1. INTRODUCTION
In their infancy, stars originating from the collapse of dense interstellar clouds continue to accrete from the residual disk and envelope, while at the same time expelling powerful collimated jets. These jets, and the shocks that are produced as they propagate through the surrounding interstellar medium (ISM), can extend over distances of several parsecs (1 parsec = 2 × 105 AU = 3 × 1016 m) and are generally observed over a large spectral range (Snell et al., Reference Snell, Loren and Plambeck1980; Mundt & Fried, Reference Mundt and Fried1983; Bieging et al., Reference Bieging, Cohen and Schwartz1984). Jets often appear as a sequence of bright emission features that are consistent with internal shock produced by small velocity variations along the flow (Reipurth et al., Reference Reipurth, Raga and Heathcote1992, Reference Reipurth, Heathcote, Morse, Hartigan and Bally2002). However, the mechanism responsible for such variability is not clear. For instance, it is not known whether this knotty structure, as traced by the so-called Herbig-Haro objects, is a consequence for example of instabilities occurring during the jet propagation, or if it is due to an intrinsic variability of the jet ejection process. Whereas jet launching is linked to magnetic fields anchored to a disk, and which are responsible for accelerating and collimating the jet near the star, magnetic fields at larger distances from the source seem to be too small to have any influence on the jet dynamics (Hartigan et al., Reference Hartigan, Frank, Varniére and Blackman2007). This can thus be accurately described by hydrodynamics, and in this context, we discuss experiments investing the physics of astrophysical jets. The article is organized as follows. To be able to link laboratory to astrophysical flows, certain scaling requirements need to be satisfied (Ryutov et al., Reference Ryutov, Drake, Kane, Liang, Remington and Wood-Wasey1999, Reference Ryutov, Drake and Remington2000, Reference Ryutov, Remington, Robey and Drake2001), and the basic ideas will be reviewed in Section 2. The link from laboratory to astrophysics and the interpretation of the results are performed with appropriate multi-dimensional codes, which are described in Section 3. In Section 4, using the case of curved jets produced on Z-pinch experiments performed on the mega ampere generator for plasma implosion experiments (MAGPIE) facility (Lebedev et al., Reference Lebedev, Ampleford, Ciardi, Bland, Chittenden, Haines, Frank, Blackman and Cunningham2004; Ciardi et al., Reference Ciardi, Ampleford, Lebedev and Stehlé2008), we discuss how scaling may be used to understand the dynamics of the curved jets from young stellar objects (YSOs). In Section 5, we will present preliminary interpretation of new experiments on the Prague astrix laser system (PALS) laser facility, which use innovative laser focusing geometries to generate slab-jets in the relevant astrophysical parameter range. The question of shocks in stellar jets, and more specifically of radiative shocks is discussed in Section 6.
2. SCALING
The issues related to the scaling astrophysical flows in the laboratory were addressed by Ryutov et al. (Reference Ryutov, Drake, Kane, Liang, Remington and Wood-Wasey1999, Reference Ryutov, Drake and Remington2000, Reference Ryutov, Remington, Robey and Drake2001) in the framework of ideal (negligible viscosity, thermal conductivity, and resistivity) compressible magneto-hydrodynamics. Here we shall only be concerned with hydrodynamic scaling between laboratory (L) and astrophysical (A) flows, which have typical lengths L*, velocity V*, density ρ*, and temperature T*, which relies on the invariance of the inviscid hydrodynamic equations to the transformation:
where r denotes the position, t the time, and the other quantities ρ (density), P (pressure), and u velocity, are functions of position and time. The constants a, b, c are determined by the initial conditions, which have to be geometrically similar for both the astrophysical and laboratory systems. Under these conditions, and provided that the so-called Euler number, Eu = V*(ρ*/P*)1/2, is the same for the two systems, the dynamics of these flows will be indistinguishable up the time-scale transformation. Although producing geometrically similar initial conditions is rarely possible, experimental flows and shocks in the correct regime represent a unique tool to study astrophysically relevant processes in the laboratory. The “correct regime” assumption here means that the laboratory flows produced can be described by the inviscid Euler equations so that Peclet number Pe = L*V*/χ (χ being the heat diffusion coefficients), and Reynolds number Re = L* V*/ν (ν being the viscosity diffusion coefficient), are much larger than unity. Typical physical conditions for astrophysical and laboratory jets are given in Table 1.
Table 1. Scaling parameters of typical jets: YSO jets, Z–pinch jets and laser jets. Values from YSO jets are taken from Cabrit (2002, 2007). In the case of the W experimental jet, the values are taken from Ciardi et al. (2008). The values for the PALS Fe jet are taken from GORGON simulations at 10 ns, on the jet axis and at a distance of 1 mm from the target surface
Obtaining an exact similarity is even more difficult in the presence of a radiation field (Ryutov et al., Reference Ryutov, Drake, Kane, Liang, Remington and Wood-Wasey1999, Reference Ryutov, Remington, Robey and Drake2001; Castor, Reference Castor2007). The nature of the coupling between radiation and hydrodynamics is determined by the value of the optical mean free path compared to typical lengths, or equivalently by the optical depth τ = κL* where κ is the medium's opacity. Jets from YSOs are assumed to be optically thin (τ ≪ 1), with the exception of jets propagating with relatively larger velocities (>200 kms−1) and which can generate radiative shocks with a developed precursor (Raga, Reference Raga, De Colle, Kajdic, Esquivel and Canto1999).
Scaling remains theoretically feasible for optically thin plasmas, where it may be included as a cooling (sink) term in the energy equation. If the cooling terms vary as ραP β with the same power exponents for the two systems, then another condition between P* and ρ* is required for scaling (see Eq. (20) in Ryutov et al., Reference Ryutov, Remington, Robey and Drake2001). In practice, such precise scaling remains mostly intractable and the strategy consists then in checking that both systems are in a similar regime expressed by the dimensionless parameter χcool = V*τc*/L* = L cool/L*, where τc is the ratio of the gas thermal energy to the radiated energy per unit time and L cool is the cooling length. Adiabatic jets have χ > 1, while radiatively cooled flows, such as YSO jets, have χ <1.
Scaling fails for the radiative bow shock produced at the head of high-velocity jets. In this case, the unshocked gas absorbs the ultraviolet (UV) photons emitted by the shock, where temperatures reach about 3 × 105 K, and a radiative precursor is generated. The Euler equations need then to be complemented with the equations for radiation transport, which are inherently non-local, and which are coupled to the population equations for all ionic and excitation stages of the chemical species in the gas.
3. NUMERICAL MODELING
While scaling helps developing experiments in the appropriate regime, to understand the limitations and relevance of laboratory flows to astrophysical models, we need to rely on numerical simulations. In this work, we present simulations of experiments performed on both laser and z-pinch facilities. Astrophysical and laboratory jet simulations are performed with GORGON, a three-dimensional (3D) resistive magneto-hydrodynamic code (Chittenden et al., Reference Chittenden, Lebedev, Jennings, Bland and Ciardi2004; Ciardi et al., Reference Ciardi, Lebedev, Frank, Blackman, Chittenden, Jennings, Ampleford, Bland, Bott, Rapley, Hall, Suzuki-Vidal, Marocchino, Lery and Stehle2007). In the case of laboratory plasmas, local thermodynamic equilibrium (LTE) is assumed; the average ionization is calculated by a Thomas-Fermi model. The ion and electron energies are solved separately and include electron and ion thermal conductions, and optically-thin radiation losses. To model astrophysical flows, GORGON includes the time-dependent ionization of hydrogen by taking into account the recombination and collisional ionization, and uses rate coefficients as tabulated in Raga et al. (2007). For temperatures above 15000 K, cooling is implemented by a function appropriate for interstellar gas composition (Dalgarno & McCray, Reference Dalgarno and Mccray1972). For temperatures below 15000 K, cooling is calculated by including the collisional excitation and ionization of hydrogen, radiative recombination of hydrogen, and the collisional excitation of Oi and Oii. The populations of Oi and Oii are assumed to follow closely those of hydrogen because of charge exchange (Hartigan & Raymond, Reference Hartigan and Raymond1993).
The simulations related to the experiments on radiative shocks have been performed with HERACLES, a 3D radiation hydrodynamics code, which solves the Euler equations for hydrodynamics coupled with the moment equations of the radiative transfer equation. The M1 model allows us to bridge the transport and diffusive limits (González et al., Reference González, Audit and Huynh2007). The LTE approximation is assumed. The equation of state is computed using the hydrogenic model described in Michaut et al. (Reference Michaut, Stehlé, Leygnac, Lanz and Boireau2004). Opacities are calculated using the super transition array model (Bar Shalom et al., 1989) and are used for the grey radiation transport (González et al., Reference González, Stehlé, Audit, Busquet, Rus, Thais, Acef, Barroso, Bar-Shalom, Bauduin, Kozlova, Lery, Madouri, Mocek and Polan2006, Reference González, Audit and Stehlé2009).
4. JET DEFLECTION
A number of bipolar Herbig-Haro jets exhibit a distinguishing C-shape morphology indicative of a steady bending (Bally & Reipurth, Reference Bally and Reipurth2001). This curvature is attributed either to the motion of the jet source relative to the local ISM or to the presence of an extended flow, such as a wind from a nearby star. In general, this give rise to an “effective” transverse wind that curves the jet, with expected “cross-wind” velocities varying from a few kms−1 to few tens of kms−1 (Jones & Herbig, Reference Jones and Herbig1979; Salas et al., Reference Salas, Cruz-Gonzalez and Porras1998; Bally & Reipurth, Reference Bally and Reipurth2001). The effect of jet bending by a lateral flow has been studied experimentally on the MAGPIE facility (Lebedev et al., Reference Lebedev, Ampleford, Ciardi, Bland, Chittenden, Haines, Frank, Blackman and Cunningham2004, Reference Lebedev, Ciardi, Ampleford, Bland, Bott, Chittenden, Hall, Rapley, Jennings, Sherlock, Frank and Blackman2005). The schematic of the experimental configuration (Fig. 1a) consists of a conical array of micron-sized metallic wires driven by a current of 1 MA rising to its peak value in 240 ns. The basic mechanism of plasma formation in wire arrays is the following: resistive heating rapidly converts the wires into a heterogeneous structure consisting of a cold (<1 eV) dense, liquid-vapor core surrounded by a relatively hot (10–20 eV), low density (~1017 cm−3) plasma. Most of the current flows in the low resistivity plasma, which undergoes acceleration by the J × B force toward the array axis. These streams of plasma have characteristic velocities of about 100 kms−1, corresponding to Mach numbers M~5. The wire cores act as a reservoir of plasma, replenishing the streams during the entire duration of the experiment (several hundred ns). The converging plasma streams are virtually magnetic field-free and their collision on axis produces a standing conical shock. Although part of the kinetic energy is thermalized at the shock, it is important to note that these streams are not perpendicular to the surface of the shock. The component of the velocity parallel to the shock is continuous across it, and thus the flow is effectively redirected upward into jet (Fig. 1a). Typical jet velocities attained are about 100–200 kms−1 and hypersonic jets with M > 10 can be produced by this mechanism. The jet collimation and the Mach number depend predominantly on the amount of radiation cooling in the plasma, which can be altered by varying wire material (Al, Fe, or W). Increasing the atomic number of the wire material increases the rate of energy losses from the plasma, lowers the temperature, and leads to the formation of more collimated jets with higher Mach numbers (Ciardi et al., Reference Ciardi, Lebedev, Frank, Blackman, Chittenden, Jennings, Ampleford, Bland, Bott, Rapley, Hall, Suzuki-Vidal, Marocchino, Lery and Stehle2007; Lebedev et al., Reference Lebedev, Chittenden, Beg, Bland, Ciardi, Ampleford, Hughes, Haines, Frank, Blackman and Gardiner2002). Typical parameters for a tungsten jet are listed in Table 1.
Fig. 1. Schematic representation of the jet generation using a conical wire array (a), XUV experimental and synthetic images of the bent jet (b) (Ciardi et al., Reference Ciardi, Ampleford, Lebedev and Stehlé2008).
In the curved jet experiment, the wires are made of tungsten, while the cross-wind is produced by a radiatively-ablated plastic foil appropriately placed in the jet propagation region (Ledebev et al., 2004, 2005; Ciardi et al., Reference Ciardi, Ampleford, Lebedev and Stehlé2008). Typical “wind” velocities of about 30–50 kms−1 can be produced in the laboratory, with the important parameters characterizing the interaction in the range V jet*/V wind*~2–4 and ρjet*/ρwind*~0.1–10.
In Figure 1b, an experimental X-ray ultraviolet (XUV) image of a curved jet shows the presence of internal shocks. The scaling to astrophysical jets is performed by taking a jet to wind speed ratio of four, and a ratio jet to wind density of 10, which are in a similar range of those characteristic of the laboratory interaction. For the astrophysical simulations of the jet and wind, we take V jet* = 100 km/s, n jet = 1000 cm−3, and V wind* = 25 km/s, n wind = 100 cm−3. The initial temperature of both media is 5000 K. In the simulations, we only follow the time-dependent populations of atomic and ionized hydrogen. Comparison of the astrophysical and laboratory jet simulations has shown that the dynamics of the interaction is similar for the two systems. Concentrating on the astrophysical jets, the simulations have shown the formation of internal shocks in the jet and the development of a “knotty” flow (Ciardi et al., Reference Ciardi, Ampleford, Lebedev and Stehlé2008). The curved jets are liable to be Rayleigh-Taylor unstable, with the growth of the instability responsible for disrupting the jet and producing a heterogeneous clumpy flow. A 3D view of the resulting flow is shown in Figure 2. Beside disrupting the flow, it is clear that the instability promotes the mixing between the ISM and the jet. The development of the Rayleigh Taylor instability is also expected in the laboratory jets; however, for the condition currently produced in the experiments, the growth time is on the order of the dynamical time and new experiments will be needed to observe its full development.
Fig. 2. (Color online) 3D isodensity contour (n = 400 cm−3) of a curved astrophysical jet showing the formation of a clumpy flow. The size of the computational box is 2004 × 2004 × 4864 AU.
5. LASER PRODUCED SLAB-JETS
In the last 10 years, a number of laboratory experiments on high-power lasers have been developed to study high-Mach number jets (Shigemori et al., Reference Shigemori, Kodama, Farley, Koase, Estabrook, Remington, Ryutov, Ochi, Azechi, Stone and Turner2000; Logory et al., Reference Logory, Miller and Stry2000; Foster et al., 2002). Although laser produced jets have generally required energies in the kJ range, it was recently shown by Kasperczuk et al. (Reference Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Rohlena, Skala and Hora2006) that direct irradiation of a massive metal target with smaller laser energies (less than about a few hundred J) can produce collimated, jets in the correct scaling regime (Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Pfeifer, Rohlena, Skala and Pisarczyk2007, Reference Kasperczuk, Pisarczyk, Kalal, Martinkova, Ullschmied, Krousky, Masek, Pfeifer, Rohlena, Skala and Pisarczyk2008, Reference Kasperczuk, Pisarczyk, Nicolai, Stenz, Tikhonchuk, Kalal, Ullschmied, Krousky, Masek, Pfeifer, Rohlena, Skala, Klir, Kravarik, Kubes and Pisarczyk2009; Schaumann et al., Reference Schaumann, Schollmeier, Rodriguez-Prieto, Blazevic, Brambrink, Geissel, Korostiy, Pirzadeh, Roth, Rosmej, Faenov, Pikuz, Tsigutkin, Maron, Tahir and Hoffmann2005).
Here we present simulations of a variant of this jet generation mechanism, which results in the formation of slab-jets with laser energies of about 30 J. Beside the low energy required, these slab-jets are interesting because of their reduced geometry, essentially two-dimensional (2D), which makes them easier to diagnose and simulate. In particular, they may be useful to develop tests for 2D numerical simulations and to develop experiments aimed at addressing instabilities (e.g., Kelvin-Helmoltz) linked to the propagation of radiatively cooled jets in the ISM.
The experiments were carried out at the PALS laser facility (Jungwirth, Reference Jungwirth2005; Kozlová et al., Reference Kozlová, Rus, Mocek, Polan, Homer, Stupka, Fajardo, De Lazzari and Zeitoun2007) with a beam energy in the range of about 30 J and a pulse duration of 300 ps (ω = 1.315 µm), irradiating a planar massive target consisting of an iron foil. The laser focal spot consists of two parallel strips stretched about 1 mm in the x-direction. Their intensities (~1.6 × 1013 W/cm2) along the y-direction have nearly Gaussian distributions (full width at half maximum of 100 µm) and the peaks are separated by about 400 µm. A schematic of the experimental configuration is presented in the Figure 3. A typical measurement of the XUV emission recorded through an aluminum window on a XUV charge-coupled-device camera is shown in Figure 4, where an elongated jet-like plasma sheet (~1 mm) forms along the symmetry plane (xz) between two focal spots.
Fig. 3. (Color online) Schematic representation of the PALS laser irradiation (λ = 1.315 µm, 30 J, 0.3 ns) on a massive iron target for laminar jet generation. The peak laser intensity on the target is 1.6 × 1013 W/cm2.
Fig. 4. (Color online) FFT processed image with low and high frequencies removed of the time integrated XUV emission from the slab-jet. The IR PALS laser pulse comes from the right and the solid iron target is located to the left of the main plasma emission. The positions of the two parallel focal spots are visible in white on the surface of the target (Kozlova et al., 2007).
To understand more precisely the jet formation and the subsequent plasma evolution, we have performed 2D simulations (y-z slab-geometry) using the 3D code GORGON. The laser energy deposition mechanism, at the relatively low irradiation intensities used in this experiment, is modeled assuming inverse bremsstrahlung absorption. The temporal profile of the laser pulse was approximated by a 300 ps full width at half maximum Gaussian function and given a elongated double-peaked spatial distribution as discussed earlier. A sequence of electron isodensity contours are presented in Figure 5 and show snapshots of the evolution of the system at 5 ns, 10 ns, and 20 ns after the initial laser pulse. The jet formation process is essentially due to the collision on the mid-plane of the two expanding plasma plumes, which begins at about 5 ns. The converging flows form a shock on the mid-plane, which serves to redirect the momentum of the jet in the axial direction, in a mechanism similar to the jets produced from laser irradiated conical targets. At early times (~5 ns), the jet temperature is about 10 eV at 600 µm, with a relatively high degree of ionization (~6 at 600 µm). Over time, the jet undergoes strong radiative cooling, which aids the collimation. The characteristic jet conditions 1 mm above target change over a time of 20 ns as follows: density ρ is 2 × 10−5 to 2 × 10−3 g/cm3, temperature T from 7 to 3 eV, average degree of ionization <Z> from 4 to 1, sound speed c from 9 to 4 km/s, and flow velocity u from 40 to 20 km/s. The Mach number in the jet reaches has typical values of five. The comparison with the characteristic conditions found in astrophysical and z-pinch jets are presented in Table 1, which also shows that the dimensionless numbers Re, Pe, and χcool are in the correct regime for scaling. By modifying the energy and the profile of the two laser focal spots, it is possible to tune the jet velocity and density. Simulations reveal that it might be possible to achieve a Mach number of about 30 by increasing the laser energy by a factor of five, with the same focal spot geometry.
Fig. 5. (Color online) Electron isodensity (m−3) maps of laser produced jets on PALS at 5, 10, and 20 ns obtained with GORGON.
To complete our investigation and to compare with the experimental results, we have computed the radiative emission of the plasma in the XUV range, including recombination (free-bound) radiation in the range 10 to 100 eV. Figure 6 shows the isocontours of the radiative emission integrated along the x-direction and integrated in time between 0 and 100 ns. The simulated emission is in good agreement with the experiments.
Fig. 6. Time and space integrated synthetic XUV image of the PALS jet (arbitrary units).
6. SHOCKS IN YSO JETS
A large variety of shocks are associated with the propagation of YSO jets in the ISM. The strongest shocks are found at the head of the jet: the bow shock that accelerates the ambient medium and the Mach disk that decelerates the jets. There are also weaker shocks between the source and the head, identified in observations by bright knots. Shocks observed in YSO jets are strongly cooled by radiation and present a recombination zone in a thin layer after the shock discontinuity (Hartigan, Reference Hartigan1994). The description in terms of a cooling function is insufficient to follow the evolution of the different species in the flow (Teşileanu et al., Reference Teşileanu, Mignone and Massaglia2008) and these NLTE effects are not scalable in laboratory flows. In general, the coupling between hydrodynamics and the time evolution of the populations of different species is difficult to handle because of the stiffness of the latter equations. Furthermore, the coupling between hydrodynamics and radiation transport, which is crucial for modeling the radiative shocks at the head of the fastest jets, introduces another complexity. Although these processes may not be fully scalable, experiments are helpful to test the simulation tools and to understand the physics of these shocks, and a number of radiative shocks experiments were conducted on high-energy laser installations (Bozier et al., Reference Bozier, Thiell, Lebreton, Azra, Decroisette and Schirmann1986; Fleury et al., Reference Fleury, Bouquet, Stehlé, Koenig, Batani, Benuzzi-Mounaix, Chièze, Grandjouan, Grenier, Hall, Henry, Lafon, Leygnac, Malka, Marchet, Merdji, Michaut and Thais2002; Bouquet et al., Reference Bouquet, Stehlé, Koenig, Chièze, Benuzzi-Mounaix, Batani, Leygnac, Fleury, Merdji, Michaut, Thais, Grandjouan, Hall, Henry, Malka and Lafon2004; Gonzalez et al., 2006; Reighard et al., Reference Reighard, Drake, Dannenberg, Perry, Robey, Remington, Wallace, Ryutov, Greenough, Knauer, Boelhy, Bouquet, Calder, Rosner, Fryxell, Arnett and Koenig2005).
In a recent experiment, performed at PALS (Gonzalez et al., 2006), shock waves of about 60 km/s were launched in Xenon at 0.2 bar in squared cells of glass with inner section of 0.7 × 0.7 mm2 and length of 4 mm. The cells were closed by a composite foil made from polystyren (10 µm) and a gold film (0.5 µm). The main beam at 435 nm (150 J, 0.3 ns) was focused through a phase zone plate (PZP) and a lens on a spot of diameter of 0.7 mm on the foil. A scheme of the target is shown in Figure 7. The ablation of polystyren foil by the laser generates a strong shock, which propagates through the gold foil and the gas. The gold foil, at the interface between the plastic and the xenon gas, aims at preventing the parasitic X-ray radiation generated by the coronal plasma of the laser—plastic interaction to pre-heat the gas inside the cell. Due to the high velocity, the shock front is heated at temperature of 10–20 eV. The photons generated at the front propagate in the cold upstream gas, which they heat and ionize. This process thus creates a radiative warm precursor, which precedes the shock front (Fig. 8).
Fig. 7. (Color online) Typical gas target design used for radiative shock experiments: the laser (in green) impacts the gilt plastic foil. The ablation generates a shock wave which propagates in the z direction. Spectroscopic investigations, for instance from the rear face in XUV may be used to follow the shock radiative signatures.
Fig. 8. (Color online) Snapshot of temperature profile (in eV) of the shock, for two conditions of the walls losses (F = 10% and 60%). The shock propagates at a constant velocity of 60 km/s in a tube of square 0.7 × 0.7 mm2 section (HERACLES simulation), filled with Xenon at 0.1 bar. The temperature in the middle of the tube is reported versus y (along the direction of shock propagation), which is the distance from the position of the maximum of temperature.
In one-dimensional (1D) description of the shock wave, all the XUV photons emerging from the shock propagate in the gas and are used for the precursor ionization. However, due to the finite section of the shock tube in the experiments, the photons reach the walls of the tube, and are not necessarily re-injected in the gas, because a fraction F of the flux is lost on the walls (by either absorption or transmission at the walls).
As a consequence of the radiative losses at the walls of the shock tube, the shock waves and the ionization fronts are not flat but become curved, leading to 2D effects on the shock front. To illustrate this point, we performed numerical simulations in 2D with the radiation-hydrodynamics Eulerian code HERACLES code (Gonzalez et al., 2007). The shock is driven by a cold piston at a constant velocity of 60 kms−1 in xenon at 0.1 bar. When the radiation flux reaches the walls of the cell, a fraction of the flux (F) is lost, while the rest (R = 1-F) is reflected secularly into the cell (which is a simplification of the interaction between the radiation and the warm tube walls). We used realistic opacities (Bar Shalom et al., 1989) and equation of state (Michaut et al., Reference Michaut, Stehlé, Leygnac, Lanz and Boireau2004) and different conditions for the radiation losses F at the lateral walls (F = 10% resulting to a behavior close to 1D because almost all photons are re-injected in the cell, and F = 60% with stronger losses). These losses have an important effect on the shock temperature, especially the precursor extension, which decreases from 1.1 mm for F:10% to 0.5 mm for F = 60%, as shown in Figure 8.
Radiation losses have thus a strong impact on the extension but also on the dynamics of the radiative precursor (Gonzalez et al., 2009). In Gonzalez et al. (2007), the radiation losses fraction F at the glass tube walls was deduced from the dynamics of the ionization front, measured by shadowgraphy (Fig. 7) and estimated to F = 60%.
In these strong radiative shocks, the transverse optical depth τ, which tunes the lateral losses and the structure of the precursor, varies form large values (>10 in the shocked part), intermediate values in the precursor (~1), and again large values in the cold gas before the ionization front. (Gonzalez et al., 2006). It is expected that radiation losses F will have a strong impact on the monochromatic radiative flux, as a consequence of the different sizes of the precursors, and of the different temperatures reached in the shock. The influence of the extension of the precursor is illustrated in Figure 9, which shows the radiation flux emerging at 30 ns from a small hole on the axis, placed at the rear face of a 6 mm tube or at 1.5 mm from the end of the tube (Fig. 8), with an angle of view parallel to the tube. These computations have been using the plasma conditions at the canal center obtained by HERACLES 2D for F = 10% and F = 60% at 30 ns, with using a 1D LTE radiative transfer code. This code used monochromatic opacities obtained with hydrogenic model, as described in Michaut et al. (Reference Michaut, Stehlé, Leygnac, Lanz and Boireau2004). Whereas more adapted mochromatic opacities would be necessary for a spectroscopic analysis of the radiation, this numerical study shows the influence of the losses on the flux through the modification of the precursor structure and the complex variation of the flux within the precursor.
Fig. 9. (Color online) Calculated radiative flux along the direction of the tube at 30 ns (in arbitrary units) at different positions of the tube (x = 0, i.e., at the end of the tube on the left, and at x = 1.5 mm from end of the tube on the right) for two values of the losses at the walls (F = 10% in black and F = 60% in blue).
7. CONCLUSIONS
We have discussed laboratory experiments to study phenomena relevant to stellar jets. These include the effects of a cross-wind on the propagation of jets, which may lead to turbulence, and the formation of knots in curved YSO jets. We have also presented new results related to 2D slab-jet experiments, which may be useful for code validation, and to study jet instability in reduced simpler geometries. Finally, we have presented new results on the radiative properties of experimental radiative shocks, illustrating the limitations of scaling for these shocks in real gases.
ACKNOWLEDGEMENTS
We acknowledge financial supports from the Access to Research Infrastructures activity in the Sixth Framework Program of the EU (contract RII3-CT-2003-506350 Laserlab Europe), from the European RTN JETSET (contract MRTN-CT-2004 005592) and from CNRS (PICS 4343). TL gratefully acknowledges financial support from Observatoire de Paris during the past several years. M.G. acknowledges the financial support provided by the Spanish Ministry of Science and Innovation through the Juan de la Cierva grant.
