As a fundamental and fascinating process in plasma physics, magnetic reconnection occurs widely in astrophysical environments, space plasmas, and laboratory plasmas.1–3 With the topological rearrangement of magnetic field lines, magnetic reconnection can effectively convert magnetic energy into plasma thermal or kinetic energy via plasma heating or particle acceleration.4–6 As an important energy dissipation mechanism, magnetic reconnection was first postulated to explain solar flares, in which magnetic energy in the solar atmosphere is suddenly released.7–10 While the classical Sweet–Parker model7,8 provides a two-dimensional (2D) framework for magnetic reconnection, a number of satellite observations and experiments have demonstrate the inherent three-dimensional (3D) characteristics of magnetic reconnection.1–3,9–17 In particular, magnetic flux ropes consisting of helical magnetic field lines occur routinely in the solar corona and planetary magnetospheres.18–21 They may play a crucial role in solar flares and coronal mass ejections (CMEs), the most energetic eruptive phenomena in the solar system.22–25 In the corona, magnetic flux ropes represent twisted magnetic field configurations storing substantial magnetic energy. When these magnetic flux ropes become unstable, magnetic reconnection will be triggered, which enables the release of magnetic energy through solar flares and CMEs. In addition, the reconnection of helical magnetic flux ropes has long been observed in magnetically confined plasma devices such as tokamaks and reverse field pinches.1,26–29 Although magnetic flux ropes have attracted extensive and continuing interest, it is still difficult to finely control their formation and reconnection in experiments.30

With developments in laser technology, the interactions of high-power lasers with matter provide a novel way to simulate high-energy astrophysical processes such as magnetic reconnection in a laboratory environment.31,32 In laser–matter interactions, strong magnetic fields of the order of kilotesla can be generated via different mechanisms in laser-ablated high-energy-density plasmas.33 Owing to the Biermann battery effect, for instance, a toroidal magnetic field can be generated along the surface of an expanding plasma, where the gradients of plasma density and temperature are noncollinear. Consequently, magnetic reconnection can be triggered in the interaction of plasmas with oppositely orientated self-generated magnetic fields using the appropriate geometric configuration of multiple driver laser beams.34–39 The reconnection and annihilation of oppositely directed magnetic fields can generate a strong transient electric field within the current sheet, thereby accelerating high-energy particles as well as producing electromagnetic bursts.34,35 In magnetic reconnection driven by relativistic laser–plasma interaction, the microphysics of the topological rearrangement of magnetic fields as well as the plasma heating and particle acceleration during the magnetic reconnection can be studied in a well-controlled manner.34–40

In this paper, we propose to generate magnetic flux ropes by using two-color Laguerre–Gaussian (LG) laser pulses copropagating in an underdense plasma. This may provide a new avenue for studying the reconnection of magnetic flux ropes in the laboratory. Driven by the ponderomotive force of two LG laser pulses with different frequencies and opposite topological charges, twisted plasma currents can be effectively excited. Along with the twisted plasma currents, twisted magnetic flux ropes are also generated. Half of the magnetic flux ropes have axial magnetic fields along the positive z axis, while the other half have these fields along the negative z axis. More importantly, the reconnection of these magnetic flux ropes can be triggered by convection of the twisted plasma currents. With the occurrence of magnetic reconnection, magnetic islands with closed magnetic field lines can be formed, and the plasma around the reconnection region can be heated to a temperature as high as 10 keV. More interestingly, a strong axial magnetic field can be generated on the axis, which is as strong as those of the magnetic flux ropes before reconnection. This strong axial magnetic field is induced by the azimuthal current generated during the reconnection of the magnetic flux ropes. This implies that the energy transfer process in the reconnection of magnetic flux ropes is more intricate. Specifically, the energy is not solely transferred from the magnetic field to the plasma unidirectionally.

To study the reconnection of magnetic flux ropes, we first excite twisted plasma waves by using two-color LG laser pulses. In a cylindrical coordinate (r, θ, z) system, the electric field of an LG laser pulse that propagates along the z axis can be written in the paraxial approximation as41–44E=ês∑p,lEp,lFp,l(X)coskz−ωt+lθ−ϕp,l−kwb2(z)X24f(z),(1)where ês is the polarization unit vector, E_p,l is the electric field amplitude of the p, l mode, ϕ_p,l = (2p + l + 1) arctan (z/z_r) is the Gouy phase, f(z)=z+zr2/z is the front surface curvature, and zr=kwb,02 is the Rayleigh length. The radial eigenfunction F_p,l(X) is given byFp,l(X)=Cp,lX|l|/2e−X/2Lpl(X),(2)where X=2r2/wb2(z) is the normalized radial coordinate, wb(z)=wb,01+z2/zr2 is the beam width, Cpl=2p!/[π(p+|l|)!] is a normalization constant, andLpl(X)=X−leXp!dpdXpe−XXp+l=X−lp!ddX−1pXp+lare the Laguerre polynomials. Here, p and l are the radial and azimuthal indices, respectively, of the topological charge. In the region z ≪ z_r, one can ignore the terms with f(z) and ϕ_p,l and have w_b(z) = w_b,0. Consequently, the ponderomotive potential of a monochromatic LG laser pulse can be simplified asΦpond =e24meω2⟨|E(r,t)|2⟩=e24meω2Ep,l2Fp,l(X)2.(3)We now introduce the electric field of the two-color LG laser pulses with different topological charges l₁ and l₂:41E=êsE0Fp,l(X)cosk1z−ω1t+l1θ+cosk2z−ω2t+l2θ,(4)In the case l₁ = −l₂ = −l, the ponderomotive potential of the two-color LG laser pulses can be written asΦpond =e2E022meω02Fp,l2(X)[1+cos(−Δkz+Δωt+2lθ)],(5)where Δk = k₁ − k₂ and Δω = ω₁ − ω₂.

As depicted in Fig. 1, two LG laser beams with different frequencies and opposite topological charges l each exhibit a pair of opposing electric field twisted structures. Upon the superposition of these two LG laser beams, the amplitude of the resulting electric field has not only a beat-wave structure, but also a spiral curve in space. The ponderomotive potential, obtained after time averaging, becomes azimuthally dependent and exhibits a twisted structure, as displayed in Fig. 1. As will be illustrated below, this twisted ponderomotive potential will give rise to twisted plasma waves. Along with the twisted plasma waves driven by such a twisted ponderomotive force, magnetic flux ropes can be generated. The corresponding magnetic fields can be estimated following the analysis in Ref. 41:Bz=−4lπj0̃cwb2Δk3Fp,l3∂Fp,l∂X{1−cos[2(−Δkz+Δωt+2lθ)]},Bθ=−2πcj0̃wbΔω2X2Fp,l3∂Fp,l∂X{1−cos[2(−Δkz+Δωt+2lθ)]},Br=πlcj0̃2wbΔω22X−X2Fp,l4⁡sin[2(−Δkz+Δωt+2lθ)],(6)where j0̃=−en0τ2c4Δk3a04/ωp, a₀ = eE₀/(m_eω₀c) is the dimensionless vector potential, τ is the pulse duration, n₀ is the plasma density, ω₀ = (ω₁ + ω₂)/2, ω_p is the plasma frequency, e is the unit charge, and c is the speed of light.

To obtain distinctly separated magnetic flux ropes, we employ a composition of a low-order LG mode with radial eigenfunction F_0,±1 and a high-order LG mode with radial eigenfunction F_1,±1 instead of a simple low-order LG mode. Figure 2(a) compares the radial eigenfunction of the composed mode, F_1,±1–F_0,±1, with that of the low-order mode, F_0,±1, and it is clear that the strongest light intensity in the case of the composed LG mode is farther from the laser axis. As a result, as shown in Fig. 2(b), the peak of the axial magnetic field amplitude generated in the composed mode case will also be farther off the axis, making the twisted magnetic flux ropes more distinctly separated from each other and facilitating a clear observation of the reconnection process between them.

To illustrate the generation and reconnection of magnetic flux ropes, we have performed three-dimensional particle-in-cell (PIC) simulations using the EPOCH code.45 In the simulations, a two-color LG laser pulse with frequencies ω₁ = 1.025ω₀ and ω₂ = 0.975ω₀ is incident into the plasma along the z axis, where ω₀ is the frequency corresponding to a laser wavelength of 0.8 μm. The LG laser pulse has a composed mode with radial eigenfunction F_1,±1–F_0,±1 and is linearly polarized in the x direction. It has a Gaussian intensity profile with a FWHM duration of τ_g = 133 fs and a beam width of ω_b = 5 μm. The LG laser pulse has a peak laser intensity of I_p = 2.33 × 10¹⁷ W/cm². The corresponding normalized amplitude of the laser electric field a₀ = eE₀/m_eω₀c ≈ 0.33. The plasma target is set as a fully ionized hydrogen plasma with an initially uniform density n₀ = 4.5 × 10¹⁸ cm⁻³ and zero temperature. Here, the plasma density has been set according to the beating condition ω_p = Δω = 0.05ω₀, where ωp2=4πn0e2/me. The simulation box (25 × 25 × 40 μm³) is divided into (500 × 500 × 800) cells, and four macroparticles per cell are allocated for each particle species.

Figure 3(a) shows that with the incidence of the two-color LG laser pulses, the amplitude of the superposed electric field exhibits a twisted beat wave structure, which is aligned with the theoretical prediction displayed in Fig. 1. Figure 3(b) clearly illustrates that when the laser frequency difference Δω and the plasma density n₀ satisfy the beating condition Δω=(4πn0e2/me)1/2, two pairs of twisted plasma waves can be effectively excited, with one pair consisting of two waves with positive axial currents and the other pair consisting of two waves with negative axial currents.

Along with these two pairs of twisted plasma waves, four pairs of magnetic flux ropes (i.e., twisted magnetic field structures) can be excited by the two-color LG laser pulses as depicted in Fig. 4(a). As illustrated in Fig. 4(b), because a composition of a low-order LG mode with radial eigenfunction (F_0,±1) and a high-order LG mode with radial eigenfunction (F_1,±1) is employed for the LG laser pulse, these magnetic flux ropes are relatively far from the axis, and the axial magnetic field near the laser axis is relatively small. As shown below, this will enable us to clearly detect the reconnection process between these magnetic flux ropes. Figure 4(b) shows that in these four pairs of magnetic flux ropes, the four ropes with positive axial magnetic fields are on the outside and the four ropes with negative axial magnetic fields are nested inside. Furthermore, the amplitudes of the positive axial magnetic fields are weaker than those of the negative axial magnetic fields, which is also consistent with the theoretical prediction shown in Fig. 2(b).

It is worth pointing out that these magnetic flux ropes are dynamic structures evolving rapidly in space and time. As shown in Fig. 4(c), the axial magnetic field of the flux ropes at t = 800 fs becomes obviously weaker than that at t = 400 fs. By contrast, the axial magnetic field around the axis becomes very strong and appears as a rod-like structure on the axis. The cross-sectional distributions in Fig. 4(d) clearly show that the axial magnetic field on the axis becomes dominant over that of the flux ropes. Since the laser pulse has already left the simulation box at around 300 fs, this strong axial magnetic field on the axis will not have been generated directly by the laser–plasma interaction. Furthermore, Eq. (6) and Fig. 2(b) also indicate that the axial magnetic field originating directly from the laser–plasma interaction should be nearly zero on the axis. Therefore, the strong magnetic field on the axis observed in the PIC simulation suggests a novel mechanism for magnetic field generation.

To better understand the evolution of the magnetic field structure, we plot the magnetic field lines in the transverse plane at z = 13.4 μm, where the magnitude of the axial magnetic field on the axis achieves its maximum. Figure 5(a) shows that the magnetic field lines in the transverse plane exhibit twisted V-shapes in the upstream regions (marked by purple boxes), but are not closed in the downstream regions (marked by black boxes) at t = 400 fs. Figure 5(b) shows that with the reconstruction of the magnetic field line structure, especially the linking of adjacent magnetic field lines along opposite directions in the downstream regions, four closed island structures (two large and two small) are formed on the magnetic field lines at t = 600 fs. More interestingly, these four magnetic islands merge into two large magnetic islands as shown in Fig. 5(c) at t = 800 fs. The formation of these magnetic islands represents a substantial change in the magnetic field topology, which is often considered an important criterion for the occurrence of magnetic reconnection in tokamaks or reversed field pinches.46

To clarify the triggering mechanism of magnetic reconnection, it is imperative to know the spatiotemporal evolution of the plasma current. It is known that magnetic reconnection in plasmas may be caused by either collision of plasma flows or convection of plasma currents.2–4 As shown in Fig. 3(b), twisted plasma currents can be effectively driven by two-color LG laser beams with opposite topological charges l. More importantly, there are some convection regions for the plasma currents. From the analysis in Ref. 41, the dominant first-order plasma current density is given byjθ(1)=0.5en0lc2a02τwb2XFp,l2(X)sin(−Δkz+Δωt+2lθ),jr(1)=−2en0c2a02τwbX2Fp,l∂Fp,l∂Xcos(−Δkz+Δωt+2lθ),jz(1)=−0.25en0c2a02τΔkFp,l2(X)sin(−Δkz+Δωt+2lθ).(7)It follows that the sign of the radial current term j_r depends on the derivative of F_p,l [denoted by (F_p,l)′] as well as on the term cos(−Δkz + Δωt + 2lθ). The radial current j_r will change from negative to positive as the radius increases when cos(−Δkz + Δωt + 2lθ) < 0, which corresponds to the regions of our simulation result shown in the upper-left and lower-right corner regions in Fig. 5(d). This means that in these regions, the electrons around the axis will move outward, while the outer electrons move inward, and they will form a pair of convective currents. As a result, the magnetic field lines can be brought together in these regions along different directions. We note that the region in Fig. 5(d) where the radial current j_r rapidly changes its sign is exactly the upstream region in Fig. 5(a) where the magnetic field lines have been reconnected to form a V-shaped structure at t = 400 fs. Furthermore, we notice that the azimuthal current j_θ in Fig. 5(g) is significantly strengthened in the upstream region, which can be attributed to the enhanced magnetic tension at the corner of the V-shape.

On the other hand, it can be seen from Eq. (6) that the phase of the magnetic field is Φ_B = 2(−Δkz + Δωt + 2lθ), while the phase of the plasma current in Eq. (7) is Φ_J = (−Δkz + Δωt + 2lθ). Owing to this difference in phase velocity between the magnetic field and the plasma current, the convection region of the radial current j_r will gradually slide from the upstream region to the downstream region. This results in closure of the magnetic field lines in the downstream region and the formation of four magnetic islands, as shown in Fig. 5(b). As the convection region of the radial current j_r moves farther, the four magnetic islands merge into two larger magnetic islands at 800 fs, as shown in Fig. 5(c). Meanwhile, the radial current j_r appears in a more complex multistripe structure in Fig. 5(f). More importantly, the balance between the positive and negative azimuthal currents j_θ is disrupted further, as shown in Fig. 5(i). As a result, a strong axial magnetic field will be generated on the axis. On the basis of the above analysis, we can conclude that the twisted magnetic flux ropes driven by two-color LG laser beams have intrinsic instability to trigger magnetic reconnection because of the convection of the plasma currents.

Using the azimuthal current j_θ obtained from the PIC simulation, the axial magnetic field B_z(z) on the axis at height z can be estimated by the following Biot–Savart law:Bz(z)=μ04π∭Vjθ(r′)r′zez−r′3dr′,(8)where μ₀ is the vacuum permeability, j_θ(r′) is the electron azimuthal current density at position r′ = (r′, θ′, z′), e_z is the unit vector along the z axis, and V represents the whole simulation box space. The spatial distribution of B_z on the axis estimated by Eq. (8) is depicted in Fig. 6. It indicates that the strength of the axial magnetic field on the axis can reach 20 T, which is as high as the axial magnetic field of the magnetic flux ropes in the early stage. More importantly, the magnetic field B_z(z) estimated by Eq. (8) is in quantitative agreement with that obtained from the PIC simulation. This reveals that the strong axial magnetic field on the axis is primarily caused by the imbalance between the positive and negative azimuthal currents j_θ, which is a consequence of the reconnection of the magnetic flux ropes.

To identify the X-point of the magnetic reconnection, we display in Fig. 7 the distributions in the x–y plane of the transverse current density J_xy, transverse magnetic field B_xy, and longitudinal current density J_z. In Figs. 7(a)–7(c), where the orientation and magnitude of the transverse magnetic field are represented by the direction and length, respectively, of the red arrows, magnetic reconnection is clearly evidenced by the convergence of arrows at the X-point. Furthermore, Figs. 7(d)–7(f) reveal that an out-of-plane current J_z is induced near the reconnection X-point, which plays a critical role in energy conversion and particle acceleration during the magnetic reconnection. In this simulation, the electron inertial length and electron gyroradius are ∼d_e = c/ω_pe ≃ 2.55 μm and R_ce = v_ine/ω_ce ≃ 1.32 μm, respectively. Here, the electron cyclotron frequency ωce=(4πnee2/me)1/2 is calculated with a magnetic field strength B = 30 T and an electron inflow velocity v_ine = 1.05 × 10⁷ m²/s. The simulated current sheet width is observed to be about 2.31 μm, which is comparable to the electron inertial length. This observation aligns with key signatures of magnetic reconnection in collisionless plasmas.3

Moreover, the plasma beta β = p/p_mag = n_ek_BT_e/(B²/2μ₀) is calculated as β ≃ 0.17, where the averaged electron temperature T_e ≈ 10⁶ K, the averaged electron density n_e = 4.5 × 10¹⁸ cm⁻³, and the magnetic field strength B = 30 T. This indicates that the plasma system is strongly magnetized and the magnetic field dominates the plasma dynamics. Consequently, the plasma can respond collectively to the magnetic field, enabling the occurrence of magnetic reconnection. It is noteworthy that plasma environments with β ≈ 0.17 occur widely in astrophysical environments: similar plasma parameter characteristics are found in CMEs (β ≪ 1),47 the solar corona (β ≤ 0.2),48 the Earth’s magnetopause (β ≈ 0.3),49 and solar flares (β = 0.01–100),50 among other typical astrophysical systems. In these environments, the magnetic field strength significantly exceeds the plasma pressure, as a consequence of which the magnetic field plays a decisive role in plasma dynamics.

Owing to the energy conversion from the magnetic field to the plasma particles, a significant increase in the plasma temperature has been observed during reconnection of magnetic flux ropes. Although an initially cold plasma is assumed (i.e., T_e = 0 at t = 0), Fig. 8(a) shows that the electron temperature can reach several keV in the region where magnetic reconnection occurs. The peak of the electron temperature at t = 800 fs is even higher than 10 keV, as shown in Fig. 8(b). More interestingly, the hot electrons tend to gather around the axis, which can be attributed to the strong axial magnetic field generated on the axis during magnetic reconnection. To verify the energy balance during magnetic reconnection, we show the temporal evolution of electromagnetic field energy, particle energy, and their sum within the simulation box in Fig. 8(d). During the early stage (t < 120 fs), the electromagnetic field energy increases rapidly as the laser pulse is entering the simulation box. Correspondingly, particles in the plasma gain energy through oscillatory motion in the laser field and heating/acceleration mechanisms, leading to a rapid rise in particle energy within this initial phase. During 120 fs < t < 240 fs, the electromagnetic field energy declines sharply as the laser pulse is leaving the simulation box. Correspondingly, the particle energy decreases partially: the oscillation-related energy gradually diminishes to zero, while the energy associated with the heating and acceleration is retained. In the t > 240 fs post-laser phase, magnetic reconnection results in a relatively slow decline in the electromagnetic field energy (primarily comprising static magnetic and electric field energies). This is accompanied by a gradual increase in the particle energy, while their sum remains essentially conserved. This demonstrates that energy is transferred from static magnetic fields to particle kinetic energy while energy conservation is maintained during magnetic reconnection.

It is worth pointing out that reconnection of magnetic flux ropes can occur over a broad range of laser–plasma parameters, provided the plasma density and the beat frequency difference Δω of the driver laser pulses satisfy the matching condition n₀ = m_eΔω²/4πe². More interestingly, both the magnetic field of the magnetic flux ropes and the resulting axial magnetic field can be enhanced by appropriately increasing the laser beat frequency difference Δω (raising the plasma density correspondingly). Figure 9 illustrates that when the beat frequency difference increases from Δω/ω₀ = 5% to 10%, the axial magnetic field strength approximately doubles, while the pitch of the magnetic flux ropes is correspondingly halved. Figure 9(f) shows that when Δω/ω₀ is further increased to 15%, the pitch of the current ropes decreases to one-third of its initial value, in agreement with the theoretical prediction. However, the structure of the magnetic flux ropes no longer remains stable in this case, as illustrated in Fig. 9(c).

The plasma system in our simulation features a helical 3D magnetic flux rope structure with a plasma thermal pressure lower than the magnetic pressure (β < 1). Consequently, magnetic reconnection occurring within such a plasma may be susceptible to tearing or kink instabilities. Notably, we find that the kink instability will become significant when the beat frequency difference Δω of the laser pulses is increased (with a corresponding rise in plasma density). Generally, the stability condition for helical magnetic configurations against kink instabilities is governed by the Kruskal–Shafranov criterion51p0Bθ<2πρBz,i.e.,lg2πρBzp0Bθ>0,(9)where the pitch of the magnetic flux rope is given by p₀ = λ₀ω₀/(2Δω), and the radius ρ approximately equals the laser beam waist w_b. Figure 10(a) shows that in the case of Δω/ω₀ = 5%, the Kruskal–Shafranov criterion is well satisfied across most regions, including the magnetic reconnection zone. When Δω/ω₀ increases to 15%, however, it can be seen from Fig. 10(b) that the Kruskal–Shafranov criterion will fail in most regions. This occurs because, despite the decrease in pitch with increasing Δω, the poloidal magnetic field B_θ grows even more rapidly, ultimately triggering kink instability. This explains the disappearance of stable magnetic flux rope structures at Δω/ω₀ = 15% in Fig. 9(c). The Kruskal–Shafranov criterion is no longer satisfied at Δω/ω₀ = 15%, and the rapidly developing kink instability will quickly disrupt the structure of magnetic flux ropes. Therefore, considering plasma instabilities such as the kink instability, the frequency difference Δω of the driver laser pulses should not be larger than 0.1ω₀ for the stable generation of magnetic flux ropes.

We have studied the generation and reconnection of magnetic flux ropes in a plasma driven by two LG laser pulses with a frequency difference Δω and opposite topological charges. As long as the plasma density satisfies the beating condition n₀ = m_eΔω²/4πe², two pairs of twisted plasma waves can be effectively stimulated: with one pair consisting of two waves with positive axial currents and the other pair consisting of two waves with negative axial currents. Along with the twisted plasma currents, four pairs of magnetic flux ropes (i.e., twisted magnetic field structures) are formed, in which the axial magnetic fields of the outer four ropes are along the positive z axis, while those of the inside four ropes are along the negative z axis. More importantly, these magnetic flux ropes are dynamic structures evolving rapidly in space and time. Because of the convection of the twisted plasma currents, these magnetic flux ropes are subject to intrinsic instability that triggers magnetic reconnection. With the change in the magnetic field topology, magnetic islands with closed magnetic field lines can be formed during the reconnection of magnetic flux ropes. As one of the most important features of magnetic reconnection, the plasma temperature can significantly increase up to 10 keV, owing to the conversion of magnetic energy to plasma particle energy. More interestingly, we have found that a strong axial magnetic field can be generated on the axis during magnetic reconnection, with strength as high as that of the magnetic flux ropes in the early stage. This strong axial magnetic field is mainly caused by the azimuthal current generated during magnetic reconnection rather than by direct laser–plasma interaction.

Our work provides a novel approach to the generation of magnetic flux ropes in the laboratory, which may play a crucial role in understanding the evolution of magnetic topology, energy dissipation, and particle acceleration in the reconnection of magnetic flux ropes relevant to solar flares and CMEs. It has been demonstrated that reconnection of magnetic flux ropes can occur over a broad range of laser–plasma parameters. Both the magnetic field strength and pitch of the magnetic flux ropes can be controlled by adjusting the plasma density and frequency difference of the driver laser pulses. The geometric similarity between the magnetic flux ropes produced in the interaction of two-color LG laser pulses with a plasma and those occurring in astrophysical plasma systems provides an ideal platform for studying the astrophysical processes related to magnetic flux ropes such as solar flares and CMEs. In particular, a strong axial magnetic field can be generated on the axis in the reconnection of magnetic flux ropes. This strong axial magnetic field can effectively guide charged particles, which may facilitate the collimation of relativistic plasma jets52,53 and CMEs.54 Furthermore, our work may also contribute to improving the plasma confinement and plasma heating in magnetic confinement fusion devices such as tokamaks and reverse field pinches,1,26–29 in which magnetic structures similar to magnetic flux ropes are ubiquitous. The magnetic flux ropes generated in the interaction of two-color LG laser pulses with a plasma have extremely small spatial scales (a few micrometers) and undergo rapid spatiotemporal evolution. Therefore, it will be extremely challenging to diagnose such small and fast-evolving magnetic flux rope structures in experiments. The electron radiography technique55 that employs femtosecond high-energy electron beams generated in laser–plasma acceleration may provide an approach to resolving the dynamics of such magnetic flux ropes.

Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant Nos. 12375236 and 12135009) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDA25050100 and XDA25010100). Simulations were carried out on the Sugon supercomputer at Shanghai Jiao Tong University.