Relativistic magnetic reconnection in laser laboratory for testing an emission mechanism of hard-state black hole system

Magnetic reconnection in a relativistic electron magnetization regime was observed in a laboratory plasma produced by a high-intensity, large energy, picoseconds laser pulse. Magnetic reconnection conditions realized with a laser-driven several kilotesla magnetic field is comparable to that in the accretion disk corona of black hole systems, i.e., Cygnus X-1. We observed particle energy distributions of reconnection outflow jets, which possess a power-law component in a high-energy range. The hardness of the observed spectra could explain the hard-state x-ray emission from accreting black hole systems.

Figure 1

(a) Bidirectional current is produced by laser irradiation on two separate positions of the microcoil. (b) The 3D PIC simulation results with $\frac{1}{30}$ downsized microcoil shows that antiparallel magnetic field structure $B_z$ (component perpendicular to the cross section) formed inside the single microcoil. This field reconnect with each other within the boundary. The boundary of the region with electron dissipation measure [27] $D_e>0.5v_A{B}_0{j}_0$ is plotted by black solid lines, indicates magnetic reconnection sites. (c) Current sheet $J_y$ in same simulation, plotted together with the boundary of $D_e>0.5v_A{B}_0{j}_0$. $v_{A0}$, $B_0$, and $j_0$ are the Alfvén velocity, magnetic field, and current density in simulation, respectively, as in the previous study [27].

Figure 2

Magnetic field topology extracted from PIC simulation, at snapshots of before, during, and after the magnetic reconnection. (a)–(c) Reconnection magnetic field component $B_z$ on $x\text{−}y$ plane at $z=0$. (d)–(f) Streamline plot of magnetic field on $x\text{−}z$ plane at $y=6.5$ $\mu \mathrm{m}$. Color map shows the out-of-plane component $B_y$.

Figure 3

The curved RCF stack surrounding the microcoil was used to measure the proton beam along the field boundary and also to detect spatial profiles of proton beams deflected by the magnetic field in the microcoil. A pair of RCF stacks was used to detect the angular distribution of the protons in the outflow jets. The two proton patterns, which appeared to be symmetric, were obtained from the same laser shot. In the selected shots, electron energy spectrometer (ESM) and Thomson parabola ion energy analyzer (TPS) were placed instead of the two RCF stacks.

Figure 4

Experimental setup for magnetic field characterization. A grid is placed between the proton source and the microcoil for analysis purposes. Angular distribution of the deflected proton is measured by the curved RCF stack.

Figure 5

Proton beam spatial pattern obtained in the experiment. Proton pattern (a) without magnetic field deflection and (b)–(e) under magnetic field deflection are shown, which probed the magnetic field generated by the microcoil. Four proton patterns in the same measurement shot are shown in descending order of proton KE, which is equivalent to showing the probed magnetic field from the earlier one to the later one. In all measurements, a grid is placed between the proton source and microcoil.

Figure 6

Current model constructed based on experimental results. (a) Schematic of current model, consisted of current flow in $\theta$ direction along the microcoil $I_{\mathrm{coil}}$ and current sheet $I_{\mathrm{sheet}}$ across the microcoil. Positive value of $I_{\mathrm{coil}}$ corresponds to clockwise current flow in diagram. (b) Distribution of $I_{\mathrm{coil}}$ along $\theta$ direction. $\theta =0$ correspond to one end of $I_{\mathrm{coil}}$, which is the incident laser focus spot in the experiment.

Figure 7

Electric field $E_x$ at $z=0$. Vectors of electric field $x\text{−}y$ component are plotted in region of green box, showed how the electric field contributed on the proton flow along the reconnection field boundary.

Figure 8

Distribution of protons detected in the radial direction of the microcoil. (a) Polar plot of average RCF signal from $-5^{\circ }$ to $5{}^{\circ }$. (b) RCF signal obtained in experiment. The highly collimated signal observed at $145{}^{\circ }$ is a typical signature of proton beam. The direction of this proton beam provided information of the magnetic field geometry inside the microcoil. No probing protons produced from the auxiliary target were used in this laser shot.

Figure 9

Some examples of the synthetic proton patterns during the parameter scan. Within the range $0.1<c<0.2$ the size of the void scales with the value $I_0$. For example, when $c=0.3$ the void will no longer be reproduced for any value of $I_0$. Also, synthetic proton patterns for the best fit when $c=0.1,0.2$ are shown in the rightmost column. The effect of the metal grid in experiment was also applied to the best fit proton pattern.

Figure 10

Temporal evolution of microcoil maximum magnetic field measured in the experiment. Vertical axis represents the maximum magnetic field in the estimated magnetic field map, as well as the value of $I_0$ in our magnetic field model. The data points correspond to both ordinate axes because the two quantities are directly related.

Figure 11

Cross section of an example of B-field map with $c=0.2$, produced by the magnetic field model used in our Monte Carlo simulation analysis.

Figure 12

Proton and electron energy distributions in (a), (b) experiment ($l=100$ $\mu \mathrm{m}$) and (c), (d) PIC simulations ($l=3.3$ $\mu \mathrm{m}$). (a) The proton energy distribution in KE $>6$ MeV was measured with Thomson parabola spectrometer (black crosses). The distribution is fitted with the power-law curve whose slope index is $p_i=3.013$ (blue dotted line). (b) The electron energy distribution was measured with ESM for $E>$ 100 keV (black dots). Both thermal and nonthermal components are observed. There are the Maxwell distribution curve (blue dotted line), power-law curve (red dashed line) with slope $p_e=1.535$, and power-law fitting with superexponential cutoff ($p_e=1.215,E_c=1.742$) (black solid line) in this graph. (c), (d) Plot energy distributions of (c) protons and (d) electrons escaped from the simulation box in the outflow direction. Both thermal and nonthermal components were observed in the electron energy distribution as the experimental result.

Figure 13

Initial electron density profile of PIC simulation plotted on the $x\text{−}y$ plane.

Figure 14

Results for the (a)–(d) microcoil and (e)–(h) open-cylinder cases. (a), (e) Current density $J_y$ at $z=0$. An intense $-y$ component on two sides was observed for the microcoil case, indicating bidirectional current generation. For the open-cylinder case, reversal of the sign of the $y$ component was observed at the lower end, and bidirectional current was not generated. (b), (f) Magnetic field $B_z$ at $z=0$. Here, $B_z$ in opposite directions is observed in both cases, despite the difference in current generation. (c), (g) Dissipation measure $D_e$ at $z=0$, normalized by $v_{A0}{B}_0{j}_0$, with $v_{A0}=0.023c$, $B_0={10}^4$ T, and $j_0={10}^{16}$ $\mathrm{A}/{\mathrm{m}}^2$ the typical values of Alfvén velocity, magnetic field, and current density, respectively. Efficient energy transfer from the electromagnetic field to plasmas was observed only in the microcoil case, where bidirectional $B_z$ was generated by the initial bidirectional current and then reconnected. (d), (h) Reconnection outflow proton angular distribution. The momentum vector direction distribution of the proton that escaped from the simulation box across the $-z$ boundary is plotted, while the $+z$ side showed similar results. All protons with KE $>400$ keV are integrated, and the origin of the plot indicates the direction parallel to the $z$ axis. The outflow proton beam is only observed in the microcoil case, as a consequence of magnetic reconnection.

Figure 15

Energy partition between proton and electrons. The contributions of electron and proton on the total particle kinetic energy are shown.