Jorge Filevich et al- Bow shocks formed by plasma collisions in laser irradiated semi-cylindrical cavities

8/3/2019 Jorge Filevich et al- Bow shocks formed by plasma collisions in laser irradiated semi-cylindrical cavities

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Bow shocks formed by plasma collisions in laser irradiated

semi-cylindrical cavities

Jorge Filevicha,*, Michael Purvis a, Jonathan Grava a, Duncan P. Ryan b, James Dunn c, Stephen J. Moon c,Vyacheslav N. Shlyaptsev a, Jorge J. Rocca a,b

a NSF ERC for Extreme Ultraviolet Science and Technology and Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523, USAb Department of Physics, Colorado State University, Fort Collins, CO 80523, USAc Lawrence Livermore National Laboratory, Livermore, CA 94551, USA

a r t i c l e i n f o

Article history:

Received 26 February 2009

Received in revised form

3 April 2009

Accepted 3 April 2009

Available online 16 April 2009

PACS:

52.50.Jm

52.65.-y

52.70.-m

42.55.Vc

Keywords:

Soft X-ray lasersPlasma shocks

Interferometry

Plasma simulations

a b s t r a c t

The formation of shocks in plasmas created by short pulse laser irradiation (l 800 nm,

Iz1 1012 W cm2) of semi-cylindrical cavities of different materials was studied combining visible and

soft X-ray laser interferometry with simulations. The plasma rapidly converges near the axis to form

a dense bright plasma focus. Later in time a long lasting bow shock is observed to develop outside the

cavity, that is shown to arise from the collision of plasmas originating from within the cavity and the

surrounding flat walls of the target. The shock is sustained for tens of nanoseconds by the continuous

arrival of plasma ablated from the target walls. The plasmas created from the heavier target materials

evolve more slowly, resulting in increased shock lifetimes.

2009 Elsevier B.V. All rights reserved.

1. Introduction

The collision and subsequent interaction of dense plasmas

created by intense laser irradiation of cylindrical cavities are of

interest for fundamental and practical reasons [13]. We have

recently reported the study of semi-cylindrical cavity plasmas

using soft X-ray laser interferometry and hydrodynamic simula-

tions [4]. Aluminum and carbon plasmas were created by irradi-

ating half-cylinder cavities at intensities of 1 10

12

W cm

2

with120 ps duration optical laser pulses. The plasmas were interfero-

metrically probed with 46.9 nm laser light to obtain electron

density maps at different times throughout their evolution. The

reduced refraction of the soft X-ray probe relative to an optical

probe allows the mapping of the electron density in plasma regions

with higher density gradients [5,6]. In this semi-cylindrical target

geometry pressure gradients at the walls radially accelerate the

plasma towards a location near the cavity axis, where it collides

forming a bright high density plasma focus with an electron density

> 1 1020 cm3. During the study of these plasmas we also

observed extreme ultraviolet plasma self-emission from a long and

narrow arc outside the cavity (see Fig.1), indicative of the presence

of a bow shock. Bow shocks are of interests in astrophysics [7,8] and

have been studied in the laboratory [9].

Herein we report the study of these shocks using interferometry

and two-dimensional radiation hydrodynamic code simulations.

Optical interferometry was used to complement soft X-ray laserinterferometry in mapping the lower density regions where the

shorter wavelength probe is insensitive. The combination of both

interferometry techniques provides the ability to measure, for

these particular plasmas, electron densities within the range from

5 1017 cm3 to 1 1020 cm3, with the highest value limited by

probe beam refraction.

2. Experimental setup

The plasmas were created using a Ti:Sapphire laser beam to

heat 500 mm diameter semi-cylindrical grooves machined into* Corrresponding author.

E-mail address: [email protected] (J. Filevich).

Contents lists available at ScienceDirect

High Energy Density Physics

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / h e d p

1574-1818/$ see front matter 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.hedp.2009.04.003

High Energy Density Physics 5 (2009) 276282
mailto:[email protected]://www.sciencedirect.com/science/journal/15741818http://www.elsevier.com/locate/hedphttp://www.elsevier.com/locate/hedphttp://www.sciencedirect.com/science/journal/15741818mailto:[email protected]


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1 mm thick slabs of different materials with intensities of

w1 1012 W cm2. The 120 ps short duration of the heating laser

pulse results in rapid deposition of laser energy, making it possible

to study the evolution of the plasma without further laserplasma

interaction. Studies were performed for carbon, aluminum, copper

and silver targets. The Ti:Sapphire laser beam was focused into the

groove forming a line focus ofw470 mm FWHM and ofw1.3 mm

length. The position and intensity distribution of the line focus

were monitored for every laser shot by imaging the reflection of

the beam off an optical flat onto a CCD camera placed at a distance

equivalent to that of the target.The plasmas were imaged onto an MCP/CCD (Multi Channel

Plate/Charged-Coupled Device) detector system with 25 magni-

fication using a spherical Sc/Si multilayer-coated mirror. The

plasmas were probed using two different interferometers to map

the high and low electron density regions. The first is a Mach-

Zehnder interferometer that operates at l 46.9 nm [6] using

diffraction gratings to split the beam of a table-top 46.9 nm Ne-

like Ar capillary discharge laser. In this laser a fast electrical

discharge current pulse compresses the plasma generated in an

argon-filled capillary tube to generate a population inversion and

amplification in the J 01 3p3s line of Ne-like Ar [10]. The laser

delivered pulses ofw1 ns duration and w0.15 mJ of energy [11].

The temporal jitter between the capillary discharge laser probe

and the plasma heating laser pulse was reduced to less than 2 nsby laser triggering the capillary discharge main spark gap. This

short wavelength probe can access the densities present in the

early stages of the evolution of the plasma, in particular the region

of the high density plasma focus. The second interferometer, used

to probe the lower density regions in the plasma, is a Mach-

Zehnder interferometer that operates at l 532 nm. The temporal

resolution of this visible interferometer is determined by the

relatively long pulse, w8 ns FWHM, of the frequency doubled

Q-switched Nd:YAG laser probe used. This pulse duration is

nevertheless sufficiently short to probe the regions of the plasma

with a relatively slow varying density. The probe laser and the

Ti:Sapphire plasma heating laser were synchronized with a jitter

of less than 1 ns. The target was positioned to intersect one of the

arms of the interferometer by using motorized translation stages.

The plasma was probed using one of the two probe wavelengths at

a time.

The experimental geometry is shown in Fig. 2(a). The cavity was

irradiated at normal incidence with respect to the flat front surface

of the target while the probe beam propagated along the axis of the

1 mm long semi-cylindrical cavity. The plasma was imaged onto

a CCD camera with a magnification of 20 using an f 20 cm lens.

A narrow band filter centered at l 532 nm was used to reduce the

plasma self-emission collected by the imaging system. The reso-

lution of this imaging system determined by the 1090% rise on

a knife edge image wasw10 mm.

Electron density maps wereobtainedfrom the interferogramsby

assuming that the plasma is uniform along the direction of propa-

gationand that theindexof refraction of theplasma is dominated by

the free electrons [12]. Under these conditions the electron density

can be directly obtained from the measured number of fringe shifts

Fig. 1. Time integrated extreme ultraviolet emission from a Cu plasma created by laser

irradiation of a semi-cylindrical target.

Fig. 2. (a) Schematic of the semi-cylindrical target showing the incident plasma

heating laser beam (from right to left) and the direction of propagation of the soft

X-ray laser probe beam (perpendicular to the page). (b) Soft X-ray laser (46.9 nm)

interferogram of a copper plasma showing the dense plasma build up near the axis.

J. Filevich et al. / High Energy Density Physics 5 (2009) 276282 277


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in the interferograms (Nf ne l=2 ncrit l where ncrit is the

critical density of the plasma at wavelength l). For a l 1 mm long

plasma, one fringe shift at 46.9 nm probe wavelength corresponds

to w5 1019

cm3

, while at 532 nm probe wavelength, one fringeshift corresponds tow4 1018 cm3. More detailed descriptions of

the experimental setup used to create the plasma and of the soft

X-ray laser probe can be found in recent publications [4,6,13].

3. Experimental data

Fig. 1 shows the time integrated extreme ultraviolet plasma

emission distribution corresponding to a copper plasma. Two

bright regions are visible. The brightest region is located close to

the axis of the semi-cylinder where the expanding wall plasma

converges and collides forming the plasma focus. The second is

located close to the target wall at the bottom of the cavity. A third

dimmer structure with the shape of an arc is seen to develop

outside the cavity, far from the region directly heated by the laser.

It was noticed that this arc structure appears in the self-emission

images when the width of the plasma heating laser line focus was

wide, i.e.w470 mm FWHM, approaching the grooves width. In this

case the wings of the heating beam illuminate the frontal flatsurface surrounding the 500 mm groove target creating a plasma. In

contrast, the arc structure was not observed in plasmas generated

by a narrower line focus (w350 mm FWHM).

The dynamics of the denser regions of the plasma where large

density gradients are present were mapped using the soft X-ray

laser interferometer. Fig. 2(b) shows a soft X-ray laser interfero-

gram of a Cu plasma obtained 7.6 ns after laser irradiation. The

white line indicates the target surface position. The wall plasma

converges into a small region near the axis where it collides to form

a plasma focus identifiable by a sharp increase in the electron

density. The plasma focus develops as early as 1.7 ns, reaching

densities higher than 1 1020 cm3 at 7.6 ns in agreement with

simulations. The simulations predict that the electron temperature

in the plasma focus region reaches 35 eV. The plasma in this region

Fig. 3. Sequence of interferograms depicting the evolution of a Cu plasma. The probe beam wavelength used was 532 nm.

J. Filevich et al. / High Energy Density Physics 5 (2009) 276282278


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is observed to remain dense well after the time of its build up. This

increase in plasma density matches the region of strong localized

emission of radiation seen in Fig. 1. A series of soft X-ray laser

interferograms describing the early part of the evolution of similar

plasmas created by irradiation of aluminum and carbon targets was

reported in Ref. [4].

Fig. 3 shows a sequence of selected l 532 nm interferograms,that describe the evolution of the lower density regions of the Cu

plasma. The interferograms clearly show the development of

a quasi-stationary bow shock structure outside the cavity. This

plasma structure starts as two narrow arcs close to the axis of the

semi-cylinder. As the plasma evolves, the arcs are stretched in

length and the distance and angle between them widens slowly.

Simultaneously, the width of the shock is observed to increase with

time. This continues until the shock fades after about 70 ns. Fig. 4

shows the electron density maps obtained from the interferograms

under the assumption that the plasma is uniform along the axial

direction. The density maps show that the shock reaches a peak

electron density ofw6 1018 cm3 at 20 ns. The first three frames

of Fig. 4, that illustrate the early stages of the evolution, show

plasma expanding from the flat frontal surface of the target.

Similar bow shock structures were observed following the

irradiation of carbon, aluminum and silver targets, corresponding

to plasmas with atomic numbers ranging from 6 to 47. As expected,

the speed at which the shocks evolve was observed to be

progressively slower as the atomic mass of the material increases.

For all materials the shocks are observed to evolve from a curved to

a straight shock front. The speed at which this transition occursdepends on the atomic mass. Fig. 5 shows interferograms and

electron density maps of C plasmas, the lightest material probed.

A significantly faster plasma evolution is observed in which the

shock fronts are already straight in the 5 ns frame. For the heavier

materials, Al, Cu and Ag, the shock fronts are first observed to be

straight at 35, 50 and 75 ns, respectively. The absence of significant

radiation cooling contributes to the disproportionately faster

evolution of the C plasma.

4. Simulations and discussion

The plasmas were modeled in two dimensions using the three-

dimensional single fluid radiation hydrodynamics code HYDRA

[14]. HYDRA is an Arbitrarily LagrangianEulerian code capable of

Fig. 4. Electron density maps obtained from the interferograms in Fig. 3. The density scale is logarithmic.



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running in an assortment of hydrodynamic mesh strategies to avoid

the mesh tangling that commonly occurs when modeling

a converging plasma. Inverse Bremsstrahlung absorption was

assumed to be the dominant laser deposition mechanism at our

irradiation conditions. The equation of state was modeled using the

Lawrence Livermore National Laboratorys LEOS library [15]. Radi-

ation transport within the plasma was treated using multi-groupdiffusion techniques with 100 bins spanning photon energies

between 1 and 3 KeV. Heat conduction was simulated using the

conductivities of Lee and More [16]. The electron flux limiter was

set to a value of 0.05 though, at our relatively small laser fluxes, this

parameter is not critical.

Simulated electron density maps of the copper plasma are

shown in Fig. 6. The density distribution in the focal region is in

very good agreement with the density build up seen in the soft

X-ray interferometer maps. However, the opacities used in HYDRA

are not accurate for the plasma conditions in the shock. Best

agreement with the experiment is observed when radiation is

turned off at 1 ns. In this case, the simulations reproduce well the

plasma evolution including the density within the shock region

(w

6 10

18

cm

3

for Cu at 20 ns after the laser irradiation).

The origin of the shock formation is well illustrated by the

computedmap of plasmavelocity vectors shown in Fig. 7. The shock

arises when the plasma that originated from the groove, after

having converged on axis, expands and collides with the plasma

that originated from ablation of the flat target wall surrounding the

groove. The collision re-directs the velocity of the side plasma to

follow the contour of the central expanding plasma producinga localized increase in plasma density, temperature and degree of

ionization. The continuous arrival of material creates a quasi-

stationary shock wave [17]. Fig. 8 shows the computed temperature

and mean degree of ionization distribution maps of the Cu plasma

at 20 ns in its evolution. The maps show that in the shocked region

the electron temperature increases by about 50 percent (w4 eV)

and that the degree of ionization also increases. Computation of the

ionion collision mean-free path following Braginskii [18] gives

a value always less than 1 mm, significantly smaller than the width

of the shock, an indication that this is a collisional shock.

Simulations for the Cu plasma show that when the flat wall

surrounding the semi-cylindrical groove is not directly irradiated

by the laser or by the plasma self-emission the arc-shaped shock

does not develop. The shock is strongest when both types of

Fig. 5. Sequence of interferograms and density maps for a C plasma. The density scale is logarithmic. The main observed difference respect to the Cu plasma in Fig. 3 is a faster

evolution.



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irradiation are present. Simulations show that in the case of the

heavier targets plasma radiation plays a role in ablating the front

wall material, which contributes to the shock formation. In

contrast, simulations performed for C plasmas reveal that radiation

does not contribute tothe ablation of the front wall.In any case, it is

the continued ablation of the wall by either radiation or heat

conduction that sustains the shocks for several tens ofnanoseconds.

Comparison of the evolution of plasmas from the different

materials shows that the main difference between them is the

slower dynamics of the heavier element plasmas, resulting from

their larger mass. Simulations for C and Cu plasmas show that close

to the target wall the initial temperatures and pressures are similar,

but the difference in mass causes the C plasma to evolve more

rapidly. For C the shock is first seen to form a few ns after laser

irradiation and to reach its peak electron density at 10 ns. The

computed temperatures at 5 ns and 10 ns are 14 eV and 5 eV and

the degrees of ionization are Z 4 and Z 2.5, respectively. In

contrast, the Cu shock is observed to develop later, and to reach its

peak density atw35 ns where the electron temperature is 6 eV and

the degree of ionization is Z 4. The peak temperature, 15 eV,

Fig. 6. Simulated electron density maps of Cu plasma at times corresponding to the experimental data of Fig. 4. The density scale is logarithmic.

Fig. 7. Velocity vector field map at 20 ns in the evolution of the copper plasma. The

arrow colors assist in visualizing the magnitude of the velocity.



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occurs at 8 ns when the degree of ionization is Z 8. The slowerevolution of the plasma corresponding to the heavier target

materials was observed to result in increased shock lifetimes:

w40 ns for C,w50 ns for Al,w70 ns for Cu and w90 ns for Ag.

5. Conclusions

The dynamics of plasma collisions and shock generation created

by short pulse (120 ps) laser irradiation ( Iz1 1012 W cm2) of

semi-cylindrical cavities machined into flat C, Al, Cu and Ag slab

targets were studied combining visible and soft X-ray interferom-

etry with hydrodynamic simulations. Measured and computed

electron density maps agree well in describing the evolution of the

plasma. Theconvergence of material ablated from thewallsnear the

axis results in a plasma collision that forms a dense bright plasma

focus,which reaches an electron density ofw1 1020 cm3. Later in

time, a quasi-stationary bow shock is observed to develop as a result

of the collision between the expanding central plasma and plasma

generated by ablation of the flat walls that surround the semi-

cylindrical groove. The shock,that is collisional in nature, reaches in

theCu plasmas a peak measured electron density ofw6 1018 cm3

and at that time is characterized by an electron temperature of 6 eV

and a degree of ionization of Z 4. The shocks are sustained for

several tens of nanoseconds by the continuous arrival of plasma

from the target walls. The slower dynamics of the plasmas corre-

sponding to the heavier materials results in an increasedpersistence

of the shocks, that in Ag are observed to last forw90 ns.

Acknowledgments

The authors would like to thank M. Marinak for helpful

discussions regarding the HYDRA simulations. This research was

sponsored by the National Nuclear Security Administration under

the Stewardship Science Academic Alliances program through U.S.

Department of Energy Research Grant #DE-FG52-06NA26152,

using facilities from the NSF ERC Center for Extreme Ultraviolet

Science and Technology, award EEC-0310717. Part of this work was

performed under the auspices of the U.S. Department of Energy by

Lawrence Livermore National Laboratory under contract DE-AC52-

07NA27344. The work of M. Purvis was partially supported by

a fellowship from the Institute for Laser Science Applications.

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evolution of the Cu plasma.


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Jorge Filevich et al- Bow shocks formed by plasma collisions in laser irradiated semi-cylindrical cavities