Application de la spectroscopie à l’étude des décharges ... · Gaussian Profile Natural Broadening Doppler Broadening Broadening mechanisms Instrumental Broadening Pressure Broadening

•  1

Application de la spectroscopie à l’étude des décharges électriques dans les milieux denses.

N Bonifaci

CNRS, G2Elab, F-38000Grenoble, [email protected]

Joel Rosato, Jussi Eloranta, Zhiling Li , Vladimir Atrazhev, Vyacheslav Shakatov, Sebastien Flury

•  2

Application:Dischargeinliquid The plasma produced by electrical discharges in liquids are finding important applications in modern technology : Electrical Insulation, High power switching, Electro discharge machning Nanomaterials synthesis, Water sterilization, Plasma medecine

LN2 77 K, 1 bar LN2 77 k 1 bar

Water sterilization

LN2 77 K 1 Bar

superconducting tape Resistive SuperConducting Fault Current Limiter

Liquid N2

G2E. Lab covers the wide spectrum of the electrical engineering science

•  Molecular spectra

•  Atomic spectra

•  Continuum

0

5000

10000

15000

20000

25000

30000

35000

650 700 750 800 850 900 950

Inten

sité

[U.A

.]

longeur d'onde [nm]

8000

10000

12000

14000

16000

18000

20000

22000

350 400 450 500 550 600 650

Inte

nsité

[U.A

.]

longueur d'onde [nm]

365 370 375 380

0

200

400

600

800

1000

1200

1400

380.46 (0-2)

375.5 (1-3)

371.05 (2-4)

Intensité relative

Longueur d'onde (nm)

R. Stringanow and N. S. Sventitskii, Tables of Spectral Lines of Neutral and Ionized Atoms Plenum New York 1968.

NIST ASD Output: Lines http://physics.nist.gov/cgi-bin/ASD/lines1.pl

Atomic Spectral Line Database http://cfa-www.havard.edu/

B. Pearse and A. G. Gaydon The identification of Molecular Spectra Chapman and Hall 1976 G. Herzberg, Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules, 2nd edn. (Van Nostrand, Princeton, NJ, 1950) I. Kovacs, Rotational structure in the spectra of diatomic molecules (Adam Higer Ltd., London, 1969)

OES

Spectral Line Profile

Line width ΔλFWHM Line shift d=λmax-λvacuum Asymmetry Satellite band Forbidden line Self-absorption

Blue wing Red wing

Microscopic probe

Line center

e- e-

700 702 704 706 708 710

P=0,1MPa

λ (nm)

700 702 704 706 708 710

P=1,4MPa

P=2,3MPa

700 702 704 706 708 710

Δλnatural~10-4 Å

Particle Temperature

Gaussian Profile

Natural Broadening

Doppler Broadening

Broadening mechanisms

Instrumental Broadening

Pressure Broadening

72

2 22 7.157 10DkTLn TMc M

λ λ λ−Δ = = ×

T ΔλD

He 10000 0,02 nm Ar 10000 0,0057 nm Hβ 5000 0,025 nm

Gaussian profile

Pressure Broadening

( ) p pp p

C hCV r

r r

ω ν

= ± = ±h

1pm s−Stark Neutral (van der Waals) Resonant

Semi empirical potential

ab initio potential

•  7

Linear Stark -------

Quadratic Stark

-------

Resonant

van der Waals

L-J

W. Behmenburg J. Quant. Spectrosc. Radiat. Transfer 4, (1964) 177 W. R. Hindmarsh, A. D. Petford, G. Smith, Proc Roy Soc A 297 (1967) 296 W. R. Hindmarsh, A. N. Du Plessis et J. M. Farr (1970) J. Phys. B: At. Mol. Opt. Phys. 3, L5-L8 Butaux, F Schuller, R Lennuier J de Phys, 33, (1972), 635.

( ) 22

CV rr

ω

= ±h

( ) 44

CV rr

ω

= ±h

( ) 33

CV rr

ω

= ±h

( ) 66

CV rr

ω

= −h

2

3 2016r r

e

e fCm c

ω λπ ε

=

2 26

0

12

C e rh

ω αε

=

Semi empirical Potential

( ) 61212 6

CCV rr r

ω⎛ ⎞= −⎜ ⎟

⎝ ⎠h

m6s-1 *2

2 2 *20 2 5 1 ( 1)2 i

nr a n l lz

= + − +

2 26C e rω α= ergcm6

* Hi

i u

En zE E

=−

α atomic polarizability m3

•  8

Blue satellites

R

Vupper

ΔV(R)= Vupper-Vlower

Maximum of ΔV

hν

Internuclear distance R

Maximum

hump

λs

Extrema of ΔV satellites

Vlower

-C6/R6

C3/R3

H G Kuhn : Does your treatment predict satellite line? A Jablonski: The theory does not predict this mysterious effect. 1968

λ0

(repulsive part)

MOLPRO 2009 package http://www.molpro.net Laboratoire de Physique et Chimie Quantique Toulouse

•  9

Stark Van der Waals (-C6/r6) Resonant (+-C3/r3)

Interaction Physical classification

Spectral line Profile

Potentiel ab initio

?

•  10

Historical development

( ) 0dtdtη

ω ω= + 0( )V r

ω ωΔ

= +h

Quasistatic approximation

Line shape formalism based on the Fourier transform of the autocorrelation function

( ) [ ] τωττφπ

ω diP ∫=+∞

0

1 expRe)( ( ( ) ( ))( ) i t te dtη η τφ τ+∞

− −

−∞

= ∫Autocorrelation function (wave train) P. W. Anderson, Phys Rev 76 (1949) 647.

P. W. Anderson, Phys Rev 86 (1952) 809.

Weisskopf (1932), Lindholm (1941), Foley (1946) Holtsmark (1919), Kuhn and Margenau (1937),

Impact approximation Phase shift

11


11

∫∞

⋅=0

)()0(Re1)( tietdddtI ω

πω

!!

)()0()()( tUdtUtd!!

+=

)())()(()( 0 tUtVtHtdtdUi +=!

time-dependent Schrödinger equation for the evolution operator U(t)

Quantum treatment

Code

d is the dipole moment U(t) evolution operator relative to the electrons

U-matrix

H0 is the Hamiltonian of the unperturbed emitter

12


12

( ) [ ] τωττφπ

ω diP ∫=+∞

0

1 expRe)(

( ( ) ( ))( ) i t te dtη η τφ τ+∞

− −

−∞

= ∫

Autocorrelation function (wave train)

The autocorrelation function measures the average evolution of the wave train over a time interval τ

from an initial time t

Classical theory Isolated line!!

( )( ) pert pN Vi

te e τηφ τ −−= =

This concerns most of atomic lines emitted from non-

hydrogenic systems.

{ } titi uleetdd ωη −−∝⋅ )()()0(!!

•  13

Perturber density Npert

{ }])'))'((1exp(1[2)(00∫∫ ∫ −−=

+∞ +∞

∞−

τ

πτ dttRVidxbdbVp!

( ) ( )[ ] 2/1202 tv++= xbtR b

R(t)

perturber

classical Perturber trajectory

Emitter


Rectilinear classical path

b is the impact parameter

( )( ) pert pN Vi

te e τηφ τ −−= =

Vp: collision volume

•  14

Unified theory

( ) ( )( )( )( )

( )( ) ( )( )⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

∫= ∑ ∫ ∫∑

∞ ∞+

∞−

0~~021'

*''

0'

'

2'

),(0 RdRdeRdxdd

dg eeee

tRdti

ee ee

eeee

fi τρπρτ

τ

α

α

V!

dee’ Dipole transition moment (ab initio calculation )

Allard N F, Royer A, Kielkopf J F and Feautrier N 1999 Phys. Rev. A 60 1021

( ) [ ]( )1

' '( ) ( ) eV R tkT

ee eed R t d R t e− ⎡ ⎤⎣ ⎦

=%

•  15


Experimental profile

Lorenztian profile (Voigt profile)

Impact approximation

N<<, core

Red Asymmetric profile

Quasi static approximation

N>>, wing

Unified theory N, ω

The quasistatic and impact approx ima t ions repre sen t important theoretical limits that are in many cases sufficient for practical purposes and have been used to guide and develop new methods that are more generally applicable and, in fact, satisfactorily solve the line b r o a d e n i n g p r o b l e m i n

practically all cases. S. Alexiou / (2009)

Kjj: 0,9-1,8

Stark -------

Resonant

van der Waals

2 3/52/56 0.7v

2ul

vdwPA C N

c Tλ

λπ

⎛ ⎞Δ = Δ ∝⎜ ⎟

⎝ ⎠

A : 8.08 ou 8.16 πµ

kT8v =752,VDW

vdwS λλ

Δ=

Impact Approximation

K: 0,9-1,8

2 20

20

14

ul r rres

r e

e fg PK Ng m c T

λ λλ

π πεΔ = ∝

0resSλ ≈

•  17

Quasistatic Approximation

Stark -------

Resonant

Van der Waals

( )( ) ( )⎟

⎟⎠

⎞⎜⎜⎝

⎛

−

Δ−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

Δ=

ul

qs

ul

qsQSP λλ

λπ

λλ

λλ

421

21

3exp

/

( ) 0=λQSP

ulλλ >

ulλλ ≤

( ) ( ) ζζζλ dPPP QSLorT −Δ= ∫+∞

∞−

H. Margenau Phys. Rev. 48, (1935) 755. H. Margenau Phys Rev 82 (1951) 156.

H. R. Zaidi , Can. J. Physics 55, (1977) 1243.

resQS resQSSλ ε λ≈ Δ

22 2

60.411 ulQS C N

cλ

λ πΔ =

( )1resQS res Nλ λ βΔ = Δ −

•  18

Stark

Hα 656.2 nm, Hβ 486.1 nm

Linear Stark effect Hydrogen lines

H.R. Griem, Plasma Spectroscopy, Academic Press, New York, 1964.1964 H Griem Spectral line broadening by Plasmas London Academic 1974 H. Griem, Principles of Plasma Spectroscopy, Cambridge University Press, 1997.

M. Gigosos et V. Gardeñoso, J. Phys. B: At. Mol. Opt. Phys., vol. 29, no 20, p. 4795, oct. 1996. M. Gigosos , M Gonzalez V. Gardeñoso Spectrochimica Acta Part B 58 (2003) 1489–1504

Table full width at half area

Ne=C(Ne,T)*Δλ3/2 Where C(Ne,T) is in A-3/2 cm-3.

0.68116

23( ) 4.810

estark

Nnmλ ⎛ ⎞Δ = ⎜ ⎟⎝ ⎠

Hα

Hβ

•  20

H-β C6 [ m6s-1] Δλ vdw

4s-2p 7.59*10-43 2.20×10-5PT-7/10

4p-2s 6.85*10-43 2.12×10-5PT-7/10

4d-2p 5.82*10-43 1.98×10-5PT-7/10

H-α C6 [ m6s-1] Δλ vdw

3s-2p 2.75*10-43 2.40×10-5PT-7/10

3p-2s 1.696*10-43 2.20×10-5PT-7/10

3d-2p 1.18*10-43 1.93×10-5PT-7/10

( ) ( )NTN vdweestarklor λλλ Δ+Δ=Δ ,

Hβ quadratic Stark, Hα self –absorption

Example : Helium Gas Linear Stark effect + van der Waals

Quadratic Stark Effect

( ) ωαλ 2)75.01(75.11 rStark

−+=ΔNe, Te

 H. R. Griem (1964) Plasmas Spectroscopy , McGraw-Hill Book Compagny, New York.  H .R. Griem (1974) Spectral Line Broadening by Plasmas , New York : Academic Press.  H. R. Griem (1997) Principles of Plasma Spectroscopy , Cambridge.

( )( )∫

∞

−+=

022341

W1

β

ββπ /

)(Ax

dxJ

p. 97 Griem 1974

Quasistatic Approximation Impact Approximation electrons ions

( ) ( ) ( ) ( )3 2

02 sin expW dβ π β χ βχ χ χ

∞= −∫

ωλ )75,01(2)( rAdS Stark −±=

Holtsmark distribution

•  22

Stark : Line shape Code Quantum treatment, Numerical calculation

Simulation code

LSNS Rosato, J. et al J. Quant. Spectrosc. Radiat. Transfer 2015, 165, 102–107

computer simulation method The particle motion is simulated and the Schrödinger Eq. is solved numerically it is time consuming

SimU Stambulchik, E. et al Phys. Rev. E 2007, 75, 016401

….. Models

PPP Frequency Fluctuation Model Rapid calculations for neutral and charged emitters

QC-FFM Stambulchik, E.et al Phys. Rev. E 2013, 87, 053108.

Frequency Fluctuation Model

Zest Gilleron, F et al Atoms 2018, 6, 11

Quasi-static description of ions and impact approximation for electrons

……

Calisti, A et al Phys. Rev. A 1990, 42, 5433–5440.

•  23

Stark (C2/r2, C4/r4) Van der Waals (-C6/r6) Resonant (+-C3/r3)

Interaction Physical classification

Spectral line Profile

Potentiel ab initio Code MOLPRO

http://www.molpro.net

Classical theory Quantum treatment

Unified theory Impact approximation Quasitatic approximation

•  24

Examples

1.  Self-healing of a metallized polypropylene film 2.  Positive streamers in liquid nitrogen 3.  Streamers in chlorinated alkane and alkene liquids 4.  Helium cryoplasma

•  25

Modeling of the spectroscopic emission lines of Aluminum emitted by a self-healing of a

metallized polypropylene film.

Rel

ativ

e in

tens

ity

394 396 398

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Simulation

Experiment

394.5 and 396.15 nm

•  26

385 390 395 400 405 410

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e in

tens

ity

Wavelength (nm)

Self-healing Hollow cathode

lamp of Al

385 390 395 400 405

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e In

tens

ity

Wavelength (nm)

Confined discharge

Modeling of the spectroscopic emission lines of Aluminum emitted by a self-healing of a

metallized polypropylene film.

T=6500-7000K Ng=0,8-1 1026 m-3

Ne=2-3 1024 m-3

Two distinct phases

The streamer propagation Streamer reaches the plane Re-illumination

Weak emitted light Intense emitted light

~100 streamers 1 streamer

Streak photograph of filamentary

streamer propagating up to plane

time

d

Positive filamentary streamers in liquid nitrogen

80mm, 102kV

0,4/1400µs 100-200 mA

Light emitted by one positive streamer in LN2 when it stops

on the insulating plane

Intense NI Atomic line (3s4P-3p4S0 and 3s4P-3p4P transition)

Experimental Results

Tbreakdown T=0 No N2 emission time


When one positive streamer stops on the insulating plane, a large current pulse and a bright emitted light are recorded at tb

Re-illumination

Broadening of Atomic line of NI

Re-illumination


Propagation velocity : 10-30 km/s

735 740 745 750 755

0,0

0,2

0,4

0,6

0,8

1,0

Normalized

Intens

itya.u.

λ(nm)

Tb= 2.6µs v=30km/s

Tb= 6.4µs v=12,4km/s

Tb= 8.6µs v=9,3km/s

Ne~1,5x1024 m-3

Ng~6x1026 m-3

Simulation of atomic line Re-illumination


735 740 745 750 755

0,0

0,2

0,4

0,6

0,8

1,0

Intens

itya.u.

λ(nm)

s imula teds pec trumexperimenta ls pec trum

Tb=2,6µs

2 3 4 5 6 7 8 9 10 11

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

neutrald

ensity1026

m-3

elec

tron

den

sity1024

m-3

B reakdowntime(µs )

e lec tronic dens ityneutra ldens ity

Re-illumination

R= 124 µm

Ng (2.6µs) > Ng (8.6µs) ?

P Gournay and O Lesaint 1994

Rm=130µm

21µs

Tb=2.6 µs Tb=8.6 µs Time

streamer channel radius

Collapse of gaseous filament

R= 78 µm

Tb The plasma column has expanded Ng

Expansion of gaseous filament

Positive filamentary streamers in liquid nitrogen Laser beam

Photodiode

10 µm

200 µm

t0

h

8 µm

tc tmax

gmax

100 ns

100µm 50 µm

A

B

C


2000 K- 3000 K Internal Pressure of the gas ~200 B V=30 km/s Internal Pressure of the gas ~30 B V=10 km/s Ne=1-5 1023 m-3

•  33

Spectral analysis of the light emitted from streamers in chlorinated alkane and

alkene liquids

Trot =3000-4000 K P=86-136 bar Ne=4-8 1023 m-3

725,6 nm

20-30 km/s

•  34

Optical Emission from Helium Cryoplasma Discharge in dense fluids (liquids or high-pressure gases :1-100 bar)

Corona-discharge

Liquid Helium

Gas liquid

Temperature: 300 K Density N: 2 1019 cm-3

4.2 K 2 1022 cm-3

T

Ø  pure liquid Ø  intense luminescenceØ  helium is atomic.Ø  Low electronic mobility.Ø  physical and Thermodynamic

propertiesØ  interaction potential ab initio He*-

He and He2*- He

V ~ kV DC, I ~ 0,1-50µA

P=0,1-100mW,

gap distance~5-8 mm

Rtip ~ 0,1-2µm

Important input parameters for the collision-radiative model in the theoretical study of the corona-discharges

Goal: Determine Ne ,Te, T, NHe

•  35

4.2 K 11 K 150 K 300 K

Helium Cryoplasma

•  36

Temperature : Rotational temperature measurements

300 K (P) 4.2 K (P)

N2, N2+

He2

150 K (P) 11 K (P)

N2, N2+

He2

He2 He2

388 389 390 391 392 393

0,0

0,2

0,4

0,6

0,8

1,0

B2Σ+u-- X2Σ+g

Inte

nsity

(u.a

)

λ(nm)

Exper Simulation

P=0.04MPaNegativeTrot=250K

N+2

He

(0-0)

T=150K

630 635 640 645 650

0.0

0.2

0.4

0.6

0.8

1.0 T =150KP =0.04MP a

Δλ=0.1nmS =0.28nmT

r=165K

Intensité(u.a)

λ(nm)

E xpérienceS imula tion

Trot=240 K Trot=200 K

N2+

He2

The rotational line of Nitrogen molecular bands was a probe to thermodynamic temperature at non equilibrium plasma. The values of

•  37


3300 K (P)(P) 4.2 K

0,0 0,3 0,6 0,9 1,2 1,5 1,8 2,1 2,4

300

330

360

390

420

450

480

510

H e2659,5nm

N2

+391nm

H e2639,6nm

Trot(K)

P res s ure P ,MP a

300K

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,940

60

80

100

120

140

160

180

200

220

240

260

T rot(K)

659,5nm639,6nm

P res s ure P ,MP a

11K

150 K (P) 11 K (P)

300-500 K 240-280 K 80-240 K Trot= 31 P +370 Trot= 33 P +263 Trot= 208 P +62

0,0 0,2 0,4 0,6 0,8 1,0200

220

240

260

280

300

320

T

rot(K

)

H e2639,6nm

N2391nm

H e2659,5nm

P res s ure P ,MP a

150K

N2+ He2

N2+

He2 He2

•  38

?

MolecularexcimersHe2*

630 635 640 645 650

0.0

0.2

0.4

0.6

0.8

1.0

T =4.2K

Intens

ité(u

.a)

λ(nm)

P =0.1MP aP =0.6MP aP =1.4MP a

L IQ U ID E

Strongly Blue Shifted


R

D1Σu+-B1Πg

(659nm)

d3Σu+-b3Πg

(639,6nm)

P

No boltzmann distribution High degree of rotational excitation

Trot=800 K

P(18)

•  39

Electron number density : Ne

300 K (P) 4.2 K(P)

Hα : 656 nmHβ : 486 nm

He I : 492 nm He 492 nm

Forbidden line 1s4f-1s2p

150 K 11 K

300 K

•  40

The 4th Spectral Line Shapes in Plasmas code comparison workshop– Baden – March 20th to 24th, 2017

Code comparison code workshops http://plasma-gate.weizmann.ac.il/slsp/

corona discharge in helium 300 K

492 nm line

•  41

Code comparison code workshops

Comparison of the FWHM of the H-β Line

•  42

H-β Line in a Corona Helium Plasma: A Multi-Code

Line Shape Comparison

RR Sheeba, M Koubiti, N Bonifaci, F Gilleron, C Mossé… - Atoms 2018, 6(2), 29; https://doi.org/10.3390/atoms6020029

•  43

Broadening of the Neutral Helium 492 nm Line in a Corona Discharge:

Code Comparisons and Data Fitting

1.5 bar 300 K

RR Sheeba, M Koubiti, N Bonifaci, F Gilleron, JC

Pain… - Atoms 2018, 6(2), 19; doi:10.3390/atoms6020019

•  44

A New Procedure to Determine the Plasma Parameters from a Genetic Algorithm Coupled with

the Spectral Line-Shape Code PPP

C Mossé, P Génésio, N Bonifaci, A Calisti- Atoms 2018, 6(4), 55; https://doi.org/10.3390/atoms6040055

•  45

A New Procedure to Determine the Plasma Parameters from a Genetic Algorithm Coupled with

the Spectral Line-Shape Code PPP

•  46

492 493

0

1

2

3

4

5

6

Spe

ctrum(arb.units)

e xperimenta ls pec trumadjus tment,N

e= 1 .8x1015cm -3

λ(nm)

H e I492nmP = 1 ba r

Electron number density : Ne 492 nm

Line Shape Modeling for the Diagnostic of the Electron Density in a Corona Discharge

J Rosato, N Bonifaci, Z Li, R Stamm - Atoms, 2017

Te= 104 K

300 K Computer simulation method

•  47

Electron number density : Ne

300 K (1-10 bar) 4.2 K (P)

1015-1016 cm-3

Forbidden line

Self-absorption allowed line

In Progress

150 K 11 K

•  48

Neutral Perturbers Density : NHe

300 K (P)

Blue satellite

Unified line shape semi-classical theory (N. Allard et al Phys Rev A 60 p1021 1999)

706 nm(3S-3P)

Main line disappears

696 698 700 702 704 706 708 710 712 7140.0

0.2

0.4

0.6

0.8

1.0

Intens

ity(arb.units)

λ(nm)

P = 10ba rP = 16ba rP = 24ba rP = 32ba rP = 39ba rP = 59ba r

T = 300K

Fourier Transform of the dipole autocorrelation function

4.2 K

706 nm(3S-3P)

( ) ( )( )e HeN g sαφ τ−

=

•  49


He*-HePotential

Blue satellite

•  50


50

N=2.4 1020 cm3

N=3.8 1020 cm3

N=4.8 1020 cm3

The agreement for a pressure of 1 and 16 Bar is excellent

Comparison between experiment and theory

ResultsforHeline706nm(3S-3P)at300K

N ALLARD, et al EPL 88 (2009) 53002

N ALLARD, et al EPJ D 61 (2011) 365-372

P=10 Bar P= 16 Bar P= 20 Bar

ω (cm-1) ω (cm-1) ω (cm-1) ω (cm-1)

•  51


300 K (P) 706 nm

Discrepancyobservedathighpressures

width

Comparisonbetweenexperimentandtheory

Width Shift

Unified Theory

•  52

Computer simulation method


•  53


685 690 695 700 705 710 715 720-0,2

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

Inte

nsity

λ (nm)

P=0.1MPa P=0.6MPa P=1.6MPa P=3.5MPa

Strongly

Blue shifted symmetrical

Gaussian profile 696 698 700 702 704 706 708 710 712 7140.0

0.2

0.4

0.6

0.8

1.0

Intens

ity(arb.units)

λ(nm)

P = 10ba rP = 16ba rP = 24ba rP = 32ba rP = 39ba rP = 59ba r

T = 300K

4.2 K

706 nm

•  54


Unified semiclassical theory

Allard, N. F. 2012, J. Phys. Conf. Ser., 397, 012065

4. 2 K 706 nm

Line Shape calculations

•  55

Interpretation ? 4.2 K

630 635 640 645 650

0.0

0.2

0.4

0.6

0.8

1.0

T =4.2K

Intens

ité(u

.a)

λ(nm)


L IQ U ID E

685 690 695 700 705 710 715 720-0,2

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

Inte

nsity

λ (nm)

P=0.1MPa P=0.6MPa P=1.6MPa P=3.5MPa

•  56

The mobility decreases rapidly when transitioning from the gas to the liquid phase

The repulsive interaction occurring between e- and helium atoms.

He localizes electrons in «bubbles»

Re ~20 Å P=0.1 MPa T= 4.2 K

e-

R~20Å

He atom

Electron bubbles in liquid 4He

Microscopic cavity: « Bubble » PRREE eltot32

344 πσπ ++=

surface energy PV energy L He is characterized by its density and surface tension parameter

P is the He pressure

•  57

Atomic–bubble model

A.  Hofer, P. Moroshkin, S. Ulzega, D. Nettels, R. Müller-Siebert, and A. Weis, Phys. Rev. A 76 , 022502 (2007)

Alkali-metal atoms implanted in condensed He reside innanosize spherical cavities

These bubbles are formed around each impurity atom due to the Pauli principle that forbids any overlap between the closed S shells of He atoms and the valence electron of the impurity

Schematic model of a Cs atom inside a spherical He bubble.

Ralkali ~ 5–7 Å

•  58

He* He2* Rydberg electron

Interpretation:

Microscopic void around the He*3s and He2*3d

Repulsion between Rydberg e- and surrounding atoms in the ground state forms bubble

?

•  59

He*(3s)

Atomic bubble

Bulk helium

New autocorrelation function with « bath » interaction

( ) ( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ Δ−−=Φ ∫

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−

rdrtrVi

ei

fi

3

/1exp ρτ

!

Difference pair potential b e t w e e n t h e s t a t e s corresponding to the emission line

Molpro code

Liquid density in the electronic ground state around 3s calculated using Bosonic Density

Functional Theory DFT

•  60

Bubble Radius (Rb) depends on applied

pressure (P).

1 bar

Liquid density around He*(3s3S)

Liquid density around 3s3S calculated using DFT

Empty cavity around excited atom (emitter)

Phys. Rev. A 85 042706 (2012).

3S

•  61

706.5 nm He* line (3S-3P)

the line position is extremely sensitive to the He*(3s) - He pair potential

Experimental (continuous) vs theoretical (dashed)

Line shift

DFT b1, b2

•  62

He2*(d3Σu)-He ab initio potential

J. Eloranta and V. A. Apkarian J. Chem. Phys. 115, 752 (2001). N Bonifaci, Z Li, J Eloranta and S L Fiedler J. Phys. Chem. A, 120 (45), pp 9019–9027 2016

Linear He2 (3d) - He

He(3s)-He

630 635 640 645 650

0.0

0.2

0.4

0.6

0.8

1.0

T =4.2K

Intens

ité(u

.a)

λ(nm)


L IQ U ID E

T-orientation He2 (3d) - He

•  63

Liquid density around He2 d3Σu+

R=12,7 Å 1 Bar R= 10,8 Å 24 Bar

DFT

Shift

He2(3d-3b)

AAo

&o

•  64

Conclusion

Impact theory Unified semiclassical theory Localized bubble state

300 K 4.2 K

The good agreement observed between the simulations and the experimental fluorescence data suggests that both He2 and He emit from a liquid environment at 4 K.

NHe, Ne, T Liquid Helium

He 3s Bubble R~10 Å

He2 d3Σu+

Bubble

R~10-13 Å

•  65

Outlook: Comparison between Andronikashvili's and the molecular probe approaches.

Andronikashvili’s experiment Molecules He2*/liquid He

Macroscopic Microscopic

Two-fluid model Local two-fluid model

Observable: torsional frequency Observable : OES

Interaction of He2*molecules with helium nanoscopic probes

Tλ=2,17 K

4 K 1 K Superfluid phase

300 K

Thank you for your attention

Documents

Application de la spectroscopie à l’étude des décharges ... · Gaussian Profile Natural Broadening Doppler Broadening Broadening mechanisms Instrumental Broadening Pressure Broadening