advances.sciencemag.org/cgi/content/full/3/11/e1700982/DC1

Supplementary Materials for

Laboratory unraveling of matter accretion in young stars

Guilhem Revet, Sophia N. Chen, Rosaria Bonito, Benjamin Khiar, Evgeny Filippov, Costanza Argiroffi,

Drew P. Higginson, Salvatore Orlando, Jérôme Béard, Marius Blecher, Marco Borghesi,

Konstantin Burdonov, Dimitri Khaghani, Kealan Naughton, Henri Pépin, Oliver Portugall,

Raphael Riquier, Rafael Rodriguez, Sergei N. Ryazantsev, Igor Yu. Skobelev, Alexander Soloviev,

Oswald Willi, Sergey Pikuz, Andrea Ciardi, Julien Fuchs

Published 1 November 2017, Sci. Adv. 3, e1700982 (2017)

DOI: 10.1126/sciadv.1700982

The PDF file includes:

Supplementary Information

section S1. Astrophysical accretion modeling using the PLUTO code

section S2. Experimental diagnostics

section S3. Comparative table of the laboratory and astrophysical plasma

parameters

section S4. Temporal animation of the 2D-resolved plasma electron density

measurements of the magnetized accretion of the laboratory plasma at 20 T

section S5. Temporal animation of the 2D-resolved density and temperature

simulated maps of magnetized accretion dynamics in young stars

section S6. Experimental observations in the case of a 6- or 30-T applied

magnetic field

section S7. Laboratory 3D MHD simulations using the GORGON code

fig. S1. Sketch of the astrophysical simulation box.

fig. S2. Radiative losses per unit EM for an optically thin plasma.

fig. S3. Cartoon showing the top view of the central coil region of the

experimental setup and the diagnostics paths.

fig. S4. Shocked plasma density profiles as measured in the laboratory and

simulated at the surface of a young star.

fig. S5. Illustration of the step transition observed in the transmitted x-rays

between the target and vacuum or an ablated plasma expanding toward vacuum.

fig. S6. Results of the analysis of the x-ray radiographs.

fig. S7. Spectral response of the combined streak camera and filter set system

used in the SOP diagnostic.

fig. S8. Best fit of the x-ray spectrum measured near the obstacle (PVC target, the

stream being generated from a CF2 target) in the case of a magnetic field strength

of B = 20 T and as obtained by the PrismSPECT code in steady-state mode for an

electron temperature of 200 eV or 2.32 MK.

fig. S9. Comparison of experimental spectra (in black) recorded near the obstacle

target for the cases of 20 T (left, here the obstacle is a PVC target, whereas the

stream is generated from a CF2 target) and 6 T (right, here the obstacle is an Al

target, whereas the stream is still generated from a CF2 target) applied B field,

together with simulations (in red) of the He-like line series obtained using a

recombination plasma model.

fig. S10. The spectrum measured for an applied magnetic field of 20 T (here, the

obstacle is a PVC target, whereas the stream is generated from a CF2 target), in

the range from 14.5 to 15.4 Å and containing the Lyα line and its dielectronic

satellites.

fig. S11. Laboratory observation of magnetized accretion dynamics using a 6-T

strength for the applied magnetic field.

fig. S12. Laboratory observation of magnetized accretion dynamics for various

strengths of the applied magnetic field and using a larger distance between the

stream-source target and the obstacle.

fig. S13. 2D slices of the decimal logarithm of the electron density of the

accretion shock region at three different times for a carbon plasma.

fig. S14. 2D slices of ion and electron temperatures as well as plasma thermal beta

at t = 22 ns (that is, 12 ns after the stream impacts the obstacle).

table S1. Parameters for the MHD models of accretion impacts.

table S2. Parameters of the laboratory accretion, with respect to the ones of the

accretion stream in CTTSs for three distinct regions, namely, the incoming

stream, the score, and the shell.

table S3. Parameters, experimentally retrieved from the interferometry diagnostic,

of the jet, shell, and core in the case of an applied magnetic field of 20 T.

table S4. Parameters, experimentally retrieved from the interferometry diagnostic,

of the jet, shell, and core in the case of an applied magnetic field of 6 T.

Legends for movies S1 and S2

References (57–82)

Other Supplementary Material for this manuscript includes the following:

(available at advances.sciencemag.org/cgi/content/full/3/11/e1700982/DC1)

movie S1 (.mp4 format). An animation of the accretion dynamics recorded as a

function of time in the laboratory in the case of an applied 20-T magnetic field.

movie S2 (.mp4 format). An animation of the accretion dynamics recorded as a

function of time in the astrophysical simulation (case D5e10-B07 of table S1, that

is, as for Fig. 1D of the main text).

Supplementary Information

section S1. Astrophysical accretion modeling using the PLUTO code

fig. S1. Sketch of the astrophysical simulation box.

The stream impact is modeled in the PLUTO code by numerically solving the time-dependent

MHD equations of mass, momentum, and energy conservation, described as below in a non-

dimensional conservative form

∂ρ

∂t+ ∇ ∙ (𝜌𝒖) = 0

∂ρ𝐮

∂t+ ∇ ∙ (𝜌𝒖𝒖 − 𝑩𝑩) + ∇ ∙ 𝑃∗ = 𝜌𝒈

∂ρ𝐄

∂t+ ∇ ∙ [𝒖(𝜌𝑬 + 𝑃∗) − 𝑩(𝒖 ∙ 𝑩)] = 𝜌𝒖 ∙ 𝒈 − 𝛁 ∙ 𝑭𝒄 − 𝑛𝑒𝑛ℎ𝛬(𝑇)

∂𝐁

∂t+ ∇ ∙ (𝒖𝑩 − 𝑩𝒖) = 0

where 𝒈 is the gravity, which is set equal to zero in the present case to allow a more direct

comparison of the model results with those of our laboratory experiment, for which gravity

effects are negligible

𝑃∗ = 𝑃 +𝐵2

2 and 𝐸 = 𝜀 +

1

2𝑢2 +

1

2𝐵2

are respectively the total pressure, and the total gas energy (internal energy, ε, kinetic energy,

and magnetic energy) respectively, t is the time, 𝜌 = 𝜇𝑚𝐻𝑛𝐻 is the mass density, 𝜇 = 1.28

is the mean atomic mass (assuming metal abundances of 0.5 of the solar values (57), which

are also consistent with deductions from X-ray observations of CTTSs (50)), 𝑚𝐻 is the mass

of the hydrogen atom, 𝑛𝐻 is the hydrogen number density, u is the gas velocity, 𝑇 is the

temperature, 𝐵 is the magnetic field, 𝑭𝒄 is the conductive flux, and 𝛬(𝑇) represents the

optically thin radiative losses per unit emission measure derived with the PINTofALE spectral

code (58) with the APED V1.3 atomic line database (59), assuming the same metal

abundances stated above. The function 𝛬(𝑇) is represented in fig. S2. We use the ideal gas

law, 𝑃 = (𝛾 − 1)𝜌𝜖, where the fluid is assumed to be fully ionized with a ratio of specific

heats 𝛾 = 5/3.

table S1. Parameters for the MHD models of accretion impacts. |B0| is the initial magnetic

field strength and 𝛽𝑠𝑙𝑎𝑏 = 𝑃𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑃𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐⁄ is the average plasma β in the hot slab; the

parameters 𝑛𝑠𝑡𝑟0 and 𝑢𝑠𝑡𝑟0 are the initial density and velocity of the stream. The model used

for Fig. 1D of the main text is D5e10-B07.

Model

abbreviation

|𝐵0| [𝑇]

𝛽𝑠𝑙𝑎𝑏 𝑛𝑠𝑡𝑟0

[1011𝑐𝑚−3] 𝑢𝑠𝑡𝑟0

[𝑘𝑚 𝑠−1] D1e11-B10 1e-3 10 – 100 1 500

D1e11-B50 5e-3 1 – 10 1 500

D2e11-B14 1.4e-3 10 – 100 2 500

D5e10-B07 7e-4 10 – 100 0.5 500

In order to track the original chromospheric material (as shown in fig. S4B), we use a tracer

that is passively advected in the same manner as the density. We define Cchrom the mass

fraction of the chromospheric material inside the computational cell. The chromospheric

material is initialized with Cchrom = 1, while Cchrom = 0 in the corona and stream. During the

stream impact, the chromospheric and stream material mix together, leading to regions with 0

< Cchrom < 1. At any time t the density of chromospheric material in a fluid cell is given by

chrom = Cchrom and that of the stream material by stream = (1 - Cchrom).

The thermal conductivity in an organized magnetic field is known to be highly anisotropic

and it can be extraordinarily reduced in the direction transverse to the field (e.g. 60). Thus we

split the thermal flux into two components, along and across the magnetic field lines, 𝑭𝑐 =

𝐹⫽ 𝒊 + 𝐹⊥ 𝒋 , where

𝐹⫽ = (1

[𝑞𝑠𝑝𝑖]⫽

+1

[𝑞𝑠𝑎𝑡]⫽)

−1

𝐹⊥ = (1

[𝑞𝑠𝑝𝑖]⊥

+1

[𝑞𝑠𝑎𝑡]⊥)

−1

to allow for a smooth transition between the classical and saturated conduction regime (61,

62). In the above equation, [𝑞𝑠𝑝𝑖]∥ and [𝑞𝑠𝑝𝑖]⊥

represent the classical (Spitzer) conductive flux

along and across the magnetic field lines (60, 63)

where [∇𝑇]∥ and [∇𝑇]⊥ are the thermal gradients along and across the magnetic field, and

𝑘∥ and 𝑘⊥ (in units of erg.s-1.K-1.cm-1) are the thermal conduction coefficients along and

across the magnetic field lines, respectively. The classical (Spitzer) thermal conductivity is

based on the assumption that the mean free path is much lower than the temperature scale

height. When this condition is not yet verified, the heat flux cannot be represented in the form

−𝑘∇𝑇, and this effect is known as saturation. In this case, the saturated flux along and across

the magnetic field lines, [𝑞𝑠𝑎𝑡]∥ and [𝑞𝑠𝑎𝑡]⊥, can be represented as

where cs is the isothermal sound speed, and is a number of the order of unity; we set = 1

according to the values suggested for stellar coronae (64–66).

fig. S2. Radiative losses per unit EM for an optically thin plasma. This is derived from the

APED V1.3 atomic line database (59), assuming the metal abundances of 0.5 of the solar

values (57).

The spatial domain of the simulations includes only the portion of the stellar atmosphere close

to the star, and is schematically represented in fig. S1. We solve the MHD equations using

cylindrical coordinates in the plane (r, z), assuming axial-symmetry. The coordinate system is

oriented in such a way that the stellar surface lies on the r-axis and the stream axis is

coincident with the z-axis. The 2D cylindrical (r, z) mesh extends between 0 and 1.2 ×

1010𝑐𝑚 in the r-direction and between −1.4 × 109𝑐𝑚 and 2.26 × 1010𝑐𝑚 in the z-direction;

the transition region between the chromosphere and the corona is located at 𝑧 = 0 𝑐𝑚. The

radial grid is uniform and made of Nr = 512 points with a resolution of ∆𝑟 ≈ 2.3 × 107𝑐𝑚.

The vertical grid is nonuniform, and made of Nz = 896 points. This allows a better spatial

resolution at the shock location, near the chromosphere. It consists of the following: i) a

uniform grid patch with 512 points and a maximum resolution of ∆𝑧 ≈ 5.4 × 106𝑐𝑚 that

covers the chromosphere and the upper stellar atmosphere up to the height of ≈ 3 × 109 𝑐𝑚

and ii) a stretched grid patch for 𝑧 > 3 × 109𝑐𝑚 with a mesh size increasing with z, which

leads to a minimum resolution at the upper boundary of ∆𝑧 ≈ 5 × 107𝑐𝑚. The boundary

conditions are the same as adopted in (24): axisymmetric boundary conditions at r = 0 (i.e.

along the symmetry axis of the problem). This means that the variables are made symmetrical

across the boundary, and both radial and angular ϕ components of vector fields (𝒖, 𝑩) change

their sign. The other conditions are: free outflow (i.e. we set zero gradients across the

boundary) at 𝑟 = 1.2 × 1010𝑐𝑚, fixed boundary conditions at 𝑧 = −1.4 × 109𝑐𝑚 (imposing

zero material and heat flux across the boundary), and a constant inflow in the upper boundary

at 𝑧 = 2.26 × 1010𝑐𝑚.

section S2. Experimental diagnostics

fig. S3. Cartoon showing the top view of the central coil region of the experimental setup

and the diagnostics paths. The grey rectangle represents the Helmholtz coil, inside the

airtight structure, delivering a magnetic field in the central region up to 20 T (35). The conical

apertures allow the insertion of the stream-source target as well as the main laser beam to

reach the stream-source target without clipping the obstacle target. The obstacle target is

inserted from the bottom of the coil through a vertical aperture. The probe beam travels along

the coil following the perpendicular aperture, going through the interaction region.

2.1 Optical interferometry

As illustrated in fig. S3, the optical probing exploits an interferometric technique to retrieve

the plasma electron density in the low-density regions (density below 1020 cm-3) of the

plasma. It consists in a standard Mach-Zehnder interferometer and uses a compressed probe

laser pulse delivering 100 mJ in 350 fs, at the wavelength of λ = 528.5 nm, to probe the

plasma. Using a Glan polarizer, we split the probe beam, before entering in the interferometer,

in two equal energy beams having crossed (S and P) polarizations (fig. S2). Then, these two

beams follow two different paths having two different optical lengths. This technique allows

us to probe the plasma at two different times for each laser shot. The two beams are sent into

the interferometer, in one arm of which is located the plasma. After exiting the target

chamber, the probe beam is separated again in its two time-separated polarizations, each of

which is sent to a specific CCD detector. The interferograms recorded on each CCD are

analyzed using the Neutrino code (67). A wavelet model enables to fit the fringes

arrangement, from which a phase map is then unwrapped. Using an Abel transform (68), the

plasma electron density is retrieved from the phase map assuming an axisymmetric

distribution of the plasma. This allows us to produce density maps, as the ones shown in Fig.

1C of the main text, from which lineouts have been taken, like the one shown in fig. S4A,

which highlights the density jump at the reverse shock front that can be extracted.

fig. S4. Shocked plasma density profiles as measured in the laboratory and simulated at

the surface of a young star. Snapshots of the longitudinal plasma electron density profiles

(A) for the laboratory experiment (at t = 37 ns, radially averaged over 100 µm around the

axis) and (B) the astrophysical simulation (at t=350 s, averaged along the radial direction)

cases, respectively, highlighting the presence of the shocked region (the stream and

chromospheric plasmas in the astrophysical MHD simulation are separated thanks to a passive

tracer - see section s1 above). The laboratory plasma profile is a composite of visible optical

measurements (full line) for the low-density regions, and of X-ray radiography measurements

(dashed line) for the high-density regions.

This electron density jump seen in the experiment, about x10 between the unperturbed region

(𝑛𝑒 = 1.5 × 1018𝑐𝑚−3) and the shocked one (𝑛𝑒 = 1.5 × 1019𝑐𝑚−3), is in good agreement

with what is expected from Rankine-Hugoniot equations. Indeed, in a strong shock

approximation (𝑀𝑠𝑡𝑟𝑒𝑎𝑚 = 𝑣1/𝐶𝑠 >> 1) and for a polytropic index of 5/3, we have (69)

𝜌2 = 4𝜌1

Where the label 1 designates the unperturbed region, while the label 2 designates the shocked

one. Then

𝑛𝑒2= 4𝑛𝑒1

×𝑍2

𝑍1

From the partially ionized, i.e. Z = 2.67, unperturbed plasma, to the assumed fully ionized, i.e.

Z = 5.3, shocked plasma, one then gets: 𝑛𝑒2= 8𝑛𝑒1

.

We note that the density jump at the reverse shock front observed in the laboratory is also

well seen in the astrophysical simulation, as shown in in fig. S4B. Figure S4B shows also that

the shocked plasma is mostly composed of stream material, which we also observe in the

laboratory. This is done by changing the target material of the stream and of the obstacle.

From it, we can deduce, through the change in the total amplitude of the X-ray emission (see

below) by ionized F atoms recorded in each case, the relative number of F ions that are in the

heated accretion plasma in each case (i.e. when the F ions are in the stream, or in the

obstacle). Indeed, we observe the same plasma density dynamics in both cases (using the

interferometry diagnostics), and also in both cases, that the visible self-emission and the X-

ray spectra are the same (but the X-ray signal is much weaker in intensity when using CF2 as

the obstacle material since there are much less F ions in the plasma). This means that the

plasma dynamics and heating (i.e. the electron density and temperature) is the same when the

composition of the laser target and obstacle targets are swapped. By comparing the F-ion

emission X-ray signal strength when using CF2 as the stream material, or as the obstacle

material, we can assess that in the laboratory the obstacle material participates to only ~5% of

the shocked plasma.

2.2 Density probing close to the obstacle target surface by X-ray radiography

To have access to the electron density measurement at higher density value than the one

accessible by the interferometry (as shown in fig. S4A), X-ray radiography is performed. This

is needed, not only because the plasma density will become over critical when approaching

the obstacle surface, and thus prevents the optical probe to penetrate the plasma, but also

because of the large density gradients that refract the optical probe beam away from the

target.

fig. S5. Illustration of the step transition observed in the transmitted x-rays between the

target and vacuum or an ablated plasma expanding toward vacuum. The blue curves are

showing the step transition of the X-ray probe transmission in a cold, non-impacted target (the

target is on the left, heavily absorbing the X-rays), while the red curves show the smoother

transition occurring when a plasma expands from the target surface, i.e. following the impact

of the obstacle target by the incoming stream (the PSL unit in ordinates stands for “Photo

Stimulated Luminescence”, which is the unit of the readout instrument (FujiFilm Co.) of the

Image Plate detector we used, and which can be related in absolute to the incident X-ray

photon flux (71)). The solid lines are experimental lineouts while the dashed lines are the fits

of the latest. The plasma transition, i.e. the red curve, is taken from a radiography occurring

35.5 ns after the stream impact on the target.

The X-ray radiography is performed by focusing the 2.5 J/320 fs/528.5 nm compressed laser

pulse arm of the ELFIE facility (43) onto a thin SiO2 (glass) stalk situated at one of the

entrance of the radial aperture, i.e. in the same path as the interferometry diagnostic (the two

diagnostics are alternated, i.e. the X-ray probe is also transverse to the axis z). It generates an

isotropic, short duration (ps) X-ray emission, strongly dominated by the Silicon cold K-

emission line at ~ 1740 eV (70). As the glass stalk is oriented in the same axis as the radial

tube managed in the coil, and as the stalk is tapered into a point-like tip on which the short-

pulse laser is shooting, the X-ray emission will originate from a point source from the point of

view of the plasma. It produces on an Image Plate (71), situated at the opposite side of the

radial tube, a sharp projected 2D transmission map of the X-rays as they go through the

denser plasma regions.

From the projected images collected on the image plates, we take a series of lineouts parallel

to the axis z, passing through the stream-impacted zone and on its sides. Two typical lineouts,

one taken at the center of the impact region, and one away (where the obstacle target is still

cold) are shown in fig. S5.

To quantitatively reconstruct the expanding plasma density profile, we record such lineouts

all along the target surface, which are then fitted by a two-slopes sigmoid function, i.e.

𝑆𝑡𝑒𝑝𝛼𝑟(𝑧) = 𝑎 ±

(𝑎−𝑏)

1±𝑒𝑠1(±𝑧±𝑙1)+𝑒𝑠2(±𝑧±𝑙2) . It is then possible to retrieve the transmission of the

X-rays as follows: 𝑇𝑟(𝑧) = 𝑆𝑡𝑒𝑝𝑝𝑙𝑎𝑠𝑚𝑎𝑟(𝑧)/𝑆𝑡𝑒𝑝𝑐𝑜𝑙𝑑(𝑧).

Figure S6 (a) shows the deduced transmission along the target surface, at z=5 µm away from

the target surface. We note the drop of the transmission in a peak shape at the jet impact

location, corresponding to an increased density as the jet hits the obstacle. The radial

extension of this transmission drop is well corresponding with the measured incoming jet

diameter, equal to 1.5 mm (see table S3) and which is represented by the two vertical dashed

lines in fig. S6 (a). Figure S6 (b) shows the longitudinal evolution of the transmission as we

go away from the target surface. It is there taken at r=0, the middle of the impacted region by

the incoming stream.

Because the X-ray radiation is strongly dominated by the Si K-alpha at 1740eV, we calculate

the optical depth of 1740 eV X-rays going through different couples (ne, Te) of plasma

electron density and temperature conditions, which we chose to encompass our experimental

plasma conditions, by running the 0-D atomic code FLYCHK (41).

fig. S6. Results of the analysis of the x-ray radiographs.(a) Recorded radial transmission of

the X-rays along the target surface, at z=5 µm from the target surface. (b) Longitudinal

transmission of the X-rays, going away from the target surface, i.e. along the z axis, taken at

r=0. The transmissions are calculated here from a radiography occurring 35.5 ns after the jet

impact.

Then, using the plasma electron temperature retrieved from the X-ray spectrometry

measurement (see below) and analysis, the electron density is here inferred (see the dashed

line in fig. S4a) as the one allowing to match the experimental transmission with the

FLYCHK-calculated transmission.

2.3 Visible self-emission measurement (SOP) of the accretion phenomenon in the

laboratory

This measurement is performed by using a Streaked Optical Pyrometer (SOP) that collects the

self-optical-emission coming from the plasma. The light is filtered by a bandpass from 400-

600 nm described in fig. S6 and then measured by a streak camera (Hamamatsu C7700

equipped with a S20 photocathode sensitive to 200–850 nm wavelengths). The wavelength

band shown in fig. S7 is narrow and far from the peak of emissivity of the plasmas we are

diagnosing since they have a priori temperatures ranging from ~0.1 MK (for the incoming jet

(37, 44) to several MK in the shocked and shell plasmas (see below), which corresponds to

blackbody emissivities peaking at wavelengths of 25 nm to <2.5 nm, respectively. The light

originating from the plasmas is imaged along the axis z of propagation of the stream. Only the

light emitted from a zone of 80 µm around the z axis is collected into the camera. This light is

then streaked in time by the camera, leading to a time-resolved 1D image of the self-emission

of the plasma (Fig. 2A of the main paper and fig. S11B).

fig. S7. Spectral response of the combined streak camera and filter set system used in the

SOP diagnostic. The spectral response is here normalized.

Wavelength (nm)

In order to retrieve an estimated temperature from this visible self-emission collected by the

streak camera, two extreme models of the emissivity can be used: either the plasma is

considered like a black body (BB, valid in the case of optically thick plasmas), or is optically

thin (OT). The free-free mean free path of a photon with a wavelength of 0.5 µm is,

approximately, ff (cm) = 0.62 Te1/2/ne

2, with Te in eV and ne in units of 1019 cm-3 (from Eq.

10.92 of (72)). Typically, using the parameters typical of the shell in the 20 T case, we get ff

= 8 cm, i.e. the plasma conditions are in between the optically thick and optically thin

regimes.

From Fig. 2A of the main text, we observe the following ratio of SOP brightness (Br) at 20 T:

Brshell/Brstream=7.43.4

Brcore/Brshell=13.56.5

The reduced brightness in the shell is consistent with higher temperature being present there,

as inferred from the X-ray spectroscopy measurement (see main text and the next section) and

the laboratory simulations. Indeed, for an optically thin plasma, for a given density, the

emission decreases for increasing temperature.

The repeatability shot to shot of the SOP during the experiment is a witness of the

repeatability of the plasma dynamics investigated here. It is quite good since it exhibits a

standard deviation that is between 10 and 20%.

2.4 Analysis of the X-ray spectrometry in the laboratory

Focusing spectrometer with spatial resolution (FSSR) in one direction (along the axis z of the

incoming stream) was used to record the temporally-integrated X- ray emission spectra of the

plasma (73). The spectrometer was equipped with a spherically bent mica crystal (2d = 19.9

Å) and set up to observe X-ray wavelength range of 13.5 to 15.5 Å (750–950 eV photon

energies) containing the emission of H- and He-like fluorine ions. The diagnostic was aligned

along nearly the same line- of-sight as the interferometer with a slight angle in the upwards (∼

5◦) and lateral (∼ 2◦) directions, which were small enough to neglect the skewing of the

image.

We concentrate our analysis on the first 2 mm of the plasma along z, starting from the

obstacle surface (z=0), i.e. where the core and shell are present (as indicated by the

interferometry and SOP data). For the analysis of the spectra, the exact spatial geometry of

the plasma was inferred from the interferometer diagnostic.

As shown in Fig. 2B of the main paper, the spectrum contains remarkably intense series of

high-n transitions in He-like fluorine ions (He, He, and Hetogether with a dominating

Ly line of H-like F.

In attempting to model the observed ratio between the He and Ly lines with an atomic

kinetics modeling in a steady-state approach (as can be made using the FLYCHK (41) and/or

PrismSPECT codes (74)), a fit can be achieved for the plasma with an electron plasma

temperature of Te = 2.32 MK, or 200 eV and an electron plasma density of Ne = 31019 cm-3

as shown in fig. S4. However, such fitting yields a clear underestimation of the rest of the He

series lines. In general, the observed relative intensities of the He, HeHe lines can occur

only in a recombining plasma, i.e. in the conditions when the recombination processes

dominate ionization ones, and the electron temperature of the plasma in a given moment is

rather lower than the ionization temperature. As a consequence, we can deduce that the

observed spectrum of He-like ions should originate from a plasma with electron temperature

below 100 eV (1.16 MK) due to the fact that the ionization potential of the high-n levels in

He-like F is below or about this value.

All together, the observed spectrum gives a clear evidence that at least two regions of plasmas

(one being “hot”, i.e. having temperature of hundreds of eV, and another one being a

recombining “cold” plasma) with various parameters contribute to the observed spectrum,

both of which are located near the obstacle surface.

fig. S8. Best fit of the x-ray spectrum measured near the obstacle (PVC target, the

stream being generated from a CF2 target) in the case of a magnetic field strength of B =

20 T and as obtained by the PrismSPECT code in steady-state mode for an electron

temperature of 200 eV or 2.32 MK.

In the cold plasma case, the emission of the He-like series can be analysed following the

procedure for recombining plasma having non-steady ionization state that is detailed in Ref.

(37). The relative intensities of the transitions 1snp 1P1 – 1s2 1S0 where n = 3 – 7 in multiple

charged He-like ions (He, He, He, He, He lines correspondingly) are sensitive to the

electron density in the range of 1016 — 1020 cm-3 when the temperature ranged from 10 to 100

eV (0.1 to 1 MK) for ions with nuclear charge Zn ~ 10. This allows us to retrieve the electron

temperature and density of the “cold” plasma fraction.

As shown in fig. S9, such procedure applied to the spectra recorded over the first 600 µm

along the axis z from the obstacle surface yields the following estimations for the “cold”

plasma component near the obstacle surface

For B = 20 T: Te = 50 eV (0.6 MK), Ne = 2.31019 cm-3

For B = 6 T: Te = 40 eV (0.46 MK), Ne = 3.31018 cm-3

Note that these density values retrieved from the recombining spectra modeling correspond

well to the values obtained from the interferometry measurements for the inner shocked core

region of the plasma, as given in tables S3 and S4.

fig. S9. Comparison of experimental spectra (in black) recorded near the obstacle target

for the cases of 20 T (left, here the obstacle is a PVC target, whereas the stream is

generated from a CF2 target) and 6 T (right, here the obstacle is an Al target, whereas

the stream is still generated from a CF2 target) applied B field, together with

simulations (in red) of the He-like line series obtained using a recombination plasma

model. The experimental intensity values are scaled according to instrumental functions of

the spectrometer and the readout system in order to compare them to the real emissivity of the

plasma in the two cases. The scale for the modeled spectra emissivity (in W/cm3) is given on

the right.

Since at such low temperatures (~0.5 MK), the population of H-like ions is low, the

contribution of this “cold” plasma component to the Ly line can be considered negligible.

Hence, we can retrieve the electron temperature of the “hot” plasma fraction independently,

analyzing the relative intensities of Ly line and its dielectronic satellites, which appear at

longer wavelength (see fig. S10 and Fig. 2B of the main text). As the hot plasma is assumed

to be in the range of several hundreds of eV (several MK) temperature range, the steady-state

approach of the PrismSPECT code can be applied for the spectra modeling.

Although the relative intensities between particular satellite components are strongly

dependent on the plasma density, the overall intensity of the satellite group is not sensitive to

the plasma density in the range considered, but to the electron temperature only. The inset of

fig. S10 shows how the ratio between the Ly line and the dielectronic satellites depends on

the electron temperature. The best correspondence of the modeled ratio to the measured one is

obtained for Te ~ 320 eV (3.7 MK). The quite low signal-to-noise ratio in the satellite

spectrum gives us a confidence interval for the temperature of 250 - 400 eV (2.9 – 4.6 MK).

For the 6 T case the Ly/satellite ratio is observed to be of the same order, within the

measurement precision.

fig. S10. The spectrum measured for an applied magnetic field of 20 T (here, the obstacle is a PVC target, whereas the stream is generated from a CF2 target), in the range from 14.5 to 15.4 Å and containing the Lyα line and its dielectronic satellites. The modeled spectra is calculated by PrismSPECT code in the steady-state approach for plasma temperatures of 175 eV (2 MK) and 320 eV (3.7 MK). The dependence of the ratio of the Ly line intensity to the one of the satellites with respect to the plasma electron temperature is given in the inset, from which the precision on the temperature determination can be inferred.

In summary, from what is observed in the SOP and interferometer diagnostics, along the same

light of sight as the X-ray spectrometer, we observe a two components plasma: the inner

shocked core region, surrounded by a shell region that is taller (along z), and thicker (in

radius) but less dense, as detailed in tables S3 and S4. The analysis of the X-ray spectra

recorded for magnetic field strengths of 6 and 20 T, as shown in Fig. 2 of the main text and

here above, confirms this observation as the spectra can be only modelled as the emission

from two distinct plasma components having densities consistent with the interferometry

measurement, and temperatures are derived from the X-ray spectrum analysis and detailed

above.

section S3. Comparative table of the laboratory and astrophysical plasma

parameters

table S2. Parameters of the laboratory accretion, with respect to the ones of the

accretion stream in CTTSs for three distinct regions, namely, the incoming stream, the

score, and the shell. The parameter is equal to the ratio of the plasma pressure to the

magnetic pressure. The laboratory stream average temperature of 0.1 MK, or 10 eV is

extracted from previous measurements aimed at investigating solely the collimated stream

generation (37, 44). For the laboratory case, the density values are taken from the

experimental measurements. The stream velocity range indicates the variation of the stream

velocity as it decreases over time (44), starting from the velocity measured at the detectable

edge of the stream (1000 km/s). For all the stream parameters calculated in the Table below

the given value of the stream velocity, we use a fixed value of the velocity (750 km/s) as it

corresponds to the peak velocity of the highest density part of the stream (1.51018 cm-3). For

the laboratory core, we start with the temperatures that are derived from the Rankine-

Hugoniot equations, i.e. that correspond to what is expected after the shock. From the shock

front where only the ions are heated, we consider that the electron and ion temperatures in the

core region correspond to the ones expected after the particles have travelled 125 µm inside

the core shocked region, at the flow velocity given, in the frame of the shock, by 𝑣𝑓𝑙𝑜𝑤_𝑐𝑜𝑟𝑒 =

𝑣𝑓𝑙𝑜𝑤_𝑠𝑡𝑟𝑒𝑎𝑚/4. To determine these temperatures, we use thermal equilibration equations,

coupled with a Thomas-Fermi model for the ionization as well as optically-thin free-bound

radiative losses. We note that the obtained temperatures are completely consistent with the

ones retrieve by the 3D-MHD model of the laboratory dynamic (see Section 7 below detailing

the GORGON code simulation results). The temperatures in the shell region are directly

extracted from the 3D-MHD code GORGON, at locations having electron densities consistent

we the ones measured experimentally. Note that the stated electron temperature of 600 eV is

resulting from electron-ion equilibration over a few ns as the electrons transit from the core to

the shell. The indicated cooling times for the laboratory plasma are obtained by running the 0-

D atomic code FLYCHK (41). In the CTTS case, the density values and temperatures in the

stream and core regions are extracted from the PLUTO simulations used in the main text (Fig.

1D). For the CTTS shell, the density and temperature values are taken from the shell area

having for coordinate (𝑟1 − 𝑟2, 𝑧1 − 𝑧2) = (7.5 × 109 − 8.5 × 109𝑐𝑚, 3 × 109 − 4 ×109𝑐𝑚) in the 1250 s frame of PLUTO astrophysical simulation. This area corresponds to the

shell part being composed by the shocked stream material ejected away from the core, and not

by the cold chromosphere material, for a better correspondence with the laboratory-defined

shell. The similar 𝛽𝑑𝑦𝑛~1 in the astrophysics shell and the laboratory one, reflects that

correspondence.

A detailed comparison of the plasma parameters in the incoming stream, core shocked and

shell regions is given in table S2 for both the laboratory and simulated CTTS plasmas.

In table S2, the Reynolds number, Re, which is the ratio of the inertial force to the viscous

one is defined in the usual manner, i.e. as

𝑅𝑒 =𝑟𝑣

ν

Where v is the flow speed, r is the typical scale length, in our case typically the stream, core

or shell radii, and ν is the kinematic viscosity, taken from Ref. (75)

ν = 2 × 1019[𝑇(𝑒𝑉)]5/2

Λ√𝐴𝑍4𝑛𝑖(𝑐𝑚−3)

Where Λ is the Coulomb logarithm. While in the case where the electrons are magnetized

ν = 2 × 108𝛼𝑇(𝑒𝑉)

Z B(G) with 𝛼 = 𝑙𝑚𝑎𝑔𝑛/𝑟𝐿𝑖

Here, lmagn is the typical length at which the magnetic field line changes its direction by π/2,

rLi is the ion Larmor radius. To determine if the electrons are magnetized, or not, we calculate

the following Hall number

ℍ𝑒 = 𝜔𝑒𝜏𝑒 = 3.4 × 106𝑒𝐵[𝑇(𝑒𝑉)]3/2

Λ𝑚𝑒n𝑒(𝑐𝑚−3)

This number, defined as the cyclotron frequency times the electron collision time, is

representative of the number of cyclotron orbits a particle performs before undergoing a

collision. Thus for high Hall numbers (i.e. >> 1), we consider the plasma to be magnetized.

In order to get a system for which the ideal MHD equations apply, the viscous effects have to

be negligible and then Re >> 1.

The Peclet number, Pe, is also defined in the usual manner, i.e. as the ratio of heat convection

to heat conduction

𝑃𝑒 = 𝑟𝑣

χ

Where v is the flow speed, r is the spatial scale length, in our case, typically the stream radius,

and χ is the thermal diffusivity for electrons, taken from Ref. (75)

χ = 2 × 1021[𝑇(𝑒𝑉)]5/2

ΛZ(Z + 1)𝑛𝑖(𝑐𝑚−3)

While in the case where the electrons are magnetized

χ = 8.6 × 109𝛼√𝐴

𝑍

𝑇(𝑒𝑉)

B(G)

The ideal MHD equations also require, in order to be valid, the Peclet number to be large (i.e.

>> 1).

The magnetic Reynolds is also defined in the usual manner, i.e. as the ratio of the convection

over ohmic dissipation

𝑅𝑒𝑀 =𝑟𝑣

D𝑀

Where DM is the magnetic diffusivity

𝐷𝑀 =1

𝜇0𝜎

Where µ0 is the vacuum permeability, and σ is taken as the Spitzer conductivity

𝜎 =𝑛𝑒𝑒2𝜏𝑒

𝑚𝑒

As for the previous dimensionless numbers, the ideal MHD equations require, in order to be

valid, the Magnetic Reynolds number to be large (i.e. >> 1).

For all the above quantities (and the ones given in table S2), the atomic number and mass

number are defined as stoichiometrically averaged over the different components in the multi-

ion plasma, either PVC or CF2, leading to Zmean and a Amean. We have verified, in the case of

the calculation of the plasma viscosity, that such approach leads to similar results (within a

factor 3) compared to more accurate calculations performed detailing the contribution of each

species within a multi-species plasma (76).

In table S2 are also defined the parameters βther, which is the ratio of the thermal pressure over

the magnetic pressure

𝛽𝑡ℎ𝑒𝑟 =𝑛𝑖𝑘𝐵𝑇𝑖 + 𝑛𝑒𝑘𝐵𝑇𝑒

𝐵2 2𝜇0⁄

and dyn, which is the ratio of the dynamic pressure over the magnetic pressure

𝛽𝑑𝑦𝑛 =𝜌𝑣2 2⁄

𝐵2 2𝜇0⁄

Note that the Euler and Alfven numbers given in table S2 are defined in Section 2 of the

Methods.

The optically thin cooling time given in table S2 is taken from Ref. (75)

where ΛN is the normalized cooling rate (77). In the case of large temperatures ( ~ keV), one

can use the expression from (78): ΛN = 1.7×10 − 25Z2T(eV)1 ⁄ 2. We choose this expression for

the laboratory case even if it is very questionable, in order to give an upper limit. In the

astrophysical case, we use values given by (24) at the corresponding densities and

temperatures.

section S4. Temporal animation of the 2D-resolved plasma electron density

measurements of the magnetized accretion of the laboratory plasma at 20 T

movie S1. An animation of the accretion dynamics recorded as a function of time in the

laboratory in the case of an applied 20-T magnetic field. The time (starting at zero when

the stream impacts the obstacle) is displayed in the top-right corner of the images. The black

dashed vertical lines represent the limit of the incoming stream, as determined by the Full

Width at Half Maximum (FWHM) of a Gaussian fit of the radial profiles of the incoming

stream over time. The thin black arrows indicate the direction of the 20 T omnipresent

magnetic field. The colorbar (identical for all images) gives the value of the plasma electron

density in cm-3. At late times, we observe that the plasma ejected from the shock into the shell

quickly overtakes (along z) the propagating reverse shock. Eventually, it drives shocks into

the incoming streaming modifying considerably its pre-shock density.

From these measured of the interferometry plasma electron density measurements, we

observe the following average values

table S3. Parameters, experimentally retrieved from the interferometry diagnostic, of

the jet, shell, and core in the case of an applied magnetic field of 20 T.

Incoming stream Central core post-

shock near the

obstacle

Shell

Plasma electron

density (cm-3)

(1.50.5)1018 (1.50.5)1019 (42)1018

Radius (mm) 0.7 0.1 0.50.25 1.550.25 – from

core edge to outer

shell edge

section S5. Temporal animation of the 2D-resolved density and temperature

simulated maps of magnetized accretion dynamics in young stars

movie S2. An animation of the accretion dynamics recorded as a function of time in the

astrophysical simulation (case D5e10-B07 of table S1, that is, as for Fig. 1D of the main

text). The simulation starts when the stream impacts the obstacle and runs until 1650 s. The

thin white lines materialize the magnetic field lines. The colorbars (identical for all images)

give the value of the logarithm of the plasma electron density in cm-3 and of the temperature

in Kelvins, respectively.

section S6. Experimental observations in the case of a 6- or 30-T applied

magnetic field

When we reduced the applied magnetic field to 6 T, or increase it to 30 T, we observe

globally the same plasma dynamics as detailed in the main text in the case of an applied field

of 20 T (Figs. 1 and 2 of the main text), with the presence of a shell surrounding the central

core (figs. S11 and S12). We also clearly observe in these figures, and by also comparing

them to Fig. 1 of the main text, that by progressively increasing the magnetic field strength,

the shell has a smaller radius and an increasing density, as it is increasingly confined by the

magnetic field.

From the interferometry plasma electron density measurements, we observe the following

average values in the case of 6 T

table S4. Parameters, experimentally retrieved from the interferometry diagnostic, of

the jet, shell, and core in the case of an applied magnetic field of 6 T.

Incoming stream Central core post-

shock near the

obstacle

Shell

Plasma electron

density (cm-3)

(1.250.5)1018 (70.3)1018 (0.90.4)1018

Radius (mm) 0.750.1 0.750.25 2.50.5 – from core

edge to outer shell

edge

fig. S11. Laboratory observation of magnetized accretion dynamics using a 6-T strength

for the applied magnetic field. Here, compared to Figs. 1 and 2 of the main text, the strength

of the magnetic field is reduced from 20 T to 6 T. Shown are (A) a map of the laboratory

plasma electron density retrieved by Abel inversion from the experimental phase map

obtained using time-resolved optical interferometry at the time 87 ns after the incoming

stream impact on the obstacle. The contours highlight the core (contour at 6 × 1018𝑐𝑚−3) and

the shell (contour at 7 × 1017𝑐𝑚−3). (B) Visible (time-and space-resolved) SOP

measurement of the plasma self-emission. The full red line marks the edge of the emission

associated to the shocked core, while the dotted red line marks the edge of the emission

associated to the shell. A shock speed transition is evidenced by the change of slope of the red

line around 90 ns. As suggested by hydrodynamic simulations performed in these 6 T

conditions, this could be due to the fact that the stream takes longer to be shaped from the

laser-irradiated target from which it originates. As the stream collimation in this case takes

place close to the obstacle, it is perturbed by the presence of a low-density plasma we observe

to be there present, induced by the pre-heating of the obstacle (induced by the X-rays

generated at the level of the stream-source target). This induces perturbations in the flow

impacting the obstacle.

The SOP (fig. S10B) at 6 T displays a similar pattern as in the 20 T case: a bright core region,

here expanding in z at a velocity of 5.7 km/s (we note the presence of a second slope, after

90ns, corresponding to a speed of 24.8 km/s) by a thick shell, more expanded in z. Close to

the background, the emission from the cold incoming jet can be detected as well. The

observed ratio, in the SOP, for the brightness (Br) of these different regions are:

Brshell/Brstream=12.53.1

Brcore/Brshell=8.02.0

The hypothesis of the flow being perturbed near the obstacle in the case of the results shown

in fig. S11 is backed by the measurements shown in fig. S12, in which we moved the obstacle

further away from the stream-source target (from 11.7 mm in the case of the results presented

for all the other reported experimental data, e.g. Fig. 1 or fig. S11, to 18 mm in the

configuration used for fig. S12). In this case, we did not observe strong perturbations of the

stream and shell formation as observed in fig. S11.

fig. S12. Laboratory observation of magnetized accretion dynamics for various strengths

of the applied magnetic field and using a larger distance between the stream-source

target and the obstacle. Here, compared to Figs. 1 and 2 of the main text, as well as the other

data shown in this Suppl. Info., the distance between the stream-source target and the obstacle

is enlarged from 11.7 to 18 mm. The other parameters are kept the same. We observe that the

formation is less perturbed than evidenced in fig. S11. We also clearly observe, as expected,

that by increasing the magnetic field strength, the shell has a smaller radius and a higher

density as it is increasingly confined by the magnetic field.

section S7. Laboratory 3D MHD simulations using the GORGON code

To model the experiments we use the 3D resistive MHD code GORGON (54, 55). The code,

originally developed to model Z-pinches, has been widely used to model laboratory

astrophysics laser experiments (35) and astrophysical plasmas (79). The code uses a finite

volume scheme on a 3D uniform Cartesian grid. The single-fluid, two-temperature resistive

magneto-hydrodynamic equations implemented in the code are

where ρ is the mass density, v is the plasma velocity, pe  ⁄ i = ne/ikBTe/i is the electronic/ionic

pressure (ne/i is the electron/ion density, Te/i is the electron/ion temperature and kB is the

Boltzmann constant), and j is the current density obtained from Ampere's law. The evolution

of the electromagnetic fields is followed using a vector potential formalism, with the magnetic

induction given by B=A. Regions with densities below 10-7 g.cm-3 are treated numerically

as a vacuum, where momentum, mass, energy and current densities are zero. In the vacuum

regions, the vacuum form of Maxwell’s equations is solved and the displacement current in

Ampère’s law is retained. Shocks are captured using a Von Neumann artificial viscosity, with

Fvisc and Qvisc the volumetric force and heating term respectively. The electron/ion internal

energy εe ⁄ i are given by εi=pi(γ-1) for the ions, and by εe=pe(γ-1) + Q(Z) for the electrons,

where γ=5/3 is adiabatic index and Q(Z) the ionization potential energy density which

depends on the average ionization charge Z of the plasma. The latter is obtained from an

analytical approximation to a LTE Thomas-Fermi model (80). The thermal fluxes are given

by qe⁄i= -Κe/i∇Te/i, where the isotropic thermal conduction coefficients Κe/i are taken from

Ref. (81) with the addition of a standard flux limiter (28). Note that, although the anisotropy

on the thermal conduction induced by the presence of the magnetic field is not here taken into

account, the fact that the electron temperatures found in the simulation are close to the ones

inferred from the X-ray spectrometry diagnostic (as detailed in Section 2.4) seems to show

that such anisotropy effects do not play a major role. The plasma resistivity η is given by

Braginskii (82). The volumetric energy transfer rate, Qei, between ions and electrons is given

by

where me/i is the electron/ion mass, νei the electron-ion collision frequency and qe the electron

charge. The code assumes an optically thin plasma with Qrad being the volumetric energy loss

rate due to radiation escaping the plasma. This rate is computed assuming recombination

(free-bound) and Bremsstrahlung radiation (80) with an upper limiter given by the black body

radiation rate (Stefan–Boltzmann's law).

The computational domain is defined by a uniform Cartesian grid of dimension 3mm x 3mm

x 12.8 mm and a number of cells equals to 300 x 300 x 640. The spatial resolution is

homogeneous and its value is dx=dy=dz = 20 μm. The laser irradiation of the solid target is

modelled with two-dimensional Lagrangian fluid code DUED (56). The code solves the

single fluid, 3-temperatures equations in 2D cylindrical geometry in Lagrangian form. The

code uses the material properties of a two-temperatures equation of state model (EOS)

including solid state effects, and a multi-group flux-limited radiation transport module with

tabulated opacities. The laser-plasma interaction is performed in the geometric optics

approximation including inverse-bremsstrahlung absorption. At the end of the laser pulse (1

ns), the plasma profiles of density, momentum and temperature (electronic and ionic) from

the DUED simulations are remapped onto the 3D Cartesian grid of GORGON with a

superimposed uniform magnetic field of 20 T (in the z-direction) and used as initial

conditions. To remove the symmetry imposed by the initial conditions and to account for the

effect of inhomogeneities in the laser intensity over the focal spot, we introduce uniformly

distributed random perturbation on the plasma velocity components, with a maximum

amplitude of ±5% the initial value. We also refer the reader to previously published results

using the same initial setup (25, 54).

In fig. S13, we show 2D slices of the plasma electron density at three different times (t = 0 ns

corresponds here to the start of the laser pulse, the stream impacting the obstacle target after

10 ns). For a 17 J laser pulse, the resulting expanding flow takes the shape of a very well

collimated column with its front traveling with a velocity of ~ 1000 km.s  − 1. The distance

between the first target and the obstacle is 12 mm, and we can see that the accretion process

starts at 12 ns, i.e. 2 ns after the stream first impact on the obstacle (see the left panel of fig.

S13). The simulation reproduce well the experimental plasma density distribution, and ten

nanoseconds later we clearly see (fig. S13-middle panel) the central conical shock structure

(delimiting the core) and on the sides the shell interacting with the magnetic field (black lines

in the middle panel). The shocked plasma begins to form the shell due to the magnetic field

recollimation (a process which can occur because of the high magnetic Reynolds number in

this region, see table S2). At later time (40 ns after the laser irradiation, i.e. 30 ns after the

stream impact), the shell is building-up a significant “cocoon” around the incoming flow.

Using a passive tracer, we are able, in our simulations, to follow the material coming

specifically from the obstacle and we observe a strong mixing of this material with the

column material in the so-called shell. It is a very interesting point since one can consider

using different obstacle materials in order to modify the plasma properties in this shell

(increasing radiative losses with higher Z materials for example).

fig. S13. 2D slices of the decimal logarithm of the electron density of the accretion shock

region at three different times for a carbon plasma. Magnetic field lines (black lines) are

shown in the middle panel. Times are given with respect to the end of the laser irradiation.

Hence the first frame corresponds to 2 ns after the stream impact on the obstacle.

At late times, fig. S13-third panel, a substantial left-right asymmetry is seen. This is the result

of a Rayleigh-Taylor (RT) type instability which develops on the plasma column outer

surface, and which modulates the flow into filaments. Its development during the collimation

phase of laser-produced plasmas in a magnetic field was pointed out in Ref. (36). The

asymmetries observed in the shell region are only captured by 3D simulations, and are a

consequence of both the density modulations already present in the incoming streams, and of

the subsequent development of RT modes on the surface of the shell during its recollimation

by the magnetic field.

Now if we look at the particular time t = 22 ns (i.e. 12 ns after the stream impact on the

obstacle), we can see in fig. S14 a specificity of the laboratory accretion experiments. In this

case the equilibration times in the post-shock plasma are generally larger than the

characteristic hydrodynamic time (contrary to the astrophysical case, see table S2). Thus, one

can see in the two first panels of fig. S14 the decoupling of the ion and electron temperatures

after the shock. Ions are hotter in the core whereas electrons are heated along their

trajectories, which results in hot electrons being located predominantly in the shell. A very

important point regarding the comparison with the astrophysical case concerns the fact that

the plasma dynamics is quite insensitive to where the energy goes after the shock since in the

MHD approximation, considered as valid here, it is the total pressure (electrons + ions) that

drives the post-shock dynamics. Thus, one can expect to reproduce correctly this dynamics

even with a two temperatures plasma. In the third panel in fig. S14, we show the plasma

thermal beta at the same time. One can see the thin layer where the shock is located. From this

panel, it is very clear that the plasma in the shell around the incoming flow has a relatively

high beta, and that it is driven by the strong pressure gradients present near the core region.

fig. S14. 2D slices of ion and electron temperatures as well as plasma thermal beta at t =

22 ns (that is, 12 ns after the stream impacts the obstacle).