Radiatively Cooled Magnetic Reconnection Experiments Driven by Pulsed Power

We present evidence for strong radiative cooling in a pulsed-power-driven magnetic reconnection experiment. Two aluminum exploding wire arrays, driven by a 20 MA peak current, 300 ns rise time pulse from the Z machine (Sandia National Laboratories), generate strongly-driven plasma flows ($M_A \approx 7$) with anti-parallel magnetic fields, which form a reconnection layer ($S_L \approx 120$) at the mid-plane. The net cooling rate far exceeds the Alfv\'enic transit rate ($\tau_{\text{cool}}^{-1}/\tau_{\text{A}}^{-1}>100$), leading to strong cooling of the reconnection layer. We determine the advected magnetic field and flow velocity using inductive probes positioned in the inflow to the layer, and inflow ion density and temperature from analysis of visible emission spectroscopy. A sharp decrease in X-ray emission from the reconnection layer, measured using filtered diodes and time-gated X-ray imaging, provides evidence for strong cooling of the reconnection layer after its initial formation. X-ray images also show localized hotspots, regions of strong X-ray emission, with velocities comparable to the expected outflow velocity from the reconnection layer. These hotspots are consistent with plasmoids observed in 3D radiative resistive magnetohydrodynamic simulations of the experiment. X-ray spectroscopy further indicates that the hotspots have a temperature (170 eV) much higher than the bulk layer ($\leq$ 75 eV) and inflow temperatures (about 2 eV), and that these hotspots generate the majority of the high-energy (>1 keV) emission.


I. Introduction
][9][10] Reconnection occurs when anti-parallel magnetic field lines advected by plasma flows generate a current sheet, also known as a reconnection layer.In the current sheet, the frozen-in flux condition breaks locally, allowing an abrupt reconfiguration of the magnetic field topology. 3,11,12This process explosively converts magnetic energy into thermal and kinetic energy inside the reconnection layer.
6][27][28][29] In astrophysical systems with strong reconnection-driven radiative emission, radiative cooling can be significant enough to rapidly remove internal energy from a) Current address: Commonwealth Fusion Systems, Devens, MA 01434, USA the system. 14,15,23In particular, radiative cooling becomes important when the cooling rate τ −1 cool dominates the Alfvén transit rate τ −1 A in the reconnection layer, resulting in a large cooling parameter R cool ≡ τ −1 cool /τ −1 A ≫ 1.Here, τ cool ≡ p/P cool is the thermal pressure divided by the net volumetric cooling rate P cool , and τ A ≡ L/V A,in , where L is the layer halflength, and V A,in is the Alfvén speed, calculated just outside the layer.In this regime, the plasma cools significantly before being ejected from the reconnection layer.
][32][33][34][35][36][37][38][39][40][41] Building on earlier work by Kulsrud and Dorman, 30 Uzdensky and McKinney 23 presented the first theoretical description of radiatively-cooled Sweet-Parker-like reconnection.In this theory, the loss of internal energy via radiative emission cools the reconnection layer, leading to compression by the upstream magnetic pressure.This in turn increases the radiative emission rate.When an increase in layer compression causes radiative losses to increase faster than Ohmic dissipation, rapid runaway compression and cooling of the reconnection layer occurs; this process is termed radiative collapse. 23,30Uzdensky and McKinney 23 showed that the Sweet-Parker reconnection rate is modified by a factor equal to the square root of the density compression ratio A, i.e.E/V A,in B in ∼ A 1/2 S −1/2 L .
Here, E and B in are the reconnecting electric and magnetic fields respectively.The lower layer temperature results in a smaller (Spitzer) resistivity η ∼ T −3/2 .Because of the strong compression (A ≫ 1) and lower temperature (hence, lower Lundquist number S L = V A,in L/ η), this theory predicts an increased reconnection rate due to radiative collapse. 23umerical simulations of astrophysical systems in the nonrelativistic resistive MHD regime show evidence for this cooling-driven compression of the reconnection layer, 30,[42][43][44][45] consistent with theoretical predictions.2][33][34][35][36][37][38][39][40][41] Simulations of current sheets unstable to the plasmoid instability in electronpositron pair plasmas cooled via synchrotron emission have additionally shown cooling-driven compression of the density and reconnected magnetic flux inside magnetic islands or 'plasmoids', 46,47 making them sites of enhanced radiative emission in the current sheet. 35,36espite various numerical studies, experimental investigation of radiatively-cooled reconnection remains largely unexplored, in part due to the difficulty in achieving the cooling rates necessary for observing radiative collapse on experimental time scales.
Yamada, Kulsrud, and Ji provide a review of major laboratory experiments of magnetic reconnection. 3The earliest experimental validation of Sweet-Parker theory in a laboratory experiment was provided by the Magnetic Reconnection eXperiment (MRX), which generated a quasi-2D collision-dominated S L > 10 3 reconnection layer in a toroidally symmetric geometry. 48,49MRX, and other magnetically-driven devices such as TREX, 50,51 access a low-density magnetically-dominated regime (n e ∼ 10 12 − 10 13 cm −3 , T e ∼ 10 eV, β ≪ 1) where radiative cooling is negligible.These experiments have provided significant insight into a variety of reconnection physics, such as evidence for strong ion heating, 52 two-fluid effects and Hall reconnection, 50,51,53 as well as magnetic flux pile-up. 51n contrast to low-β magnetically-driven experiments, laser-driven experiments of magnetic reconnection provide access to a strongly-driven β ≫ 1 high-energy-density (HED) regime (n e ∼ 10 20 cm −3 , T e ∼ 1000 eV). 54,55In these experiments, adjacent sub-millimeter spots on a solid target are irradiated with an intense Terawatt-class laser beam.The reconnecting magnetic fields are either self-generated by the Biermann battery effect, 54,[56][57][58] or supplied via external coils 59 or laser-driven capacitor coils. 60Laser-driven experiments have provided evidence for two-fluid effects, 54,58,59 magnetic flux pile-up, 59 and particle acceleration in magnetic reconnection. 60However, despite the high operating pressure, the cooling parameter in these experiments was small as the plasma ions become fully-stripped at these high temperatures, [55][56][57] eliminating strong cooling by atomic transitions.
Pulsed-power-driven experiments are another class of strongly-driven β ≈ 0.1 − 1 HED magnetic reconnection experiments. 613][64][65][66] Each wire array generates radially-diverging (with respect to the array center) flows of magnetized plasma, which collide in the mid-plane, generating a reconnection layer.Experiments on the MAGPIE facility (n e ∼ 10 18 cm −3 , T e ∼ 50 eV) using aluminum wires demonstrated cooling of the ions at a low S L < 10, measured via collective spatially-resolved optical Thomson scattering. 62,67Using lower-Z carbon wires, these experiments accessed higher Lundquist numbers S L ∼ 100, 63,64 at which plasmoid formation was observed, unlike in the lower Lundquist number aluminum experiments. 62,67However, in these carbon experiments, there was negligible cooling of the reconnection layer, as the carbon ions were fully stripped.

Inductive
In this paper, we present results from the Magnetic Reconnection on Z (MARZ) experiments, which build on previous pulsed-power experiments and simultaneously demonstrate both a high S L ≈ 120 and a high cooling parameter R cool > 100.The MARZ experimental platform generates a radiatively-cooled reconnection layer by driving a dual exploding wire array using the Z machine (20 MA peak current, 300 ns rise time, Sandia National Labs). 68The reconnection layer undergoes strong cooling, which is characterized by the rapid decline in X-ray emission generated from the layer.Furthermore, high-energy emission from the layer is dominated by localized fast-moving hotspots, which are consistent with magnetic islands produced by the plasmoid instability 36,46,47 which were seen in three-dimensional resistive magnetohydrodynamic simulations of the experiment. 69hese experiments provide the first quantitative measurements of reconnection and plasmoid formation in a strongly radiatively-cooled regime, and directly characterize the highenergy radiative emission from the reconnection layer, using temporally-and spatially-resolved X-ray diagnostics.This, as mentioned earlier, is of particular astrophysical significance, because of the generation of high-energy emission in reconnecting astrophysical systems. 14,15wo-and three-dimensional radiative resistive magnetohydrodynamic (MHD) simulations of the MARZ experiments were previously reported in Ref. 69.The simulations were performed using GORGON -an Eulerian resistive MHD code with van Leer advection. 70,71The simulations implemented both volumetric radiative loss and P 1/3 multi-group radiation transport, using spectral emissivity and opacity tables generated by the atomic code SpK. 72Line emission dominated in the simulations, providing strong cooling of the reconnection layer.Key results from these simulations are summarized as follows -(1) strong radiative cooling (R cool ≈ 100) drove radiative collapse of the current sheet, resulting in decreased layer temperature and strong compression; and (2) the current sheet was unstable to the plasmoid instability, forming strongly-emitting plasmoids in the reconnection layer, which eventually collapsed due to radiative cooling. 69n this paper, we additionally compare our experimental findings with results from these simulations.Our previous paper 73 provided details on the X-ray diagnostic results from these experiments; this present paper not only expands on the X-ray results, but also contributes results from additional diagnostics, providing context and further characterization of these experiments.
This paper is structured as follows.In §II, we describe the load hardware and the experimental diagnostics.Results from the experiments are described in §III, while analysis of experimental data and discussion of key results, including radiative cooling and plasmoid formation, are provided in §IV.Finally, we outline key conclusions and future work in §V.

II. Experimental and Diagnostic Setup
A. MARZ Load Hardware Figure 1(a-b) show the load hardware.The load consists of two cylindrical exploding arrays, each with 150 equallyspaced, 75 µm diameter aluminum wires.The array diameter is 40 mm, and the array height is 36 mm.The center-to-center separation between the arrays is 60 mm, giving a 10 mm distance between the wires and the mid-plane.Both wire arrays are over-massed, so they generate continuous plasma flows throughout the experiment without exploding. 74,75A scaled experiment that matched the current per wire and driving magnetic field of the MARZ experiment was reported in Ref. 75, using a single planar wire array on the 1 MA COBRA machine.Results from these experiments show good ablation from 75 µm diameter Al wires, with no closure of the interwire and the cathode-wire gaps. 75he Z machine 68 drives a 20 MA peak, 300 ns rise time current pulse through the load, which has an inductance of about 2.5 nH.When current flows through the wires, the wires heat up resistively, and the wire material vaporizes and ionizes to create low-density coronal plasma surrounding the dense wire cores.Current density is concentrated within a thin skin region which generates coronal plasma around the stationary cores.The driving magnetic field points azimuthally inside the cathode-wire gap of each array, and rapidly drops to zero outside the array. 76The global j × B force, therefore, accelerates the coronal plasma radially outwards from each array, and the ablated plasma streams supersonically and super-Alfvénically into the vacuum region outside the arrays.The ablating plasma advects magnetic field from inside the cathode-wire gap to the outside, resulting in radially-diverging flows of magnetized plasma. 77The plasma flows from each array advect frozen-in magnetic field to the mid-plane, where the field lines are anti-parallel and generate a reconnection layer (see Figure 1).
Three MARZ shots (MARZ1, MARZ2, and MARZ3) have been conducted on the Z machine so far.Each shot was fielded with identical load hardware and driving conditions, and an evolving set of diagnostics, as detailed in §II B.

B. Diagnostic Setup
Figure 1(c-d) show the diagnostic setup.We categorize the diagnostics into current, inflow, and reconnection layer diagnostics.Current diagnostics, which include B-dot probes in the magnetically insulated transmission line (MITL) of the Z machine and Laser Photonic Doppler Velocimetry (PDV), monitor current delivery to the load.Inflow diagnostics, which include inductive probes and streaked visible spectroscopy, characterize the plasma ablating from the wires, which in turn, form the inflows into the reconnection layer.Finally, the reconnection layer diagnostics characterize the plasma in the current sheet, and consist of filtered Xray diodes, X-ray imaging, and time-integrated X-ray spec- troscopy.We provide more details on each diagnostic below.

Current Diagnostics
Dual-polarity B-dot probes in the MITL of the Z machine monitor the load current. 78These probes are calibrated, and their signals are numerically integrated to determine the current.PDV 78,79 is used to monitor the current delivered to each individual wire array.PDV tracks the velocity of a copper flyer plate which forms a section of the central conductor of each array, which accelerates due to the driving magnetic pressure. 78A comparison of the measured flyer plate velocity with 1D-MHD simulations is used to calculate the delivered current.Each array contains 4 separate PDV probes which record the flyer plate velocity at different azimuthal locations around the central conductor.The MITL B-dots and PDV are routinely fielded on the Z machine to characterize power flow; details of these systems are provided in Ref. 78.

Inductive probes
We position inductive probes at multiple radial locations around the wire arrays to measure the time-and spaceresolved magnetic field advected by the plasma ablating from the wires.Each inductive probe consists of a single-turn loop created by connecting the inner conductor of a coaxial cable (2 mm outer diameter) to the outer conductor. 80In MARZ1, inductive probes were positioned at radial distances of 5 mm, 8 mm, 11 mm, and 14 mm from the wires, with the normals to the wire loops parallel to the azimuthal magnetic field.In MARZ2 and MARZ3, the probes were at 5 mm, 10 mm, and 20 mm.2][83] We position two probes of oppo-site polarity at each location, separated vertically by 1 cm (see Figure 1d).This allows us to eliminate the contribution of electrostatic voltages via common mode rejection. 81,83Each probe is calibrated before use, and we numerically integrate the signals to determine the magnetic field.

Streaked Visible Spectroscopy
Streaked visible spectroscopy (SVS) 78,84 makes measurements of visible emission spectra from the plasma, along paths in the xy plane, as shown in Figure 1c.Optical fibers collect and transmit light to a spectrometer (1 m McPherson Model 2061 scanning monochromator; 140 mm × 120 mm, 50 G/mm, 6563 Å blaze diffraction grating) and a streak camera (Sydor streak camera; SI-800 CCD) setup.The tip of each fiber (Oz Optics, LPC-06-532-105/125-QM-0.8-1.81CL)consists of a MgF 2 anti-reflection coated collimating lens ( f = 1.85 mm, NA = 0.22).The beam divergence is 57 mrad, resulting in a spot diameter of about 5 mm at the center of the collection volume.The spectral range and resolution of the system are 300 nm and 1.5 nm respectively.The sweep time is about 550 ns, and the temporal resolution is 0.3 ns.In MARZ1, we simultaneously record emission from the plasma ablating from the backside of the arrays at 8 mm and 17 mm from the wires (green line in Figure 1c), using separate SVS systems.In MARZ3, the visible spectroscopy line-of-sight (LOS) includes plasma ablating from both arrays and the plasma in the reconnection layer (blue line in Figure 1c), along y = 26.5 mm and y = 34 mm.

Visible Self-Emission Imaging
In MARZ1, we positioned an additional inductive probe with a 10 mm long 1 mm diameter glass rod attached to its tip, at 15 mm from the wires (hereafter, referred to as the 'T-probe') (see Figure 1c).It provides an extended obstacle that creates a detached bow shock when the flow interacts with the probe.We observe the bow shock using a selfemission gated optical imager (SEGOI). 78SEGOI is an 8frame camera that records 2D self-emission images in the visible range (540-650 nm) on 8 separate micro-channel plates (MCPs).We record images between 320-367 ns, with a 7 ns inter-frame time, 1 ns exposure, and a 8 mm diameter field of view.SEGOI also captures a 1D streak image (sweep time = 300-400 ns) along a line parallel to the T-probe axis, 2 mm below the probe.

X-Ray Diodes
Silicon diodes 78 record the X-ray power generated from the reconnection layer.In MARZ1 and MARZ2, the diode viewed the reconnection layer from the side (side-on).The diode was filtered with 2 µm of aluminized Mylar (Figure 1c).The T = 0.5 transmission cut-off for this filter is at about 100 eV.In MARZ3, the diode viewed the reconnection layer from the top (end-on) [Figure 1d], and was filtered with 8 µmthick beryllium.The T = 0.5 cut-off is at roughly 1 keV.Each diode has a 22.5 µm active layer and a nominal 0.6 mm diameter.The diode response is 0.276 A/W.

X-Ray Imaging
We image the reconnection layer using two time-gated ultra-fast X-ray imaging (UXI) cameras. 78The cameras provide a 25 × 12.5 mm 2 (1025px × 512px) field of view through a 500 µm diameter pinhole (magnification = 1×, geometric resolution ≈ 1 mm).The cameras view the reconnection layer with polar angles of θ = 9 • and θ = 12 • with respect to the z-axis (see Figure 1d), and with azimuthal angles (from the x−axis) of φ = 170 • and φ = 40 • (not shown in Figure 1), thus viewing both the top and side of the layer.The pinholes are filtered with 2 µm thick aluminized Mylar, which filters out photons with energies < 100 eV.Each camera records 4 images with a 20 ns inter-frame time, and a 10 ns exposure time.Data from this diagnostic is only available for MARZ3.
In addition to time-gated imaging, we record timeintegrated X-ray images of the reconnection layer, using two pinhole cameras viewing the layer from the top with polar angles of roughly 5 • .Pinhole diameters of 300 µm and 500 µm are used.Each camera has 3 pinholes of the same diameter but different filtration that generate three images (magnification ≈ 0.5, resolution ≈ 450 − 750 µm) of the reconnection layer on a 64 mm × 34 mm image plate.

Time-integrated X-Ray Spectroscopy
An X-ray scattering spectrometer (XRS 3 ) 78,85 with a spherically-bent quartz crystal provides time-integrated spatially-resolved (along the out-of-plane z direction, resolution: ∆z ≈ 200 µm) measurements of X-ray emission spectra from the reconnection layer.The range and spectral resolution of the spectrometer in the MARZ experiments were 1.5-1.9keV and ∆E ≈ 0.5 eV respectively.We record the X-ray spectrum on an image plate (Fuji TR), filtered with a 11 µm thick beryllium filter.Data was recorded in either of two configurations -(1) 150 mm radius crystal, crystal-to-target separation = 800 mm, and a 8 µm kapton filter on the spectrometer entrance slit; and (2) 200 mm radius crystal, crystal-to-target separation = 500 mm, and no kapton filter.Configuration 1 was used for MARZ1 and MARZ2, while configuration 2 was used for MARZ3.

III. Results
We describe the experimental results from our diagnostics in this section.In MARZ2, damage to one of the arrays during installation produced results which were unreproducible.Therefore, we show results primarily from MARZ1 and MARZ3, with some exceptions.

A. Current Measurements
Figure 2a shows the averaged current measured by the MITL B-dot probes in MARZ1 and MARZ2.The Z machine consistently delivered a peak current of roughly 21 MA, with a rise time of about 300 ns across the two shots.The shot-toshot variation in the delivered current was < 5%.
Figure 2b shows the current measured by the PDV diagnostic for all three shots.We show the averaged current for the east (solid line) and west (dashed line) arrays in each shot.Figure 2b shows equal current division between the arrays.As expected, the shape of the current pulse measured by PDV matches that of the current measured by the MITL B-dots.The peak value in each array is roughly 10 MA, showing negligible current loss between the MITL and the load.Current measurements by the MITL B-dot probes are not available for MARZ3, but the PDV measurements in Figure 2b show that the current delivered to the load in this shot was consistent with the other two shots.

B. Magnetic Field and Velocity in the Inflow Region
Figure 3a shows the voltage signals from probes in MARZ1.We only show the inductive component of the signals V = 0.5(V + −V − ), determined from common mode rejection of signals from the two opposite-polarity probes at each location.The signals in Figure 3a are all similar in shape, but displaced in time, which is expected due to the advection of the frozen-in magnetic field by the plasma between the locations of the probes. 77,83We note that the probes are placed on the side of the arrays opposite to that of the reconnection layer (as shown in Figure 1), so they measure the 'unperturbed' magnetic field in the inflow, not affected by reconnection.
We numerically integrate the signals in Figure 3a to determine the magnetic field, as shown in Figure 3b.][83] In Figure 3b, two separate probes at 5 mm from the wires record the magnetic field from different arrays.Both probes exhibit similar magnetic fields, consistent with equal current splitting between the arrays, as described in §III A. Figure 3c shows the magnetic field recorded in MARZ3.The recorded magnetic field is slightly larger than that in MARZ1.Here, inductive probes measuring the magnetic field from the two arrays at 20 mm from the wires show identical magnetic fields, consistent with equal current splitting.We note that in MARZ3, the two opposite-polarity probes at 5 mm recorded significantly different signals.The signal on the bottom probe was consistent with the expected field magnitude (based on measurements in MARZ1), while the other was anomalously high.Therefore, we discard the anomalous signal and only report data from one probe at 5 mm in Figure 3c.
Finally, we note that probes measuring the advected magnetic field from different arrays at the same radial distance in MARZ2 measured significantly higher advected magnetic field on the west array, despite equal current splitting observed in Figure 2b.The west array was partly damaged during installation on this shot, and the probes were measuring the magnetic field from the damaged section of the array.
The delay in the voltage signals between probes at different locations provides an estimate of the average flow velocity. 83igure 4a shows the voltage signals recorded by probes in MARZ1 at 5 mm and 8 mm respectively.The signals show several identifiable features, indicated via circles in Figure 4a.By tracking the transit time of these features, we estimate the flow velocity, as shown in Figure 4b.The flow velocity is roughly 110 km s −1 , consistent with flow velocities previously recorded in pulsed-power-driven wire arrays. 61,66In Figure 4c, we show the inductive probe voltage measurements at 5 mm and 10 mm from the wires for MARZ3, together with the estimated flow velocity in Figure 4d.On this shot, the recorded flow velocity varied between 100 − 200 km s −1 .

C. Measurements of Visible Spectra in the Inflow
Figure 5 shows streak images of the visible emission spectra collected at 8 mm and 17 mm from the wires respectively in MARZ1.Note that these spectra are from the side of the wire arrays opposite the reconnection layer (see Figure 1c).We have applied corrections to these spectra for distortions by streak camera optics, timing corrections for spectral differences in photon transit delay over the fiber length, as well as relative intensity corrections due to the wavelength-dependent response of the spectrometer. 84Wavelength calibration and instrument broadening (about 1.5 nm) were determined using preshot images of 458 nm and 543 nm laser lines recorded by each SVS system.
The streak camera first records emission at roughly 90 ns for the 8 mm system (Figure 5a).This corresponds to an average flow velocity of roughly 90 km s −1 between the wire and probe locations; the estimated velocity is consistent with that estimated from inductive probe measurements (Figure 4).Compared to the spectra at 8 mm, emission at 17 mm is first recorded later at roughly 140 ns, corresponding to an average velocity of roughly 120 km s −1 (Figure 5c).Finally, by integrating the spectral intensity in wavelength space, we find that the temporal evolution of intensity I(λ )dλ (which depends on the plasma density) roughly matches that of the advected magnetic field shown in Figure 3.
Figure 5(b and d) show lineouts of the streak images at different times, each averaged over 10 ns.The spectra at both radial locations show well-defined Al-II and Al-III emission lines, which correspond to transitions in singly-and doublyionized aluminum respectively.Later in time, continuum emission begins to dominate over line emission.This occurs at around 300 ns and 450 ns for the 8 mm and 17 mm observations respectively.Late in time, the spectra also exhibit absorption features corresponding to Al-II and Al-III transitions, as indicated in Figure 5.We use the Al emission lines to estimate time-resolved values of ion density and electron temperature in the inflow region.This analysis, performed using collisonal-radiative and radiation transport modeling, is described in §IV B.
In MARZ3, the diagnostic LOS included plasma in the reconnection layer and that ablating from both wire arrays, as shown in Figure 1c (blue line).The spectra, shown in Figure 5(e-f), are similar to that recorded in MARZ1 (Figure 5), with well-defined Al-II and Al-III emission features.However, between 150-350 ns, the Al-II 624 nm transition, which appears as an emission line in Figure 5(a-d), now appears as an absorption feature in Figure 5(e-f).We discuss the origin of this absorption feature in §IV B.
In addition, the spectra exhibit features associated with the coatings on the optical components.The streak images show a stray Na-I line at roughly 485 nm early in time, as well as a strong Na-I absorption feature later in time.These features are not generated by the aluminum plasma, but are instead stray features generated from the optical coatings in the system.These stray features appear at around the same time in all streak images.

D. Bow shock Imaging
Figure 6 shows an optical self-emission image of the T-bar probe at 346 ns.A bow shock, which appears as a curved re-gion of enhanced emission, forms around the T-probe.Shock formation around the T-probe provides visual confirmation of wire array ablation and generation of supersonic flow.Multiframe self-emission images, as well as the 1D streak image of the bow shock, show that the shock front remains invariant in time between 300-400 ns.The shock angle, determined from the derivative of the shock front position (red curve in Figure 6), asymptotes to about 30 • .

E. X-Ray emission from the reconnection layer
We now present results from the reconnection layer diagnostics, which characterize the temporal, spatial, and spectral properties of X-ray emission from the reconnection layer.

X-Ray diodes
The X-ray diodes characterize the temporal evolution of Xray emission from the reconnection layer.Figure 7 shows the signals from the side-on (blue, grey) and end-on (red) diodes.All three diode signals exhibit a peak in X-ray emission at about 220 ns.For the side-on diodes, which measure > 100 eV photons, the emission first ramps up around 150 ns, and the full-width-at-half-maximum (FWHM) of the signal is about 80 − 90 ns.Similarly, the signal from the end-on diode, which records comparatively harder X-rays with energy > 1 keV, initially ramps up around 200 ns, and exhibits a FWHM of roughly 50 ns.The X-ray emission peaks around 220 ns on all diodes, and then falls sharply.The shape of the X-ray emission is much sharper than that of the driving current pulse, which peaks about 100 ns after the peak in X-ray emission (see Figure 2).This shows that the emission feature is related to the dynamics of the current sheet, rather than the driving current.In addition, the diodes consistently record a small emission feature at about 100 ns.This feature may be related to the initial arrival of plasma at the mid-plane.of the emission, the width of the emitting region (along x) also decreases with time.Peak emission is recorded between 210 − 220 ns.By 250 ns, the emission has fallen significantly, and the layer is no longer visible on the X-ray cameras.

Time-gated X-ray Imaging
The X-ray images provide information about the spatial distribution of emission from the reconnection layer.Emission is highly inhomogeneous -Figure 8(a-b) shows sub-millimeter scale regions of enhanced emission embedded within the less brightly emitting layer.The intensity of emission from the hotspots is > 10 times higher than the average intensity from the rest of the layer.The presence of emission hotspots indicates localized regions of plasma with higher temperature or density relative to the rest of the layer.
These hotspots, indicated via green and yellow arrows in Figure 8(a-b), can be observed in images from both cameras to travel away from the center of the layer.We track the translation of the hotspot centroids between successive frames to estimate their velocities.Figure 9 shows the estimated hotspot velocity calculated using images from camera A between 220-240 ns (green), and from camera B between 190-210 ns (yellow).The hotspot velocities are consistent between both cameras.Hotspots accelerate along the ±ydirection, away from the center of the layer.Hotspot velocity increases from 0 km s −1 to about 50 km s −1 over a distance of roughly 10 mm.We will show in §IV F that the observed hotspot velocity is consistent with the expected velocity of the outflows from the reconnection layer.

Time-integrated X-ray Imaging
Figure 8c shows a time-integrated X-ray image of the reconnection layer.The image is recorded with a 300 µm diameter pinhole, filtered with 2 µm aluminized Mylar, identical to the time-gated X-ray cameras in §III E 2. Figure 8c shows an elongated region of bright emission.The extent of the emission region in the y−direction is about 60 mm, while the FWHM along the x−direction is 1.6±0.5 mm.The FWHM of the emitting region was determined by fitting a Gaussian function to the intensity variation along x at different y−positions.Here, we only show one of the recorded time-integrated X-ray images; however, the features of the image in Figure 8c are consistent with the other images recorded in the experiment.

X-ray spectroscopy
Figure 10(a-b) show the time-integrated spectrum of the X-ray emission from the reconnection layer for MARZ1 and MARZ3.Emission lines with energies 1570-1600 eV were observed in both shots.Although the output is timeintegrated, the end-on diode signal (filtered with 8 µm Be), which measured > 1 keV X-ray emission (see Figure 7), shows that the spectrum was generated around 220 ± 25 ns.
Lineouts of the recorded spectrum averaged over z = 10 ± 0.5 mm and z = −10 ± 0.5 mm are shown in Figure 10(c-d).We label the Al K-shell emission lines, which include He-like and Li-like satellite transitions.The He-like lines correspond to transitions in Al-XII ions (2 bound electrons, Z = 11).Identified He-like lines include the He-α resonance line (1598 eV), the He-α inter-combination (IC) line (1588 eV), and He-α resonance lines with 3p and 3d spectator electrons (1594 eV, 1596 eV).The He-α resonance line (2p 1 P 1 → 1s 1 S 0 ) repre- sents a transition to the ground state 1 S 0 from the next highest energy state 1 P 1 of the singlet system, while the inter-combination transition (2p 3 P 1 → 1s 1 S 0 ) occurs between the upper term of the triplet system 3 P 1 and the lower term of the singlet system 1 S 0 . 86,87The transitions shielded by spectator electrons appear at energies lower than the resonance transition.In the recorded spectra, the He-α resonance and IC lines exhibit roughly similar intensities, while the He-α transitions with spectator electrons have lower intensities.
The intensity and spectral position of the recorded lines exhibit modulations along the z-direction.This can be observed in Figure 10, which shows a higher intensity of the lines for z < 0 mm.In Figure 10b, red crosses indicate the position of He-α IC line; the spectral position varies with z, and the magnitude of this deviation is < 1 eV.We discuss potential reasons for the observed modulation in a later section.
Although we only show data from MARZ1 and MARZ3 in Figure 10, results from MARZ2 also exhibit the same emission lines, and the line ratios are consistent with that in MARZ1 and MARZ3.In §IV E, we use the line ratios of the observed He-like lines and Li-like satellites to constrain the density, temperature, and homogeneity of the emitting plasma in the reconnection layer.

A. Current and Magnetic Field Measurements
In §III A, we observed equal current division of the MITL current between the two wire arrays.In addition, inductive probes measuring the advected magnetic field from separate arrays at the same radial distance (5 mm in MARZ1, 20 mm in MARZ3) recorded similar magnetic field strength, consistent with equal current splitting (Figure 3).
The advected magnetic field, however, does not reproduce the shape of the driving current, but instead exhibits a slower initial rise, followed by a faster ramping up later in time.This happens at around 320 ns for the 5 mm probes in MARZ1 and MARZ3, as seen in Figure 3(b and c).This effect was also observed in simulations of the experiment, and was found to be a consequence of a change in the wire ablation due to heating of the wire cores. 69In the simulations, the wire cores cool initially, but eventually begin to heat up due to re-absorption of emission generated by the surrounding plasma.The hotter cores are more conductive, and restrict the transport of magnetic field into the plasma flow from the cathode-wire gap.Although this effect is an important consequence of radiation transport observed both in the experiment and simulations, 69 we note that the rise in the magnetic field occurs well after the onset of strong cooling in the experiments (around 220 ns), as discussed later in §IV D.

B. Density and temperature in the inflow region
We estimate the ion density n i and electron temperature T e in the inflow to the reconnection layer by performing leastsquares-fitting of synthetic spectra to the measured visible spectroscopy data shown in Figure 5(a-d).The synthetic spectra I ω are generated by solving the steady-state radiation transport equation (Equation 1) 88 along the spectrometer's line-of-sight (LOS) s [see Figure 1], using spectral emissivity ε ω (n i , T e ) and absorption opacity α ω (n i , T e ) values calculated by PrismSPECT. 89 The PrismSPECT model uses a steady-state non-local thermodynamic equilibrium (nLTE) model with Maxwellian free electrons.The PrismSPECT calculations additionally assume a zero-width plasma with no background radiation field; comparison of finite width PrismSPECT simulation results with the zero-width results show that the effect of background radiation is negligible in this regime. 90s shown by the green line in Figure 1c, the diagnostic LOS samples plasma ablating from only one array in MARZ1.To solve radiation transport, we assume constant electron temperature along this LOS s.Previous experimental measurements in exploding wire arrays show little spatial variation in the temperature due to high thermal conductivity in pulsedpower-driven plasmas.Because the density falls with radial distance from the wires, 81,82 we expect density along the LOS to peak at the center and fall towards the edges.The rocket model provides a simple description of the variation of mass density generated from wire arrays: 74,92 ρ r,t Here, r is the radial location around the wire array, R 0 = 20 mm is the radius of the wire array, and V is the ablation velocity.A Gaussian function n i (s,t) = n 0 (t) exp[(s − s 0 ) 2 /2σ (t) 2 ], with peak value n 0 (t) and standard deviation σ (t) is a good approximation to the expected density along s calculated from Equation 2. Here, s 0 is the center of the diagnostic LOS.Furthermore, using the measured value of the flow velocity V ≈ 110 km s −1 (see Figure 4), we constrain the value of σ (t) for our analysis, reducing the number of unknowns for fitting.
Figure 11a shows a synthetic fit (orange) to the measured spectrum (black) for the Al-II and Al-III inter-stage lines between 440-480 nm at 220 ± 5 ns, collected at 8 mm from the wires in MARZ1.The synthetic fit reproduces the experimental spectrum well.Ion density is sensitive to the width of the well-isolated Al-II 466 nm line, and electron temperature is sensitive to the line ratio of the inter-stage Al-II 466 nm and Al-III 448 nm and 452 nm lines.Temperature variations modify the relative population densities of the Al-II and Al-III ionization states.Increasing the temperature therefore increases the relative intensity of Al-III lines, while the Al-II lines become weaker, and completely disappear for temperatures T e > 4 eV, thus placing an upper bound on the electron temperature.
The time-resolved ion density and electron temperature determined from this analysis at 8 mm from the wires are shown in Figure 11b ance of the line emission is consistent with a rise in the ion density n i ⪆ 3 × 10 18 cm −3 and temperature T e ⪆ 3 eV.The increasing density is also consistent with the increasing total emission I(λ )dλ measured at this time in Figure 5a.Further from the array, at 17 mm from the wires (Figure 5d), the electron temperature is found to be roughly 2 eV between 220-380 ns, and the ion density is lower, at about 2 − 6 × 10 17 cm −3 further away from the wires.This shows that the temperature remains roughly constant in the plasma flows, while the density falls with radial distance from the wires, as expected due to divergence.
Finally, we perform synthetic spectral and radiation transport modeling to better understand the absorption features observed in MARZ3 [Figure 5(e-f)], which samples plasma emission and absorption along a chord that includes both arrays and the layer plasma (blue line in Figure 1c).We model the plasma from each array with a Gaussian density (same peak value n 0 and variance σ 2 ) and a homogeneous temperature T 0 .The layer is modeled as a region of thickness 1.5 mm with ion density n L and temperature T L .A parametric study was performed by varying the layer density and temperature, and the synthetic modeling shows that the layer acts as a continuum backlighter, generating emission that is absorbed by the array plasma between the layer and the collection optics.The synthetic modeling allows us to qualitatively compare the layer density to the array density through inspection of emission and absorption features.When the the layer density n L is comparable to the peak array plasma density n 0 , the higheropacity Al-II 624 nm line appears as an absorption feature, whereas the other Al lines appear as emission features, which is what is seen in the experiment.For layer densities much greater than the array plasma density, all of the Al lines appear as absorption features, whereas for layer densities less than the array density, all Al lines are emission features.Therefore, the presence of the Al-II 624 nm absorption feature in our experimental spectra [(Figure 5(e-f)] is consistent with the layer density being similar to the array plasma density at this location (y = 26.5 mm), which is far away from the center of the layer.Spectra collected further downstream in MARZ3 (y = 35 mm) only show emission features and no absorption features, indicating that the layer density decreases as the plasma flows away from the center of the reconnection layer, consistent with resistive MHD simulations of the experiment. 69

C. Bow Shock Analysis
The measured Mach angle of the bow shock around the T-probe (Figure 6) can provide information about the Mach number in the inflow region.The estimated Mach angle µ of the shock is about µ ≈ 30 • , which corresponds to an upstream Mach number of about M up = 1/ sin(µ) ≈ 2. The shock standoff distance, estimated from the width of the emission region at the leading edge of the probe, is about 0.2 mm.The negligible change in the shock structure between 300-400 ns also indicates that the Mach number remains roughly constant.
The resistive diffusion time of the magnetic field through the obstacle and the stagnated plasma is about τ η ∼ (1 mm) 2 / ηglass + (0.2 mm) 2 / ηplasma ∼ 0.1 − 1 ns, which is smaller than the hydrodynamic time L/V ≈ 5 ns.Here, we estimate the magnetic diffusivity ηplasma using Spitzer resistivity calculated with a temperature of T e ≈ 2 − 10 eV.The flow velocity at this time V (t = 350 ns) ≈ 200 km s −1 is determined from the transit time of the plasma to the T-probe.Since the hydrodynamic time is comparable to the diffusion time, decoupling of the magnetic field and the plasma can result in hydrodynamic shock formation. 81,82From the sonic Mach number M S = V /C S ≈ 2 and the measured flow velocity, we estimate the ion sound speed C S ≈ ZT e /m i ≈ 100 km s −1 .However, this results in an estimated temperature of ZT e ≈ 2 keV, which is three orders of magnitude larger than the measured temperature in the inflow region from visible spectroscopy.
If, on the other hand, we assume that the shock is magnetohydrodynamic and magnetically dominated β ≪ 1, then M A = V /V A , and the expected Alfvén speed is V A ≈ B/ √ ρ µ 0 ≈ 100 km s −1 .In §IV F, we show that the plasma β ≈ 0.1 in the inflow region.From the measured value of the magnetic field (B ≈ 3 T) at this time, the estimated ion density from the shock shape is 2 × 10 16 cm −3 , which is an order of magnitude lower than the expected density inferred from visible spectroscopy.We note that this is an upper bound on the density estimate from the shock shape, because the probe would measure a higher compressed magnetic field for MHD shock formation.
Therefore, the observed shock shape does not match the inflow conditions measured using inductive probes and visible spectroscopy.A potential cause of this discrepancy could be the generation of photo-ionized plasma from the probe surface, because of the harsh X-ray environment provided by the Z machine.Photo-ionized plasma at the T-probe tip may increase the post-shock pressure, creating a larger shock angle.
Further investigation of this mismatch will require direct measurements of the post-shock density and temperature, and will be pursued in future experiments.

D. Radiative Cooling and Generation of High-Energy Emission from the Reconnection Layer
The X-ray diode signals (Figure 7) and the X-ray cameras (Figure 8) both show a transient burst of high-energy X-ray emission from the reconnection layer.The initial rise in X-ray emission is consistent with increasing density and/or temperature of the reconnection layer during the formation stage.The temperature in the layer is initially high enough to generate high-energy X-rays with energies > 1 keV.The subsequent (a) fall in X-ray emission after 220 ns is consistent with rapid radiative cooling of the layer.The temporal change of X-ray intensity measured by the diodes also matches the intensity evolution observed in the X-ray images (Figure 8).We also observe a sharp fall in X-ray emission from the reconnection layer in radiative resistive MHD simulations of the MARZ experiment. 69In the simulations, radiative collapse of the current sheet, characterized by a sharp fall in the layer temperature and a simultaneous rise in density, begins around 200 ns after current start.In Figure 12a, we plot synthetic diagnostic data, calculated from simulations, of the filtered X-ray emission generated from the reconnection layer as a function of time.The filtered X-ray emission is generated by post-processing the simulation results using radiation transport modeling in XP2. 69We spatially integrate the output intensity, and filter it using transmission curves for both 8 µm Be and 2 µm Mylar, in order to match the diode filters in the experiment.In Figure 12a, we additionally show the expected X-ray emission (filtered with 8 µm Be) for the case with no radiative cooling.
In the absence of radiative cooling, X-ray emission from the layer would continue to rise, as the layer density ramps up in time at a consistently high temperature > 100 eV.In the radiatively-cooled case, however, the emission peaks and then falls sharply, similar to that in the experiment.The temperature in the layer is initially > 100 eV, which is high enough to generate > 1 keV X-rays.However, the subsequent fall in X-ray emission occurs due to radiative collapse of the layer, which rapidly cools as the density increases.The simulations therefore confirm that the rapid fall in X-ray emission is an experimental signature for strong radiative cooling of the reconnection layer.Figure 12a also shows that the FWHM of the harder (> 1 keV) emission is shorter than that of softer > 100 eV emission, similar to that in the experiment.This is expected, since as the temperature of the emitting plasma falls, the spectral distribution of the emitted radiation shifts to lower energies.Thus, the higher-energy emission falls earlier than the lower-energy emission.
Simultaneous measurements of X-ray emission by the 8 µm Be and 2 µm Mylar filtered diodes in the experiment (Figure 7) provide constraints on the temperature of the emitting plasma.Figure 12c shows the emissivity of an aluminum plasma with ion density 5 × 10 18 cm −3 as a function of the plasma temperature, calculated using the atomic code Spk. 93pk uses a nLTE model and includes line, recombination, and bremsstrahlung emission. 69The unfiltered emissivity exhibits a smaller peak around T ≈ 50 eV; the emissivity is lower between 50-100 eV, and increases for T > 100 eV.The smaller peak results from L-shell line emission of photons with energies of 100 − 300 eV, while the increased emission at temperatures T > 100 eV is due to higher energy > 1 keV Al K-shell emission.We also show the emissivity filtered using X-ray transmission tables for 8 µm Be and 2 µm Mylar in Figure 12c.The 8 µm Be filter significantly attenuates radiation with energies < 1 keV, whereas the 2 µm Mylar filter exhibits a smaller window of transmission around photon energies ≈ 200 eV.Therefore, the filtered emissivity through 2 µm Mylar is significant for temperatures T > 25 eV, while for 8 µm Be the signal is only significant for temperatures T > 100 eV. 94he different responses of the filtered diodes shown in Figure 12c allows us to constrain the temperature of the emitting plasma.Initially, in region A (see Figure 7), where neither diode records any signal, we expect the plasma temperature to be T < 25 eV.In region B, where the Mylar diode records signal, while the Be diode does not, the temperature of the emitting plasma is constrained to be 25 < T < 100 eV.In C, where both diodes simultaneously record signals, the temperature must be T > 100 eV.Similarly, the expected temperature is 25 < T < 100 eV, and T < 25 eV in regions D and E respectively.Therefore, the diode signals indicate an initial heating of the reconnection layer to temperatures > 100 eV, followed by a sharp fall below T < 25 eV due to radiative cooling.We show later that the expected temperature at the time of peak emission (region C), is consistent with results from X-ray spectroscopy analysis in §IV E.
The diodes collect time-resolved emission integrated over the entire reconnection layer.The time-gated X-ray images (Figure 8) complement this measurement by providing spatial resolution at discrete times.These images were also filtered with 2 µm Mylar, and at around 190-200 ns both the layer and hotspots generate emission in the spectral range transmitted by the Mylar filter, indicating both the hotspots and the layer have T > 25 eV.Later in time (230-240 ns), the hotspots remain bright, while emission from the layer has significantly decreased.This indicates that the layer has cooled to T < 25 eV, while the hotspots have remained above 25 eV, such that the signal on the Mylar filtered diode is dominated by hotspot emission.By 250 ns, there is no emission recorded on the X-ray camera or the Mylar filtered diode, consistent with both the hotspots and the layer cooling to T < 25 eV.
Figure 12(d-g) show synthetic X-ray images of the reconnection layer generated from post-processing the 3D simulation results in XP2 between 190-250 ns.The synthetic images are filtered with 2 µm Mylar, and use the same LOS as X-ray camera B in the experiment (see Figure 1d).As observed in Figure 12(d-g), emission from the reconnection layer falls as a result of radiative cooling, consistent with the experimental images in Figure 8.The synthetic images also show hotspots of emission within the elongated reconnection layer, similar to that in the experiment.These hotspots correspond to the position of magnetic islands or plasmoids in the simulations, which are generated by the tearing instability. 47,95The plasmoids appear as localized regions of enhanced emission due to their relatively higher electron density and temperature. 69Enhanced emission from plasmoids has also been reported in relativistic-PIC simulations of extreme astrophysical objects. 35he majority of the high-energy emission is generated by the plasmoids in our simulations because of their higher temperature.This can be observed in Figure 12b, which shows X-ray emission from the reconnection layer filtered with 8 µm Be.Emission recorded by the 8 µm Be filtered diode in the experiment may thus be dominated by higher energy emission from the hotspots with temperature T > 100 eV.This is further supported by the analysis of X-ray spectroscopy from the experiment, which is provided in the following subsection.

E. Analysis of X-Ray Spectroscopy
We estimate the temperature and density of the plasma in the reconnection layer by comparing the measured spectra shown in Figure 10 with synthetic spectra.We use the atomic code SCRAM to generate nLTE spectral emissivity ε ω (n i , T e ) and absorption opacity α ω (n i , T e ) tables, 96 which are then used to solve the radiation transport equation 88 (Equation 1) along the diagnostic LOS to model the output intensity spectrum.For this analysis, SCRAM includes spectral line broadening effects (Stark and thermal Doppler), and incorporates a background radiation field by assuming a homogeneous cylindrical plasma of diameter 1 mm.A characteristic length of 1 mm is chosen because it is comparable to the width of the X-ray emission region, as observed in X-ray images of the reconnection layer (Figure 8, Figure 8c).The contribution of scattering to the total opacity is expected to be small in this regime, and is thus, excluded from the SCRAM calculations.
The SCRAM results show that Al K-shell lines do not appear for temperatures below 60 eV.Furthermore, as expected for inter-stage transitions, 87 the relative emissivities of the Li-like satellites and He-like lines are strong functions of temperature.Li-like satellites exhibit higher emissivities at lower temperatures, whereas the emissivity of Helike lines dominates at higher temperatures.The He-α resonance transition exhibits much higher emissivities and opacities compared to the other He-like lines, consistent with the relatively higher probability of the resonance transition. 86,87t T e ≈ 100 eV, the Li-j,k,l satellites and the He-α resonance line have similar emissivity values; however, the opacity of the He-α resonance line is several orders of magnitude higher than both the Li-like satellites and other He-like lines.For instance, at n i = 1 × 10 18 cm −3 and T e = 100 eV, the attenuation length scale α −1 ω for the He-α resonance line is about 0.1 mm, while that for the other He-like lines and Li-like satellites is > 10 mm.Therefore, due to the high opacity of the He-α resonance line, radiation transport calculations are required to accurately model the spectral intensity of the emission from the reconnection layer.
To solve the 1D radiation transport problem along the diagnostic LOS, we first assume emission from a plasma of length d with homogeneous ion density n i and electron temperature T .Values of n i , T , and d are then randomly sampled from uniform distributions to find solutions that match within 20% the experimentally observed line ratios.The model includes the effect of source and instrument broadening, but neglects Doppler shift, which is < 0.25 eV, as calculated from the hotspot velocities in Figure 9.In particular, we compare three different line ratios shown in Figure 10d -(A) He-α IC / He-α Resonance (blue), (B) He-α IC / Li-j Satellite (red), and (C) He-α IC / He-α with 3p spectator (green).Figure 13 shows a corner plot of the solutions that individually satisfy these line ratios at z = 10 mm in MARZ3 (see Figure 10d).The corner plot shows one and two-dimensional projections of the three-dimensional parameter space --Figure 13(b, d, and e) are 2D scatter plots for solutions, while Figure 13(a,c  and f) show the probability distribution functions for the values of n i , T and d of the solutions.The solid contours in Figure 13(b, d, and e) enclose 90% of the solutions.The intersection of the solutions for these line ratios constrains the properties of the emitting plasma.
As seen in Figure 13b, which shows a scatter plot of the ion density against temperature, solutions for the B (red) and C (green) line ratios constrain T e to a narrow band around T ≈ 170 ± 20 eV, and provide an upper bound of about n i ≲ 5 × 10 18 cm −3 on the ion density (indicated via the black dashed line).These bounds are determined from the intersection of these solutions.The size of the plasma d is poorly constrained from these line ratios, since line ratios B and C are for the optically thin lines, and optical depth (α ω (n i , T e )d) thus has a limited effect.Figure 13(d and e) also clearly show overlapping solutions at T ≈ 170 ± 20 eV and n i ≲ 5 × 10 18 cm −3 respectively, but exhibit a wide range of possible values for d.
The size of the emitting plasma can, however, be con-strained through solutions for line ratio A (blue).Line ratio A is the relative intensity of the He-α IC compared to the higher opacity He-α resonance line, which is a strong function of optical depth.This line ratio is well satisfied for a wide range of T , n i and d; however, from Figure 13d, we observe that for temperatures T = 170 ± 20 eV that satisfy line ratios B and C, line ratio A is only satisfied for d ≤ 0.8 mm (indicated via the black dashed line).If the size of the emitting plasma exceeds this value, we can no longer satisfy all line ratios simultaneously because of over-damping of the high-opacity He-α resonance line.Notably this value for d is significantly lower than the length of the reconnection layer observed in Figure 8c, which implies that only a small region of the layer is contributing to the the emissivity and opacity of the system for these photon energies.This is further illustrated in Figure 13h, which compares two synthetic spectra to the experimental spectrum at z = 10 mm (MARZ3).Both synthetic spectra are calculated for T = 170 eV and n i = 1 × 10 18 cm −3 , but using sizes of d = 0.5 mm (red) and d = 5 mm (blue) respectively.As expected, the synthetic spectrum for d = 0.5 mm reproduces the line ratios and line widths of the experimental spectrum well.The synthetic spectrum for d = 5 mm reproduces the relative intensities of the Li-like satellites and the He-α IC and spectator transitions, but fails to reproduce the He-α resonance line.This analysis therefore indicates that Al K-shell emission from the reconnection layer is predominantly generated by sub-millimeter size hotspots in the layer.This is further supported by the X-ray images of the layer (Figure 8) that show the presence of strongly-emitting hotspots of size < 1 mm, as well as by the simulations, which show strong localized emission of > 1 keV photons from the plasmoids (Figure 12b).Assuming that the hotspot density lies between the upper bound of n i ≤ 5 × 10 18 cm −3 and the lower bound of n i ≥ 5 × 10 17 cm −3 , which is the inflow density from visible spectroscopy (Figure 11), we find, from Figure 13e, that 0.3 ≤ d ≤ 0.5 mm, consistent with the plasmoid widths observed in simulations. 69o estimate an upper bound on the bulk temperature of the layer, we consider a simple model that includes a single hotspot of size d embedded in a homogeneous layer with emissivity ε L and opacity α L , as shown in Figure 13g.Radiation transport solutions for this model indicate that the bulk layer temperature must be less than about T bulk ≤ 75 eV.At around T bulk ≈ 75 eV, contribution from the layer is not negligible and modifies the spectral intensity from the hotspots; however, solutions that satisfy the line ratios in the experiment are still possible.At higher layer temperatures, the He-α resonance line becomes strongly absorbed by the layer, and the experimental spectrum can no longer be reproduced.
Figure 10 shows that the hotspots form elongated structures of length ∼ 10 mm along z.The above analysis was repeated at multiple z-positions for the different shots.Although bounds on the inferred hotspot density, temperature, and size show slight variations along z, the values remain largely consistent.This is unsurprising because the same Al K-shell lines are observed at different z and the line ratios remain largely similar, despite small modulations, as seen in Figure 10.The mod- ulation in the spectral position of the lines is unlikely to be caused by Doppler shift -as mentioned before, the maximum Doppler shift expected is 0.25 eV, which is smaller than the 1 eV modulation seen in Figure 10.The spectral modulations could be a result of modulations in the position of the hotspots in the object plane along x.Deviations in the source position can lead to deviations in the position of the lines recorded on the image plate.From ray tracing simulations, 85 the observed deviation in spectral position corresponds to a roughly 1 mm deviation in the position of the hotspots.This deviation is comparable to the amplitude of the modulations in the plasmoid position generated by the MHD kink instability in the 3D simulation of the experiment. 69Thus, the spectral deviation of the lines along z may be a preliminary indication of the MHD kink instability of the plasmoids.

F. Cooling Rate
Analysis of experimental data in the previous sections has provided quantitative estimates of the plasma properties.In this section, we use these experimental results to further characterize the net cooling rate in the reconnection layer at the time of the onset of strong radiative cooling.
The temporal evolution of the reconnection layer temperature depends on the relative magnitudes of the terms in the internal energy equation: 97 Here, ρε = p/(γ − 1) is the internal energy density, ∇ • (ρεv) is the advective term, η| j| 2 , −p∇ • v, and ∇v : τ are the compressional, resistive, and viscous heating terms respectively.Lastly, P rad is the volumetric radiative loss from the layer.We can estimate the order-of-magnitude of these terms based on the plasma parameters in the layer and in the inflow, as shown in the second column of Table I.Here, B in , p in and V in are the magnetic field, thermal pressure, and velocity in the inflow just outside the layer, and p L and V out are the layer pressure and the reconnection outflow velocity.The half-length and the half-width of the layer are denoted by L and δ respectively.Lastly, η and µ are the (Spitzer) resistivity and plasma viscosity, 98 while γ is the adiabatic index. 88o determine the net cooling rate, we require estimates of the inflow and layer parameters listed above.In our previous paper, Ref. 73, we presented approximations of these parameters at the time of onset of radiative cooling (t ≈ 220 ns).We do not repeat this analysis here, but instead, summarize the key results.Based on the measured values of ion density n i , electron temperature T e (see §IV B), magnetic field B, and flow velocity V (see §II B 2) in the inflow region, we find that the inflows are super-Alfvénic (M A = V /V A ≈ 7).We reiterate that these quantities are measured on the side of the array opposite the reconnection layer.Therefore, by taking advantage of the azimuthal symmetry of the outflows from the arrays (which form the inflows to the layer), we diagnose the inflow conditions, unaffected by the reconnection process.Super-Alfvénic inflows have previously been shown to generate shock-mediated magnetic flux pile-up upstream of the reconnection layer, dividing the inflow into pre-shock and postshock pile-up regions. 51,62,67,99In simulations of the MARZ experiment, magnetic flux pile-up results in fast perpendicular MHD shocks upstream of the reconnection layer. 69Ref. 73  estimates the parameters in the post-shock inflow region by solving the Rankine-Hugoniot jump conditions, the solution to which is a function of the upstream M A , plasma beta β , and adiabatic index γ. 97The plasma parameters in the pre-shock and post-shock inflow regions are listed in the first and second columns of Table II.
The plasma properties in the post-shock pile-up region set the inflow conditions just outside the reconnection layer.Ref. 73 uses two additional assumptions, both supported by simulation results, to approximate properties in the reconnection layer -(1) the reconnection layer exists in pressure balance with the post pile-up inflow region; and (2) at 220 ns, which is right at the onset of strong cooling, there is negligible compression of the layer.The first assumption simply states that the kinetic ρ in V 2 in /2, magnetic B 2 in /2µ 0 and thermal p in pressures just outside the reconnection layer must be balanced by the thermal pressure p L inside the layer.The second assumption argues that the temperature of the layer T L has not fallen enough at 220 ns to trigger the radiative collapse and run-away density compression of the reconnection layer.The estimated plasma properties in the reconnection layer are listed in the third column of Table II.We note that the estimated layer temperature at this time is T bulk ≈ 60 eV, which is consistent with the upper bound (T e,bulk ≲ 75 eV) determined from X-ray spectroscopy ( §IV E), and the predicted ion density is n i ≈ 6 × 10 18 cm −3 , slightly greater than the upper bound of n i ≲ 5 × 10 18 cm −3 ) from X-ray spectroscopy.The estimated Lundquist number is S L = LV A / η ≈ 120, and the predicted Sweet-Parker layer halfwidth is δ SP ≈ L(S L ) 1/2 ≈ 1.4 mm, 3,11 which is comparable to the FWHM= 1.6 ± 0.5 mm of the X-ray emission region observed in the time-integrated image of the reconnection layer (Figure 8c).We approximate the layer half-length L = 15 mm, using half the radius of curvature of the magnetic field lines at the mid-plane.Lastly, an estimate of the reconnection rate is determined by comparing the post-shock inflow velocity V in ≈ 20 km s −1 to the outflow velocity V out ≈ 72 km s −1 , estimated by extrapolating the linear trend in the hotspot velocity observed in Figure 9.The inferred reconnection rate at this time is V in /V out ≈ 0.3.This is roughly comparable to the expected reconnection rate from Sweet-Parker theory S −1/2 L ≈ 0.1. 11sing the quantities listed in Table II, we now estimate the relative magnitudes of the terms in the energy equation (Equation 3).As observed in the third column of Ta-TABLE II: Plasma parameters at the time of onset of radiative cooling (220 ns).Bold values are measured experimentally, while others are estimated/inferred.In column 1, we report values of n i , T e , and Z from visible spectroscopy analysis at 8 mm from the wires (see §IV B), magnetic field from averaging the values recorded by the inductive probes at 5 mm and 10 mm in MARZ3 (Figure 3c), and the flow velocity is estimated from the transit time of the magnetic field between the two probes (Figure 4d).Parenthetical values show bounds from X-ray spectroscopy ( §IV E) ble I, Ohmic heating, compressional heating, and net enthalpy advection into the layer, are estimated to have similar magnitudes, whereas the contribution of viscous heating is small.We also note that comparing the conductive heat flux −κ∇T ∼ κ(T L − T in )/δ SP with the advective flux p in V in /(γ − 1) along the x−direction shows that conduction losses from the layer to the upstream inflow are expected to be small (q cond,x /q adv,x < 0.1).Here, κ is the parallel thermal conductivity in the layer, which is a function of the layer density and temperature T L , 98 and T in is the inflow temperature.
We estimate the radiative loss rate P rad from the layer by solving the radiation transport equation (Equation 1) for an isotropically emitting and absorbing medium. 69,93 Here, ε ω and α ω are the spectral emissivities and opacities respectively, and τ ω = 2α ω R is the optical depth.R is the characteristic distance traveled by the radiation leaving the reconnection layer, which we approximate using the volume-tosurface area ratio R = (1/δ SP + 2/L) −1 of a cuboidal slab of width 2δ SP , and height and length 2L.Spectral emissivity and opacity values for the estimated layer temperature and density are determined from SpK. 72 The radiative loss rate calculated using Equation 4 is P rad ∼ 10 18 W m −3 , which is significantly

FIG. 1 :
FIG. 1: (a) In-chamber image of the MARZ load hardware.(b) A 3D schematic of the MARZ load hardware, showing two exploding wire arrays, each with 150, 75 µm diameter aluminum wires.Each array generates radially-diverging plasma flows (red) with frozen-in magnetic fields (blue), that generate a reconnection layer at the x = 0 midplane.(c) Top (xy-plane) view of the load, showing the arrangement of inductive probes (black), and lines-of-sight of streaked visible spectroscopy (SVS) [green, blue], X-ray spectroscopy (XRS 3 ) and side-on X-ray diodes (purple), and the self-emission gated optical imager (SEGOI) [magneta].(d) Side (xz-plane) view of the load, showing the lines-of-sight of the end-on X-ray diode (green), and the two X-ray cameras (black).

FIG. 2 :
FIG. 2: (a) Averaged current measured by B-dot probes in the magnetically insulated transmission line (MITL) of the Z machine for two different shots (MARZ1 -red; MARZ2 -blue).The peak current is about 21 MA, and the rise time is about 300 ns.(b) Current measured by Photonic Doppler Velocimetry (PDV) in the east (solid) and west (dashed) arrays, showing equal current division between both arrays on all three shots.

FIG. 3 :
FIG. 3: (a) Inductive voltage signals from probes placed at radial distances 5, 8, 11, 14, and 15 mm from the wires in MARZ1.Signals are delayed with respect to one another due to the transit time of the magnetic field advected by the plasma between the probe locations.(b) Time-resolved magnetic field measurements at different radii around the array in MARZ1.(c) Magnetic field measurements in MARZ3.

FIG. 4 :FIG. 5 :
FIG. 4: (a) Inductive voltage signals from probes placed at 5 mm and 8 mm from the wires in MARZ1, showing delay between the signals.(b) Estimate of the average flow velocity between 5-8 mm from the time delay of the inductive probe signals in MARZ1.(c) Inductive voltage signals from probes placed at 5 mm and 10 mm from the wires in MARZ3.(d) Estimate of the average flow velocity between 5-10 mm from the time delay of the inductive probe signals in MARZ3.
FIG. 6: Gated optical self-emission image of a bow shock around the T-probe.The bow shock exhibits a Mach angle of about 30 • .

Figure 8 (
Figure 8(a-b) shows time-gated images of the reconnection layer.Camera A (θ = 9 • , φ = 170 • ) recorded images between 190-250 ns at 20 ns intervals, while camera B (θ = 12 • , φ = 40 • ) recorded images between 180-240 ns, again at 20 ns intervals.Images from both cameras show an elongated layer of bright emission.The intensity of (> 100 eV) X-ray emission increases initially, consistent with the formation of the reconnection layer, and falls thereafter.Along with the brightness

FIG. 8 :FIG. 9 :
FIG. 8: (a-b) Time-gated X-ray images (10 ns exposure time) of the reconnection layer at between 180-250 ns, recorded using camera A (top row) and camera B (bottom row).X-ray images show brightly emitting hotspots (green and yellow arrows) embedded in an enlonged layer.(c)Time-integrated X-ray image of the reconnection layer.The image was recorded with a 300 µm diameter pinhole, filtered with 2 µm aluminized Mylar.

FIG. 10 :
FIG. 10: (a-b) Time-integrated X-ray emission spectra recorded in MARZ1 and MARZ3.(c-d) Lineouts of the X-ray spectra at z = 10 mm (red) and z = −10 mm (blue), showing Al K-shell emission lines.These include the He-α resonance and inter-combination (IC) lines, the He-α transitions with spectator electrons, and the Li-like satellite transitions.Shaded regions represent the standard deviation of the spectra inside the integration window.
FIG. 11: (a) A least-squares fit of synthetic data (orange) generated from radiation transport and Prismspect simulations to the experimental spectrum (black) at t = 220 ± 5 ns for visible spectra collected at 8 mm from the wires.(b) Temporal variation of electron temperature (black) and ion density (blue) in the inflow region determined by fitting synthetic spectra to the visible spectroscopy data collected at 8 mm from the wires.

FIG. 12 :
FIG. 12: Synthetic diagnostics from simulations of the MARZ experiment: (a) Filtered X-ray emission from the reconnection layer.The emission is filtered with 8 µm Be (red) and 2 µm Mylar (blue) to match the diode filters in the experiment.The black curve shows the expected X-ray emission (filtered with 8 µm Be) for the simulation with no radiative cooling.(b) X-ray emission from the layer filtered with 8 µm Be.Plasmoids primarily generate high-energy > 1 keV emission from the layer.(c) Filtered emissivity of the aluminum plasma generated using Spk tables.(d-g) Synthetic X-ray images of the reconnection layer, filtered with 2 µm Mylar, and using the same line of sight as X-ray camera B in Figure 8. X-ray emission from the layer decreases with time due to radiative cooling.

FIG. 13 :
FIG. 13: Corner plot of solutions which match the line ratios of (A) He-α IC / He-α Resonance (blue), (B) He-α IC / Li-j Satellite (red), and (C) He-α IC / He-α with 3p spectator (green).(b, d, and e) show the 2D scatter plots for n i , T e , and d; (a, c, and f) show the probability density distributions of these values for valid solutions.Solid lines represent contours enclosing 90% of the solutions.(g) Radiation transport model for emission from a single hotspot with emissivity ε H and opacity α H , embedded in a homogeneous layer with ε L and opacity α L .(h) Comparison of synthetic spectra with the experimental spectrum (z = 10 mm, MARZ3).Both synthetic spectra are calculated for T = 170 eV and n i = 1 × 10 18 cm −3 , but using sizes of d = 0.5 mm (red) and d = 5 mm (blue) respectively.

TABLE I :
Estimated magnitudes of terms in the energy equation