Author Correction: Direct observations of pure electron outflow in magnetic reconnection

Magnetic reconnection is a universal process in space, astrophysical, and laboratory plasmas. It alters magnetic field topology and results in energy release to the plasma. Here we report the experimental results of a pure electron outflow in magnetic reconnection, which is not accompanied with ion flows. By controlling an applied magnetic field in a laser produced plasma, we have constructed an experiment that magnetizes the electrons but not the ions. This allows us to isolate the electron dynamics from the ions. Collective Thomson scattering measurements reveal the electron Alfvénic outflow without ion outflow. The resultant plasmoid and whistler waves are observed with the magnetic induction probe measurements. We observe the unique features of electron-scale magnetic reconnection simultaneously in laser produced plasmas, including global structures, local plasma parameters, magnetic field, and waves.

images are observed in astrophysical plasmas 11 but electron-scale measurements are limited. We use laboratory experiments to observe both local and global information simultaneously in a controlled manner 26 .
In laser produced plasmas, magnetic reconnections have been studied using self-generated magnetic field by Biermann battery, which is an azimuthal magnetic field around the laser spot [3][4][5][6] . By irradiating a solid target with multiple laser beams, the azimuthal magnetic fields are advected with the plasma flow and anti-parallel magnetic fields collide and reconnect. The typical magnetic field strength and velocity are ∼ 1 MG and ∼ 100 km/s , respectively 3 . The typical gyroradius is ∼ 10 nm for electron and ∼ 10 µm for proton, therefore, the electron-scale is too tiny to resolve in the experiments and tends to be overlooked. Alternatively, there are experiments with external magnetic field using magnet 7 , pulsed power discharge 8 , and capacitor-coil target 9 . This allows us to control the parameters corresponding to the magnetic field such as gyroradius, gyrofrequency, and magnetization. We have used an external magnetic field strong enough to magnetize the electrons but not the ions. We briefly review our previous work 7 . In the previous work, the plasma collimation in the presence of a perpendicular external magnetic field is observed with interferometry, while there is no such collimation in the absence of the magnetic field 7 . The ion gyroradii estimated with the plasma flow velocity are much larger than the system size but electrons are well magnetized 7 . The plasma flow with dynamic pressure much larger than the magnetic pressure distorts the applied magnetic field, resulting in the charge separation across the magnetic field, since the electron is magnetized but ion is not. This leads to E × B drift only for electron. The electron moves along the distorted magnetic field rather than drift across the magnetic field and plasma is collimated. The collimation scenario is verified with particle-in-cell simulations 7,27 . The cusp and plasmoid propagation at electron Alfvén velocity with self-emission imaging indicates the magnetic reconnection at electron scale 7,28-30 . However, there was no observational evidence of the different motion between electron and ion, and the magnetic field relevant to reconnection event.
In this paper, we report the local observations of electron-scale magnetic reconnection in addition to global observations focusing on the electron dissipation region. The local velocity measurement clearly shows pure electron outflow that is not accompanied with the ion motion. The magnetic field measurements show the magnetic field inversion corresponding to the plasmoid, and also the whistler waves associated with electron-scale dynamics. The pure electron outflow demonstrates the magnetic energy is released to only the electrons on the onsets of the magnetic reconnection.
The experiment is performed with Gekko XII laser facility at Institute of Laser Engineering, Osaka University. The setup of the experiment and configuration of initial magnetic field are shown in Fig. 1, and the experimental details are found in the caption. We measure plasmas at the rear-side of the target. We use self-emission imaging as global diagnostics, and collective Thomson scattering (CTS) 32 and a magnetic induction probe 33 as local diagnostics. Figure 2a-c, d-f compare the measurements at 50 ns after the laser irradiation with and without an applied magnetic field, respectively. We obtain global information in Fig. 2a,d as well as local information in Fig. 2b,e simultaneously. The global images in Fig. 2a,d show collimated plasma flow originating from the main laser arriving from the left and interacting with a target at (x, y) = (0, 0) mm. The purple region in 0 x 10 mm and −4 y 4 mm indicates emission from the resulting nitrogen plasma. The shocks result in bright emission regions centred near (9, 0) mm. Note that the increased emission at (5, 0) mm is due to the CTS probe beam interacting with the plasma and the plasmoid is smeared. Although the probe beam heats the plasma locally ionizing and increasing the electron density, the velocity is unchanged during this process. Figure 2b is the shifted wavelength and θ is the scattering angle. Because the wavelength shift is ∼ 250 pm at d = 0 mm in Fig. 2c, the ion flow velocity is ∼ 100 km/s . A red shift seen in the CTS spectrum indicates that the ions move in the positive x direction, i.e. along the laser propagation direction. In Fig. 2b,c, at position d ∼ 1.5 mm (red spectrum), the spectrum shows an asymmetry about the shifted central wavelength. This asymmetry is not seen in the equivalent spectrum in Fig. 2e,f. This spectral feature suggests the electron velocity exceeds the ion velocity 32 , and that both move in the positive x direction. In contrast, the symmetric spectrum in Fig. 2e, the equivalent measurement with no applied magnetic field shows the electrons and ions move with the same velocity.
A plot of the velocity difference with and without the applied magnetic field is shown in Fig. 3. We define v e,i as the change in flow velocity by applying the external magnetic field. As the Biermann battery process self-generates a magnetic field and the reconnection by the Biermann battery magnetic field is also observed in our setup 6 , we compare the results in the presence and absence of the applied magnetic field in order to pick up the electron and ion motions related to the applied magnetic field (and the magnetic reconnection illustrated in Fig. 1e). Note that the reconnection outflows by the Biermann battery magnetic fields are perpendicular to the direction observed by CTS. This data shows that the differences in ion velocities are negligible, while there are significant spatial differences in the electron velocities. The analysis of the CTS spectra indicate ion velocities are not influenced by an applied magnetic field. The ion velocities are consistent with previous measurements made using a streaked optical pyrometer 7 . The electron velocity with the applied magnetic field is slower than that without the applied magnetic field at d 0 , whereas the electron changes the propagation direction of the relative velocity at d 1 . This is an indication of pure electron outflow.
We estimate electron and ion gyroradii before the reconnection in ref. 7 , which shows the electrons are magnetized but not for ions. Here we estimate the relevant parameters after reconnection, electron and ion gyroradii [ r g = mvc/(qB) ] and magnetization parameter [the ratio of a magnetic pressure to dynamic pressure Here m, c, q, and n are the mass, speed of light, charge, and the particle number density, www.nature.com/scientificreports/ respectively. The estimates use fits to the CTS spectra to infer ionization states of +1 for proton and +3 for carbon, typical flow velocities of 100 km/s, the electron temperature of 10 eV, and the ion temperature of 50 eV, the initial-at-target magnetic field of 3 kG, and the lowest electron density of e17cm −3 . We use the averaged  www.nature.com/scientificreports/ and the electron dynamics is coupled to the magnetic field dynamics. Note that, in principle, the earlier the timing from the laser irradiation is, the faster the plasma velocity in laser produced expanding plasmas (see Fig. 1 in ref. 7 ). Before the reconnection, the ion gyroradii are much larger than the system size. Even after the reconnection, it is still larger than the observed reconnection region of ∼ 2 mm . Since the ion skin depths for proton and carbon are d p ∼ 0.2 mm and d c ∼ 2 mm, respectively, the spatial scale of reconnection is on the order of the several skin depths and the magnetic reconnection can be electron-only 19 .
Because only the electrons are magnetized, the reconnected magnetic field pushes only the electron component of the plasma from the reconnection region. This occurs along the x axis as illustrated in the inset of Fig. 3. The difference in electron velocity is ∼ 2500 km/s in Fig. 3, which is twice of outflow velocity 7 . Using the measured electron density and initial magnetic field strength, the Alfvén velocity defined with the electron mass m e is v Ae = B/(4πn e m e ) 1/2 ∼ 900 km/s (note that we underestimate v Ae due to the overestimation of density). This leads to the conclusion that the spatial distributions in the velocity differences depicted in Fig. 3 result from pure electron outflow. The ions are not involved in magnetic reconnection process. Figure 4 shows the local magnetic field measurements. The data were obtained in case2 in order for magnetic field to transport to the induction probe. In the presence of the shock wave with higher gas pressure (case1), the signal shows unique upstream wave feature (not shown). We focus on the magnetic reconnection where a plasmoid is generated and propagates toward the probe 7 . This is measured as a magnetic field inversion at the induction probe. In our experiment, Fig. 1, the magnetic field inversion is most significant in B 2 component. The plasmoid propagation velocity is ∼ 100 km/s 7 and the probe locates ∼ 5 cm away from the target, hence, the magnetic field inversion should occur around t ∼ (5 cm)/(100 km/s) = 500 ns . The plasmoid velocity is close to the ion velocity measured with CTS. Although the electrons and ions move differently at the reconnection region, we assume that the electrons cannot be significantly apart from the ions at the probe where the spatial scale is several times larger than the ion gyroradius. The measured voltage (blue curves in Fig. 4c,d) is approximately proportional to the time derivative of the magnetic field. The magnetic field in Fig. 4d is likely the self-generated Biermann battery magnetic field 38 . While B 1 and B 3 are similar in both cases (see Supplementary Fig. 1), B 2 is considerably different with and without the applied magnetic field. The shape of blue curve in Fig. 4c,d are in qualitative agreement with that in Fig. 4a,b around t ∼ 500 ns , respectively. This indicates the magnetic field inversion. We calculate the absolute value of the magnetic field in the red curves in Fig. 4c,d. It is clear that only B 2 in Fig. 4c is inverted at t ∼ 400 and 700 ns. The magnetic field inversion can be understood as the propagation of the plasmoid or the low frequency magnetic fluctuation. If the inversion is a wave propagation, there should be the magnetic inversion not only in B 2 component but also in B 3 component (two components perpendicular to the background magnetic field). The magnetic field in B 3 component shows no inversion (see Supplementary  Fig. 1c). Thus, the magnetic field inversion strongly indicates the passage of a plasmoid, the former and latter inversions correspond to the arrival and passage of plasmoid, respectively.
There is a oscillation of magnetic field at t ∼ 400 ns, see Fig. 4c, when the applied magnetic field is present. We use wavelet analysis of the three magnetic field components, shown in Fig. 5a-c, to identify a ∼ 10 MHz oscillation around t ∼ 400 ns in the field components perpendicular to the nominal background magnetic field. www.nature.com/scientificreports/ The oscillation is only observed when the applied magnetic field is imposed as shown in Supplementary Fig. 2. This oscillation occurs in the range � i < ω ≪ � e , where i is the ion gyrofrequency at ∼ 1 MHz. The phase difference of B 2 and B 3 in Fig. 5d shows ∼ 90 • , which corresponds to right-hand polarization. The oscillation is recognized as the whistler wave. The higher and lower frequencies of the whistler wave in Fig. 5 propagate faster and slower, respectively. We model the timing at which the whistler wave arrives at the probe in the presence of expanding plasma. The wave propagation velocity in the laboratory frame is sum of plasma velocity (u) and group velocity of the whistler wave ( v g ). We simplify to one-dimension propagation. We assume the expansion velocity of plasma as u = s/t , where s is the position of wavefront from the target, and t is the time after the laser irradiation. Therefore, the wave propagation velocity is expressed as ds/dt = (s/t) + v g . Solving the differential equation, we obtain the arrival timing of whistler wave. The initial conditions are s = 0 mm and t = 50 ns from CTS results. In the frequency range of � i ≪ ω ≪ � e , ω pe , the group velocity is approximated to v g /c = 2(ω� e ) 1/2 /ω pe ∝ (ωB/n e ) 1/2 , where ω pe is the plasma frequency. This shows that the group velocity is determined by n e /B . As only the electrons are magnetized we assume that n e /B is near constant in the plasmoid, although the electron dynamics can change the density and magnetic field change in time. The value for n e /B at the reconnection region uses n e0 ∼ 1 × 10 17 cm −3 measured with CTS, and the initial strength of B 0 ∼ 3 kG. The density is likely overestimated as the CTS probe beam ionizes the plasma. The black curves in Fig. 5d show the predictions from the model for the arrival time of whistler waves with the range of B 0 /(2n e0 ) ≤ B/n e ≤ 2B 0 /n e0 . These qualitatively match the ∼ 90 • phase difference region and illustrate that these oscillations are whistler waves.
In summary, we report the local observations of magnetic reconnections driven by electron dynamics in laser produced plasmas. The local velocity measurements directly reveal the pure electron outflow occurs at both sides of a reconnection region. Magnetic reconnection generates a plasmoid or magnetic island. The local magnetic  . (a,b) A schematic illustrating the relation between magnetic field (B in red) and time derivative of magnetic field ( ∂B/∂t in blue) in bipolar and unipolar magnetic field, respectively. When the sign of magnetic field inverts (a), the signal of ∂B/∂t is tripolar. On the other hand, when a Biermann magnetic field approaches and passes through the probe (b), the signal of ∂B/∂t is bipolar. (c,d) Magnetic field measurements with and without the applied magnetic field in case2, respectively. The plots show the B 2 component where the magnetic field inversion is most significant. The blue and red curves represent the measured voltage and magnetic field, respectively. The velocity of fast plasma is ∼ 500 km/s 7 , thus, the signal before 100 ns is attributed to be the electromagnetic noise. This region ( t < 100 ns ) is shaded gray. The voltage curves at t ∼ 200 ns briefly saturate. The magnetic field before the saturation is expressed as dotted red curves and our analysis likely underestimates the B 2 magnetic field before saturation. The dotted and solid horizontal lines represent the initial magnetic field strength and B = 0 , respectively. The voltage returns to 0 at the end of the trace. We integrate the signals from the end of time to avoid problems caused by noise and saturation at times before ∼ 250 ns. www.nature.com/scientificreports/ field measurements show the magnetic field inverts twice, this corresponds to the passage of a plasmoid, and the whistler waves resulting from electron-scale dynamics. The electron outflow, magnetic field inversion, and resultant whistler waves are the direct evidences of electron-scale magnetic reconnection. We showed the electron dynamics governing macroscopic phenomena of magnetic reconnection in laser produced plasmas. This indicates the magnetic energy is converted to only the electrons on the onsets of the magnetic reconnection. Our experimental results provide simultaneous measurements of global structures, local plasma parameters, magnetic fields, and waves in a controlled manner. In the presence of whistler waves, the electrons can be further accelerated by the cyclotron resonance. The next milestone is the direct observation of nonthermal electron acceleration by the whistler waves. We are developing diagnostics to intrinsically measure the wave growth 39,40 , leading to identify the excitation location and timing of whistler and other waves. The recent 3D simulation shows the reconnection rate increases as a result of localized reconnection region 41 . The 3D reconnection rate can be observed using multi-channel CTS measurements or electric/magnetic field measurements at the reconnection region with proton radiography 4,5,8 . Moreover, the experiment can be extended to relativistic regime using ultraintense laser pulses 42,43 and turbulent regime using multiple beams 44,45 . Laboratory experiments will contribute further understanding the magnetic reconnections.

Data availibility
The data that support the findings of this study are available from the corresponding author upon reasonable request.  Fig. 4c and Supplementary Fig. 1. As shown in Fig. 4, the electromagnetic noise is filled with gray. While there are distinct signals above 10 MHz at t ∼ 400 ns in B 2 and B 3 , the signal in B 1 is weak. According to the magnetic field strength in Supplementary Fig. 1, the magnetic field is almost parallel to B 1 . (d) Phase difference of B 2 and B 3 . We pick up the region where the signals are correlated with each other and they are not correlated with the dummy signal (see Supplementary Fig. 2). We fill the removed region with gray. The blue and red curves represent the contours of 45 • and 135 • , respectively. The phase difference at the oscillation is ∼ 90 • . Because the frequency domain is between the electron and ion gyrofrequencies, the magnetic fluctuation is considered to be the whistler wave. We plot the whistler wave propagation model in black curves.