Optical measurement of the expansion of a laser plasma created on a planar microtarget

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Optical measurement of the expansion of a laser plasma

created on a planar microtarget

C. Popovics, R. Benattar

To cite this version:

C. Popovics, R. Benattar.

Optical measurement of the expansion of a laser plasma created on

a planar microtarget.

Journal de Physique Lettres, Edp sciences, 1982, 43 (17), pp.633-639.

�10.1051/jphyslet:019820043017063300�. �jpa-00232104�

L-633

Optical

measurement of the

_expansion

of

a

laser

plasma

created

on a

planar microtarget

C.

_{Popovics (*)}

and R. Benattar

_(*)

Laboratoire P.M.I.,

Groupe

de Recherche n° 29 du _C.N.R.S., Ecole

_{Polytechnique,}

91128 Palaiseau Cedex, France

(Refu le 28 _{juin 1982, accepte} le 19

_juillet

1982)

Résumé. 2014 Pour mesurer par interférométrie la densité dans la couronne d’un

_plasma

_{créé par}

laser, il faut utiliser de

_petites

cibles afin d’atteindre la densité la

_plus

élevée

_possible.

_Ici, nous avons choisi de créer un

_plasma

au bout de

_{micro-cylindres}

de même diamètre que la tache focale du laser. Avec ce _type de cible, le

_plasma

créé en dehors de la tache focale _{par conduction latérale} est situé

sur la

_périphérie

du

_{micro-cylindre}

et peut être sondé

_{optiquement indépendamment}

du

_plasma

principal.

En utilisant de telles cibles illuminées par une

_impulsion

laser à

_néodyme

de 1 à 3 J et de _{durée 50 ps,}

nous avons mis en évidence

_pendant

_{l’impulsion laser,} des effets non

_linéaires

tels que modification

du

_profil

de densité et filamentation. Après

l’impulsion

laser, nous avons _mesuré la distribution de

densité, montrant que les isodensités ont une forme

_{sphérique. Quelques}

_pourcents de

_l’énergie

laser incidente sont retrouvés dans

_{l’expansion}

latérale d’un

_plasma

de

_quelques

électrons volts de

température

qui

s’étend sur environ 100 03BCm le _long du

_{micro-cylindre.}

Abstract. 2014 Interferometric

density

measurements in the corona of a laser created

_{plasma require}

small targets in order to reach the _highest

_{density possible.}

Here we have chosen to create the

_plasma

on the end of

_{microcylinders}

which diameter is of the size of the focal _spot of the laser. With this

type of _target, the

_plasma

created outside the focal _spot of the laser

_by

lateral conduction is located

at the

_periphery

of the

_{microcylinder}

and can be

_{optically probed}

_separately

from the main _plasma.

Using such _targets illuminated with a 1-3 J, 50 ps duration

neodymium

laser

_pulse,

we have evi-denced

_during

the laser _pulse non linear effects such as

density profile

modifications and

filamen-tation. After the laser

_pulse,

we have measured the

density

distribution

showing

that the

_density

contours are _nearly

spherical.

A few _percent of the incident laser energy is found in a lateral _plasma

whose _temperature is a few electron volts and which

_expands

about 100 03BCm

along

the

microcylinder.

J.

_Physique

- LETTRES 43

(1982) L-633 - L-639 1~’ SEPTEMBRE 1982,

Classification

Physics Abstracts 52.50J

In laser

_target

_interaction,

the energy transfer from the laser to the dense

_regions

of the

_plasma

is

_{greatly dependent}

on what occurs in the corona. The

knowledge

of the _parameters of this

outside

_plasma,

in

_particular

its electronic

_{density profile}

is

_important

for the

_study

of

absorp-tion and _transport processes, and instabilities. The laser

absorption

is

directly

related to the

density gradients

in the subcritical and critical

_plasma,

and the heat transfer across the laser

axis or toward the dense

regions depends

on the presence of

magnetic

fields and

_suprathermal

(*)

Contributing to the GRECO-ILM of the C.N.R.S.

634 JOURNAL DE PHYSIQUE - LETTRES

electrons. Density contours can be modified by these two last processes and also by instabilities.

Optical probing and in particular interferometry is a good approach for the corona study as it

gives in this region qualitative and quantitative informations on the contour lines and gradient

scale lengths of the density.

In the case of the interaction of a laser beam at 1.06 um wavelength, the density profile around the cutoff density for the main beam can be measured by UV interferometry if the extension of the plasma is sufficiently small [1, 3]. In the experiences on large planar targets, optical probing

is difficult as the edges of the target and the large low density plasma alters the measurement of the centre of the plasma : indeed, a first source of error is the presence of diffraction fringes

creat-ed by the edge of the target; this can be eliminated by choosmg a target with a large curvature

instead of a plane target. Also, refraction may become so important that the probe beam does

not reach the critical density for the main laser. Moreover, the contribution of the cold peripheric plasma to the interference order can become as important as the axial plasma one and intro-duce an important error on the measurement. Then, in order to measure the density on a planar

target, we use as a target the end of a microcylinder which diameter is of the order of the focal

spot diameter. For this type of target, the lateral expansion of the plasma is located on the cir-cumference of the cylinder so the cold lateral plasma does not alter the axial plasma

measure-ment, and it can itself be also measured.

The plasma is created by a neodymium laser (~, = 1.06 ~m) on the end of glass cylinders of 50 or 100 um diameter. Pulse duration is 50 ps and the incident energy varies between 1 and 3 J,

giving 5 x 1014 to 1.5 x 10" W/cm2 m a 70 ~m focal spot. A Wollaston interferometer [4]

is illuminated by a 0.26 ~m wavelength probe beam of 25 ps pulse duration. The temporal evolu-tion of the plasma is measured by varying the delay between the probe beam and the main beam

(At = 0 when the two maxima are simultaneous). Spatial resolution is limited to 5 um by the

precision of the set up of the target in the object plane of the imaging microscope.

The observation of the plasma evolution shows well separated axial and lateral expansion.

During and just after the laser pulse, the axial expansion is very fast, and non linear effects occur

in a sharp density gradient. In this first stage, mterferometric measurements are not quantitative

and are _interpreted as shadowgraphy. In a second stage, the expansion becomes more quiet

and quantitative density measurements are then possible. A lateral plasma is rapidly established

along the cylindrical target, and can be studied during the two stages of the expansion.

In the first stage of rapid expansion, during and after the laser pulse, mterferograms present

a few closed up fringes around a opaque zone. This mdicates a very sharp density gradient (Le 5 ~m) which is not resolved in the experiment. Simultaneously, interferograms evidence

non linear effects : figure 1 shows a density crater which can be associated to the radiation

pres-sure of the laser. The importance of the ponderomotive effects m the experimental conditions

Fig. 1. - Formation of a density crater on a target of 50!lm diameter with a 1.5 x1015 W/cm2 laser

635 EXPANSION OF A LASER PLASMA

can be verified

_{by evaluating}

the ratio a between the

gradients

of radiation _pressure and kinetic

pressure. The

density gradient being

of the same order as the laser

wavelength,

the ratio a can

be written

_{[5] :}

with

₁₀

in

_{Wjcm2, À.}

in _Jlm

_{and Te}

in eV.

_{Taking Te}

= 1

_keV,

and the measured

we find a =

0.56,

which _means that the

ponderomotive

effects _are

important

[6-7].

On

_figure

_{2 appears} a more

_complex

structure which can be attributed to a filamentation of

the laser beam in the

_plasma.

This structure, very similar to what is observed in other

experi-ments

_[8],

_presents

8 to _{9 Jlm} diameter filaments. The distance between the filaments is at least

20 to 25 _~m. The filaments can be initiated

_by

hot

_spots

in the laser beam. The measured filaments

diameter is in accordance with the calculation of

_stability

of a filament

propagating

in a

_{plasma [9].}

Indeed,

the stable diameter is :

where _c0p is the local

_plasma

_{frequency, vo}

the

_{oscillating speed}

of an electron in the

electroma-gnetic

field,

and vt

the thermal

_velocity.

This

_gives

and

The _{8 ~m} diameter measured in the underdense

plasma

is close to the

_prediction,

and the

figure

2 shows that the filament diameter decreases when the

_density

increases.

Although

the exact

_position

of an

_isodensity

contour cannot be measured

_during

and

_just

after

the laser

_pulse

from the

_{interferograms,}

we can show that the

_edge

of the opaque zone can be

associated to a

_density

of the order of 5 x

1019

cm - 3

to 2 x

1020

cm -

3.

_Indeed,

this transition

corresponds

to a

_{sharp density gradient}

from the

_density

of maximal

_penetration

of the main

beam until a

_density

which is

sufficiently

small for the

fringes

be not much _{shifted. The opaque}

zone is characteristic of a

region

where the

probe

beam is refracted out of the

_imaging

_optics

and must be associated to a

_density

_greater

than 2 x

1020 cm- 3.

The

_fringes

which are not

Fig.

2. - Filamentation of the subcritical

plasma. (Target diameter : 100 ~m, laser intensity :

636 JOURNAL DE PHYSIQUE - LETTRES

Fig. 3. - Axial

expansion

of the

_plasma.

The

_position

of the

_edge

of the dark zone

_surrounding

the _target

is

_reported

in the dashed area. It is

_compared

to the evolution of the 5 x 1019 and 2 x 1020 cm-3 isoden-sities calculated in a

_spherical

_planar calculation with the

hydrocode

FILM (-- : 5 x 1019

cm- 3 ;

2 x 102 0

cm-3).

much

shifted

_correspond

to a low

_{density plasma. Figure}

4c indicates that a

_density

_greater

or of

the order of 5 x

1019 cm- 3

can be

reasonably

associated to the low

_density

side of the

_sharp

gradient.

So the

_temporal

evolution of the _opaque zone can be

_compared

to the

_plasma

evolution

calculated with an

_hydrocode.

The calculation is done with the monodimensional

_hydrocode

FILM

_[5-10]

with a laser

intensity

of 5’ x

1014

W/cm2

and a 50 ps duration

pulse.

The _energy

is absorbed

_by

Inverse

_{Bremsstrahlung (8 %)}

and

_locally

at the critical surface

₍₁₀

_%).

The

ther-mal flux inhibition factor is

_0.12,

value obtained for best fit of

_{density profiles [3, 7]. Spherical}

and

_planar

cases are considered. The

spherical

case is calculated with a

_target

diameter of 50 ~m

~ and for the

comparison

of

_spherical

and

_planar

_{calculations,}

the centre of _symmetry is

_supposed

to be on the

planar

_target

surface.

On

_figure

_3,

we have

_reported

the

_density

contours 5 x

1019 cm- 3

and 2 x

1020 cm- 3

calcu-lated in the

_spherical

and

_planar

case. We have also indicated

by

hatchings

the

position

of the

dark zone. This

_comparison

shows that after the laser

_pulse,

the

_{plasma expands}

much less

than the

_prediction

of the

_{planar simulation,}

and is better

_{represented by}

the

_spherical

model.

On the other

_hand,

_during

the laser

_pulse,

the

_planar

and

_spherical

models

_give

a similar

expan-sion,

and the

_experiment

is not conclusive on the

_type

of

_geometry

of the

_plasma.

The

_analysis

of the

_{interferograms}

obtained after the laser

_pulse

show also that the subcritical

plasma expands spherically. Figure

4 shows the

_{interferogram}

obtained 210 _ps after the maximum

of the laser

_pulse,

on a 100 _Jlm diameter

_target,

and the results obtained from Abel inversion of

the

_{interferogram.}

The

_density

_{profile (Fig. 4c)}

has a 13 _± 5 _~m

_gradient

scale

length

at half critical

_density.

The

_isodensity

contours show

_clearly

a

spherical

_symmetry

around a centre which

moves off from the

_target

during

the

expansion.

The

plasma

diameter is of the same order as the

focal

_spot

diameter.

In this

_experiment,

we have also measured the lateral

_expansion

of the

_plasma

which can be

reached from the

_study

of the

_plasma

created on the

_periphery

of the

cylindrical

_target,

on a

non irradiated area.

Figure

5 is the

superposition

of two

_{interferograms,}

obtained before the

laser shot

_(initial

_target

_image)

and

_during

the laser shot

_(At

= 90

ps).

It shows that the dark _zone

637 EXPANSION OF A LASER PLASMA

Fig.

4. -

Sphericity

of the subcritical _plasma after the laser _{pulse (At} = 210

ps).

(Target

diameter : 100 um, laser

_{intensity :}

1015

_Wjcm2.)

_{a) Interferogram. b)}

_Isodensity

contours densities are indicated in 1020 cm- 3

unit. _{c) Density profile}

_along

the laser axis.

Fig. 5. - Lateral and axial

expansion of the _plasma. Two

_{interferograms,}

obtained before the laser shot and 90 ps after the laser maximum are

superposed.

In the dark _region

corresponding

to the dense _plasma

638 JOURNAL DE PHYSIQUE - LETTRES

Fig.

6. - Self-similar

expansion

of the lateral

_plasma

on a

_cylindrical

_target. From the measurement of the radius

_R1

and

_R2

of the

_plasma

around the _target at

_{times t,}

and _t2, the

_{density gradient}

scale

_lengths

L, 1 and

L2

are deduced.

measurement of the variation of the diameter of the

_cylinder

in a non irradiated area leads to a

value of the _energy

_{deposited by}

lateral

_transport

_along

the _target.

_Indeed,

we _{may suppose that}

the radial

_expansion

of the

_cylinder

is self-similar in this case as the lateral

_plasma

is heated

_by

a

thermal wave. Then the measurement of the diameter of the

_plasma

at two different times

_gives

the sound

_speed

and the electronic

_temperature

of the lateral

_plasma.

In a

cylindrical

self-similar

expansion,

the sound

_speed

is related to the

_{density gradient}

scale

_{lengths L1}

and

_L2

measured

at

_{times t, and t2 by :}

Figure

6 indicates the _way to deduce

_{L 1}

and

_L2

from the

_position

of the

_edge

of the dark zone.

Supposing

that this frontier

_corresponds

to a

_density

of 5 x

1019 cm-3

or 2 x

1020

cm-3,

the

order of

_magnitude

of the electronic

_temperature

can be evaluated as :

- for

a _{100 gm} diameter

_target

_Te

= 8 eV

- for

a 50 gm diameter

_target

_Te

= 4 to 20 eV.

The

_particles

of the

_plasma

are

_initially

in a

_cylindrical

corona which

_{depth e}

is the

_penetration

of the thermal front. This

_depth

can be evaluated to _{1 gm} or less

_{[11]. Then,}

we estimate the _energy

contained in the lateral

_plasma

to :

where

_Te

is the measured electronic

_temperature,

is

the electron

_density

in the

_solid,

’

Do

is the diameter of the initial

_target,

and

L is the

_length

of the heated

_{cylinder (L ~}

100

_~m).

So,

we find the order of

_magnitude

of the

_{laterally deposited}

_{energy, in}

_percent

of the incident

laser energy :

- for

a 100 _~m diameter

_target

- for

639 EXPANSION OF A LASER PLASMA

The above calculation could

support

the

_hypothesis

of a lateral

_transport

_{by suprathermal}

elec-trons.

_Indeed,

the

_length

of about _{100 lim} of heated

_plasma

_corresponds

to the _range of

supra-thermal

_electrons,

and the

_percentage

_{of energy found in this lateral}

_expansion

is in

_agreement

with

_{previous experiments [12]. Nevertheless,}

a return current

_along

the

_target

could be also a

possible

mechanism to reach such lateral

_plasma

conditions.

_And,

in this case of

_targets

of 50 Jlm

diameter,

a

_part

of the incident _{energy may} also

directly

heat the

periphery

of the

cylinder

as

the focal

_spot

is

_larger

than the _target diameter.

In summary, this

_experiment

of interaction on small size

_planar

_targets have evidenced the

following points :

-

during

the laser

_pulse,

non linear

_phenomena

such as

_density

crater formation and

filamen-tation occur in the

_plasma;

- after the laser

pulse,

the subcritical

_{plasma expands spherically;}

- about 1

%

of the incident laser energy is

deposited

indirectly

on the

periphery

of the

cylin-drical

_targets,

on a distance of the order of 100 _gm. This lateral

_heating

can be attributed either

to

_suprathermal

electrons or to a return current in the _target.

Acknowledgments. - We acknowledge

assistance from the GRECO Interaction Laser

Matiere technical staff. We

_{particularly appreciate}

support

from and fruitful discussions with

E. Fabre.

References

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