

39 An Extremum Principle: V φ,s 2V φ,b for any mutual solution between GBc and IAW relations. 2 equations, 2 unknowns... BUT HOW DOES THE PLASMA DO THAT? gds (USD φysics) ptsg seminar 22 Jun / 22

40 What does happen to ions at the plasma boundary in multiple-ion species plasmas?: The GBc is satisfied gds (USD φysics) ptsg seminar 22 Jun / 22

41 What does happen to ions at the plasma boundary in multiple-ion species plasmas?: The GBc is satisfied in multiple-ion species (electropositive) plasmas, by all ions reaching (close to) the ion sound speed of the system. gds (USD φysics) ptsg seminar 22 Jun / 22

42 What does happen to ions at the plasma boundary in multiple-ion species plasmas?: The GBc is satisfied in multiple-ion species (electropositive) plasmas, by all ions reaching (close to) the ion sound speed of the system. The theoretical GBc is wrong: gds (USD φysics) ptsg seminar 22 Jun / 22

43 What does happen to ions at the plasma boundary in multiple-ion species plasmas?: The GBc is satisfied in multiple-ion species (electropositive) plasmas, by all ions reaching (close to) the ion sound speed of the system. The theoretical GBc is wrong: sheath formation appears to be insensitive to details of slow moving ions. The < v 2 > seems to matter! gds (USD φysics) ptsg seminar 22 Jun / 22

44 What does happen to ions at the plasma boundary in multiple-ion species plasmas?: The GBc is satisfied in multiple-ion species (electropositive) plasmas, by all ions reaching (close to) the ion sound speed of the system. The theoretical GBc is wrong: sheath formation appears to be insensitive to details of slow moving ions. The < v 2 > seems to matter! Q: What about for an arbitrary number of ion species? gds (USD φysics) ptsg seminar 22 Jun / 22

45 What does happen to ions at the plasma boundary in multiple-ion species plasmas?: The GBc is satisfied in multiple-ion species (electropositive) plasmas, by all ions reaching (close to) the ion sound speed of the system. The theoretical GBc is wrong: sheath formation appears to be insensitive to details of slow moving ions. The < v 2 > seems to matter! Q: What about for an arbitrary number of ion species? How does the plasma satisfy the GBc in the general case? The ion sound speed of the system is no longer the obvious choice. Is a new paradigm necessary to understand this special medium like behavior in general? gds (USD φysics) ptsg seminar 22 Jun / 22

46 What does happen to ions at the plasma boundary in multiple-ion species plasmas?: The GBc is satisfied in multiple-ion species (electropositive) plasmas, by all ions reaching (close to) the ion sound speed of the system. The theoretical GBc is wrong: sheath formation appears to be insensitive to details of slow moving ions. The < v 2 > seems to matter! Q: What about for an arbitrary number of ion species? How does the plasma satisfy the GBc in the general case? The ion sound speed of the system is no longer the obvious choice. Is a new paradigm necessary to understand this special medium like behavior in general? THANKS FOR YOUR ATTENTION! gds (USD φysics) ptsg seminar 22 Jun / 22