Study of magnetic reconnection at low- $β$ using laser-powered capacitor coils Open Access

Magnetic reconnection^1,2 efficiently converts magnetic energy to plasma energy in the form of bulk flow, thermal particle, and non-thermal particles through alteration of magnetic field topology. Magnetic reconnection occurs throughout the Universe³ often as part of explosive phenomena such as solar flares and Earth's magnetospheric substorms. Magnetic reconnection has been confirmed to occur in the near-Earth space plasmas and in the laboratory plasmas via in situ measurements of local electromagnetic fields and plasma particles in and near the diffusion regions around the X-line where magnetic field lines change their connectivity. Magnetic reconnection has been also long considered to occur in solar and more distant astrophysical plasmas via remote-sensing measurements of enhanced global morphological emission and ex situ measurements of accelerated particles. There has been substantial progress over the past 70 years in understanding the rate of magnetic reconnection in nearly collisionless plasmas. In theoretical and numerical research,⁴ this includes identifying the electron dynamics responsible for breaking field lines, corroborated via space in situ measurements.^5,6 The associated kinetic structures and some energy conversion processes have also been identified via laboratory experiments.⁷ However, many open questions about the magnetic reconnection problem remain.

The major scientific challenges and research opportunities to meet them have been summarized in a number of recent community whitepapers^8,9 submitted to several recent decadal surveys. Ten major problems are listed below:

1. Multiple scale problem: How does reconnection couple global fluid (magnetohydrodynamic or MHD) scales to local dissipation (kinetic) scales?

2. 3D problem: How does reconnection take place in three dimensions on global and local scales?

3. Energy problem: How are particles heated and accelerated?

4. Boundary problem: How do boundary conditions affect the reconnection process?

5. Onset problem: How does reconnection start?

6. Partial ionization problem: How does partial ionization affect reconnection?

7. Flow-driven problem: What role does reconnection play in dynamos of flow-driven plasmas?

8. Turbulence and shock problem: What role does reconnection play in turbulence, collisionless shocks, and plasma transport?

9. Explosive phenomena problem: How and under what conditions does magnetic reconnection drive or follow explosive phenomena such as solar flares and coronal mass ejections?

10. Extreme condition problem: How does reconnection operate in extreme conditions such as intense radiation and relativity in astrophysics?

Each of these interconnected problems can be tackled by a combination of theory, simulation, observation, and laboratory experiment. The latter has been important for testing theoretical and numerical predictions, to confirm observational evidence, and to discover new physics. Reference 7 concisely summarizes important results obtained over the past two decades in well-controlled and well-diagnosed laboratory experiments on collisionless reconnection. The experimental campaigns for these results, however, were performed on basic magnetized plasma facilities that include devices specifically designated to study reconnection. In contrast, reconnection experiments performed in high-energy-density (HED) plasmas, powered either by lasers^10–26 or by pulsed power,^27,28 are more recent and less developed due to diagnostic and control difficulties but have incurred rapid progress.

Many of these experiments in HED plasmas have used platforms based on colliding plasma plumes and focus on the flow-driven regimes at high plasma $βup≡(neTe+niTi)/(Bup2/2μ0)≫1$ in the upstream region of the magnetic reconnection site.^27,28 Here, $ne$ and $ni(=ne/Z)$ are electron and ion number densities, respectively, and Z is the ion charge. $Te$ and $Ti$ are the upstream electron and ion temperatures, respectively. Note that only the reconnecting component of the magnetic field within the reconnection plane, $Bup$⁠, is used to define $βup$⁠; the uniform guide field component in the out-of-plane direction, while important for the plasma dynamics, is not included in the definition because its energy is not tapped in the conversion of magnetic to kinetic energy during reconnection.

On the other hand, a new class of experiments^21–26 uses the platforms based on laser-powered capacitor coils and focuses on magnetically driven regimes at low upstream plasma $βup(≪1)$⁠. Most of the basic magnetized plasma experiments are also in the same regime, but with Z typically $∼1$⁠. In contrast, the capacitor coil platform typically offers $βup≪1$ and $Z≫1$ simultaneously. These special characteristics, combined with unique diagnostic capabilities explained below, provide much needed advantages for the capacitor coil platform to be used to study particle acceleration in addressing problem No. 3 (Energy problem) and problem No. 2 (3D problem) listed above.

Although both the basic magnetized plasma experiments and laser-powered capacitor coil experiments have low $βup$⁠, there is a significant advantage of the latter for diagnosing non-thermal particle acceleration. While in situ measurements of non-thermal particles are impossible for laser experiments and also generally difficult for basic magnetized experiments due to short Debye length for electrostatic energy analyzers,⁴² laser experiments are ideal for ex situ measurements, analogous to many astronomical observations. The ex situ measurements of electrons are generally difficult in basic magnetized plasma experiments due to the presence of cold plasma, dense neutral gas, and complex coils and vacuum structures in the plasma edge. The advantage of laser-powered capacitor coil platforms motivated our first set of micro-magnetic reconnection experiments (MRX)²⁴ to be discussed in this paper. For comparison, key parameters and characteristics of each research platform of magnetic reconnection are listed in Table I.

The laser-powered capacitor coil platform offers an important advantage over the basic magnetized experiments for studying current-driven kinetic instabilities of magnetic reconnection at high Z values, and specifically $Z≃18$ for the copper plasma made from our targets. In the cases described here, ion acoustic waves (IAWs)^46–49 are not subject to ion Landau damping since the ion acoustic speed, Eq. (3), is much faster than the ion thermal speed, $Vth,i=Ti/M$⁠, since $Z≫1$⁠. IAWs have been long conjectured to be important in providing a local, current-dependent anomalous resistivity required to sustain Petschek-type⁵⁰ fast reconnection,^51–54 but rarely studied⁵⁵ due to ion Landau damping, which is strong when $ZTe∼Ti$ as in typical basic magnetized plasma experiments.

In Sec. II, the experimental setup and diagnostics are described, followed by description and discussion of experimental results on electron acceleration,²⁴ and ion and electron acoustic waves (EAWs)²⁶ in Sec. III. Discussion and future prospects are provided in Sec. IV.

The laser-powered capacitor coil platform is facilitated by recent advances in strong external magnetic field generation using laser irradiation of a metallic coil target.^56–66 Such targets usually consist of two parallel metallic foils connected by a thin wire that is bent into different coil shapes for generating various magnetic field configurations. High-energy lasers pass through the entrance hole in the front foil and irradiate the foil in the back. Hot electrons are generated during the intense laser-foil interaction and escape from the back foil, building up an electrical potential between the two foils. This produces a large current flowing through the connecting coil and therefore strong magnetic field generation.

The capacitor coil targets for the magnetically driven reconnection experiments discussed here consist of two connecting parallel coils²³ designed after successful measurement of the field generation by a single coil.⁵⁹ An example of the experimental schematic is shown in Fig. 1 using the OMEGA EP laser facility at the University of Rochester, NY. The targets were made from $50 μm$-thick Cu and comprised of two square parallel plates with length $1.5 mm$ and two parallel U-shaped coils separated by $600 μm$⁠. The U-shaped Cu coil, with a wire cross section of $50×100 μm2$⁠, had two 500- $μm$-long straight wires joined by a half-circular wire with a radius of curvature of 300  $μm$⁠. The targets were fabricated by laser-cutting $50 μm$-thick sheet Cu and then bending the coils into the desired shape. Target designs for other laser facilities in the US and abroad were similar to those used on OMEGA EP, with slight modifications to accommodate laser configurations and optimize diagnostic output. Two EP long-pulse UV beams passed through the front holes and irradiated the back plate delivering a combined $∼2.5$ kJ in 1 ns. The plasma in the coil region comes from the x-ray heated wires first as the preexisting plasma for magnetic reconnection, followed by the plasma from the Ohmically heated wires. The diffusion of plasma generated by the intense laser–foil interaction comes last, creating a situation of asymmetric reconnection in the downstream relevant to Earth's magnetotail and solar surface.² 

In the double coil configuration, the voltage difference between the foils drives very similar currents in both coils, creating a quasi-axisymmetric magnetic reconnection geometry as a result of the anti-parallel magnetic fields in between the coils. The plasma between the coils is magnetized by the coil-driven anti-parallel magnetic field, forming a reconnection current sheet. This concept is very similar to that used for MRX, but at a much smaller scale, and the experiments are therefore named micro-MRX. For MRX, a quadrupole magnetic configuration is formed by two flux cores, providing one public region where field lines wrap around both flux cores and two private regions where field lines wrap around only one flux core. Magnetic reconnection is induced thereby either increasing or reducing current in the flux cores by “pushing” or “pulling” flux between the public and private regions, by charging capacitors to high voltages and then discharging.⁶⁷ For micro-MRX, the current generated in the connecting coils increases while the laser pulse is on and decays after the laser pulse is turned off, providing magnetically driven, quasi-axisymmetric “push” and “pull” reconnection.

Proton radiography was used to measure the current strength in the coils and any fine-scale structures in the reconnection region during reconnection.⁵⁹ This includes ultrafast proton radiography using high-energy protons generated by target normal sheath acceleration (TNSA) and monoenergetic proton radiography using 14.7 MeV protons generated from D-³He fusion inside an imploding capsule. The TNSA protons are broadband with energies up to 55–60 MeV (Refs. 68 and 69) and provide a spatial resolution of 5–10  $μ$ m and a temporal resolution of a few picoseconds.⁷⁰ The monoenergetic protons provide $∼$45  $μ$ m spatial resolution and $∼$130 ps temporal resolution.⁷¹ As energetic protons probed the reconnection region, the proton beam spatial profile incurred variations from deflections by the Lorentz force, allowing inference of the field geometry.

Collective Thomson scattering was used to characterize plasma parameters such as electron temperature and density and capture plasma waves in the reconnection region.⁷² In micro-MRX experiments, a 527 nm probe laser was focused onto the plasma $600 μm$ above the X-line of the reconnection plane in Fig. 1. The scattered light in a volume $60×60×50 μm3$ was collected by an $f/10$ reflective collection system,⁷³ and the scattering angle was $63.4°$⁠. The collected scattered light was temporally and spectrally resolved by narrowband (7 nm window for ion acoustic waves) and broadband [320 nm window for electron plasma waves (EPWs)] spectrometers, coupled with streaked cameras with a 5 ns streak window.

Two time-integrated electron spectrometers—the Osaka University electron spectrometer (OU-ESM) and the single channel electron spectrometer (SC-ESM)—were used to measure the electron energy spectra. The OU-ESM is located $37.5 cm$ away from the coils at a polar angle of $39°$⁠, and it scans an azimuthal range of $179°–199°$ with five equally spaced detection channels [see Figs. 1(b) and 1(c)]. The azimuthal angle spread was chosen to allow distinguishing between acceleration mechanisms in an axisymmetric setup, with symmetry in the polar direction. The SC-ESM is positioned 9.5 cm away from the coil center and the measurement line of sight is perpendicular to the center reconnection plane as shown in Fig. 1(a). After reaching the spectrometer, an electron first passes through a pinhole $700 μm$ wide and $2 cm$ deep. Separation of electron energies is accomplished with permanent magnets placed along the detector line of sight, creating a magnetic field perpendicular to the line of sight. The Lorentz force deflects differently energized electrons to different distances along the detector length onto an image plate. In general, impacts closer to the detector entrance represent lower-energy electrons. In the experiment, magnets were chosen corresponding to electron energies in the $20 keV–1 MeV$ range. During the electron spectral measurements, the proton radiography measurement was turned off to avoid contamination of the particle spectra due to laser-plasma instabilities (LPIs).

An example of the raw proton radiographs of the coil target after laser irradiation in the face-on radiography geometry is shown in Fig. 2(b). The data were obtained at $t=t0+3.158$ ns for 24.7 MeV protons generated by TNSA, where $t0$ is the arrival time of the drive beams at the surface of the back Cu foil. The data show the rectangular Cu foil, the fiber stalk that holds the entire target, and the straight-part of the two U-shaped coils as viewed from the face-on direction to the target. The dashed line overlaid on top is the contour of the original target in a face-on view, in good agreement with the experimental measurement. The primary features are the formation of two prolate voids generated by the magnetic fields of the driven coil currents, and a center flask-shaped structure between the voids that indicates the occurrence of magnetic reconnection.

The amplitude of the coil current and the current-generated magnetic fields is estimated by matching the theoretically calculated and measured proton voids in the proton radiographs. Synthetic radiographs are generated via a particle ray tracing code using the same radiography geometry as in the experiments. The proton beam generated by TNSA propagates through the coil target. The amplitude and distribution of the three-dimensional magnetic fields are calculated using the Biot–Savart law. As the energetic proton beam traverses the field region, the beam's spatial profile varies from Lorentz force deflections. Synthetic proton images are constructed by tracing each proton trajectory and counting the accumulated protons at the detector plane. Figure 2(a) shows the synthetic proton image with matching voids as measured in the experiment, indicating a coil current of $I=44$ kA at $t=t0+3.158$ ns. Electrical fields were found to be negligible in contributing to the proton features.⁵⁹ 

Figure 2(c) shows the time evolution of the coil current measured by the proton radiographs at different probe times. The blue line overlaid on top is the coil current calculated by a lumped-circuit model using our experimental parameters.^60,74 The coil current profile is approximated by a linear rise during the laser pulse, followed by exponential decay after laser turn-off at 1 ns. Extrapolating the experimentally measured current magnitude to $t=1$ ns, the maximum coil current is inferred to be $∼57±4$ kA, which corresponds to a coil center magnetic field strength of $∼110$ T and an upstream reconnection magnetic field strength of $50.7 T$⁠.

A striking “flask-like” feature with high proton fluence is observed in between the two prolate voids. This feature is not present in synthetic radiographs simulated with only the coil magnetic fields [Fig. 2(a)]. Analytical calculations,²³ MHD simulations using the code FLASH,²⁶ and PIC simulations using the code VPIC²⁴ were carried out. All point to the conclusion that this center feature is formed by the out-of-plane current from magnetic reconnection.

Figure 3 shows results of the VPIC simulations. Details of the simulation setup can be found in Ref. 24. Electromagnetic fields from the VPIC simulations of the experiments were prescribed in the particle ray tracing calculations to generate synthetic proton radiographs. Figure 3(a) shows the out-of-plane current $jθ$ profiles at $t=1.4 trise$⁠, where $trise$ is the current rise time of 1 ns. Strong push reconnection is seen at this time. The corresponding synthetic proton image is shown in Fig. 3(b) where the center feature is reproduced. Two primary features in the out-of-plane current $jθ$ profiles are potentially responsible for creating this center feature: the push reconnection current sheet and diamagnetic return current. To de-convolve the effects of each on the synthetic proton radiographs, ray tracing is performed on a “zoomed” field, where the diamagnetic return current is largely shielded out [Fig. 3(c)]. The center feature is maintained in this radiograph [Fig. 3(c)], indicating the source of the center feature as the push reconnection current sheet. Thus, the presence of a similar center feature in experimental radiographs is indicative of push reconnection and the corresponding electromagnetic fields.

Collective Thomson scattering was used to measure plasma conditions in the reconnection region. Assuming Maxwellian distributions for ions and electrons, the plasma temperature (⁠ $Ti$ and $Te$⁠), plasma density (⁠ $ni$ and $ne$⁠), and ion charge state Z can be determined from the measured spectra of ion acoustic waves (IAWs) and electron plasma waves (EPWs). Figures 4(a) and 4(b) show temporally and spectrally resolved IAW and EPW spectra from collective Thomson scattering measured at 600  $μ$ m downstream of the central point between the top of the coils (see Fig. 1 for Thomson scattering setup), with a propagation direction within the reconnection plane and pointing $∼$ 17° away from downstream. The measurement time was at 1–5 ns with respect to the onset of the laser irradiation to the capacitor coil target. (See Sec. III D for the analysis of Thomson spectra at a later time.) Figures 4(c)–4(f) show the time evolution of plasma temperature, velocity directed to the downstream, plasma density, and ion charge state by forward fitting the synthetic IAW and EPW spectra, respectively, to the experimentally measured broadband spectra.⁴⁵ A single Maxwellian for electrons and ions was assumed. In the IAW analysis, the relative drift velocity between electrons and ions is set as a parameter to explain the asymmetry of two IAW peaks. The analyses were performed every 0.1 ns, including the spatial gradients of density and velocity. The error bars correspond to the standard deviation of each parameter estimated by the least squares fitting.

To cross-benchmark the above analyses, Fig. 5 shows the results of using the TSADAR code⁷⁵ to analyze the IAW and EPW spectra simultaneously from the same Thomson scattering data as Fig. 4. The raw data are divided into individual lineouts representing the spectrum at a single temporal slice, the measured conditions are found by matching the Thomson scattering spectral model to the data and the best matching spectra are stacked temporally to produce the images in Figs. 5(a) and 5(c). The data are only analyzed in the neighborhood of the data, i.e., 450–600 nm for the EPW and 526–528 nm for the IAW, ignoring the temporal calibration fiducials recorded at the top and bottom of the data images. This analysis corroborated that of Fig. 4 and checked for the influence of temporal gradients and super-Gaussian electron velocity distribution functions as well as accounting for all instrumental effects such as finite aperture corrections. These considerations were found to have negligible effect on the inferred parameters in this regime.

At 600  $μm$ downstream from the X-line, the nominal plasma parameters are as follows: $Z∼18$⁠, $ne∼3×1024$ m⁻³, $ni∼1.7×1023$ m⁻³, $Te∼$ 400 eV. This results in $β≈βe∼0.05$ for $B=100$ T, since $ni≪ne$⁠. This low- $β$ condition is favorable for studies of particle heating and acceleration and also for IAW excitation since $Z≫1$ as discussed in Sec. I. Note that the EPW spectra show EAW peaks that are explained by non-Maxwellian electron distribution functions.²⁶ As a result, the Lundquist number is large at $S=103–104$ but the system size $L=600μ$m is not too large compared to the ion skin depth due to heavy copper ions, so the normalized size $λ=L/di∼1.4$⁠. This places our current experimental setup in the electron-only regime⁷⁶ of the magnetic reconnection phase diagram.^2,3 In this regime, ions are unmagnetized by the reconnecting magnetic field but they can still respond to the resulting electric field if sufficient time is given. It is this case in our setup where IAWs have been observed, see Sec. III D below.

Theoretically and numerically, non-thermal particle acceleration has recently been studied extensively,^36,37 and various acceleration mechanisms have long been proposed.² These include parallel electric field acceleration,⁷⁷ Fermi acceleration,⁷⁸ betatron acceleration,⁷⁹ and direct acceleration by reconnection electric field.^80,81 Figure 6 illustrates these proposed particle acceleration mechanisms in and near the reconnection site. In the electron-only reconnection, electron heating and acceleration can be studied if electrons have sufficient space and time to receive energy from the magnetic field, as in our case.

Our primary diagnostic is the time-integrated measurement of electron energy spectra by the Osaka University Electron Spectrometer (OU-ESM). This is aimed nearly tangentially along the X-line with five channels at different azimuthal detection angles that range from 179° to 199° toward one of coils. Channel No. 5 has an angle of 179° and is most tangential to the X-line direction.

Figure 7(a) exemplifies the measured electron energy spectra in the magnetic reconnection case with two capacitor coils. A peak in the energy range of 40–70 keV is identified, and it becomes clearest in channel No. 5, which measures along the most tangential direction to the reconnection X-line. That no such peaks exist in the control cases shown in Fig. 7(b) with only one coil and Fig. 7(c) with no coil establishes that the peak is due to reconnection.

The measured angular dependence suggests that the acceleration of non-thermal electrons is due to the reconnection electric field, $Erec$⁠, in the out-of-plane direction of the anti-parallel reconnection.⁸⁰ The required sign of $Erec$ to be directly responsible for the observed acceleration points to the push reconnection driven by the increasing current in both coils, which is expected after lasers irradiate the capacitor coil target but possibly with some delays suggested by matching simulation (see below).

The magnitude of $Erec$ can be estimated as $Erec=αVAB0$ where $α$ is the reconnection rate, $B0$ is the upstream reconnecting magnetic field of 50.7 T (see Sec. II), and the Alfvén speed $VA=B0/μ0niM$⁠, where $ni$ is the ion density at the X-point. The reconnection rate $α$ is typically $∼0.1$ for electron-ion reconnection but for electron-only reconnection it is a function of the normalized size.⁸² For the small size limit that applies to our case, $α≃0.6$⁠. Therefore, for a range of $ne=(1–5)×1024$ m⁻¹, we estimate $Erec=(1.3–3.0)×107$ V/m. If we take the characteristic acceleration distance $d=1000 μ$m in the out-of-plane direction, the accelerated electrons by the reconnection electric field should have an energy of $Erecd=13–30$ keV, which is within a factor of 2 of the measured energy of $30–70$ keV for the spectral peak. We consider this consistent with our interpretation given the uncertainties in the relevant parameters.

To further test the above interpretation, a series of axisymmetric particle-in-cell simulations²⁴ were performed using the VPIC (Vector PIC) code.⁸³ Due to computational resource limitations, choices were made to achieve a real mass ratio of copper ions to electrons as well as a realistic plasma $β$⁠. This meant using an artificially stronger magnetic field and hotter plasma, reducing the ratios of electron plasma frequency to gyrofrequency, $ωpe/ωce$⁠.

Figure 8(a) shows the reconnection rate $α$ as a function of time measured in the reconnection region, indicating that the peak $α∼0.6$ is approximately confirmed when $ωpe/ωce$ approaches the realistic value of 6.33. As a consequence of reconnection, the accelerated electron energy spectra shown in Fig. 8(b) exhibits an angular dependence qualitatively consistent with the experimentally measured spectra shown in Fig. 7(a). The energy of the spectral peak is also consistent with the experimentally measured range of 40–70 keV.

The electron energy spectra measured by the single channel electron spectrometer SC-ESM further supports that the direct electric field acceleration by push reconnection is likely the acceleration mechanism. In Fig. 1(c), $Erec$ in the push phase points from the front plate to the back plate. Therefore, SC-ESM measures electrons moving against the force they experience, $−eErec$⁠. The measured electron energy spectra are shown in Fig. 9 for both reconnection cases with two coils and no reconnection cases with only one coil. No characteristic peaks are seen in both cases in the OU-ESM measurements [Fig. 7(a)], consistent with the expectation from the direct reconnection electric field acceleration. Furthermore, less energetic electrons are detected in the reconnection cases than the no reconnection cases, again consistent with the expectation that the directional reconnection electric field accelerates electrons away from the SC-ESM direction toward the OU-ESM direction.

The second set of experiments using micro-MRX is to study current-driven instabilities, notably ion acoustic waves (IAWs). These can be destabilized by a large relative drift between electrons and ions at low- $β$ without being subject to ion Landau damping since the ion acoustic speed, $VS≈ZTe/M$⁠, is much faster than the ion thermal speed $Vi≈Ti/M$⁠.

Historically, IAWs were once considered to be a promising candidate to generate anomalous resistivity^51,52 in the reconnection diffusion region in order to realize the Petschek-like reconnection model.⁵⁰ However, their importance has been dismissed due to the realization that IAWs are strongly stabilized by ion Landau damping in plasmas often found in the laboratory and in space where $Ti≃ZTe$⁠. In the micro-MRX where $Ti≪ZTe$⁠, however, IAWs are not subject to ion Landau damping and can be destabilized relatively easily. Figures 4(a) and 4(b) show spectra from collective Thomson scattering measured at 1–5 ns from the laser irradiation and at 600  $μ$ m downstream of the central point between the top of the coils, with a propagation direction within the reconnection plane and pointing nearly (17° away from) downstream. The two IAW peaks in Fig. 4(a) indicate that ion Landau damping is not large in the micro-MRX.

Figure 10(a) shows IAW spectra at later times during 7–11 ns from the laser irradiation. A strong, asymmetric IAW burst, indicating large relative drift between electrons and ions, appears at $∼$ 7.2 ns. The strongly asymmetric IAW spectra cannot be fitted with the theoretical spectra assuming a single Maxwellian. A spectrum is shown in Fig. 10(b) right before the burst at 7.1 ns along the dashed vertical line in Fig. 10(a). A relative drift speed between ions and electrons, $Vd$⁠, can explain the asymmetry between two peaks (green dashed line) while ion flow gradient, $ΔV$⁠, can explain the broadening of each peak (orange line). Combining both $Vd=0.17Vth,e$ and $ΔV=2×104$ m/s $∼Vth,i$ can explain both features (red line). Large $Vd$ and $ΔV$ are expected at the immediate downstream of the diffusion region where both large electric current and velocity gradients exist as part of the reconnection dynamics.

In addition to the IAW burst, EAWs are also destabilized in micro-MRX. Figure 11(a) shows both IAW and EAW spectra and the latter have about 0.12 ns delay in time, implying that it is a consequence of the former. Both IAW and EAW spectra at 9 ns along the dashed vertical line are shown in Fig. 11(b). The strong asymmetry in the EAW cannot be explained by the synthetic spectrum (dashed red line spectrum) constructed for a single Maxwellian distribution (dashed red line in the inset) of electrons, but it can be explained by a two-stream electron distribution (solid red lines for the spectra and in the inset). Furthermore, the Doppler shift of the peak spectrum is consistent with the phase velocity of the EAWs, which is on the order of $Vth,e$ and matches the velocity at the valley of the distribution shown in the inset of Fig. 11(b).

The causality between IAW and EAW bursts is reproduced by 1D and 2D PIC simulations.²⁶ The nonlinear evolution of IAWs in the 1D simulation shows formation of an electrostatic double layer, which reflects low-energy electrons while accelerating high-energy electrons. The resultant two streams of electrons trigger EAW bursts consistent with the measurements both on the time delay between IAW and EAW bursts as well as on the EAW phase velocity. The EAW burst eventually leads to electron heating. This scenario is also reproduced successfully in the outflow region of a 2D PIC simulation of magnetic reconnection using OSIRIS code⁸⁴ with a cold ion population in the background, albeit at a reduced mass ratio.

We have developed a unique experimental platform, the micro-MRX, to study magnetically driven reconnection at low upstream beta using high-power lasers. The platform is based on strong electric currents generated by targets of capacitor coils, distinctly different from the reconnection experimental platform using lasers by colliding plasma plumes, which are flow-driven at high upstream beta. Compared with traditional magnetized plasma experiments studying reconnection at low upstream beta, the uniqueness of the micro-MRX platform is twofold: (1) the ex situ detection capabilities of particles and photons and (2) high-charged majority ions so that ion acoustic waves are unstable due to large electric current without ion Landau damping.

Taking advantage of this uniqueness, two initial experimental campaigns haven been successfully carried out on micro-MRX detecting electron acceleration and excitation of ion acoustic waves by magnetic reconnection. There are ample further opportunities along each of these research lines. On the topic of electron acceleration, acceleration mechanisms other than direct acceleration by reconnection electric field can be studied also in the electron-only reconnection regime. These include Fermi acceleration by multiple plasmoids, betatron acceleration when magnetic field is compressed, and parallel electric field acceleration especially during the presence of a guide field. Each of these mechanisms can be studied with properly designed targets in the electron-only regime, even though these mechanisms were originally proposed in the electron-ion reconnection regime. For example, by having multiple coils on each side of the reconnection upstream region, an elongated current sheet can be driven to form multiple plasmoids in favor of Fermi acceleration of electrons. This idea has been tested numerically as described below.

Figure 12 shows the results from a 2D VPIC simulation of five-coil targets. The simulation has a mass ratio of 324, the same electron and ion temperature of 500 eV, ion charge state $Z=4$⁠, and an electron density of $1018$ cm⁻³, resulting in an ion skin depth $di=0.04538$ cm and an electron skin depth $de=0.01$ cm. The ratio between the electron plasma frequency and the electron gyrofrequency $ωpe/Ωce=8.43$⁠. The simulation has a size of $Lx×Lz=0.36$ cm $×$ 0.36 cm =35.7  $de×35.7de$⁠. The grid size is $564×564$⁠. The horizontal and vertical separations between the coils are 0.045 and 0.055 cm, respectively. The simulation has open boundary conditions along both directions, and the formation of the current sheet and the consequent reconnection is driven by electric current in the coils. The current increases linearly during a ramp-up time of $tramp=0.46Ωci−1=314.1ωpe−1$ and then exponentially decays with a decay time of $τ=1.97Ωci−1=1345.2ωpe−1$⁠. Initially, 1% of all particles were loaded as background. As the simulation proceeded, five plasma injectors were included between the five pairs of coils to mimic the Gaussian laser pulses. These Gaussian injectors have a width of 0.0423 cm, and their intensity linearly increases with time until $tramp$⁠, when the injectors are turned off. The plasma injectors result in a nearly uniform plasma density in the current sheet early in the simulation [Fig. 12(a)].

The simulation shows an elongated current sheet that thins and eventually breaks into four plasmoids [Figs. 12(a) and 12(b)]. The simulation captures two middle islands merging, with the other two ejecting from the layer. The reconnection is in an electron-only regime due to the layer's size. Early in the simulation, the acceleration was identified as direct acceleration by the reconnection electric field,²⁴ as shown in Fig. 12(c) for an anisotropic electron distribution with $pe⊥>pe∥$⁠, where $pe⊥$ and $pe∥$ are the perpendicular and parallel electron pressure, respectively. As the current sheet breaks into magnetic islands, the acceleration is primarily due to the Fermi mechanism,^79,86,87 resulting in $pe∥>pe⊥$ at the two ends of the magnetic islands [Fig. 12(d)]. During these processes, electrons are accelerated to over 100 keV, forming a significant non-thermal tail with a power-law-like distribution [Fig. 12(e)]. These initial results illustrate the potential of the multi-coil targets in exploring electron acceleration mechanisms by magnetic reconnection. Further consideration and optimization will be needed in terms of target design, diagnostics, and experimental setup before implementing the ideas on specific facilities.

In order to investigate the effects of a three-dimensional setup, a preliminary 3D PIC simulation of micro-MRX was carried out as shown in Fig. 13. The simulation parameters are similar to those used for the multiple coil setup of Fig. 12, but, using only a single pair of coils in a 3D domain. These coils (blue) contain both the straight and curved sections present in the experiment. The plasma formation via the laser interaction with the target plates is not modeled, and we instead inject plasma in a volume source between the coils during the ramp-up phase, as done in Fig. 12. The grid size is $280×280×560$ for a simulation domain of 0.18  $×$ 0.18  $×$ 0.36 cm³, the mass ratio is $mi/me=324$⁠, and the separation between the coils is 0.055 cm. Figure 13 shows the current density and magnetic field lines in the plane intersecting the center of the two coils at $t=0.125Ωci−1$⁠, early in the push phase of reconnection (⁠ $tramp=0.46Ωci−1$⁠). The current sheet that forms between the two coils has a thickness comparable to the electron skin depth. Consistent with electron-only reconnection,^82,87 we find that the electrons are accelerated up to the electron Alfvén speed in bi-directional jets in the $±x$ outflow direction, whereas the ions remain relatively uncoupled to the magnetic field (not shown). Future studies will examine the physics of electron acceleration as well as IAW and EAW wave generation using this 3D setup.

On the topic of ion acoustic waves on micro-MRX, the logical next steps include quantification of the effects of waves on reconnection and detection of the waves propagating in the out-of-the-plane direction of magnetic reconnection as originally speculated to be able to facilitate the realization of Petschek reconnection.^51,52 Other topics include extending the system size to large sizes so that ions are also coupled and ion acceleration in electron-ion reconnection can be studied. The realization of multiple X-line regimes at even larger scales and higher Lundquist numbers in the reconnection phase diagram^2,3 will allow study of the multiscale physics of magnetic reconnection. Many major problems of magnetic reconnection research^8,9 listed in Sec. I can be studied by using the micro-MRX platform with proper targets, diagnostics, and experimental setups. In this sense, comparative research with space observation by MMS,⁵ ground-based observation by EOVSA⁴³ and STIX,⁴⁴ and the upcoming Facility for Laboratory Reconnection Experiments (FLARE),^2,88 as summarized in Table I, will be fruitful to cover many more varieties of physics regimes and field geometry, as well as a wider parameter space.

This work was supported by the DOE Office of Science, Fusion Energy Sciences (FES) under the LaserNetUS initiative at the OMEGA Laser Facility and Jupiter Laser Facility. This work was mainly supported by the High Energy Density Laboratory Plasma Science program by the DOE Office of Science and NNSA under Grant No. DE-SC0020103. The authors acknowledge General Atomics, the University of Michigan, and the Laboratory for Laser Energetics for target fabrication, and the Jupiter Laser Facility, OMEGA, and OMEGA EP crews for experimental and technical support. The work of A.M. and R.K.F was supported by the National Inertial Confinement Fusion program by the DoE NNSA at the University of Rochester under Contract No. DE-NA0004144.

The authors have no conflicts to disclose.

H. Ji: Conceptualization (lead); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Resources (lead); Supervision (equal); Writing – original draft (lead); Writing – review & editing (equal). G. Fiksel: Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). E. G. Blackman: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). A. Chien: Formal analysis (equal); Funding acquisition (supporting); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal). S. Zhang: Formal analysis (equal); Funding acquisition (supporting); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). L. Gao: Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (lead); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). G. Pomraning: Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). K. Sakai: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). F. Guo: Formal analysis (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). X. Li: Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). A. Stanier: Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). A. Milder: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). R. K. Follett: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal).

The data that supports the findings of this study are available within the article.