The formation of reverse shocks in magnetized high energy ......The formation of reverse shocks in...

The formation of reverse shocks in magnetized high energy density supersonicplasma flowsa)S. V. Lebedev, L. Suttle, G. F. Swadling, M. Bennett, S. N. Bland, G. C. Burdiak, D. Burgess, J. P. Chittenden,

A. Ciardi, A. Clemens, P. de Grouchy, G. N. Hall, J. D. Hare, N. Kalmoni, N. Niasse, S. Patankar, L. Sheng, R.

A. Smith, F. Suzuki-Vidal, J. Yuan, A. Frank, E. G. Blackman, and R. P. Drake

Citation: Physics of Plasmas (1994-present) 21, 056305 (2014); doi: 10.1063/1.4874334 View online: http://dx.doi.org/10.1063/1.4874334 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/21/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A comparison of planar, laser-induced fluorescence, and high-sensitivity interferometry techniques for gas-puffnozzle density measurementsa) Rev. Sci. Instrum. 79, 10E717 (2008); 10.1063/1.2979871 Highly resolved measurements of defect evolution under heated-and-shocked conditionsa) Phys. Plasmas 14, 056314 (2007); 10.1063/1.2720799 The evolution of magnetic tower jets in the laboratorya) Phys. Plasmas 14, 056501 (2007); 10.1063/1.2436479 Dynamic hohlraum radiation hydrodynamicsa) Phys. Plasmas 13, 056301 (2006); 10.1063/1.2177640 Steady supersonically rotating plasmas in the Maryland Centrifugal Experimenta) Phys. Plasmas 12, 055704 (2005); 10.1063/1.1896954

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The formation of reverse shocks in magnetized highenergy density supersonic plasma flowsa)

S. V. Lebedev,1,b) L. Suttle,1 G. F. Swadling,1 M. Bennett,1 S. N. Bland,1 G. C. Burdiak,1

D. Burgess,2 J. P. Chittenden,1 A. Ciardi,3 A. Clemens,2 P. de Grouchy,1 G. N. Hall,1,c)

J. D. Hare,1 N. Kalmoni,1 N. Niasse,1 S. Patankar,1 L. Sheng,1,4 R. A. Smith,1

F. Suzuki-Vidal,1 J. Yuan,1,5 A. Frank,6 E. G. Blackman,6 and R. P. Drake71Blackett Laboratory, Imperial College, London SW7 2BW, United Kingdom2Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London, London E1 4NS,United Kingdom3LERMA, Observatoire de Paris and �Ecole Normale Sup�erieure Universit�e Pierre et Marie Curie,UMR 8112 CNRS, 75231 Paris, France4Northwest Institute of Nuclear Technology, Xi’an 710024, China5Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China6Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA7University of Michigan, Ann Arbor, Michigan 48109, USA

(Received 28 November 2013; accepted 25 February 2014; published online 1 May 2014)

A new experimental platform was developed, based on the use of supersonic plasma flow from the

ablation stage of an inverse wire array z-pinch, for studies of shocks in magnetized high energy

density physics plasmas in a well-defined and diagnosable 1-D interaction geometry. The

mechanism of flow generation ensures that the plasma flow (ReM� 50, MS� 5, MA� 8,Vflow� 100 km/s) has a frozen-in magnetic field at a level sufficient to affect shocks formed by itsinteraction with obstacles. It is found that in addition to the expected accumulation of stagnated

plasma in a thin layer at the surface of a planar obstacle, the presence of the magnetic field leads to

the formation of an additional detached density jump in the upstream plasma, at a distance of �c/xpifrom the obstacle. Analysis of the data obtained with Thomson scattering, interferometry, and local

magnetic probes suggests that the sub-shock develops due to the pile-up of the magnetic flux

advected by the plasma flow. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4874334]

I. INTRODUCTION

The collision of a supersonic plasma flow with an obsta-

cle can lead to the formation of a reverse shock in the flow

with the structure depending on many parameters—including

the degree of flow collisionality, radiative cooling of the

post-shock plasma, and the dynamic importance of magnetic

fields frozen into the plasma. Shocks formed by supersonic

plasma flows are ubiquitous in astrophysics and include

accretion shocks,1 internal shocks in astrophysical jets,2 and

more locally in the interaction of the solar wind with space-

craft and planets.3–5 Shocks are also of interest in inertial

confinement fusion (ICF) research, such as those produced

by ablated material in laser driven hohlraums and in z-

pinches.6–8 An understanding of the dynamics of reverse

shock formation and of their properties is far from complete

despite considerable computational, observational, and ex-

perimental efforts. This is particularly true in relation to

shocks in magnetized, high energy density physics (HEDP)

plasmas, where a pile-up of the magnetic field could affect

plasma compressibility and the shock structure, and are

therefore of interest for scalable studies of astrophysical phe-

nomena9 and ICF.

In this paper, we describe and present data from a new

experimental platform designed to study magnetized shocks

formed at HED using the ablation flow produced by an

inverse wire array z-pinch. The plasma flow is produced by

the ablation of fine metallic wires driven by a MA level elec-

tric current pulse, which introduces a strong (�1–2 T) mag-netic field, embedded into and advected by the flow and

sustained for the duration of the experiment (�250 ns). Thecollision of the plasma flow with a conducting (metallic) ob-

stacle leads to the formation of a reverse shock in a configu-

ration which allows good diagnostic access for detailed

studies of the formation, evolution, and properties of the

shock.

The experiments show that in addition to the expected

accumulation of stagnated plasma in a thin layer slowly

expanding from the surface of the obstacle, an additional

detached density jump is formed in the upstream plasma

flow ahead of the stagnated plasma. This additional sub-

shock is first detected at a distance of �c/xpi from the obsta-cle, and remains almost stationary for the duration of the

experiment. Initially, at the time of formation, both the den-

sity and flow velocity jumps in the sub-shock are relatively

small ( 5)of the upstream flow. Later in time, the measurements by the

Thomson scattering (TS) diagnostic show a larger (factor of

�3.5) jump in the flow velocity at the sub-shock, while stillno significant heating of the plasma is observed. The analysis

of the experimental data suggests that the sub-shock

a)Paper BI3 6, Bull. Am. Phys. Soc. 58, 25 (2013).b)Invited speaker. E-mail addresses: [email protected] and

[email protected])Present address: Lawrence Livermore National Laboratory, California

94550, USA.

1070-664X/2014/21(5)/056305/10/$30.00 VC 2014 AIP Publishing LLC21, 056305-1

PHYSICS OF PLASMAS 21, 056305 (2014)


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http://dx.doi.org/10.1063/1.4874334http://dx.doi.org/10.1063/1.4874334mailto:[email protected]:[email protected]://crossmark.crossref.org/dialog/?doi=10.1063/1.4874334&domain=pdf&date_stamp=2014-05-01

develops as a result of evolution of a magnetic precursor,

due to the pile-up of the magnetic flux which is frozen into

the plasma electrons and advected by the plasma flow.

The paper is organized as follows. Section II describes

an inverse wire array z-pinch configuration used for the for-

mation of supersonic plasma flow, and the experimental

setup used to diagnose this. Section III presents the experi-

mental results; included here are a description of the parame-

ters of the undisturbed plasma flow used in these

experiments, the formation of a sub-shock structure in the

reverse shock produced by the interaction of the flow with a

planar obstacle, and the late time evolution of the sub-shock.

Section IV discusses the results obtained with particular

focus on the balance between the flow ram pressure and the

magnetic field pressure. Section V presents conclusions.

II. EXPERIMENTAL SETUP AND DIAGNOSTICS

The experimental set-up used to study the interaction of

the magnetized supersonic plasma flow with a planar con-

ducting obstacle is shown in Fig. 1. The plasma flow is pro-

duced by the ablation of thin metallic (Al) wires driven by a

1.4 MA, 250 ns current pulse at the MAGPIE pulsed power

facility.10 The wires are arranged to form an inverse wire

array z-pinch,11 where the current is applied through a cen-

tral (cathode) electrode and then returns through the sur-

rounding array of wires, which are positioned coaxially with

the central electrode. The formation of the ablated flow in

this configuration is similar to that of a standard imploding

cylindrical wire array;12 however, in this inverse setup the

J�B force drives the ablated plasma radially outwards intothe external region which is initially free from magnetic

field. The ablated plasma is accelerated to velocity of

�1� 107 cm/s in the close vicinity of the wires (inside thefirst �1–2 mm), and then propagates with almost constantvelocity. The plasma flow is expected to possess a frozen-in

magnetic field, the advection of the magnetic field having

been observed previously in standard wire arrays,13–15

although not measured for inverse arrays prior to these

experiments. The wire arrays used here consist of 16 Al

wires, each 40 lm in diameter and 15 mm in length, andpositioned on a diameter of 20 mm coaxially with the central

(8 mm diameter) electrode (Figs. 1(a) and 1(b)).

To create a planar flow for the interaction, the wires

were arranged in pairs so that the distance between the wires

in each pair was slightly smaller than the average inter-wire

separation (an angular separation of 20� for the pair insteadof 2p/N¼ 22.5�). This increased proximity acts to magneti-cally focus the flow from the adjacent wires, and the interac-

tion between the two plasma streams creates two standing

oblique shocks, between which the flow is essentially planar.

The resulting flow then interacts with a planar, 5 or 10 mm

wide, 10 mm tall, and 15 lm thick Al foil, installed perpen-dicular to the flow at a distance of 10 mm from the wires.

For this foil position, the flow reaches the obstacle �100 nsafter the start of the driving current. The rate of mass injec-

tion into the flow is determined by the ablation rate of the

wires, which is described with reasonable accuracy by the

“rocket” ablation model,12 giving an ablation rate dm/dt/ I2,where I¼ 1.4� 106 sin2(pt/500 ns) is a good approximationof current applied to the wire array. For the rising current

pulse (first 250 ns experimental time), the mass density in the

flow increases with time and the spatial distribution of mass

density for a fixed moment in time can be found using the

ablation rate and taking into account the time-of-flight deter-

mined by the flow velocity.11,16

The collision of the plasma flow with an obstacle leads to

accumulation of material in front of the foil and the formation

of a reverse shock in the incoming plasma. The high degree of

azimuthal symmetry of the system and the formation of eight

nominally identical plasma flows allows several obstacles to

be used simultaneously to create additional interaction regions

to maximize the amount of information that can be collected

by different diagnostics in each experiment. This also allows

parameters of undisturbed plasma flow to be measured in the

same experiment, as illustrated in Fig. 1(b).

A number of complementary diagnostics were used to

study the interaction of the flow with the obstacle. Gated

multi-frame cameras were used to obtain time-resolved

images of the interaction region and follow the temporal evo-

lution of the shocks. An optical gated camera (12 frames

with 5 ns exposure time and 10 or 20 ns inter-frame separa-

tion) imaged the interaction from the end-on (z) direction,

while the extreme ultraviolet (XUV) camera17 (photon

energy >30 eV, 4 frames gated at 2 ns with 10 ns or 30 nsinter-frame separation) recorded side-on images. Laser prob-

ing (532 and 355 nm, 0.3 ns) of the interaction region was

performed in side-on and end-on directions using interferom-

etry and shadow channels. Details on the interferometer

FIG. 1. (a) Side-on and (b) end-on views of the experimental setup and the

diagnostics. (c) The ion feature of the TS spectra measured in the upstream

plasma. kTS is the Doppler-shifted wavelength of the spectrum and k0 is thatof superimposed stray light at the original wavelength.

056305-2 Lebedev et al. Phys. Plasmas 21, 056305 (2014)


155.198.208.245 On: Thu, 01 May 2014 12:29:46

set-up and of the analysis technique used to obtain electron

density distributions from the interferograms can be found in

Ref. 18. The magnetic field in the plasma flow was measured

using pairs of identical, overlapped, inductive probes with a

loop area of 2.7mm2 (1.55 � 1.75 mm) and which werewound in opposite directions. The probes were shielded by a

thin layer of conductive paint to suppress possible electro-

static noise from variations of the plasma potential, and sig-

nals from each probe were recorded separately.

A TS diagnostic15 was used to measure the plasma flow

velocity and plasma temperature using the ion feature of the

scattering spectra. For the parameters of the plasma in these

experiments (Te� 20 eV, ne� 5� 1017�2� 1018 cm�3), theTS diagnostic operates in the collective scattering regime,19

with a scattering parameter a¼1.5–4. In most of the experi-ments, the focused probing laser beam (532 nm, 5 ns

FWHM, 3 J, �200 lm spot size) propagated through thecentre of the array as shown in Fig. 1(b). The beam propa-

gated through a small hole of �1 mm diameter in the middleof the obstacle foil and through a hole in the central elec-

trode, or, in some of the experiments, in the opposite direc-

tion through the electrode towards the obstacle. A different

probing direction was also used in early experiments, with

the laser beam passing next to the central electrode in the

direction towards the foil. In all cases, the scattered signal

was observed in the r-h plane, in the directions parallel to thefoil surface (Fig. 1(b)). Several spectra corresponding to dif-

ferent spatial positions along the probing laser beam were

obtained using fiber optic bundles with 7 or 14 fibers

(200 lm or 100 lm diameter, respectively), which deliveredscattered light to the input of a 0.5 m ANDOR SHAMROK

imaging spectrometer, coupled with an ANDOR intensified

charge-coupled device (ICCD) camera which provided a gat-

ing time of 4 ns. The spectral resolution was determined by

the size of the optical fibers used (100 or 200 lm) and for the2400 g/mm grating used in these experiments was equal to

0.25 A or 0.45 A, respectively.

III. EXPERIMENTAL RESULTS

A. Overview of the flow-obstacle interaction

We begin presentation of the experimental results by

describing the overall structure developing during the inter-

action between the plasma flow and the obstacle. Fig. 2

shows typical laser probing images of the interaction region

obtained using the perpendicular, side-on probing direction.

These images were obtained at t � 260 ns after the start ofthe current and correspond to a late phase of the interaction,

when all the observed features are well defined. The first fea-

ture observed to form is a dense thin layer of plasma at the

surface of the foil, which at the time of this image is

�0.7 mm thick (Figs. 2(a) and 2(c)). Measurements per-formed at different times and with different diagnostics

(laser probing, optical and XUV imaging) show that this

layer becomes observable from �90–100 ns after the start ofthe current and expands with a constant velocity of

�4� 105 cm/s. The delay between the appearance of thestagnated plasma at the obstacle and the start of the driving

current agrees well with the time-of-flight needed for the

plasma flow to reach the obstacle. The stagnation layer has a

sharp density jump and the initial rise of the electron density

is observable by the interferometry. There is also an increase

in intensity of XUV emission and an increase in the ioniza-

tion state of Al ions, as observed by spatially and temporally

resolved XUV spectroscopy, indicating a temperature

increase. The details of the measurements of the properties

of this stagnation shock will be published separately.

The most prominent feature seen in the images is a

detached, shock-like structure (which we refer to as a “sub-

shock”) formed upstream from the obstacle and positioned at

this time at a distance of �3.5 mm from the obstacle surface.Analysis of the interferogram using the procedure described

in Ref. 18, yields a map of electron line density (neL) which

is shown in Fig. 2(b). From this density map it is seen that

the increase of the density at the sub-shock is relatively

FIG. 2. Formation of a sub-shock during the collision of the plasma flow with a planar Al foil obstacle: (a) the side-on 532 nm interferometry recorded at

t¼ 257 ns, (b) the corresponding map of line-integrated electron density (neL), there “0” of the horizontal scale corresponds to obstacle surface, (c) side-onshadow image obtained under the same conditions and a pre-shot image (d). In all images the plasma flow is from left to right, with the foil obstacle at 10 mm

from the ablating wires.



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small: not more than a factor of �2, while the shape of theinterference fringes in Fig. 2(a) gives an apparent width of

the density jump of �0.4 mm. The actual width of the den-sity jump is smaller as due to the presence of a small curva-

ture in the sub-shock (in the r-h plane), which is seen in theend-on images at late times, and is responsible for the over-

estimation of the width of the transition as measured by the

interferometry. The shadow laser probing images (Figs. 2(c)

and 2(d)), which are sensitive to the electron density gra-

dients, suggest that the width of the sub-shock is indeed

��0.1 mm.The rest of Sec. III describes the formation, properties,

and the evolution of the sub-shock, starting from the descrip-

tion of the parameters of the undisturbed plasma flow collid-

ing with the obstacle.

B. Parameters of the upstream plasma flow

The parameters of the plasma in the upstream flow were

determined by comparing the measurements obtained with

and without the obstacle present. Such measurements were

performed either in the same experiment using flows pro-

duced by different pairs of wires of the inverse wire array (as

illustrated in Fig. 1(b)) or in different experiments using the

observed high symmetry and reproducibility of the plasma

flow generation. These measurements show that the plasma

flow parameters in the upstream region are not affected by

the presence of the obstacle, as is expected for a supersonic

flow. The density distribution was measured using side-on

interferometry images similar to that shown in Fig. 2(a), and

also using end-on interferometry images discussed later in

the paper. These measurements show that for the times rele-

vant to the experiments described in this paper the electron

density at positions just upstream of the sub-shock is in the

range of 4� 1017 cm�3 (for t� 180 ns with the foil at 10 mmfrom the wires) to 2� 1018 cm�3 (for t� 250 ns with the foilat 7 mm from the wires).

The velocity of the plasma flow and the product ZTewere measured using the Thomson scattering diagnostic and

Fig. 1(c) shows a typical TS spectra. The Doppler shift of the

ion feature provides measurements of the plasma flow

velocity, which for the upstream flow is equal to

Vfl¼ 1.1� 107 cm/s at early times (�180 ns), decreasing to0.9� 107 cm/s later (at �250 ns). The shape of the TS spec-tra shows the well-separated ion-acoustic peaks, which indi-

cates that ZTe is much greater than the ion temperature Ti,19

with the fitting of the theoretical scattering form-factor yield-

ing ZTe¼ 60 eV for the upstream plasma flow. The ionsound speed calculated using this value of ZTe is equal to

Cs¼ (cZkBTe/mi)1/2� 2� 106 cm/s, giving the sonic Machnumber of the upstream plasma Ms¼ 5. Simultaneous meas-urements of velocity in the interaction region and in an

unperturbed flow on the opposite side of the array (pre-

formed as shown in Fig. 1) show that the presence of the ob-

stacle only changes the flow parameters at positions close to

the foil surface, but does not change Vfl and ZTe upstream of

the sub-shock. In some of the experiments, the TS spectra

were recorded simultaneously from two opposite (690�)directions to the probing beam, which allowed the full

velocity vector to be determined in the r-h plane (similar tothat discussed in Ref. 20). These measurements show that in

the region of the plasma flow between the two standing

oblique shocks (Fig. 1), the plasma velocity direction is nor-

mal to the obstacle, and that the velocity component in the

direction parallel to the obstacle surface is negligible

(

the probe signals (dB/dt) in the absence of the obstacle

repeats the shape of the derivative of the driving current

(dI/dt), which is consistent with the advection of the mag-

netic field by the plasma flow, as would be expected for

plasma flow with a magnetic Reynolds number (ReM) larger

than unity. Indeed, for the measured parameters of the

upstream plasma (Vflow¼ 107 cm/s, ZTe¼ 60 eV) and a char-acteristic spatial scale of the distance between the wires and

the obstacle (10 mm), the magnetic Reynolds number is suf-

ficiently large, ReM� 50–100.Comparison of the probe signals obtained both with and

without the obstacle (Fig. 3) show that they behave identi-

cally until �175 ns. After that, which agrees well with thetime when the sub-shock is first detected, a larger magnetic

field is observed with the obstacle present. We should how-

ever emphasise that the magnetic probe measurements do

not provide quantitative information on the field strength

behind the sub-shock due to the relatively large size of the

probes which is comparable to the distance between the sub-

shock and the obstacle.

Integration of the dB/dt signals yields the magnetic field

evolution (Fig. 3(c)), showing that at the time of the sub-

shock formation at t� 170 ns the field magnitude reaches�1 T. (We note here that while the probes are designed tominimize possible perturbations to the flow and to the meas-

urements of the upstream magnetic field, it is difficult to

fully exclude possibility of this from the probe measure-

ments alone. However, recently performed measurements24

with Faraday rotation technique show the same upstream

magnetic field as measured by the probes, thus suggesting

that these perturbations are relatively small.) Using this

value of the magnetic field, and estimating the mass density

of the flow from the measured upstream electron density and

the measured ZTe¼ 60 eV (corresponding for Al to an aver-age ionisation of Z� 4 and T� 15 eV), we can estimate theAlfv�en velocity as VA� 1� 106 cm/s. Thus, we can con-clude that the upstream plasma flow is both supersonic

(Ms� 5) and super-Alfv�enic (MA¼Vfl/VA� 8), and the flowis supersonic with respect to the fast magneto-sonic speed

(VMS¼ (Cs2þVA2)1/2), with MMS¼Vfl/VMS� 4.5.The presented characterisation of the upstream flow pa-

rameters shows that the sub-structure in the reverse shock

observed in these experiments is formed as a result of the

interaction of a super-magnetosonic flow with the obstacle.

The level of magnetic field advected by the flow is relatively

small, in the sense that the ram pressure of the flow is signifi-

cantly larger that the magnetic field pressure

(qV2/(B2/8p)� 100), though the thermal plasma beta of theflow is not large (bth� 3).

C. Formation of the sub-shock

Fig. 4 shows typical images of the flow-obstacle interac-

tion observed by end-on diagnostics. The optical image in

Fig. 4(a) obtained at t¼ 210 ns after the current start showsthe plasma streams from a pair of ablating wires and the two

standing oblique shocks indicated in Fig. 1, which are analo-

gous to the oblique shocks observed in standard Al wire

arrays.18 Strong optical emission is also seen from a thin

layer positioned immediately at the foil surface. The thick-

ness of this layer increases in time with a constant velocity

of only 4� 105 cm/s, starting from zero at t¼ 90 ns when thefirst plasma arrives at the obstacle, and reaching �0.6 mm att¼ 230 ns after the current start. Laser probing images (Fig.4(b)) also show a narrow opaque region of the same thick-

ness in front of the foil surface, and the formation of this

layer is consistent with the accumulation of stagnated plasma

at the foil.

The additional shock-like feature, the sub-shock, is seen

upstream from the stagnation layer at a distance �2 mm fromthe foil. The optical camera images show that this feature

becomes detectable at t¼ 170 ns as a region of enhancedemission, which expands with a speed of �1�1.5� 106 cm/s(�10%�15% of upstream flow velocity), reaching a position�3 mm from the foil at t¼ 250 ns. Fig. 4(b) shows an inter-ferogram obtained at t¼ 225 ns using probing in the end-ondirection. Tracing the positions of interference fringes and

comparing them with the fringe positions recorded before the

experiment allows the distribution of the electron density to

be reconstructed following the procedure described in Ref. 18.

The resulting electron density map (Fig. 4(c)) shows that the

density inside the two oblique shocks is fairly uniform in the

direction parallel to the foil, which is consistent with the 1-D

character of the flow. The density map shows an increase of

the electron density at �2 mm from the foil, at the same posi-tion where the sub-shock is seen in other diagnostics. The

FIG. 4. Experimental images showing the interaction of the plasma flow with the obstacle, including (a) end-on fast-frame optical emission, (b) end-on inter-

ferometry, and (c) the areal electron density (neL) obtained from the interferogram. In all images plasma flow is from the left, with the foil surface at the right

(“0” of the horizontal scale corresponds to obstacle surface).



155.198.208.245 On: Thu, 01 May 2014 12:29:46

electron density measured in the upstream region immediately

before the density jump is equal to 5� 1017 cm�3, and themaximum density in the downstream region directly before

the dense stagnated layer is�1.3� 1018 cm�3.Fig. 5 shows spatial profiles of the flow velocity meas-

ured with the TS diagnostic at two different times, 180 ns

and 225 ns, together with electron density profiles measured

using end-on interferometry in the same experiments at the

same times. Velocity profiles show that only a relatively

small drop in the flow velocity occurs at the sub-shock, to

about 60% of the upstream value. Thereafter, the velocity

continues to decrease reaching �30% of the upstream veloc-ity at the boundary with the dense plasma layer accumulated

at the foil surface. The electron density profiles show that

there is only a small electron density increase at the sub-

shock, of not more than a factor of �2 in. comparison to theupstream density, and the data show a steepening of the elec-

tron density profiles with time (Fig. 5).

We should note here that the interferometry provides

density averaged along the probing path, and it is possible

that due to the presence of a small curvature of the sub-

shock in the r-z plane the density immediately after the sub-

shock could be slightly higher, with the thickness of the

transition being slightly smaller. In contrast, the Thomson

scattering provides local measurements of the flow velocity,

and is thus a better indicator of the flow behaviour at the

sub-shock.

It is instructive to compare the measured electron den-

sity profiles ne(x) with mass density distributions which can

be estimated using the measured velocity profiles. For a

steady flow with time-independent density in the upstream

flow, the mass density should be inversely proportional to

the flow velocity, such that q(x)� 1/Vfl(x). Density profilescalculated in this way are shown in Figs. 5(b) and 5(d). For

the temporally increasing density of the flow, this estimate

represents the upper limit for the mass density profile.

Comparison of the electron and mass density profiles indi-

cates there could be some small increase in the average

plasma ionization at the sub-shock (due to the divergence of

their profiles in the flow immediately downstream). This is

consistent with the results of the TS measurements, which

show only a small increase in ZTe, from �60 eV in theupstream flow to �110 eV immediately after the sub-shock,decreasing to �90 eV at the boundary with the dense stag-nated layer. The TS data also do not show a measurable

increase of the ion temperature, the ion-acoustic peaks

remain well separated meaning that Ti remains much smaller

than ZTe. The absence of measurable heating of the ions will

be discussed in more detail later in Sec. III D.

These results, the small level of velocity and density

jumps at the sub-shock together with only a small tempera-

ture increase, suggest that this feature cannot be explained as

a “standard” shock formed by a high Mach number flow

(MMS� 5) which should produce a much larger jump of �4(or higher if the effective adiabatic index c is smaller than5/3). Instead, we interpret the observed global structure of

the interaction region as the development of a sub-shock at

the front edge of a magnetic precursor created by the pile-up

of the magnetic flux, advected by the flow towards the obsta-

cle. Stagnation of the plasma flow containing a frozen-in

magnetic flux creates (in the reference frame of the obstacle)

a motional electric field E¼�V2�B2 which drives an elec-tric current on the surface of the obstacle (Fig. 6). The corre-

sponding perturbation of the magnetic field in the plasma

(field pile-up) acts differently on the electrons and ions of

the flow. At a spatial scale of the order of the ion inertial

length c/xpi the ion and electron responses decouple and theperturbation of the electron pressure could propagate ahead

of the stagnation shock, e.g., as a whistler mode,21 creating a

magnetic precursor and ultimately leading to the formation

FIG. 5. Plasma flow velocity profiles measured from Thomson scattering at (a) t¼ 180 ns and (c) 225 ns, as well as profiles of electron density (interferometry)and relative mass density calculated from the velocity profiles at these times (b) and (d). The sub-shock is at xs� 2 mm from the obstacle (at x¼ 0).



155.198.208.245 On: Thu, 01 May 2014 12:29:46

of a cross-shock electric field which would decelerate the

ions. The distance between the sub-shock and the stagnated

layer (�1.5 mm) at the time when it becomes detectable isindeed very close to the c/xpi� 1 mm. The observed reduc-tion in the flow velocity (V/Vfl� 1/2 at the sub-shock) corre-sponds to the presence of the decelerating potential of

Du� 3/4Ei/(eZ)� 300 V. The presence of an electric poten-tial at the sub-shock is consistent with detection of reflected

ions, which are observed by Thomson scattering (Fig. 5(a)),

showing the reflected ions as an additional oppositely shifted

feature in the scattering spectra. The reflected ions are only

seen in the upstream flow immediately in front of the

sub-shock, and not between the sub-shock and the stagnation

plasma layer. The average velocity of these reflected ions is

the same as that in the incoming flow (Fig. 5(a)), which is

consistent with reflection by the electric potential. The

reflected ions are only observed at the time just after the

sub-shock formation, and are not seen at later times, suggest-

ing that the reflection is a transient phenomenon accompany-

ing formation of the potential, but further investigation is

needed here.

D. Parameters of the sub-shock at late time

The experiments show that the sub-shock formed ahead

of the obstacle retains its overall structure for the duration of

the experiment, which is at least �150 ns after it is firstformed. Side-on XUV images in Fig. 7 obtained in two dif-

ferent experiments at t� 170 ns and t� 270 ns after the cur-rent start show that the sub-shock remains uniform and keeps

the same shape, but the distance from the obstacle gradually

increases with time at a speed of 1.5� 106 cm/s (�15% ofthe flow velocity). It is seen that at later time the intensity of

emission becomes more concentrated at the sub-shock front,

with a more pronounced decrease towards the obstacle sur-

face. The apparent steepening of the sub-shock is seen by

several diagnostics, but the most accurate and detailed meas-

urements of the sub-shock parameters are provided by the

Thomson scattering diagnostic.

Fig. 8 shows results from TS measurements obtained at

t¼ 216 ns after the current start for an obstacle positioned at7 mm from the wires. The smaller distance between the wires

and the obstacle did not affect the sub-shock formation and

evolution, but in comparing the measurements obtained for

the two different positions of the obstacle one needs to take

into account that the closer position of the obstacle effec-

tively corresponds to the later stages of the sub-shock evolu-

tion, approximately equivalent to a time-of-flight delay of

�0.3 cm/107cm/s¼ 30 ns.The image in Fig. 8(a) represents the raw TS data from

14 spatial positions along the probing laser beam, which

propagates in the flow direction, perpendicular to the obsta-

cle surface (as illustrated in Fig. 1(b)). Accompanying the

raw data are the corresponding spectral fits for the scattered

FIG. 6. A cartoon illustrating the formation of the sub-shock. The motional

electric field drives the current (��V2 � B2) along the conducting obstaclesurface and some fraction of it closes at the edges of the plasma flow, creat-

ing a region of enhanced magnetic field (magnetic precursor) between the

obstacle and the sub-shock (which is formed at a distance of �c/xpi).

FIG. 7. XUV images obtained in two different experiments showing the

temporal evolution of the sub-shock. The edge wire of the array is seen at

the left boundary of the images, with the obstacle foil positioned at a dis-

tance of 10 mm from this and visible on the right. The first image (177 ns)

corresponds to the time close to the sub-shock formation time. The two other

images show the propagation of the sub-shock.

FIG. 8. Data from the Thomson scattering diagnostic. (a) The scattered spec-

trum obtained for 14 spatial positions covering a length of �4 mm along thedirection perpendicular to the obstacle surface, from the foil (top) towards

the wires. The four spectra at the bottom correspond to the upstream flow.

(b) The ion feature of the Thomson scattering spectra measured in the

upstream flow and (c) after the sub-shock. The Doppler shift of the spectra

provides measurement of the flow velocity, while the fit to the scattering

form-factor provides measurement of ZTe.



155.198.208.245 On: Thu, 01 May 2014 12:29:46

signals recorded at positions upstream and downstream of

the sub-shock (Fig. 8(b)).

The spatial profile of the flow velocity obtained from the

Doppler shift of the scattering spectra is shown in Fig. 9(a).

It is seen that at this late time the velocity reduction across

the sub-shock has increased to a factor of �3.4, which is sig-nificantly larger than the jump of only �2 observed for theearlier times. Such larger velocity jumps of �3.5�4 werereproducibly measured in all experiments corresponding to

the late stages of the sub-shock evolution, and could, on a

first glance, be interpreted as an evidence of the development

of a strong shock. The distribution of the average electron

density measured with the end-on interferometry in the same

experiment (Fig. 9(b)), with ne determined by dividing the

measured neL by the height of the shock, does not show a

large density jump. This is, however, primarily due to the

presence of a curvature of the sub-shock front in the r-z

plane, which leads to a significant underestimation of the

electron density immediately (inside the first �1 mm) afterthe sub-shock. Finding the local electron density distribution

from the neL measurements could be potentially possible by

combining the side-on and end-on interferometry measure-

ments, but this has not yet been attempted here.

Another way to obtain information about the local den-

sity distribution is by using the measured relative total

intensities of the TS signals (integrated over wavelength)

and Fig. 9(b) shows the corresponding spatial profile

obtained from the scattering spectra shown in Fig. 8. It is

seen that the TS intensity distribution has an abrupt increase

by a factor of �3.5 at the position of the sub-shock. At thesame position the velocity decreases by approximately

the same factor. To discuss a possible relation between the

measured TS intensity and the density distribution, it is in-

structive to compare the TS intensity profile with the

expected mass density distribution, which can be calculated

using the measured velocity profile. For a shock formed by a

steady (time-independent) flow, the mass density distribution

would be inversely proportional to the velocity distribution

due to the mass flow continuity at the shock. In this experi-

ment the flow density is not constant in time, but is propor-

tional to the ablation rate of the wires.

Our previous experiments with both the standard and

inverse wire arrays11,12,16 show that the density distributions

are well approximated by the rocket ablation model,12 and

we will use it to find the expected mass density profiles at

the sub-shock.

The mass density q1(x,t0) in the undisturbed (upstream)flow at the time of observation t0 is proportional to

q1ðx; t0Þ /dm

dtt0 �

x

V1

� �/ I2 t0 �

x

V1

� �; (1)

where x is the distance from the ablating wire and V1 is the

flow velocity in the upstream flow, and x/V1 accounts for the

time-of-flight delay. After the sub-shock, the density changes

first due to the reduction of the flow velocity (which

increases by a factor of V1/V2), and second due to the change

in the time-of-flight delay in the post-shock flow, and is

given by

q2ðx; t0Þ /V1V2� dm

dtt0 �

xSV1� ðx� xSÞ

V2

� �; (2)

where xs is the position of the sub-shock and V2 is the flow

velocity in the downstream region, which is assumed con-

stant following the measurements shown in Fig. 9(a).

The expected relative mass density distribution, deter-

mined using Eqs. (1) and (2) with the measured V1 and V2(from TS) and the shape of the driving current I(t), is shown

in Fig. 9(b), together with the relative profile of the TS inten-

sity. It is seen that the two profiles show a remarkably good,

though very unexpected, agreement and possible implica-

tions of this are discussed next.

The total intensity of the ion feature of the Thomson scat-

tering signal (ITS) is given by the well-known19 expression

ITS / neZa4

1þ a2ð Þ 1þ a2 þ a2 ZTeTi� � : (3)

For the plasma parameters relevant to the measurements

shown in Figs. 8 and 9 the scattering parameter a is greaterthan unity (a� 3), so that a2 1. In addition, the shape ofthe TS signal, i.e., the presence of the well-defined

FIG. 9. Spatial profile of the flow velocity (top), determined from the analy-

sis of TS data shown in Fig. 8. Plots at the bottom show: the electron density

profile measured by end-on interferometry (green line), the mass density

profile calculated from Eqs. (1) and (2) (blue dashes), and the profile of total

intensity of the TS signal (red dots). The sub-shock is at xs� 2.7 mm fromthe obstacle positioned at x¼ 0 (7 mm from the wires in this experiment).



155.198.208.245 On: Thu, 01 May 2014 12:29:46

ion-acoustic peaks seen in both the upstream and down-

stream regions, means that the ratio ZTe/Ti 1. This allowsEq. (3) to be simplified by retaining only a2 in the firstbracket and only the last term in the second bracket, so that

the TS intensity becomes approximately equal to

ITS � neTiTe� qTi

Z

Te; (4)

where q is the mass density and Z is the average charge ofthe ions.

The observed good agreement between the measured TS

intensity profile and the calculated mass density profile thus

could be interpreted as that the ratio TiZ/Te does not change

between the upstream and the downstream flow regions.

Moreover, for the Al plasma at the conditions of our experi-

ment (ne� 1018 cm�3, Te in the range 10�50 eV), the ratioZ/Te only weakly depends on the electron temperature and

varies by less than �20%, according to calculations withPRISM-SPECT software22 for the non-LTE ionization equi-

librium. This in turn suggests that the ion temperature does

not change between the upstream and the downstream

regions. This is contrary to the expected strong heating of

the ions in a “standard” strong shock transition. For the con-

ditions of our experiment, with the Al ions moving at a ve-

locity of �107 cm/s, an ion temperature of �100 eV could beexpected immediately after a strong shock. Thomson scatter-

ing spectra shown in Fig. 8(b), however, do not show high

ion temperatures in the post sub-shock region. Indeed, a fit-

ting of the theoretical TS form-factors to the measured spec-

tra show that ZTe increases at the sub-shock from

ZTe� 60 eV in the upstream region to ZTe� 110 eV imme-diately after the sub-shock. At the same time these fittings

suggest that the ion temperature in the downstream region

remains sufficiently small (best fit at Ti� 25 eV). Anincrease of the Ti to 50 eV or 75 eV leads to a significant and

clearly observable disagreement between the measured and

theoretical TS spectra, as can be seen in Fig. 8, and we esti-

mate from the fittings that the Ti in the downstream region

does not exceed �40 eV.The observed absence of the measurable heating of the

ions in the sub-shock suggests that even at the late stages of

the evolution the main effect on the ions is produced by the

cross-shock electric potential formed by the pile-up of mag-

netic field, which decelerates the ions with very little, if any,

increase of the ion temperature. To produce the observed

jump in the flow velocity of a factor of 3.5, a larger electro-

static potential of Du� 0.9Ei/(eZ) is needed for these laterstages of the sub-shock evolution. To explain the observed

unexpectedly low ion heating, measurements of the variation

of plasma parameters across the sub-shock front with better

spatial resolution will be attempted in future experiments.

IV. DISCUSSION

The presented experimental data show the formation of

a sub-structure developing in a reverse shock produced by

the collision of a magnetized HED plasma with an obstacle,

due to the pile-up of the magnetic field advected by the flow.

This magnetic field initially acts on the electrons of the flow,

leading to the formation of a cross-shock electric potential

affecting the ions. An interesting and important issue in this

picture is the balance of the ram pressure of the incoming

flow at the sub-shock. The observed steady motion of the

sub-shock in the direction away from the obstacle means that

the post sub-shock pressure exceeds the ram pressure (qV2)of the flow. The magnetic pressure should play a key role in

the balance since the thermal pressure, calculated using the

measured post-shock plasma parameters (ZTe, ne), is an

order of magnitude too small to achieve this balance alone.

A contribution to the thermal pressure from a non-thermal

population of ions appears to be unlikely being inconsistent

with the measurements of TS spectra in the downstream

plasma. The average post-shock magnetic field Bav, arising

from the accumulation of the magnetic flux brought by the

plasma flow, can be estimated using the magnetic field B(t)

measured by probes, such that

Bav ¼Vf l

ðBðtÞdt

xs: (5)

Using the magnetic field measurements presented in

Fig. 3, Eq. (5) yields Bav� 3 T at t¼ 225 ns. An estimate ofthe ram pressure from the plasma parameters measured at

the same time (Fig. 5) suggests that in order to balance the

jump in the ram pressure, a magnetic field larger than Bav by

a factor of �2.5 is needed.The origin for this discrepancy is not understood at pres-

ent and requires further investigation; in particular additional

measurements of the magnetic field in the flow by a different

diagnostic are required. The first attempts to measure the

magnetic field distribution using a newly fielded Faraday

rotation diagnostic23,24 indeed show the presence of a 7–8 T

magnetic field in the region between the sub-shock and the

obstacle, in the immediate vicinity to the stagnated plasma at

the obstacle surface. The field in all other regions after the

sub-shock is however smaller at �4 T, which is reasonablyclose to the Bav field estimated above, while the magnetic

field in the upstream plasma is also in close agreement with

that measured by the magnetic probes. More detailed meas-

urements of the magnetic field distribution and of other

plasma parameters will be attempted in future experiments

to address this issue. In particular it will be important to

investigate the possibility of the presence of other compo-

nents of the magnetic field in the post sub-shock region, as

the present diagnostics have only been sensitive to the

B-field directed parallel to the obstacle in r-h plane (whichshould be the only component present in the laminar flow ge-

ometry of this experiment). An additional understanding

could be gained by attempting to reproduce the formation of

the sub-shock observed in these experiments using numerical

simulations. This would require at least a two-fluid MHD

model, treating the electrons and ions separately, or possibly

full Particle In Cell (PIC) simulations of the problem, per-

formed in at least a 2-D setup to model the possible current

loop (Fig. 6) in the plasma responsible for the pile-up of the

advected magnetic field.



155.198.208.245 On: Thu, 01 May 2014 12:29:46

V. CONCLUSIONS

The HEDP z-pinch driven experiment described in this

paper presents a novel and interesting platform for creating

supersonic plasma flow with an embedded and advected

magnetic field. The generated flow is both supersonic and

super-Alfv�enic, with a fast magneto-sonic Mach number of�5, and has Reynolds and magnetic Reynolds numbersmuch greater than unity. The present paper describes the use

of this platform for the study of a reverse shock formed at

the collision of the flow with an obstacle in the geometry of

a perpendicular magnetised shock. We have observed that

the flow-obstacle interaction leads to the formation of a sub-

shock positioned at a distance of �c/xpi from the obstacle,presumably at the edge of the magnetic precursor. This

sub-shock arises due to the accumulation of the magnetic

flux advected by the flow, which is believed to act directly

on electrons of the incoming flow, resulting in the develop-

ment of a cross-shock potential decelerating the ions.

Measurements with Thomson scattering and other diagnos-

tics show that the ions decelerate at the sub-shock without

being heated, which is not understood at present.

The experimental platform described in this paper can

be modified to investigate the interaction of two counter-

streaming magnetized supersonic flows. In particular it is

possible to create the colliding flows with oppositely directed

magnetic fields and use this configuration to study the mag-

netic reconnection in high beta, radiatively cooled plasma

flows.

ACKNOWLEDGMENTS

This work was supported in part by EPSRC Grant No.

EP/G001324/1 and by DOE Cooperative Agreement Nos.

DE-F03-02NA00057 and DE-SC-0001063.

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