Introduction

Magnetic reconnection is the fundamental process for energy release in solar flares and coronal mass ejections (CMEs; P. F. Chen 2011; K. Shibata & T. Magara 2011). During reconnection, the magnetic energy stored in sheared magnetic fields is rapidly released in the form of thermal energy, kinetic energy, and particle acceleration (A. O. Benz 2017). Traditional models of reconnection, such as the Sweet-Parker model, predict reconnection rates that are too slow to account for the rapid energy release observed in solar flares. The Petschek reconnection model (H. E. Petschek 1964) predicts fast magnetic reconnection via slow-mode shocks, but it requires the formation of a very specific and narrow diffusion region, which is difficult to sustain over large scales or in resistive MHD conditions. To resolve this discrepancy, more recent models have introduced the concept of plasmoids that form within the current sheet due to the tearing mode instability. As the current sheet thins and stretches prior to reconnection, it becomes increasingly susceptible to this instability, leading to the formation of multiple plasmoids (K. Shibata & S. Tanuma 2001;N. F. Loureiro et al. 2007; A. Bhattacharjee et al. 2009; Y.-M. Huang & A. Bhattacharjee 2010; M. Bárta et al. 2011). These plasmoids enhance the reconnection process by increasing the local reconnection rate, effectively speeding up the overall process and facilitating the rapid energy conversion needed to power solar flares. The presence of plasmoids also helps explain the observed fine structures in solar flare emissions and the quasiperiodic pulsations (QPPs) often detected in extreme-ultraviolet (EUV), X-ray, and radio observations. These plasmoids play a crucial role at the high Lundquist numbers characteristic of flares, as their formation, motion, and eventual coalescence are closely linked to the acceleration of particles to high energies. Observing the emissions from these accelerated particles provides valuable insights into the underlying mechanisms of flare energy release. The acceleration of the energetic electrons resulting from the ejection and coalescence of plasmoids in the current sheet has broad implications for understanding the fast magnetic reconnection in the solar, heliospheric, and magnetospheric current sheets (L. J. Chen et al. 2008; T. D. Phan et al. 2024).

Electron acceleration in the flare current sheet, particularly from plasmoids formed by reconnection, involves several key mechanisms. These electrons gain energy from the reconnection electric field and from the betatron and Fermi acceleration mechanisms within contracting plasmoids. Additionally, the turbulent environment created by interacting and merging plasmoids enhances stochastic acceleration processes (J. F. Drake et al. 2006). Numerical simulations and observations continue to provide critical insights into the complex dynamics of electron acceleration in flare current sheets (J. T. Dahlin et al. 2014Dahlin et al. , 2017;;B. Chen et al. 2020). Particle-in-cell (PIC) and kglobal simulations suggest that the coalescence of multiple plasmoids can produce suprathermal particles (M. Oka et al. 2010;J. F. Drake et al. 2013;H. Arnold et al. 2021). Alternatively, termination shocks may form when a fast reconnection outflow collides with the top of the flare arcade, creating a site for efficient particle acceleration. These shocks accelerate electrons and ions through processes such as diffusive shock acceleration, where particles gain energy by repeatedly crossing the shock front (H. Aurass et al. 2002;H. Aurass & G. Mann 2004;B. Chen et al. 2015). This mechanism can also significantly contribute to the high-energy particle populations observed in solar flares.

Hard-X-ray (HXR) emission in solar flares is primarily produced by high-energy electron beams that are accelerated during magnetic reconnection and interact with the dense low coronal and chromospheric plasma (S. Krucker et al. 2008). Yohkoh and RHESSI observations have revealed the presence of looptop (above the flare arcade) and footpoint sources during flare impulsive energy releases (S. Masuda et al. 1994;B. Dennis et al. 2022). RHESSI observations have discovered the presence of double coronal X-ray sources during a few solar flare events (L. Sui & G. D. Holman 2003;L. Sui et al. 2004), enhancing our understanding of the fundamental processes of energy transfer and particle acceleration in flares. This doublesource configuration was interpreted as evidence of magnetic reconnection in the flare current sheet, where the lower source is typically associated with the looptop source above the flare arcade and the upper source with the reconnection outflow high in the corona (T. Wang et al. 2007;W. Liu et al. 2008). The flare energy release site is believed to lie between these double coronal X-ray sources. The nature of coronal double coronal X-ray sources is not yet fully understood. The simultaneous observations of flares at EUV, X-ray, and radio wavelengths offers a valuable opportunity to explore the mechanisms of energy release and particle acceleration.

QPPs are a common and intriguing feature observed in flare emission across a wide range of wavelengths, including radio, X-ray, and EUV (S. R. Kane et al. 1983;A. R. Inglis et al. 2008;P. Kumar et al. 2016P. Kumar et al. , 2017a;;L. A. Hayes et al. 2020). These pulsations typically manifest as periodic or quasiperiodic variations in intensity, with periods ranging from a fraction of a second to several minutes. The physical mechanisms driving QPPs are not well understood, but they are generally thought to be related to repetitive magnetic reconnection processes associated with magnetohydrodynamic (MHD) oscillations or bursty reconnection/plasmoids within the flaring region (V. M. Nakariakov & V. F. Melnikov 2009;J. A. McLaughlin et al. 2018; I. V. Zimovets et al. 2021). MHD simulations have demonstrated the formation and ejection of a series of plasmoids moving bidirectionally during explosive flare reconnection in a current sheet beneath erupting flux ropes (M. Bárta et al. 2008; J. T. Karpen et al. 2012;B. J. Lynch & J. K. Edmondson 2013;S. E. Guidoni et al. 2016; J. T. Dahlin et al. 2022).

Decimetric radio bursts, typically observed in the frequency range of 300-3000 MHz, are produced by nonthermal electrons accelerated during the magnetic reconnection process (A. O. Benz et al. 2011). The height of the decimetric (236-432 MHz) radio sources observed by the Nançay Radioheliograph generally lies above the RHESSI looptop source (N. Vilmer et al. 2002;M. Pick et al. 2005;A. O. Benz et al. 2011). Previous studies have proposed that decimetric radio bursts and pulsations (drifting toward lower frequencies) can be produced by the ejection and coalescence of multiple plasmoids in the flare current sheet (B. Kliem et al. 2000). The drifting pulsating structures (DPSs) in decimetric radio bursts likely indicate the intermittent nature of the energy release in the flare current sheet and the signature of radio emission from electrons accelerated during the ejection and coalescence of plasmoids (M. Karlický 2004; M. Karlický et al. 2010;M. Karlický & B. Kliem 2010;M. Karlický & M. Bárta 2011).

A few previous studies have linked the behavior of plasmoids with the acceleration of electrons, leading to radio and X-ray emission, during magnetic reconnection in flares. RHESSI observations suggest an increase in HXR and radio emissions during the coalescence of a downward-moving coronal X-ray source (interpreted as a plasmoid) with a looptop kernel (R. O. Milligan et al. 2010). However, EUV images of this event do not reveal any plasmoids. P. Kumar & K.-S. Cho (2013) reported the first simultaneous EUV and radio (DPS in the decimetric band) observations of bidirectional plasmoids during an X-class flare. The speeds of the upward-/downwardmoving plasmoids observed in EUV and in radio DPSs (both positive and negative) were found to be consistent. S. Takasao et al. (2016) presented radio imaging of microwave bursts (i.e., gyrosynchrotron emission) during the ejection and coalescence of downward-moving plasmoids along with their interaction with the flare arcade.

This paper presents EUV imaging of the plasmoids formed in flare current sheets underneath erupting flux ropes during two successive flares on 2015 April 22. The bidirectional plasmoids were associated with QPPs in the X-ray (soft/hard) and radio (decimetric) wavelengths. The flux rope appeared only in the hot channels (131/94 Å) during the first flare. We present direct imaging of the formation of double coronal X-ray sources at both ends of the flare current sheet during the ejection and coalescence of multiple plasmoids. The erupting flux rope during the second flare apparently undergoes kink instability and the formation of a plasma/current sheet along with multiple plasmoids propagating bidirectionally. In both cases, the flux ropes reached a height of about 45 Mm (60″) above the limb but remained confined within the overlying strapping field of the active region, thus failing to produce CMEs. In Section 2, we present the observations and results, while in Section 3 we discuss and summarize the results.

Observations and Results

We analyzed Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA; J. R. Lemen et al. 2012) fulldisk images of the Sun (field of view ≈ 1.3 R e ), with a spatial resolution of 1.  5 (0.  6 pixel -1 ) and a cadence of 12 s, in the following channels: 1600 Å (C IV+continuum; temperature T ≈ 0.1 MK, 5000 K), 304 Å (He II; T ≈ 0.05 MK), 171 Å (Fe IX; T ≈ 0.7 MK), 211 Å (Fe XIV; T ≈ 2 MK), 193 Å (Fe XII, Fe XXIV; T ≈ 1.2 MK and ≈ 20 MK), and 131 Å (Fe VIII, Fe XXI, and Fe XXIII; T ≈ 0.4, 10, and 16 MK) images. The 3D noise-gating technique (C. E. DeForest 2017) was applied to denoise the SDO/AIA images.

To investigate the particle acceleration sites during the flares associated with these stalled flux rope eruptions, we used X-ray light curves and images from RHESSI (R. P. Lin et al. 2002). We used the CLEAN algorithm (M. J. Aschwanden et al. 2004) to reconstruct the X-ray image, with an integration time of 60 s in the 6-12 keV and 12-25 keV energy channels, using detectors 3 and 5-9. RHESSI missed the impulsive phases of flux derivative and the observed HXR bursts during both flares/eruptions, as expected. No CMEfoot_1 was detected in the LASCO C2 coronagraph images during these flares. The Learmonth (25-180 MHz) and Wind/WAVES dynamic radio spectra do not show any radio bursts (type II or III) associated with these events. 2.1. Event #1 AIA images during the first flare reveal the appearance of an flux rope, which was detected only in the hot channels (AIA 94 and 131 Å; Figures 2(a1)-(a4)). One leg (L1) of the flux rope is close to the flare arcade, while the other leg extends behind the limb (Figure 2(a4)). A bright plasma sheet (PS) above the flare arcade appeared between these two legs (Figures 2(a3) and (a4)). The flux rope was confined and did not produce a successful eruption (see Movie S1). The blobs were best seen in the AIA 171, 193, and 211 Å channels; therefore, we show a sequence of AIA 171 Å images (a zoomed-in view of the region marked in Figure 2(a1) and Movie S2) covering the bright PS and blobs. AIA 171 Å images reveal the ejection of multiple plasma blobs (marked by arrows) along the bright PS above the flare arcade during 08:00-08:11 UT (Figures 2(b1-b4) and (c1-c4)). During 08:04-08:10 UT, the bright sheet has two components (PS1 and PS2) in which the plasma blobs propagate (Figures 2(b4-c3)). After 08:10 UT, we observed only a single PS. The size of the blobs ranges from 2″ to 3″. To measure the temporal evolution and kinematics of the blobs formed in the flare PS, we created time-distance (TD) EUV intensity plots along slices P1Q1 and P2Q2 (marked in Figure 2(b1)) using AIA 171 Å images during the first flare (C3.8; 08:00-08:30 UT). The TD intensity plot along P1Q1 (along the PS) shows the ejection of multiple blobs above the flare arcade during the flare impulsive phase (08:00-08:11 UT; Figure 3(a)). The speeds of the upward-moving blobs along the tracked paths are 228, 203, 208, 295, 323, 370, and 210 km s -1 . The TD intensity plot along P2Q2 (across the PS) reveals the blobs passing through the slit (Figure 3(b)). The blobs were detected in the PS until 08:20 UT and disappeared afterward. The white curve represents the average intensity of the blobs (scale given on the right y-axis), which is extracted from between the two horizontal dashed lines in Figure 3(a). The Fermi-GBM light curve shows the X-ray emission in the 6-12, 12-25, and 25-50 keV channels (Figure 3(c)). The X-ray emission reveals QPPs in the 6-12 and 12-25 keV bands during 08:00-08:20 UT, with only weak emission in the 25-50 keV band (08:00-08:06 UT). The ejection of blobs is nearly associated with the X-ray emission peaks (marked by arrows) in the 6-12 and 12-25 keV bands during the flare impulsive phase (four cycles during 08:00-08:08 UT; see Movie S2). Interestingly, QPPs also appear in the same X-ray bands during the flare decay phase, 08:11-08:20 UT. The dynamic radio spectrum shows nearly simultaneous decimetric/metric radio bursts (800-150 MHz) with the X-ray peaks during the flare impulsive and decay phases (Figure 3(d)). The radio/X-ray emission stopped at 08:20, coinciding with the disappearance of the blobs in the PS.

We utilized e-Callisto dynamic radio spectra (250-350 MHz) from the KRIM station (Crimean Astrophysical Observatory) to investigate the metric/decimetric bursts during the flares. The fine structures of the radio bursts (pulsating structures, marked by arrows) are best seen in the e-Callisto dynamic spectra (Figure A1). The radio pulsating structures, detected in metric/ decimetric frequencies, reveal strong correlation with the X-ray emission in the 12-25 keV band during the first flare (C3.8). Some of the radio bursts also show multiple substructures at 08:02, 08:12, and 08:15 UT (Figures A1(a At 08:14 UT, we observed another faint source, S3, between S1 and S2 (Figure 5(a4)). One minute later, the source had moved up about 12″ in the RHESSI image. The estimated speed of S3 is around 150 km s -1 . Simultaneously, we noticed a decrease in the height of S1 (Figure 5(b4)). RHESSI contours overlaid on AIA images reveal that source S3 coincides with blobs near the apex of the PS. Source S1 fades as its height increases during 08:17-08:19 UT, while source S2 remains bright (Figures 5(c4) and (d4)). The source S1 disappeared after 08:20 UT and source S2 also faded gradually (see Movie S3) during the decay phase of the flare.

Event #2

The second flare (M1.1) began at 08:28 UT, peaked at 08:44 UT, and ended around 08:58 UT. The GOES flux shows two stages of energy release during this flare. During the first stage of energy release (08:28-08:36 UT), AIA images (1600, 211, and 131 Å) reveal the activation of a filament close to the flare arcade from the previous C3.8 flare (Figure 6). The slow rise of the filament begins with brightening between its legs. The AIA images and associated animation (Movie S4) depict the kinking of the slowly rising filament (F) along with the formation of a bright plasma/current sheet between its legs (Figures 6(a2 The filament appears to be stable for a while and is confined during the decay phase of the first energy release (08:34-08:37 UT). During the impulsive phase of the second energy release (08:38-08:40 UT), we observed two PSs along the flux rope legs (PS1 and PS2), with blobs moving upward and downward within both sheets aligned along the legs of the filament (Figure 7). We also observed upward-moving blobs in the flare current sheet, which merge and collide with the lower part of the flux rope and change their orientation toward the southern leg (the cyan arrow in Figures 7(a2)-(a5) and 7(b2)-(b5)). AIA 131 Å images reveal bright PSs along the legs, the formation and ejection of multiple blobs, and the flare arcade during the impulsive phase of the flare (Figures 7(c1)-(c6) and Movie S6). AIA 1600 Å images reveal a ribbon near the southern footpoint of the flux rope (Figure 7); the second ribbon is likely occulted behind the limb. The flux rope stopped nearly at the same height (about 50″ above the limb) as the flux rope during the first flare (C3.8). We created TD intensity plots from AIA 211 and 131 Å images along the slices P1Q1, P2Q2, P3Q3, and P4Q4 to determine the kinematics of the erupting filament and associated upward-/downward-moving blobs in the flare current sheet during 08:20-08:50 UT. The dynamic radio spectrum from e-Callisto reveals faint decimetric/metric radio bursts (250-350 MHz) occurring prior to and during the impulsive phase of the M1.1 flare (Figure 8(a)). The AIA 211 Å TD intensity plot along slice P1Q1 captures the erupting filament and PS (Figure 8(b)). The filament rises slowly at about 35 km s -1 during 08:25-08:35 UT. Bright PSs were observed along the legs of the erupting flux rope (PS1/PS2) and at the leading edge (PS3). The PS at the leading edge disappeared between 08:36 and 08:38 UT. A rapid rise of the flux rope at 107 km s -1 was observed during 08:39-08:41 UT, during the fragmentation of the PS, accompanied by bidirectional blobs. A strong radio burst was detected at 08:39 UT during the merging of an upward-moving blob with the lower boundary of the flux rope. Multiple blobs were observed until 08:46 UT. The flux rope was confined at 08:41 UT and exhibited transverse (kink) oscillations with a period of about 2-3 minutes and an amplitude of approximately 5-6 Mm (Figure 8(a)). At least three cycles of transverse oscillation are clearly observed between 08:40 and 08:47 UT. Notably, the kinematics of the flux rope correlate with the GOES SXR flux, indicating two stages of energy release. During both stages, the formation and ejection of multiple plasmoids within the double structure of the PS were observed, along with associated decimetric/metric radio bursts (see Movie S6). The speeds of the blobs were determined by tracking the most visible paths in the TD intensity plots. The speeds of multiple upward-moving blobs (the blue dashed lines) were 134, 150, and 330 km s -1 along P1Q1 (Figure 8(b)) and 254 and 175 km s -1 along P3Q3 (Figure 8(d)). The speeds of the downward-moving blobs were 150, 82, 123, 235, and 204 km s -1 along P2Q2 (Figure 8(c)) and 162 and 88 km s -1 along P3Q3 (Figure 8(d)). The TD intensity plot along P4Q4 shows the separation of the flux rope legs during the eruption (Figure 8(e)). The brightenings between the legs are due to the downward-moving blobs in the PSs. The AIA 131 Å channel reveals the appearance of an flare arcade at 08:40 onward, due to ongoing reconnection in the flare current sheet (Figure 8(d) and accompanying Movie S6).

Discussion

Plasma/current Sheets with Multiple Plasmoids

We analyzed two flare events that occurred successively at the main PIL within the same AR. The blobs observed in the PSs during both flares are interpreted as plasmoids. For the first time, we observed a double structure of the plasma/current sheet with multiple propagating blobs below the erupting flux ropes. We interpret these blobs as plasmoids formed by reconnection in the flare current sheet. During the first flare (C3.8), we observed upward-moving reconnection outflows traced by multiple plasmoids (speed: 200-370 km s -1 ) and the formation of a hot flux rope during the eruption. Prior to the second flare (M1.1), a filament within the flux rope rose slowly (35 km s -1 ), associated with brightening between its legs. The flux rope showed evidence of kink instability and the formation of two bright PSs (PS1 and PS2) on the inner surfaces of its legs, joined by a central flare current sheet. The speeds of the upward-and downward-moving plasmoids were 134-330 km s -1 and 82-235 km s -1 , respectively, with plasmoid sizes ranging from 2″ to 3″. The sizes and speeds of the plasmoids are consistent with previous observations (S. Takasao et al. 2012; P. Kumar & K.-S. Cho 2013; P. Kumar et al. 2019Kumar et al. , 2023)).

The observations of plasma/current sheets detected below an erupting flux rope are consistent with the predictions of an MHD simulation of a kink-unstable flux rope. Figure 4 in B. Kliem et al. (2010) depicts the double structure of the PS (the helical current sheet in cyan color) along the legs of the flux rope and an flare current sheet (red color) below the flux rope. This MHD simulation exhibited current sheets and associated reconnection in a failed/confined eruption, strikingly similar to the observed events described in their Section 3. However, the spatial resolution of the B. Kliem et al. (2010) simulation does not seem to be sufficient to resolve plasmoids in the helical current sheets and flare current sheet. In contrast, we detected a separation between the legs of the flux rope during the eruption but did not observe leg-leg reconnection, as seen in the MHD simulation. As described in B. Kliem et al. (2010), the helical current sheet forms as a result of the kink instability of an flux rope, wrapping around the twisted legs of the rope. This structure is crucial for understanding the magnetic reconnection processes and energy release during stalled solar eruptions.

We interpret the plasmoid dynamics with a comparison to the results of an MHD simulation (Figure 9). This simulation, which was performed with the ARMS code (C. R. DeVore & S. K. Antiochos 2008), modeled an eruptive flare with a highresolution adaptive grid using the same configuration employed in J. T. Dahlin et al. (2022) at a lower resolution (the lower resolution was employed in order to capture the entire flare evolution, which was not computationally feasible at higher resolution). Many plasmoids were formed, the dynamics of which will be discussed in detail in J. T. Dahlin et al. 2025 (in preparation). Here, we show a selection of longitudinal slices of the density (Figures 9(a)-(d)), showing plasma blobs that correspond to plasmoids below an erupting flux rope. The running-difference animation of synthetic white-light images (constructed from the ARMS density data, following the method of B. J. Lynch et al. 2016) provides a better view of bidirectional plasmoids (Movie S7b). A TD plot of the density in Figure 9(e) illustrates the formation and ejection of multiple plasmoids (Movie S7a). The acceleration of the flux rope during the period of plasmoid proliferation, consistent with the observations, is clearly evident. In the simulations, the plasmoid speeds in the flare current sheets are higher than the blob speeds in the observations. This is probably due to the difference in the localized Alfvén speed between the simulation and the observed activity.

Double Coronal X-ray Sources

During the first flare (C3.8), we detected double coronal X-ray sources (6-12 and 12-25 keV) located at both ends of the PS (i.e., below and above the reconnection site). The lower source was located above the flare arcade, while the higher source was observed near the reconnection outflow, where multiple plasmoids merged with the underside of the halted flux rope. The flux rope appearing in the hot channels was observed during magnetic reconnection at the flare plasma/current sheet. Previous observations from RHESSI Sui et al. 2004;W. Liu et al. 2008) have interpreted the double coronal source as evidence of magnetic reconnection in the flare current sheet. However, direct imaging of the plasma/current sheet with multiple plasmoids moving bidirectionally has not been reported previously to be simultaneous with double coronal X-ray sources. Here, we present a consistent picture of plasmoidmediated reconnection in the flare current sheet associated with the formation of double coronal X-ray sources, thereby adding observational support to previous findings by RHESSI. In addition, we observed a faint X-ray source (6-12 keV) that appeared between the double X-ray sources (S1 and S2) and was cospatial with EUV plasmoids in the PS. The speeds of the upward-moving faint source and EUV plasmoids are consistent.

During the initiation of the second flare, we observed a RHESSI X-ray source (6-12, 12-25 keV) located near the PS between the legs of the flux rope (Figures 6( d2) and (d3)). This is consistent with the plasma heating and particle acceleration associated with the formation and ejection of plasmoids in a PS beneath an erupting flux rope. Previous observations have also revealed the formation of an HXR source between the legs of a kink-unstable flux rope, interpreted as magnetic reconnection in a current sheet (D. Alexander et al. 2006;K.-S. Cho et al. 2009). However, these observations did not show evidence for a plasma/current sheet or plasmoids. Our observations provide direct imaging of plasma/current sheets with multiple plasmoids, thereby supporting previous interpretations about the formation of X-ray sources between the legs of a kinkunstable flux rope.

RHESSI missed the impulsive phase of the second flare, so we do not have X-ray imaging for that interval. We observed decimetric radio bursts (evidence of electron injections) associated with the formation/ejection and coalescence of plasmoids at the trailing edge of the flux rope during the impulsive phase of the M1.1 flare.

The Fermi-GBM X-ray spectra (6-30 keV energy, assuming that the emission is generated by a thin-target bremsstrahlung radiation process) at different intervals reveal the evolutions of the temperature, emission measure, and spectral index during plasmoid-mediated reconnection in both flares (Figures A5 and A6). The estimated temperatures and emission measures near the quasiperiodic peaks (the five intervals mentioned in the Fermi spectra) during the first flare (C3.8) range from 10 to 15 MK and from 1.9 to 6.8 × 10 47 cm -3 . The spectral index varies between 3.9 and 6.7. For the second flare (M1.1), the temperature and emission measure near two peaks were [12, 13.5] MK and [30 × 10 47 , 23 × 10 47 cm -3 ]. The spectral index (δ) varies from 7.1 to 4.3 (see Table 1).

The QPPs in decimetric radio bursts associated with plasmoids in an flare current sheet are most likely due to plasma emission. This mechanism effectively explains the rapid periodic variations and fine structures observed in the radio spectrum, as it directly involves the interaction of accelerated electrons with the ambient plasma in the highly dynamic environment of the flare current sheet. The observed frequencies of 300-800 MHz correspond to plasma densities (using f n 8980

, where f p is the plasma frequency in Hertz and n e is the electron density in inverse cubic centimeters) ranging from approximately 1.1 × 10 9 to 0.8 × 10 10 cm -3 (assuming fundamental emission). The comparison of radio spectra from ORFEES (Figure 3(d)) and Callisto/KRIM (Figure A1) suggests that the ORFEES pattern (involving some of the type III burst-like features) is likely the second harmonic of the much fainter fundamental emission observed in the Callisto dynamic spectrum. If the radio emission for the frequency range of 500-800 MHz corresponds to the second harmonic (2f p ), the estimated plasma density will be approximately 0.7 × 10 9 to 0.2 × 10 10 cm -3 . These densities suggest that the emission source region should be located in the PS (i.e., the upward-moving blobs merging into the flux rope). PIC simulations suggest that accelerated electron beams trapped within the helical structure of plasmoids, particularly in the lower-density shell, are believed to produce the DPSs observed in radio bursts (M. Karlický & M. Bárta 2011). The observations indicate that the decimetric pulsation is likely associated with the electron beams injected during the coalescence of upward-moving blobs with the halted flux rope. The density of the PS (and blobs) is generally on the order of 10 10 cm -3 (based on differential emission measure or DEM analysis; Figures B1 and B2), while the flux rope density is about 5.8 × 10 9 cm -3 . The decimetric pulsations are temporally correlated with the appearance of the RHESSI upper source (S2), suggesting that upward-moving electron beams at different energies excite both X-ray (source S2) and decimetric radio emissions below the erupting flux rope (e.g., the upward-moving radio source in M. Pick et al. 2005). The major X-ray emission is generally associated with the lower source S1 (i.e., the downward-moving electron beams during reconnection).

QPPs Associated with Plasmoids

The wavelet analysis (C. Torrence & G. P. Compo 1998) of the X-ray light curve (12-25 keV) reveals a ≈100 s periodicity during the first flare (C3.8; Figure A3). The quasiperiodic X-ray bursts closely match the decimetric pulsations (400-800 MHz) observed in the ORFEES dynamic spectrum (Figure 3(d)). This 100 s periodicity is correlated with the creation of multiple plasmoids in the flare current sheet.

Moreover, the high-resolution e-Callisto dynamic spectra and Learmonth observatory (1 s cadence) radio flux profiles reveal a shorter period in decimetric bursts. The wavelet analysis of the radio flux densities reveals a ≈10 s periodicity during the first flare (C3.8; Figure A4). The 10 s period may be attributed to an MHD wave process. As the plasmoids interact and merge, they undergo MHD oscillations (e.g., the sausage mode; V. M. Nakariakov et al. 2003), leading to perturbations in the density and magnetic field within the plasmoid (e.g., see the MHD simulation by P. Jelìnek et al. 2017). These oscillations can modulate the injection of electron beams into the surrounding plasma, leading to the repetitive acceleration of electrons. The periodic injection of these electron beams, synchronized with the plasmoid oscillations, may result in the observed 10 s QPPs in the radio emission. The AIA temporal resolution (12 s) is not sufficient to detect these oscillations in the EUV images (10 s). The typical size of the plasmoids in our observations is about 2″-3″. The speed of the upward-moving plasmoids ranges from 134 to 330 km s -1 . Using the observed oscillation period of the decimetric radio bursts, we determine the ambient Alfvén speed using the formula P = L/V A , where L is the size (width) of the plasmoids and V A is the Alfvén speed at the edge of a plasmoid. For an average plasmoid size of 2000 km and an oscillation period of 10 s, the estimated Alfvén speed is about 200 km s -1 . This value is consistent with the average speed of the plasmoids in the flare current sheet.

During the second flare (M1.1), the QPPs in radio decimetric bursts are characterized by a period of about 60 s (Figure 8(a)), which is roughly consistent with the frequency of the ejected plasmoids in the PS (Figures 8(b) and (c)). The strong radio burst around 08:37 UT was correlated with the merging of the first upward-moving blob with the lower boundary of the flux rope. The other upward-moving plasmoids also merge with the flux rope and produce weaker decimetric radio bursts.

The AIA 171/211 Å running-difference images do not reveal any evidence of an EUV wave (shock/fast-mode wave) during the QPPs. Therefore, we can rule out the modulation of quasiperiodic particle acceleration via propagating fast-EUV waves. Previous observations have revealed QPPs associated with upward-propagating fast-mode waves during flare reconnection and associated radio bursts without plasmoids (P. Kumar et al. 2017b).

QPPs observed in both radio and X-ray emissions during solar flares are often linked to the dynamic processes occurring in the flare current sheet, particularly the formation and ejection of plasmoids. These plasmoids can periodically release energy as they move through the current sheet. The corresponding radio and X-ray QPPs arise from the acceleration of electrons and the associated emissions as plasmoids interact with the surrounding plasma and magnetic fields. The temporal correlation between radio and X-ray QPPs suggests a common driver, i.e., the repetitive nature of plasmoid formation/ejection and associated coalescence.

Successive or Magnetically Connected Confined Eruptions

Both eruptions occurred successively along the same PIL, with no gap between the flares. The flare arcades appeared next to each other. During the first flare, the flux rope was observed only in the hot channels (94/131 Å). However, plasmoids were seen in multiple AIA channels covering cool and warm/hot plasma. The second flare started with the eruption of a filamentcarrying flux rope along with bright PSs along the two legs. The flux ropes in both eruptions stopped at a similar height (about 45 Mm). The AIA 171 Å image reveals systems of multiple overlying loops above the erupting flux ropes (Figure 1(a)). We speculate that the flux ropes were unable to overcome the overlying strapping field, as required for escape. The presence of two bright PSs lining the flux rope legs suggests the existence of a helical current sheet in both stalled eruptions. During the second eruption, we also noticed the appearance of a PS (PS3) at the leading edge of the flux rope during its interaction with the overlying structures. PS3 disappeared rapidly during the kinking motion of the flux rope. Further acceleration of the flux rope was associated with plasmoid-mediated reconnection in the current sheets embedded in PS1 and PS2. The majority of the upwardmoving plasmoids merged into the underside of the flux rope. The flux rope halted, and no current sheet was left behind it for further flare reconnection. The flux rope plasma drained back to the solar surface after the eruption stalled. Therefore, the kinking motion, along with the inability of the flux rope to escape from the strong overlying flux system, is likely responsible for the confinement of these successive eruptions.

We have observed a similar confined eruption associated with a kink-unstable flux rope with a flare PS containing plasmoids (P. Kumar et al. 2023). However, our previous observations did not exhibit the double structure of the helical PS along the flux rope legs. In this event, we also observed a kink oscillation (period ≈ 2-3 minutes and amplitude ≈5-6 Mm) of the stalled flux rope after its encounter with the overlying loops (P. Kumar et al. 2022).

The kinematics of the flux rope and the GOES SXR flux are strongly correlated during the second flare (M1.1). The slow rise of the flux rope matches the slow rise of the X-ray flux prior to the flare (Figure 8). The flux rope remains nearly stable for about 2-3 minutes during the dip in the SXR flux, which we interpret as a pause in flare reconnection. The subsequent acceleration of the flux rope is strongly correlated with flare reconnection associated with plasmoids, suggesting that flare reconnection plays a significant role in the acceleration of the flux rope in the low corona.

Conclusion

We report direct imaging of the formation and ejection of multiple plasmoids in flare current sheets beneath erupting flux ropes, along with QPPs at X-ray and radio wavelengths. During the M1.1 (second) flare, we observed kinking of the flux rope in both the hot and cool AIA channels, along with the formation and ejection of bidirectional plasmoids in the flare PS. The current/plasma sheet is predominantly viewed edge-on in this event, allowing for a more direct comparison with the 3D MHD simulation. In contrast, during the C3.8 (first) flare, the plasma/current sheet appears more distorted and tilted, with the flux rope formation observed only in the hot AIA channels. Upward-moving plasmoids are clearly visible, while downward-moving plasmoids appear less prominent during the first flare. These observations confirm: (i) that the X-ray double coronal sources observed by RHESSI are located at both ends of the flare current sheet and are formed during plasmoidmediated reconnection in the sheet; (ii) the faint transient source that appeared between the double coronal sources is most likely associated with upward-moving plasmoids; (iii) the presence of an flare current sheet with double structure and multiple plasmoids, as predicted by an MHD simulation of a kink-unstable flux rope (B. Kliem et al. 2010); (iv) the formation of a plasma/current sheet at the leading edge of the kink-unstable flux rope during its encounter with the overlying flux system; (v) that the coalescence of the upward-moving plasmoids at the underside of the flux rope is accompanied by decimetric radio bursts; and (vi) X-ray/radio QPPs (P = 10 s, 100 s) are associated with the ejection and coalescence of plasmoids in the flare plasma/current sheet. These findings enhance our understanding of plasma heating and the quasiperiodic acceleration of electrons via plasmoid-mediated reconnection in flare current sheets below erupting flux ropes. The production of energetic electrons through the ejection and coalescence of plasmoids in the PS has broad applicability to understanding fast magnetic reconnection in solar, heliospheric, and magnetospheric current sheets. The direct imaging of plasmoids and associated QPPs provides key insights into plasmoid-mediated magnetic reconnection and particle acceleration, supporting theoretical models of these processes during solar flares. In the future, similar flare events along with simultaneous EUV, radio, and HXR imaging will yield further insights into the electron acceleration sites associated with plasmoids during magnetic reconnection in solar eruptions. Movie S3. The AIA 171, 211, and 131 Å animation (left panels; Figures 4 and 5) and the ORFESS radio dynamic spectrum (Figure 3(d)), the Fermi-GBM X-ray flux (Figure 3(c)), and the RHESSI images in the 6-12 keV channel (bottom rows of Figures 4 and 5) during the first flare (C3.8). The animation runs from 08:10 UT to 08:20 UT. Its real-time duration is 2.2 s. Movie S4. An animation of the AIA 171, 211, and 131 Å images (Figures 6(b1)-(d1)) covering the second flare (M1.1). The top panels show a large field of view, while the lower panels display a zoomed-in view of the area outlined by the red box in the top panels. The animation runs from 08:26:13 UT to 08:56:37 UT. Its real-time duration is 5.1 s. Movie S5. The AIA 171, 211, and 131 Å animation (Figures 6(b1)-(d4)) is shown in the left panels, while the right panels display the Fermi-GBM X-ray flux (6-12 keV; Figure 3(c)), the GOES SXR flux derivative (1-8 Å; Figure 1(d)), and the RHESSI images in the 6-12 keV channel during the initiation of the second flare (M1.1). The animation runs from 08:26:25 UT to 08:33:37 UT. Its real-time duration is 3.8 s. Movie S6. The first part of the animation shows a TD intensity plot along P1Q1 (Figures 7(b4) and 8(a) and (b)), using AIA 211 Å images and the associated e-Callisto radio dynamic spectrum (decimetric bursts) during the second flare (M1.1). The second part of the animation covers TD intensity plots along P2Q2 and P4Q4, using AIA 211 Å images (Figures 7(b5