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A major objective of laboratory astrophysics is to simulate the fundamental nature of astrophysical plasma physics processes in a laboratory environment so that certain astrophysical phenomenon can be studied in a controlled manner13. High energy density facilities, such as high-powered lasers and Z-pinches, can provide such opportunities14, for example, direct measurements of opacity15, equations of state16, and photoionized plasmas17,18, as well as the similarity of physics, such as certain hydrodynamic phenomena of jets19 and shocks20 where a scaling law between astrophysical and laboratory plasma systems can be applied.

As a fundamental cause of many plasma energy conversion processes, magnetic reconnection (MR) is certainly a high priority of such studies. Masuda et al.21 observed the loop-top X-ray source in solar flares using the YOHKOH satellite and proposed that two antiparallel magnetic fields were merged above an arcade of closed loops as outflow jets from the reconnection point collided with high-density plasmas on the loop to produce a hot X-ray region. Ultraviolet22 and X-ray23,24 observations of plasma jets ejected from the regions above the solar surface were also reported, and further confirm theoretical models of MR. Because of the great similarity of phenomena relating to MR in solar flares and laser-produced plasmas, here, by applying the scaling law of magnetohydrodynamics (MHD), we try to reproduce the reconnection outflow/jet and the loop-top X-ray source in the laboratory using a high-power laser facility.

Previous simulations and experiments7,8,25,26 showed that a mega-gauss (MG) magnetic field B could be generated in hot, high-density plasmas by irradiating a solid target using high-power laser beams. The B-field was approximately ‘frozen’ in the plasma bubbles. As the two bubbles expanded laterally and encountered each other with oppositely directed B-fields, MR occurred as the B-field lines became topologically rearranged in the diffusion region. It thus enabled us to simulate the solar flare loop-top X-ray source generation process in the laboratory.

The experiment was performed at the Shenguang (SG) II laser facility, which can deliver a total energy of 2.0 kJ in a nanosecond square pulse. The eight SG II laser beams, with a wavelength of λL=0.351 μm, are divided into four bunches. Each bunch then consists of two laser beams. The geometric configuration, as shown in Fig. 1, is designed to be similar to the scheme of a loop-top X-ray source in the solar flares depicted in Fig. 2a. Two synchronized laser bunches separated by 400–600 μm are focused onto one side of the Al foil with the other two laser bunches symmetrically irradiating the other side simultaneously. Each bunch is focused to a focal spot diameter of 50–100 μm full width at half maximum (FWHM), giving an incident laser intensity of ∼5×1015 W cm−2. A Cu target is set 250 μm away from one foil edge. The Al foil is 1,600 μm×500 μm with a thickness of 10–50 μm. The Cu target is 1,600 μm×250 μm with a thickness of 150 μm. The X-ray emission is measured using three X-ray pinhole cameras in the forward, side and reverse directions, to investigate the reconnection jets as well as their impact on the copper target. The image is taken through a 10 μm pinhole, filtered with 50 μm of beryllium, allowing all X-rays above ∼1 keV to pass. Most of the signal from the high-energy continuum is recorded using time-integration on an X-ray film with its highest sensitivity to X-rays in the 1–10 keV range. A flat crystal spectrometer is set in front of the targets to record the X-ray spectra from the heated plasmas. Shadowgraphy and interferometry with a 120 ps green (λL=0.53 μm) laser beam are also used to investigate the evolution of the plasma.

Figure 1: Experimental set-up.
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Four bunches of long pulse (1 ns) lasers are focused on both sides of a thin Al foil target. Shadowgraphy and interferometry are used to diagnose the plasma evolution with a short pulse (120 ps) probe beam (shown as a green dotted line). The MR occurs between the two laser focus spots, and is detected by three X-ray pinhole cameras. The reconnection outflow/jet can thus interact with a pre-set Cu target. X-ray spectra from the heated plasma are recorded by a crystal spectrometer set in front of the target.

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Figure 2: Loop-top-like X-ray source and outflows observed in the laboratory.
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a, Magnetic reconnection model for the loop-top X-ray source in a compact solar flare, with a sketch depicting the X-ray observation scheme of ref. 21. b, The pinhole X-ray image observed forward of the Al foil target. Magnetic field lines are illustrated based on the flux surface of the plasma bubbles. The Al and Cu targets are the rectangles enclosed by white dotted lines. The red arrows indicate outflow/jet directions. c, X-ray image with two laser spots separated by 400 μm and with a foil thickness of 10 μm. The asymmetry of the laser intensity on the Al target causes an imbalance of the laser spots as well as of the magnetic fields B1 and B2, and further induces the inclination of the upward outflow. The downward outflow impinges on the Cu target and results in a hot X-ray source.

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The process can be reasonably described by MHD, as the magnetic Reynolds number is very high. Ryutov et al. 13 demonstrated the scaling relations of two ideal MHD systems (ReM≫1), in which the variables of the systems remain invariant under such transformations, as r=a r1, ρ=b ρ1, p=c p1, , , , where r is the characteristic length, ρ is the mass density, p is the pressure, v is the velocity, B is the magnetic field of the systems, and a, b, c are transformation coefficients. By choosing laser parameters and target materials properly, the magnetic Reynolds number is around 4,000 (for Z=13, A=27, L=0.1 cm, T=1,000 eV), which makes the MHD processes in laser plasmas and solar flares (ReM∼5×108) comparable.

The similarity of the MHD in solar flares and laser-produced plasmas is shown in Table 1, with the transformation coefficients a=10−11, b=108, and c=1010. The scaled parameters of the solar coronal plasmas in the third column are very similar to those of the laser-produced plasmas in the second column.

Table 1 The similarity of solar flares and laser-produced plasmas, with a=10−11, b=108, c=1010.
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Two bright X-ray spots are clearly observed resulting from the laser heating the Al foil target. In Fig. 2b, the two laser spots are separated by 600 μm, nearly 6–7 laser focus diameters, in vacuum to reproduce a previously studied geometry of laser driven magnetic reconnection8. The spontaneous magnetic field has an estimated MG strength based on hydrodynamic simulations and similar experimental measurements7,8. When two plasma bubbles expand on the Al foil surface, two toroidal MG magnetic fields ‘frozen’ in the bubbles merge accordingly with each other. The breakdown of the ‘frozen in’ condition occurs when the oppositely directed fields B1 and B2 encounter each other between the spots, where a diffusion region can be clearly seen with two significant X-ray patterns showing the release of magnetic energy. The width across each pattern is on the order of the ion inertial length c/ωpi=2.28×107 z−1(μ/ni)1/2 (cm)≈100 μm, with an ion density of 1018 cm−3. In this region electrons and ions are decoupled, and MR occurs. Note that there is also a clear interface between the two X-ray emission patterns, which is possibly a magnetic separatrix between two plasmas with the dominant magnetic field component tangential to it. A similar experiment, however, was carried out with two imbalanced laser beams separated by 400 μm, as shown in Fig. 2c. Consequently, the upflow is not vertical but has an inclination of ∼10°, providing an interpretation for the plasma jet inclination in solar flares. The X-ray intensity, on the other hand, is greatly enhanced in comparison with that in Fig. 2b as a result of the small separation. The diffusion region can hardly be defined here because the emission in the region is too high to distinguish from the spots.

The most striking feature in both experiments is that a bright X-ray spot at the centre of the Cu target is observed just below the downward outflow/jet. The position and the arc shape of the spot is solid evidence that there is a high-speed outflow/jet on the Al foil impacting the plasma generated on the Cu target, a picture clearly resembling the loop-top X-ray source in solar flare observations. In Fig. 2c, the upflow ejected out of the Al target due to MR can also clearly be seen. It is more than 2 mm with a width of 300 μm, or 2×105 km with width of 3×104 km when scaled for a solar plasma; this is on the order of the typical lengths and widths of X-ray jets observed in solar flares23. The flow velocity was measured to be 400 (±50) km s−1 from time-resolved shadowgrams in the laboratory, which agrees well with the typical Alfvén speed of VA≈400 km s−1, in a magnetic field of 106 G for the experiment as well as the transverse velocity for bi-directional plasma jets of ∼150–300 km s−1 scaled from observations22. Here we assume the scaling law is valid during the whole reconnection process.

For the experiment, the initial state is not in equilibrium. On the edge of the plasma, the force balance is broken down because of an imbalance between the pressure gradient and the Lorentz force. Therefore, the reconnection process is extremely strongly driven. Next, we numerically simulated the experiment with a two-dimensional/3-component Hall MHD code, for the balanced beams with a 600 μm separation (Case 1), and for the imbalanced beams with a 400 μm separation (Case 2). The X-ray emission obtained in both the simulations agrees well with experimental results, as shown in Fig. 3a, and b. The reconnection geometry is found to be ‘Y-type’ (Fig. 3d), justifying the Sweet–Parker geometry, and the decoupling of ion and electron flows is also clearly shown by the black arrows (Fig. 3c) in the region with the ion inertia scale of di=c/ωpi≈100 μm, which is in good agreement with the experiment. A one dimensional cross section of the experimentally observed X-ray images between the two focal spots is also plotted for comparison to the numerical result. It can be seen that the X-ray signal patterns in the regions denoted by black arrows are also where the ion and electron flows are decoupled most significantly in the numerical simulation. The interface between the two X-ray peaks illustrated with red arrows shows a possible electron diffusion region around 10c/ωpe, larger than the theoretical prediction but in a good agreement with a recent MRX measurement29. We also find that reconnection is much faster (t=0.8 ns) than typical Sweet–Parker resistive reconnection, clear evidence of fast reconnection due to both the Hall effect and the boundary conditions30. The simulation of the imbalanced Case 2, as shown in Fig. 3b and d, also reproduced the experimental result in Fig. 2c well.

Figure 3: Simulation results with Hall MHD code.
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a,b, X-ray images of the numerical MR simulation corresponding to the experiments of Fig. 2b and c, respectively. c, The inflow velocity Vz (black triangle for ions and red dot for electrons), together with the one-dimensional cross-section of an X-ray image between the two laser spots in Fig. 2b (blue solid line). The distance between the two X-ray patterns denoted by black arrows is on the order of the ion inertial length 2di≈200 μm, comparable to the size of the ion-electron decoupling region. The interface between the two X-ray patterns, about 20de≈40 μm, is denoted by red arrows. d, The vector velocity of ion (black arrow) and electron (red arrow) flows plotted for the area enlarged from b. The inclination is shown to be in agreement with the experimental result in Fig. 2c.

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The experiment reported here is the first laboratory simulation of a MR induced loop-top X-ray source and outflow/jet with high-power lasers. MG magnetic fields and high-energy-density plasmas generated by intense laser pulses allow us to study astrophysical MR on a laboratory scale. Such measurements with the controlled parameters of laser-produced plasmas should greatly benefit the understanding of not only explosive energy release and particle acceleration processes such as solar flares, but also many other astrophysical phenomena related to MR.