Spectral diagnostic of a resonantly laser created non-Debye plasma

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Submitted on 1 Jan 1990

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J.C. Valognes, J.P. Bardet, C. Dimarcq, L. Giry

To cite this version:

Spectral diagnostic

of

a

resonantly

laser created

non-Debye

plasma

J. C.

_Valognes

_(1),

J. P. Bardet

_(1,

_2),

C.

Dimarcq

(1)

and L.

_Giry

₍₁₎

(1)

Laboratoire des

_plasmas

_denses, Université P. et M. _{Curie, T.12, E.5,} 4 Place Jussieu, 75252 Paris Cedex 05, France

(2)

Ecole Centrale des Arts et Manufactures, 92290

_{Châtenay-Malabry,}

France

(Received

on

February

15, 1990, revised on

April 24,

1990,

accepted

on June 7,

1990)

Résumé. 2014 L’évolution de la densité

électronique

et de la

température

est un

point

essentiel de

l’étude d’un

_{plasma (faiblement}

non

idéal)

obtenu _par résonance laser. Afin d’effectuer cette

étude, dans le but

d’expliquer

les variations inhabituelles _observées, de l’intensité des raies

4D ~ 3P et 4F ~ 3P de

_Na(I),

les auteurs utilisent un calcul de

perturbation

Stark

(tenant

compte d’un effet

dynamique

des

ions)

et basent leur

_diagnostic

sur la

_comparaison

entre les

_profils

expérimentaux

et

_théoriques.

Un bon accord est obtenu dans la

_majorité

des cas.

Quand

à la

population

du niveau 3P, son évolution est à

_rapprocher

de celle

_déjà

mise en évidence par

d’autres travaux, dans des conditions

expérimentales

différentes mais _pour des densités

_proches.

Abstract. 2014 The time

history

of electronic

density

and

temperature is a main

_point

of the

study

of a

resonantly

laser created

(weakly non-ideal) plasma.

In order to _carry out this

study,

with the aim of

_explaining

the unusual variations of the emitted 4D ~ 3P and 4F ~ 3P

_Na(I)

lines

_intensity,

the authors

_perform

a Stark calculation

(including ion-dynamic effect)

and use as a

diagnostic

a

comparison

between

_experimental

and theoretical

_profiles.

Good agreement is obtained for most

of the records. As for the Na 3P-level

population,

its time

history

is close to those

_already

obtained in other studies, with different

experimental

conditions but for

_comparable

densities. Classification

Physics

Abstracts

32.70 - 52.50J - 52.70

Introduction.

The irradiation of an alkali metal vapor

by

a laser tuned to the nS - nP resonance line is _very

efficient to

_produce

a dense

plasma

( 1016

cm-

3 )

in a _very short time. Predicted earlier

by

Measures

_{[ 1 ],}

such a

plasma

was

reported

for the first time

by

Lucatorto and Mcllrath

[2]

who

irradiated a sodium _vapor with a 1 MW

pulsed dye

laser.

Then,

the _purpose of resonant

interaction

_experiments

has been twofold : either to determine which

_microscopic

mechanisms contribute to the

strong

ionization

_during

the laser

_pulse,

or to

_diagnose

the created

_plasma

and to

_study

its time

_history

which

_presents

after the laser

_pulse

a

typical

relaxation.

Despite

the fact that this

_study

is devoted to the second

_phase,

it is essential to recall some of the main

phenomena contributing

to the

_strong

ionization mechanisms

during

the firt

_phase

_{[1] :}

-

superelastic

electronic collisions -

energy

pooling

and

Penning

ionization

- associative ionization and dissociation.

Allegrini [3]

on the

population

of energy level

by

_energy

pooling

_process, of De

Jong

[4]

on

the associative ionization and of

_{Morgan [5]}

on the time

dependent

electron _energy

distribution

_{(computation taking}

into account all electronic

_{collisions, elastic, inelastic,}

superelastic...).

As for the

_lapse

of time

_following

laser

irradiation,

we can

notice,

although

it is not

_closely

linked to our _{purpose, the}

study

of Kumar and al. of the

_strong

infrared emission observed

during

recombination

_{[6] ;}

closer to our work is the

study

of 3P

Na(I)

level

population

time

history by

Landen

_[7].

Recently,

resonant interaction has become of

_great

interest as a

possible

light

ion source for

inertial confinement

fusion,

currently

called LIBORS

_(laser

ionization based on resonance

saturation) [1,

8,

9].

Of course, the scale of our

experiment

is not at all the same : as

compared

to 800

cm2

of _{lithium vapor,}

_only

2

mm2

of sodium vapor are irradiated in our own case

[10].

However,

the irradiance of sodium _{vapor up} to 20 MW

cm-2

is

_{approximately}

40 times

_greater

than those of LIBORS.

By

coupling

theoretical

_{spectroscopic profile}

calculations and

_recordings

of

_spectral

line

shapes

emitted after the laser

_pulse,

it becomes

_possible

to follow the time evolution of the main

parameters

of the

_{plasma (electronic}

and ionic

densities,

temperatures...)

and to infer a

logical interpretation

of the

_experimental

results.

Section 1

_gives

the

_experimental

_setup

and

results ;

section II and III detail the main

_stages

of the calculation and

_give

an

approach

of the

non-Debye plasma ;

section IV will be our

conclusion.

1.

_{Expérimental}

_setup

and results.

The

_experimental

_setup,

well described in

_previous

_papers

_{[10, 11],}

is

_briefly

summarized here

(Fig. 1).

A flashtube

_pumped

_dye

laser is focused at the center of a

specially designed

cross-shaped heatpipe

oven

(length :

8 cm, diameter : 3

cm)

which contains Na vapor and Ar as a

buffer gas ; the initial pressure is 50 torr

_(against

10 torr in

[2])

and the initial

temperature

600 K. The tunable laser

_pulse

duration is 2 _f.LS

_{FWMH ;}

_{the average laser flux in the}

interaction

_region

is 20 MW

cm-2.

The main differences with

_experimental

conditions of Lucatorto and Mcllrath are the

_greater

_pressure and a

longer

irradiation time. A

gated optical

multichannel

_{analyser (OMA III)}

set in the focal

_plane

of the

_spectrometer

_{(whose dispersion}

is 0.4

_nm/mm)

enables data

_recording

_during

and

_specially

after the laser

_pulse

on a shot to

Fig.

1. -

Experimental

shot basis. The O.M.A. _response is

_carefully

calibrated

_using

a

tungsten-ribbon lamp

and a

carbon arc in the near I.R. and the visible. The O.M.A. is also calibrated in

wavelength

units

using spectral lamps.

Two consecutive

_pixels

of the O.M.A. are distant

by

0.006 nm : the

experimental

resolution is about 50 000. All

recordings

are made at

_{right angle}

from the laser beam axis. Numerous transitions of

_Na(I)

are observed :

Experimental

data,

mainly

about 4D - 3P and 3D - 3P transitions of

Na(I)

are

automati-cally

stored and

_{processed by}

a

microcomputer.

These transitions are chosen for their very

different

_{optical depths.}

Figure

2a shows

_{typical profiles}

of the 4D ---> 3P doublet and near forbidden lines 4F - 3P recorded at

_significant

times 4

kLs, 10

kts, 25 f.LS, 35 kts after

beginning

of the laser

pulse

with

an _{exposure time of 0.5 )JLS.} It

clearly

_{appears that line}

profiles

are

strongly

time

dependent :

according

to the

_recording

time,

line

_wings

are more or less

broadened ;

the red shifts of

peaks

and the forbidden _{lines emergence} on the blue

wing

are variable.

The 4D - 3P doublet

_intensity

versus time

(Fig. 2b)

falls off when the laser excitation

decreases. The

_secondary

increase of

_intensity

at 35 kts, will be discussed on section III. The

examination of

_figures

2a and 3 shows a

_great

difference between 4F4D --+ 3P and 3D --+ 3P

Na(I)

experimental profiles.

The

_strong

self reversal of the latter is an evidence of electronic

density

and

temperature

gradients.

However,

the

_plasma

can be considered as

optically

thin

for the 4F4D --> 3P doublet. ’

The _very

_strong

_{auto-absorption}

of 3D - 3P doublet

_gives

a

good opportunity

for

estimating

the

_temperature.

_Assuming

a

parabolic

transverse

_temperature

_{distribution,}

resolution of the radiative transfer

_equation

_[12]

_provides

_temperatures

between 4 000 and 5 500 K. The variation of

temperature

versus time is

displayed

in

figure

4.1. This range of

temperatures

will be useful in the

_{interpretation}

of the

_plasma

behaviour

_during

the second

phase

of its time

_{history owing}

to their values

_{always significantly higher (Fig. 4.1 )}

than those

stemming

from the numerical model

_(unified

Stark

_{theory including}

an electric field and a

dynamic

ion correction - see §

II).

Contrary

to the case of the 3D --. 3P line

profile

for which Stark

broadening

is

small,

the

profile

of the

_optically

thin

semi-degenerate

4F4D --. 3P

_Na(I)

line

_{mainly depends}

on Stark

broadening.

Thus,

the Stark

_broadening

calculation is fundamental : a first

_computer

_program

based upon Lorentzian combinations does not fit

_{satisfactorily enough}

every

experimental

profile (the

asymetry

of the

_dominating

_component

cannot be

removed ;

the forbidden line 4F - 3P cannot be

_{reached) (Fig. 5).}

In these

conditions,

in order to

_improve

theoretical

calculations,

a well tried

fitting-method [13-15]

is used.

Fast Fourier transform

_(F.F.T.)

_conditions,

_spectral

bandwith,

sampling

interval are

adjusted

in order to discretize

_identically

theoretical and

_{experimental profiles.}

Each

_profile

is reconstructed from 512

_points

which coincide with 512

_{experimental frequencies}

_{data ;}

it is then

_possible

to _compare

_{accurately experimental}

and theoretical

_profiles.

II. Stark

_broadening

calculation.

Il.1 FUNDAMENTAL RELATIONS. - As is

_customary

when Stark

broadening

tends to be

important,

normalized line

_{profiles mainly depend, by}

Fourier-transform,

on a

good

Fig.

2.

_{- a) Experimental profiles}

of the 4F4D-3P

_multiplet

at different times : 1) 4 ils,

2)

10 kts,

3)

25 iis,

4)

35 lis.

2b)

4D-3P doublet

_intensity

versus time.

operator

T ( t )

are calculated here

by assuming

independent

electronic and ionic

perturbations,

which allows to write the time

_operator

_{T( t )}

as

[13] :

Fig.

3. -

Typical profile

of self-reversal 3D-3P doublet.

the Hamiltonian H of the

system

being

written as :

Ho

is the

_{non-perturbed}

atom

_{Hamiltonian ;}

P is an

_operator

representative

of all

perturbations

which can be taken as

static ;

Vi (t)

and

Ve (t)

_represent

the

perturbations

_of

ions and electrons.

Fourier transform

_{properties imply}

that a theoretical Stark

profile

is

given by :

i.e. a sum of convolutive

products

of «

partial »

electronic and ionic

profiles :

In

_(11.1.5)

and

_{(11.1.6), la>,}

_{(b l,le)...}

are

eigenfunctions

of the static Hamiltonian

[ Ho

+

P ].

The thermal

averaged

operators

Ua(t)Av ( «

=

i,

e )

_are obtained from

« impact

4.1.

_{Temperatures Te, 7Î, TBartels .}

4.2. Electronic

_{density Ne.}

4.3.

_{Te and}

factors.

Fig.

5. -

Typical

Lorentzian fit of the 4D-3P doublet.

the (c

[ Ti(t)Av la>

are estimated

by

means of the adiabatic solutions of the

Schrôdinger

equation

[ 15] :

Finally,

d is the

_dipolar

momentum

operator.

11.2

_CONSEQUENCES

OF FIRST CALCULATIONS.

_{- Following}

sections II.2. a-c summarize

preliminary investigations intending

to describe

_precisely

the

_plasma

time

_history.

a) P

= 0. - The

validity

of the

_quasistatic

_{approximation being questionable (the}

correlation

_parameter

r, i.e. the ratio of the mean distance between ions and

Debye

radius,

is

greater

than

_0.8),

if we consider

only

electronic

profiles

of 4D-3P

doublets,

the

impact

approximation

version of the unified

_{theory (even}

with

_Magnus

_{exponential formalism) [ 15]}

never

gives

a

good

_agreement

with

experimental profiles.

More

precisely,

when line widths

match

_experimental

data

_{peaks frequencies}

do not

fit,

and

_conversely

a

good

_agreement

between

_experimental

and theoretical

_{peaks frequencies}

does not allow us to obtain

_large

enough

broadenings

for values of electronic

_{density Ne}

and

temperature

Te compatible

with

experiment.

Besides,

the forbidden 4F-3P doublet is never obtained.

b) P

is a static Stark _operator. - The forbidden 4F-3P doublet becomes

_{significantly}

present

only

if P is a static Stark

_operator.

As is well

known,

the discrete atomic levels

split

_up

into _{different sublevels in the presence of} an electric

field,

and when the auto-correlation

correlation function leads to an

implicit

Lorentzian

analysis.

The field

intensity

is determined

from the

_{experimental frequency}

difference à between the 4D-3P and 4F-3P doublets for

expected (Ne, Te ).

In these

conditions,

whatever

_{(E, Ne,}

_{Te )}

are, we obtain

profiles

which are

exceedingly

narrow. Of course, the Lorentzian nature of the theoretical electronic

_profiles

explains

the poor agreement in the

_wings.

c)

Ion

_dynamical

correction. - Since numerical values of the

_non-ideality

factor :

violate the

_validity

condition of the

_quasistatic

treatment

_{(Fig. 4.3),}

an ion

dynamical

correction is desirable

_[15,

_16].

This correction is inferred from

_[14],

after

_checking

adiabaticity

conditions.

_By

_taking

into account

_{simultaneously}

the effect of an electric field

(its origin

will be defined

in §

II.3)

and a

dynamic

contribution for

ions,

one obtains results in

very

good

agreement

with the

_experimental

_{profiles (see § III).}

Details of theoretical calculations are found

in §

II.3 and in the

_appendices

of reference

_[15].

In

_conclusion,

we have shown it is

possible

to resolve the time

_history,

one

profile

after the

other,

for times

greater

than 5 J-LS after the end of the laser

pulse.

11.3 AN APPROACH OF THE NON-DEBYE PLASMA. - The

_plasma

time evolution

_(detailed

in

§

III)

confirms that the

_plasma

is

_{consistently weakly}

non-ideal. The

_non-ideality

factor is about

0.3,

which

_implies

that the number of ions in the

_{Debye sphere}

is

_{approximately}

one or

two. This is

_typical

of a

non-Debye

plasma.

However,

since the average distance between ions

is

_{nearly equal}

to the

_Debye

radius,

this

_length

can still be used as a reference. We assume

that the ionic

_{perturbations splits}

into two

_{parts :}

- a

dynamic

effect due to a

single

ion inside the

Debye sphere (case

a) ;

- a

resulting

field for all the other unshielded ones

(case 13).

Of course, the strict calculation of

the 13

case would

imply

to use a

cluster-type expansion

as

in

_Baranger

and Mozer

_[17],

which would take into account

_increasing

orders of correlation. Even

_excluding

correlations,

we would have to use the

following expression

of the

perturbing

potential development [ 15] :

the i-sum

_including

all active ions. In this formula :

as

V (t), depends

on the

k-degree

irreducible tensorial

_operators

related to the

_spherical

harmonic

_operators

_{by [18] :}

(r,

0,

ç )

and

_(Ri(t),

_{Oi(t), (/)i(t))}

are

respectively spherical

coordinates for the valence

The time

dependence

of ion coordinates makes the treatment of such a

perturbation

difficult.

_However,

if

_only

the k = 1 terms which represent the main interaction «

monopole-dipole »

[15]

are

considered,

it can be noticed that :

bring

in the

_components

of the electric field of the i-ion at the t-time.

The mathematical

_development

is

_formally

identical to the one

corresponding

to electrons. In this last case, thanks to the

_Magnus

_exponential

formalism,

numerous terms can be

systematically

estimated,

such as «

monopole-dipole »

terms

_(k

=

1 )

and

chronological

effect ;

strong

collisions associated to «

dipole-dipole »

terms

_(k

=

2 )

_are

negligible

when

chronological

effect

_slightly

contributes to the

_{profile [15].}

In these

conditions,

good

agreement

with

_{experimental profiles mainly depends}

on the ionic

perturbation.

According

to the time

_dependence

of the electric field

_present

in formula

_(II.3.1-3),

the effect of the i-ion is

differently

treated :

- A

strong

dependànce ( a case)

is treated

_by

adiabatic solutions

_[14].

- The

/3

case is

represented by

an electric field

E,

identified in a first

approximation

(k

= 1 terms of

V(t)

without

correlation)

to the resultant E

== VE,

of

non-dynamic

ions,

i

constant

_during

the effective duration of the

_dynamic

effect. This field is introduced in the

operator

P

_(11.1.3).

Sublevels

_{1 a), 1 b)}

...

present

in

(11.1.5)

and

(11.1.6),

energies

and

energy shifts calculations are carried out

_{(as eigenvectors}

and

_eigenvalues)

from the

(Ho + P )

matrix

_using

the Jacobi method. If for

convenience,

the Oz axis is directed

_along

the field

E,

the P matrix has the

_following

reduced elements

_(with

a

no-quenching hypothesis) :

including

radial

_integrals

F(1)n,l,l- 1 .

In other

words,

each atom is in the local electric field of the ions

_present

all the time in the extended

_{Debye sphere.}

Let us

emphasize

that this field has an excitation effect on the

charged

particles,

in addition to its action on the atomic _energy

levels ;

particularly,

it

gives

greater

importance

to the ion

_dynamic

effect.

The

_{quasi-stationarity}

of the

_{experimental profile during}

a

recording

duration allows us to

use the

_present

method as the basis of our Stark

profiles

calculations. Then usual basis

approximations,

as classical

path,

maxwellian electronic velocities

distributions,

... can be

trusted,

as the calculations will show.

III. Discussion.

We have obtained

_enough

instantaneous

_{experimental profiles}

to describe the

plasma

time

history. By comparison

with « instantaneous »

experimental profiles,

an as exhaustive as

parameters

and then an historical reconstruction of the

phenomenon.

This time reconstruction

is fundamental in the

_{interpretation}

of

_figure

2b :

_particularly

the relative extremum of

_light

intensity

at 35 _JLS can now be

explained.

Moreover,

our basic

hypothesis

are « a

posteriori »

justified

since

_{they provide}

a

phenomenological description.

III.1 THEORETICAL PROFILES AND PLASMA TIME HISTORY. - In order to illustrate the

importance

of the ion

_dynamic

correction,

we

give

thereafter some

experimental

and

theoretical

_{profiles superposed}

for different values of time t.

_{Figures (6a-d) display}

on the same

diagram experimental

and

complete (corrected) profiles ; figures (7a-d) display

experimental

and electronic

_profiles

for the same data.

Figures

8a-d are a

proof

of the

outstanding

influence of the electric field E

_intensity

on the

complete

theoretical

profiles.

The

figures

8a-c

_permit

to _{compare three}

_{profiles computed}

for different values

_{of [[ E [[}

of the

same order of

magnitude (15,

20 and 25 kV

cm-’),

for the same values of

_temperatures

and

electronic

_{densities ;}

the

_figures

8a and 8d

_correspond

to two different values of the electronic

temperature

(2 000

and 1 000

_K)

for the same value

25 kV cm-1.

We can see the

_strong

Fig.

6. -

Fig.

7. -

Experimental

and electronic

_profiles.

influence of the microfield

(by

the

_splitting

of 4D and 4F

_sublevels).

First fixed

_by

the

frequency

difference Ocv between the 4D - 3P and 4F - 3P

_doublets,

it is then

_{adjusted by}

modifying

the values of electronic densities and

temperatures

in order to _agree with the

experimental

Ak line shifts and widths. It appears well-established

that,

without the presence of this

microfield,

it would be

_impossible

to fit the

_experimental

results.

At

last,

a

comparison

of

figures

6,

7,

8 shows the

leading

role of the ionic

perturbation

through

the microfield and the

_dynamic

effect.

The reconstruction indicates

_regular

variations of the main

_{parameters E,}

_Ne,

_Te,

Ti

-The field

_strength

is between 14 and

30 kV cm-1.

Three

_temporal

_stages

are to be

distinguished :

Even if a

signal

can be detected

beyond

70 J..Ls, it merges into the

background

and

a

precise

Fig.

8. - Effect of the field

_strength

and temperatures

(Ne

= 1.7 _x

1016

cm-3).

a)

The

_{strength of}

the Gaussian laser

signal

is

_negligible

at 4 _ts. The

_recording

time

_{(0.5 ps)}

of the

setup

is too

_{long compared}

to the _very fast

_change

of the

_{plasma during}

the

strong

recombination

_{phase (from}

2 to 4

_ts),

and does not

_{permit significant recordings.}

Consecu-tively

theoretical reconstruction is not

_{possible ;}

furthermore,

if it were

possible (by

an

appropriate temporal

distribution of

_profiles),

it would be

_readily

shown that the electron distribution is not Maxwellian

_[5].

_During

this

_phase,

the

_light

emission

vanishes,

the

_plasma

ionisation rate falls from 100 % to about 10 %.

Then,

from 4 to 10 _ts,

_{progressively,}

the radiative recombinations lead to a decrease of the electronic

density,

so that the critical field

Ec

becomes lower than the electric field E after 6 ts. This critical field is

given by [19] :

We can consider that the

exciting

effect of an electric field is the same for _any atom. In our

slighty

ionized

_plasma,

_{the electrons lose the absorbed field energy}

_by

collisions with ions and neutrals. This situation is similar to the case of a

completely

inhibited runaway of electrons in

weakly

ionized

_{plasmas ;}

this is

_why

we

compare ~ E ~

with

_Ec

~ .

This

presentation

matches

with low

temperatures

(energies)

and Coulombian interactions

_{(electron-ion}

collisions

frequencies

about 1.7 x

1012

s-1).

Thus after 6 ts,

strong

radiative collisions become more and more numerous. The

electronic

temperature

simultaneously

falls from 4 000 to 2 300 K while the ions are

overheated to 2 300 K

_{(see Fig.}

4.1 and

_{profiles 6a-b) :}

a

_part

of the lost electronic energy

contributes to overheat the

ions,

with a thermalization time of about 10 _kts.

b)

10 ts

is a very

typical

moment in the

_plasma

time

_history.

- The electronic

_density

shows

a relative minimum

(Ne

= 0.9 _x

1016

cm-

3).

The

temperature

is 2 300 K

(thermalisation

is

achieved) ;

the

_Debye

radius is 35 nm and the mean number of ions in the

Debye sphere

is

1.5.

- The difference

between [[ E [[

and Il Ec Il

is maximum

_{(Il E}

= 25 kV cm - 1, Il Ec Il

_~

=

16 kV

cm-1).

The

_strong

emission of the 4F4D - 3P line at this time shows that the 4F and 4D

populations

are

important.

From these

levels,

ionization is

possible

with 0.85

_eV,

_energy

only

three times the mean thermal electronic _energy.

Then,

one can think that electrons can

reach such an _energy on a distance near the extended

Debye sphere

diameter in a number

great

enough

to maintain

_(at

10

_ts)

or increase

(after 10 )JLs)

the electronic

density.

Such a

situation,

connected with the

lowering

of ionization

level,

is

already

mentioned

by

B. d’Etat and Hoe

_{Nguyen [20] :}

_according

to their

results,

a

_spontaneous

ionization can occur for microfields lower than the critical one ; this

phenomenon

is

unavoidably

enhanced

here.

Consequently,

for t > 10 _ts, the noticed modification of the

plasma

behaviour is

explained

here

_by

the relative

_strength

of the electric

_{field ~ E Il}

as

compared

to _{the critical field up} to

about 30 _{ts :} this field

compensates

the lack of radiative recombinations

_{by increasing}

the collisional excitation of the 3P level.

_Then,

an

equilibrium

is reached when electron excitation

and deexcitation are

equal.

A

long

lasting

«

trapping »

of the 3P and 4F-4D levels is

observed,

which appears

experimentally through

the increase of the emitted

_light

_{intensity (whose}

relative maximum is between 25 and 40

_iis).

As the electronic

_density

_increases,

the electronic

_temperature

_(equal

to the ionic

_one)

decreases,

which shows that the electronic energy is

dissipated

either in radiative collisions or

in

_ionizing

ones, the latter

progressively loosing

their

_importance

until it balances the radiative recombinations at about 25 lis.

It is

_important

to notice that the values of

_parameters

_{Ne, Te, Ti,}

_{Il Ec Il}

and

Il E Il

remain

_steady

after 25 kts,

Il

Ec

Il

becoming slightly

greater

than

_Il

E

_Il

_{(see Fig.}

9.1 and

profile 6c). Apparently,

there is a

long

« relaxation time » after the laser

pulse, during

_which

the

_light

emission is

_comparable

to the one of a traditional

plasma,

but for much lower

temperatures.

In

_spite

of the relative

_uncertainty

of the 3

x1017 cm- 3

estimated atomic

_{density during}

this

period,

we

emphasize

the

_agreement

of the latter with a durable

trapping

of the 3P level for a

long

time after the laser

_pulse.

Such a value of the atomic

density

favours

high

_energy

electrons,

and

_consequently

the

_ionizing

collisions and the

_increasing

of 3P level

_population.

Besides,

the

_trapping

is a

plausible explanation

since _{energy levels}

_populations

_{obtained from}

parameters

is not simultaneous :

_{Ne, Te, If,}

_Il

E

_Il

are

only

decreasing

after 45 _f,Ls.

During

this

period,

radiative recombinations have become

_again

the main cause of emission. For the reached electronic

_density,

the electric field is no

longer

_strong

enough

to

_give

_energy to the electrons and at last the more and more non-ideal

plasma

dies

(see Fig.

9.1 and

profile

6d).

III.2 RELATIONS BETWEEN ELECTRIC FIELDS, DENSITIES AND TEMPERATURES. - The time

dependence

of the non

ideality

factor

ri(t)

is in

_agreement

with our

assumption

about the

comparatively

important profile

modification

_predicted

as due to ion

_dynamic

effect. Since the electric field

_[[E[[

and the

_quasi-static

field

_(Holtsmark

normal field

_strength)

[[ EQs [[

[13] :

have similar

_strength,

it is then natural to calculate the relative difference :

A

_simple

relation between this ratio and the

_non-ideality

factor

_ri(t)

is encountered

(Fig. 9.2) :

A similar

_empirical

law is satisfied if we take as a new reference the critical field

Ec [19]. Replacing

_EQs

by Ec (Fig. 9.3)

we obtain :

This result was

predictable,

as thé ratio 201320132013

~

is close to 1 in our

expérimental

conditions.

~ EQS ~

The

_figure

9.1 shows

_{that Il}

E

_{[[ , [[}

Eos

and Il Ec Il

are

always

nearly

equal.

Figures

9.2 and 9.3

show the

_opposite

variations

of

_(resp.

d’E)

and

_ri(t)

which follow from the different

E E

temporal

variations of the main

_parameters

_(Fig.4.1-3).

These

_opposite

variations are

characteristic of the

_experiment

at _{any time.} Before 10 ws,

they

come from the

coupling

of

radiative recombinations and ions

_{heating (decrease}

of

_ri(t)

and increase of

AE) ;

after

10 _ws, the

_coupling

between

_ionizing

collisions and the

_slight

decrease of the

temperature

gives

the same result

(increase

of

Ti( t)

and decrease of

AE).

IV. Conclusion.

already

seen, this situation

_implies

two different treatments of ions

_according

to their distances to the

_perturbed

atom.

_First,

unshielded ions in the

_vicinity

of the

boundary

of

Debye

sphere

have a collective action that is more or less

represented by

the electric field E in

the

operator P,

which sets the new atomic _energy levels of the used formalism.

Secondly,

a

dynamic

effect has to be considered for the ions

_being

in the most inner

_part

of the

_Debye

sphere.

Without such a

dynamic

effect,

no theoretical

profile

has a correct width. Whatever the

_recording

time t

_(after

5

_its),

these two

_{perturbations}

have to be

_{simultaneously}

taken into

account

₍₅

_f.LS t 45

_ts).

2. The electric field

_E,

_by

which atomic _energy levels are

perturbed plays

also an

important

physical

part

in the nature of electronic

collisions ;

it remains

_remarkably

constant at

25 kV

cm-1

1

(see Fig. 9.1),

as

compared

to the critical field

_{Ec strength}

and the normal field

strength

_{EQS Il}

(which

are

good references)

which _vary

according

to the values of

Ne

and

_{Te .}

Towards the end of the radiative recombination

_phase,

the electronic

_{density Ne}

decreases

enough

to

_give

a critical field

strength Ec [[

lower

than [[

E

~ .

A revival of electrons becomes

possible ;

the rate of radiative recombinations

_decreases,

the ionization rate

increases,

and

consequently Ne

shows a minimum at 10 _ts.

Then,

our numerical results show that there is an

equilibrium

between the two

_{phenomena. Simultaneously, light intensity}

fluctuations

(Fig. 2b)

are

explained.

3.

_Empirical

relations are satisfied between

4.

_Despite

the difference in the time

scale,

the variations of the 3P level

_population

encountered for our densities are

certainly

to be related to those found

_by

Landen et al.

_[7].

But there are

important

differences between our

study

and the Landen’s one.

First,

our

conclusions,

partly comparable

with those of Landen et

al.,

are carried out

_by

an « ab initio »

calculation,

already

used and

_{improved by}

the

_present

results. It

_gives

values of main

parameters

Ne, Te,

... close to those encountered in

previous

papers but leads to very well

fitted

_{profiles only}

because it includes at the same time the ionic microfield

perturbation

and

the ion

_dynamic

effect.

_Secondly,

if the two

_plasmas

have the same

origin,

our

experimental

conditions are _very different from theirs : _pressure, laser

pulse

duration

(2

_jjbs

against

30

ns),

trapping

duration

_{(40 its}

_{against 160 ns)}

and

_especially

the increase of the

_light

emission between 10 and 35 _lis, which had not been observed

_by

Landen and is

_certainly

in relation with the relaxation time duration. When

_compared

to the « relaxation time » encountered here

(about

30

_ts),

the one

reported by

Landen

[7]

(160 ns)

seems to show a scale invariance

with

_regard

to the laser

_pulse

duration.

These results

_give

a

phenomenological explanation

of the

experiment

which agrees with all

the

_experimental

observations

_during

the

_lapse

of time : 4 _{ts -«--- t --} 45 _kts

_(i.e.

the efficient

trapping).

Acknowledgments.

We would like to thank here J. Larour for the heat

_{pipe technology}

and Y. Vitel for the

measurement

_techniques

and of course J. L. Bobin and M. Skowronek for numerous

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