Particle Acceleration In Plasmoid Ejections Derived From Radio Drifting Pulsating Structures
aa r X i v : . [ a s t r o - ph . S R ] D ec PARTICLE ACCELERATION IN PLASMOID EJECTIONSDERIVED FROM RADIO DRIFTING PULSATINGSTRUCTURES
N. Nishizuka , M. Karlick´y , and M. Janvier , M. B´arta ABSTRACT
We report observations of slowly drifting pulsating structures (DPS) in the0.8-4.5 GHz frequency range of the RT4 and RT5 radiospectrographs at OndˇrejovObservatory, between 2002 and 2012. We found 106 events of drifting pulsatingstructures, which we classified into 4 cases: (I) single events with a constant fre-quency drift [12 events], (II) multiple events occurring in the same flare with con-stant frequency drifts [11 events], (III) single or multiple events with increasingor decreasing frequency drift rates [52 events], and (IV) complex events contain-ing multiple events occurring at the same time in the different frequency range[31 events]. Many DPSs are associated with hard X-ray bursts (15-25 keV) andsoft X-ray gradient peaks, as they typically occurred at the beginning of the hardX-ray peaks. This indicates that DPS events are related to the processes of fastenergy release and particle acceleration. Furthermore, interpreting DPSs as sig-natures of plasmoids, we measured their ejection velocity, their width and theirheight from the DPS spectra, from which we also estimated the reconnectionrate and the plasma beta. In this interpretation, constant frequency drift indi-cates a constant velocity of a plasmoid, and an increasing/decreasing frequencydrift indicates a deceleration/acceleration of a plasmoid ejection. The reconnec-tion rate shows a good positive correlation with the plasmoid velocity. Finallywe confirmed that some DPS events show plasmoid counterparts in AIA/SDOimages.
Subject headings: acceleration of particles — magnetic reconnection — Sun:flares — Sun: particle emission — Sun: radio radiation — Sun: X-rays, gammarays National Institute of Information and Communications Technology, 4-2-1, Nukui-Kitamachi, Koganei,Tokyo 184-8795, Japan; [email protected] Astronomical Institute of the Academy of Sciences of the Czech Republic, 25165 Ondˇrejov, Czech Re-public Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom
1. Introduction
Various plasma ejections in solar flares are observed in the solar corona. Ejectionsof soft X-ray emitting plasma blobs and hot loops, i.e. flux ropes in 3 dimensions, arecalled plasmoid ejections. Plasmoid ejections are observed in multi wavelength emissions:soft X-ray (SXR: e.g. Shibata et al. 1995; Ohyama & Shibata 1997; Tsuneta et al. 1997;Nishizuka et al. 2010), hard X-ray (HXR: e.g. Hudson et al. 2001; Sui et al. 2003; Glesener et al.2013), UV/EUV (e.g. Liu et al. 2010; Takasao et al. 2012; Kumar & Cho 2013; Liu et al.2013) and radio emissions (e.g. Kliem et al. 2000; Kundu et al. 2001; Khan et al. 2002;Karlick´y et al. 2002; Bain et al. 2012). Plasmoids gradually rise up in the preflare phaseand are impulsively accelerated in the main phase, in association with HXR bursts. Sim-ilarly, when coronal mass ejections (CMEs) are accelerated in the main phase, both HXRbursts and a rapid increase of SXR emission are observed. (CMEs: Zhang et al. 2001;Temmer et al. 2008). Some downward ejections of plasmoids, which collide with the loop-top region, are also reported (Koloma´nski & Karlick´y 2007; Liu et al. 2010; Milligan et al.2010; Takasao et al. 2012). Plasmoid ejections are evidence of magnetic reconnection andmultiple X-lines in a solar flare (e.g. Shibata et al. 1995; Ohyama & Shibata 1997; Tsuneta et al.1997; Karlick´y 2004; Nishizuka et al. 2010).Accelerated electrons escaping from the reconnection regions in the upward direction areobserved as type III bursts in radio emissions, while downward electron beams are observedas a reverse-drift burst (Aschwanden & Benz 1997). The observed frequency correspondsto the frequency of the plasma surrounding the electron beam, so that electrons propagatingin a density gradient of the solar atmosphere show frequency shift in the radio spectra.Having these two bursts interpreted as bi-directional electron beams from one region, wecan expect magnetic reconnection or acceleration in that location. Recently it has beenshown that acceleration regions exist at several different heights during solar flares, bothin observations (Aschwanden 2002; Krucker et al. 2010; Reid et al. 2011) and numericalsimulations (Shimizu et al. 2009; B´arta et al. 2011, 2012; Nishida et al. 2013).Furthermore, some decimetric radio bursts in flares show coherent, quasi-periodic se-quences of fast-drifting pulsed structures bound by a pair of slowly drifting low- and high-frequency cutoffs. These are called slowly drift pulsating structures (DPSs: e.g. Kliem et al.2000; Kundu et al. 2001; Karlick´y et al. 2002; Khan et al. 2002; Karlick´y 2004; Karlick´y et al.2004; Tan et al. 2007; Tan 2008; Tan et al. 2008; B´arta et al. 2008; Wang et al. 2012).They are caused by quasi-periodic particle acceleration episodes that result from a highlydynamic regime of magnetic reconnection in an extended large-scale current sheet above theSXR loops, where reconnection is dominated by the repeated formation and the subsequentcoalescence of plasmoids (Kliem et al. 2000; Karlick´y 2004; B´arta et al. 2008). Electron 3 –beams trapped in a plasmoid are observed as pulsating structures in a DPS, while the motionof a plasmoid in a density gradient of the solar atmosphere is observed as a global frequencydrift.Electrons are accelerated in a DC field around the X-line in the vicinity of a plasmoid(Karlick´y & B´arta 2011). The acceleration process of electrons forms an anisotropic velocitydistribution, which excites the observed radio emission. The period of DPSs can be explainedby the time scale of plasmoids determined by the tearing-mode oscillation (Tan et al. 2007).A few spectra of DPSs are shown to correspond to SXR emitting plasma ejecta (Kliem et al.2000; Karlick´y 2004; Tan et al. 2007), in the flare ascending phase just after the onset.Previous studies have shown that all the DPS events are accompanied by GOES SXR flares(Tan et al. 2008), and they occur when the gradient of the GOES SXR curve reaches itsmaximum (Wang et al. 2012). In our 0.8-4.5 GHz frequency range, most of the DPSs takeplace at the beginning of the whole flare radio emission, i.e. before the type IV bursts, whichis in this range a common flare burst type. From several very broad radio spectra taken byseveral radiospectrographs, Karlick´y et al. (2002) found an association of DPSs with typeII bursts, generated in the metric radio range by flare shocks. It agrees with the results ofTan et al. (2008) showing a close association of DPSs with CMEs or ejection events.Plasmoid ejection is strongly related to the reconnection process, as shown in the”plasmoid-induced reconnection model” (Shibata & Tanuma 2001). When we assume anincompressible plasma around a current sheet, the conservation of mass fluxes of the inflowand the outflow leads to the following equation: v in = W pl L in v pl , (1)where v in is the inflow velocity, L in the length of the inflow region, W pl the width of theplasmoid, and v pl the plasmoid ejection velocity. This equation indicates that the plasmoidejection induces a reconnection inflow, so that the ejection velocity has a good correlationwith the inflow velocity. Even in the case of a compressible plasma, the inflow velocity andthe net reconnection rate increase with the plasmoid ejection, when magnetic flux is piled uparound a current sheet by the reconnection inflow at the same time as the plasmoid ejection(Ono et al. 2011; Hayashi et al. 2012).Plasmoid ejections also have an important role in particle acceleration, as well as un-steady impulsive energy release. Current models of particle acceleration during solar flaresconsidering plasmoid dynamics are as follows: (1) DC field acceleration in a reversed X-linebetween two colliding plasmoids (e.g. Tanaka et al. 2010; Karlick´y & B´arta 2011), (2) ac-celerations in a contracting plasmoid after coalescence (Drake et al. 2006; Tanaka et al.2010; Oka et al. 2010) and in multiple reconnection outflows by interacting plasmoids in 2 4 –dimensions (Hoshino 2012), and (3) acceleration at the fast shock above the loop-top wheremultiple plasmoids collide (Nishizuka & Shibata 2013). Furthermore, turbulence producedby plasmoid dynamics may couple with stochastic accelerations.In this paper, we classified DPSs into 4 cases with regards to the plasmoid dynamics,i.e. acceleration/deceleration, and estimated the reconnection rate by using DPSs data. Thefirst advantage of our study is that we analyze 106 DPSs we found during the time period2002-2012. The number of analyzed DPSs is larger than the previous studies and allows us tostatistically study the sample. The second is that, in a gravitationally stratified atmosphere,DPSs show direct information along the vertical direction, i.e. the vertical ejection velocityand not the apparent velocity as usually deduced from imaging observations. The ejectiondirection is not always vertical, but in many cases the ejection may occur at some angleto the density gradient. This can affect the estimation of the ejection velocity from driftvelocities in radio observations, though it would give an error of a factor √ ◦ . The third is that DPSs also contain information about electron beams, whichallow us to compare the plasmoid ejection with the particle acceleration. This is why we alsocompared DPSs and HXR data, and discussed the relationship to the particle accelerationprocess. Finally we searched for plasmoid counterparts in imaging observations by the SolarDynamics Observatory (SDO). We explain the analysis method in §
2, the analysis results in §
3, and we summarize our results and discuss them in §
2. Observations of DPS events and their Classification
We used the radio spectrum data taken by the radiospectrograph at the Ondˇrejov ob-servatory (Jiˇriˇcka et al. 1993). There are three radio telescopes (RT3, RT4 and RT5) inthe frequency range of 0.8-4.5 GHz. The time cadence is 10 ms. The set of data we usedcovers 11 years from 2002 to 2012. The DPS events between 2002 and 2005 in our paper arepartially the same as in a previous paper by B´arta et al. (2008), and we added some eventsduring the same period with a more careful analysis and during 2006 and 2012 with newdata (examples in Figures 1 and 2).During this time period, there are lots of decimetric bursts observed, including type IIIor reverse-drift bursts and DPSs. The type III or reverse-drift bursts are detached broadbandfast-drift bursts, whose typical durations are < < × cm − . Interpreting DPSs as signatures of plasmoids, the drifts towardslower/higher frequencies mean upward/downward motions of plasmoids. The DPSs withdecreasing/increasing frequency drifts mean acceleration/deceleration of plasmoids.In this paper, we found 106 DPS events during 2002-2012. We dealt with multiple DPSevents in a single flare as a single event, though B´arta et al. (2008) counted every DPSsas individual events. This is why the number of DPS events in B´arta et al. (2008) lookslarger, although the number of DPSs we analyzed is much larger than in their paper. Wesummarized the events in Table 1, where we noted some characteristics of these DPSs. SomeDPSs drift to lower frequencies, and others drift to higher frequencies or have no drift. Thefrequency drift sometimes varies in time. Some DPSs oscillate around a certain frequency.Most of the DPSs occurred at the beginning of the impulsive phase of flares and sometimesof the radio bursts known as broadband continuum (type IV burst), which is consistent withTan, C. et al. (2008). Sometimes they appear after the impulsive or main phase, and smallnumbers of events are not associated with flares (inconsistent with Tang et al. 2007; this isdiscussed in detail in § t start and t end . We also measure the low- and high-frequency cutoffs of every decimetric bursts, listed as f max and f min , at the start of the eventas well as the end time (see Fig. 2). The upper/lower edge of the DPS is determined byeye. We determine the duration as ∆ t = t end − t start . It is noted that the frequency drift ratechanges in quite a short time period <
100 ms, as shown in Figure 2, so that the frequencydrift rate shows discontinuity during the acceleration and in each period the frequency driftrate can be well fitted by a linear approximation (cases (III) and (IV) in the next paragraph).When a DPS event shows changes in the frequency drift rate, we separate the event to shorterperiods with an approximately constant frequency drift and measure t start , t end , f max and f min for each period.Following the different characteristics of DPSs, we classified our 106 DPS events intofour categories: (I) single DPS events with a constant frequency drift (drift towards loweror higher frequencies), (II) multiple DPS events occurring in the same flare with constantfrequency drifts, (III) single or multiple events with increasing or decreasing frequency driftrates and (IV) complex events containing multiple events occurring at the same time in thedifferent frequency range. Cases (I) and (II) have only three events with no frequency drift, 6 –Fig. 1.— Typical DPS events taken by Ondˇrejov radiospectrograph telescopes: (a) (I) singleevents with constant frequency drift, (b) (II) multiple events with constant frequency drifts,(c) (III) single event or multiple events with increasing/decreasing frequency drift rates and(d) (IV) complex events including multiple events occurring at the same time in the differentfrequency range.Fig. 2.— A typical DPS event (case (III)) taken by Ondˇrejov radiospectrograph telescopeon 2011 Mar 6 with the measurable parameters indicated. 7 –whereas cases (III) and (IV) include lots of events with no frequency drift preceding/followingthe acceleration/deceleration. The number of events for case (I) is 12 events, 11 events forcase (II), 52 events for case (III) and 31 events for case (IV). This leads to the fact thatcase (III) is the most common and case (IV) is the second. Therefore, DPSs usually haveincreasing or decreasing frequency drift rates. Those different categories are illustrated inFigure 1.The motions of the DPSs in case (III) have typically three patterns: no drift to drifttowards lower frequency, drift towards higher frequency to no drift, and drift towards higherfrequency - no drift - drift towards lower frequency. It seems that most of the DPSs in case(III) tend to decrease the frequency drift rate. The initial frequency and the frequency driftrate of DPSs in case (II) are random. The patterns of the DPSs in case (IV) are sometimesvery complex, composed by multiple DPSs with increasing/decreasing frequency drifts. Someof them are superposed and seem to be merged or split. Multiple DPSs appear at the sametime in different frequency ranges. The observation of multiple DPSs may indicate multipleplasmoids formed in a current sheet via the secondary tearing mode instability, which leadsto the repetition of the coalescence process and bursty ejections.Figure 3 shows the year variation of the number of detected DPS events during 2002-2012. The first peak is around 2002, and the second one is in 2012. During 2006-2009,no DPSs were observed, except for one event in 2007. This seems to correspond with the11-year period of solar activity variation. Especially case (III) shows the most sensitive anddramatic changes along the solar activity. Fig. 3.— Year variation of the number of DPS events during 2002-2012, with DPSs classifiedin four different categories. 8 –Table 1. Event list of the 106 DPS events during 2002-2012.
Date a Time b Case c RHESSI d GOES e Date a Time b Case c RHESSI d GOES e I ◦ - I ◦ - I - ◦ I ◦ - I ◦ - I - ◦ I - ◦ I - ◦ I ◦ - I - ◦ I - × I - ◦ II ◦ - II ◦ - II - ◦ II ◦ - II - ◦ II - ◦ II - ◦ II ◦ - II ◦ - † II ◦ - II ◦ - III - ◦ III - ◦ III ◦ - ∗ III - × III - ◦ III ◦ - ∗ III × - III - ◦ III - ◦ III - ◦ III ◦ - III - ◦ III ◦ - III ◦ - III ◦ - III ◦ - III - ◦ III ◦ - † III ◦ - † III ◦ - † III ◦ - III - ◦ III - ◦ III - ◦ III ◦ - III ◦ - III - ◦ III ◦ - III ◦ - III ◦ - III - ◦ III ◦ - † III ◦ - III ◦ - III ◦ - III ◦ - III ◦ - † III ◦ - III - ◦ III ◦ - III - ◦ III - ◦ III ◦ - III ◦ - III ◦ - III - ◦ III ◦ - III - ◦ III - ◦ III - ◦ III - ◦ III - ◦ IV - ◦ IV - × IV × - IV ◦ - IV - ◦ IV - ◦ IV ◦ - IV - ◦ IV ◦ - IV ◦ - † IV ◦ - IV ◦ - ∗ IV × - IV ◦ - IV ◦ - IV - ◦ IV - × ∗ IV - × IV ◦ - IV - ◦ IV × - IV - ◦ IV - ◦ IV - ◦ ∗ IV - × IV - ◦ IV - ◦ IV - ◦ IV × - IV - ◦ IV - ◦ Note. — a Date (yyyy/mm/dd), b Start time [UT], c Classification: case (I)-(IV), d RHESSI peak (with/without ◦ / × ; no data − ), e GOES time derivativepeak (with/without ◦ / × , events with RHESSI data are skipped − ). Here weconsider events occurring during different flares. † mark denotes the events withHXR peaks but without GOES SXR flares. ∗ mark denotes the events withneither HXR nor GOES SXR flares. 10 –
3. DPSs in association with HXR bursts3.1. Measurements of HXR peaks
DPSs are ensembles of type III-like bursts, i.e. emissions from high energy electronbeams via wave-particle interactions. In DPSs, electrons are trapped in plasmoids. Thereforethese trapped electrons cannot reach dense layers of the solar atmosphere where the X-rays are usually generated, i.e. the chromosphere and the photosphere. However, thereare electrons accelerated simultaneously in the same reconnection region, which are nottrapped in the plasmoids. These can then generate HXRs in deep and dense layers of theSun’s atmosphere. Therefore, some association of DPSs and HXR bursts can be expected(Karlick´y et al. 2004). This association can be further influenced by the fact that anybeam of superthermal electrons generate the X-rays in dense layers, but the radio emissionof the beam can be reduced due to an inappropriate beam distribution function, reducedwave conversion, and absorption effects. On the other hand, if the magnetic field structureassociated with many interacting plasmoids becomes complicated, all accelerated electronsare trapped in this structure and do not reach the dense layers of the solar atmosphere. In thiscase we can observe DPSs without corresponding HXRs. Since a DPS (a series of accelerationepisode) lasts much longer than a single type III bursts (one acceleration episode), we studyhere the mean association of DPSs with HXR peaks, i. e. not for individual accelerationepisodes as in the analysis of type III bursts and HXR peaks (Benz et al. 2005).To compare DPS events with HXRs, we used data taken by RHESSI (Lin et al. 2002),whose time cadence is 4 s. We checked all the RHESSI data for the 106 DPSs presentedabove, and 51% of all events (54 DPSs) turned out to be simultaneously observed withRHESSI. For these events, we drew light curves integrated on-disk in three different energyranges, 15-25 keV, 25-50 keV and 50-100 keV. For one DPS event not correlated with anyRHESSI data, we used data taken by the Czech-made Hard X-Ray Spectrometer (HXRSF´arn´ık et al. 2001) onboard the U.S. Department of Energy Multispectral Thermal Imagersatellite (MTI). HXRS has three energy bands: HXRS-S1 for 19-29 keV, HXRS-S2 for 44-67keV and HXRS-S3 for 100-147 keV, with a time cadence of 200 ms. For the other eventswith neither RHESSI nor HXRS data, we calculated the time derivative of SXR light curvestaken by GOES, whose peak is believed to be well correlated with HXR peaks, as knownfrom the Neupert effect (1968). The criterion used to distinguish whether there is a HXRcomponent is an evident increase of HXR emission up to over 40 counts with 4 s cadence(above the background level) in a short time scale, at least in an energy band of 15-25, 25-50,or 50-100 keV. As for the events without RHESSI HXR data, we picked up all the eventswith positive GOES SXR gradients occurring at the same time as DPSs. 11 –
We find that 49 DPSs events (90%) with RHESSI are associated with HXR peaks, and5 events (10%) are not (Table 2). When considering all the events with RHESSI, HXRS orGOES, we found that 95 events (90%) are correlated with HXR peaks and/or SXR peakgradients, and 11 events (10%) are not (Table 3). We summarize the results also in pie graphsof Figure 4, which indicates that most of the DPS events are related to HXR emissions andare associated with particle acceleration. Moreover, we also find that more than 90% of case(I)-(III) events are correlated with HXR peaks, whereas case (IV) shows only 74% of HXRevents. In other words, not all the DPS events are associated with HXR events. Especiallycase (IV) is less correlated with HXR peaks. Considering Neupert effect (1968), it can berewritten that not all the DPS events are in association with SXR flares.Actually we confirmed that not all the DPS events are correlated with GOES SXR flaresover C-class. Majority of DPSs occurred with HXR and SXR flares, but some DPSs withSXR flares and no HXRs (indicating soft flares), some (7 DPS events, attached with † markin Table 1) with HXRs but without SXRs (because the count of HXRs is so small like 40-200that the SXR component is covered in SXR background), and the others (5 DPS events with ∗ mark in Table 1) with neither HXRs nor SXRs (but these were also in active regions). Forthe last 12 events without SXR flares, seven of them are interpreted as independent eventsfrom SXR, because the time difference between DPSs and SXR peaks is so large. Two ofthem occurred in decay phase of GOES flares without any enhancement of SXR. One is inthe quiet SXR activity. Three of them are neglected because of the small increase of SXR likefrom GOES C5.0 to C5.4. These are probably because the magnetic structure in Case (IV)is complex, which can trap in some cases all accelerated electrons, and thus no acceleratedelectrons reach dense layers of the solar atmosphere, and then much reduced X-ray emissionis produced.Figures 5-7 show typical DPS events associated with HXR bursts. The radiospectra ofDPSs are attached with HXR light curves taken by RHESSI, with solid line (15-25 keV),dotted line (25-50 keV) and dashed line (50-100 keV). Every event shows an evident emissionin the energy band 15-25 keV, but only a small number of events show very weak ones inhigher energy bands. This indicates that DPSs are more related to particles/plasmas inthe energy range of 15-25 keV, rather than in the higher energy range of 25-100 keV. Theoccurrence ratio of different HXRs energy events is summarized in Table 4. All the DPSsassociated with HXR peaks taken by RHESSI are accompanied by an enhancement in the15-25 keV band. HXRs in the 25-100 keV bands are observed in less than 25% of all theevents which were associated with HXRs in the 15-25 keV range. Case (I) shows the largestoccurrence ratio of 50-100 keV events to 15-25 keV events, case (IV) show the second, case 12 –(II) the third and case (III) shows the smallest.HXR light curves sometimes show a small hump before the main peak in time, whichis well correlated with a DPS event. It is also noted that HXRs in different energy bandsshow time difference between their peaks, i.e. higher energy peaks are reached earlier thanlower energy peaks, and DPSs are in general more closely correlated with the higher energypeaks in terms of the timing, only when there is a HXR peak in higher energy bands. Thiscan be explained as higher energy particles can precipitate to the chromosphere faster thanlower energy ones, so the timing of higher energy particles is closer to the timing of particleacceleration in the corona near DPS-emitting plasmoids. 13 –Fig. 4.— (a) The percentage of DPS associated with a HXR peak observed by RHESSIor HXRS. “Without a HXR peak” means that there were no HXRs observed above thebackground level. “No RHESSI HXR data” means no RHESSI data during DPS events. (b)The same as (a) using the time derivative of the GOES SXR flux for “no RHESSI” events.Table 2. The number of events with or without HXR peaks for each case (I)-(IV). HXRdata is taken by RHESSI and HXRS.case (I) case (II) case (III) case (IV) Totalwith HXR peaks 5 7 28 9 49no HXR peaks 0 0 1 4 5no RHESSI data 7 4 23 18 52Total 12 11 52 31 106Table 3. The number of events with or without HXR peaks or GOES SXR gradient peaksfor each case (I)-(IV). HXR data is taken by RHESSI and HXRS.case (I) case (II) case (III) case (IV) Totalwith HXR/SXR grad. peaks 11 11 50 23 95no HXR/SXR grad peaks 1 0 2 8 11Total 12 11 52 31 106 14 –Fig. 5.— Typical DPS events taken by radiospectrograph telescopes in Ondˇrejov observatoryand HXR light curves taken by RHESSI in different energy ranges (15-25, 25-50, and 50-100 keV). (a)-(d) show events with ∆t <
0, where ∆t=t
DP S -t HXR . Furthermore, (a) has noHXR >
25 keV, (b) HXR <
25 keV coincides with HXR >
25 keV, (c) HXR <
25 keV coincideswith HXR >
25 keV and HXR peak is long, (d) HXR <
25 keV precedes HXR >
25 keV. 15 –Fig. 6.— Comparison between DPSs observed in Ondˇrejov observatory and HXRs observedby RHESSI in different energy ranges (15-25, 25-50, and 50-100 keV): (a) ∆t=0 and noHXR >
25 keV, (b) ∆t=0 and HXR <
25 keV coincides with HXR >
25 keV. (c) ∆t > <
25 keV coincides with HXR >
25 keV. (d) ∆t > <
25 keV precedes HXR > DP S -t HXR . 16 –Fig. 7.— DPS events with radio bursts known as broadband continua (or type IV burst)and HXRs observed by RHESSI in different energy ranges (15-25, 25-50, and 50-100 keV):(a)-(c) ∆t=0 and f DP S < f burst . (d) ∆t > f DP S > f burst . Here ∆t=t
DP S -t HXR . 17 –
DPS events (with HXR peaks) can be classified by their relation with these peaks. Figure5 shows events which precedes HXR peaks. Figure 6(a)-6(b) shows DPSs whose accelerationor deceleration occur at the same time as HXR peaks, and Figure 6(c)-6(d) shows eventsdelayed to HXR peaks. Here we determine the peak time of HXR (15-25 keV), t HXR , andthe start time of the corresponding DPSs, t DP S . The time difference between the two times(∆ t = t DP S - t HXR ) is illustrated in Figure 8. A positive ∆ t corresponds to a delay of DPSsrelative to HXR, while a negative ∆ t indicates the occurrence of DPSs before the onset orduring the rising phase of HXR bursts. In Figure 9, most of the events are distributed in therange of -60 s < ∆ t <
30 s, which can be fitted with a Gaussian function centered at the nullvalue for ∆ t , and with its negative-side tail enhanced (or double Gaussian functions are alsosuitable). This means that DPSs mainly occur in the flare ascending phase just after theonset of the flare, and that DPSs occur when the gradient of SXRs reaches the maximum(see also Wang et al. 2012). There are minor extreme events with | ∆ t | >
60 s, but thesemay be independent from the HXR activity. Furthermore, there is no tendency that theevents with larger/smaller ∆ t are associated with larger/shorter duration HXR peaks, i.e.when ∆ t is small the events are not always impulsive.As explained above, the association of DPSs with HXRs can be influenced by the radioemission mechanism and by the trapping in the complex magnetic fields resulting from theformation, and possibly the interaction, of multiple plasmoids. The acceleration regions inthe current sheet higher in the corona can get magnetically connected and/or disconnectedmultiple times, as the magnetic topology evolves in the layers below (see e.g. B´arta et al.2011). Namely, new plasmoid formation and coalescence, taking place below the accelerationregion influences the evolution of the magnetic connectivity of this acceleration region allthe way down to the chromosphere/photosphere. Therefore, defining a clear correspondencebetween the radio DPS emissions and HXR remains difficult. Here we propose to look atgeneral tendencies for this connection that can be deduced from observations. We interpretcases of positive ∆ t when the radio emission takes more time, for radiation process to takeplace, e.g. specific velocity distribution, than HXRs. Cases with negative ∆ t may indicatethat the trapping in a complex magnetic field or complex magnetic connectivity domain leadsto particles necessitating more time to precipitate to the chromosphere due to the trappingin the magnetic topology, or that very few high energy particles first escaped to the lowerdense layers, leading to weak HXRs, while the bulk of high energy particles emitting HXRsescaped with a slight delay.The enhancement of HXRs during the acceleration of a plasmoid is only evident forone event. Rather, during multiple plasmoid acceleration events or multiple DPS events, 18 –initially enhanced HXR emission gradually decreases (28 events, e.g. Fig. 5(c)) or reaches thebackground level (5 events, e.g. Fig. 6(a)). When the HXR curve has multiple enhancements,some DPSs also have multiple enhancements in the intensity of the radio/microwave emission(e.g. Figs. 5(d) and 6(d)).Figure 7 shows DPS events with additional radio bursts which are called broadbandcontinuum or type IV burst. 6 events out of the 48 DPS events with RHESSI HXR peaksare accompanied with radio bursts in the frequency range of 0.8-4.5 GHz. 1 event occurredduring the main phase of the radio burst, while 5 events occurred before or at the initialphase of the radio burst. It is also noted that one DPS during the main phase is observedin the higher frequency of a radio burst, while 5 DPSs before radio bursts are in the lowerfrequency. Tan et al. (2008) reported that 88% of DPSs took place at the initial phase ofradio bursts (0.6-7.6 GHz) in their analysis. In our analysis, DPSs with radio bursts knownas the broadband continuum (type IV burst) only represent 13% of all the cases, and 5/6(=83%) of the events occurred at the initial phase of the radio bursts. F´arn´ık et al. (2001)also reported that the GHz broadband radio pulses taken by the 3 GHz Ondˇrejov radiometerare delayed by 2-14 s related to the HXR emission peaks. If DPSs are synchronized withHXR peaks, DPSs should be observed 2-14 s prior to the radio bursts.Fig. 8.— The relationship between the start time of a DPS and the peak time of HXRs:(a) DPS precedes HXR, (b) DPS and HXR occur at the same time, (c) DPS is delayed withHXR. Here ∆t=t DP S -t HXR . 19 –Fig. 9.— Histogram of the time difference between the peak time of HXRs and the starttime of an isolated DPS or a series of multiple DPSs.Table 4. Distribution of DPS events observed with HXRs from the RHESSI data, fordifferent energy ranges.Low Energy Middle Energy High Energy(15-25 keV) (25-50 keV) (50-100 keV)Case (I) 5 3 2Case (II) 7 3 2Case (III) 27 14 5Case (IV) 8 5 3Total 47 25 12(1.00) (0.53) (0.25) 20 –
4. Statistical Results for the Characteristics of Plasmoids4.1. Basic equations, and Derivation of the Plasmoid properties
It has long been established that fast-drifting radio bursts (type III and reverse-driftbursts) in the decimetric frequency range are caused by radiation from plasma oscillationsexcited by electron beams (Wild et al. 1954), with typical exciter velocities of v b /c=0.07-0.25 (Dulk et al. 1987). Similarly, in DPSs the fast drifting features were proposed tobe generated by the plasma emission mechanism with electron beams (Kliem et al. 2000).With this assumption, in the next step, we convert the measured radio frequencies f max and f min into approximated values of electron densities, i.e. n max and n min , by setting theobserved radio frequency equal to the fundamental electron plasma frequency f p , f p = 8980 √ n e (2)with n e the electron density (in cgs units). Implicitly it is assumed that the observed deci-metric radio emission is related to the fundamental plasma emission. If some bursts wereemitted at the harmonic level of the plasma frequency, the inferred density would be a factor4 lower.Here we link the atmospheric density with the magnetic field strength, the height ofthe DPS event, etc. First, the plasma density in the environment surrounding the plasmoid,noted hereafter n out , is given by models from Alvarez & Haddock (1973) and Aschwanden &Benz (1997) (see also Equation 176 in Aschwanden 2002), n out ( h ) = ( n (cid:0) h h (cid:1) p ( h ≤ h ) ,n Q exp (cid:16) − hλ T (cid:17) ( h ≥ h ) (3)where h =1.6 × cm is the transition height between the lower and the higher corona, n =4.6 × , cm − , n Q =4.6 × cm − is the base density, λ T = RT /g =6.9 × cm is thethermal spatial scale of density, and the power-law index is p =2.38. We can estimate thecoronal magnetic field by considering the Sun as a magnetic spherical dipole, as suggestedin Aschwanden (1999), B cor ( h ) = B (cid:18) hh D (cid:19) − (4)where B =100 G and h D =7.5 × cm. It is noted here that, for the purpose of ourstudy, we need some simple formula approximating the dependence of the magnetic fieldon heights in the corona. In the review book of Aschwanden (2004) (page 19-20), there aretwo such approximations: the Dulk and McLean’s formula which is valid above 1.02 R sun (Dulk & McLean 1978) and the Aschwanden’s approximation. Both approximations were 21 –derived from observations. We used the Aschwanden’s approximation, because it is a com-monly used approximation of the magnetic field in the low corona. It is true that the currentlayer where the plasmoids are formed is quite a complex region, however, even in simulationsof plasmoid formation, the ambient magnetic field around the current sheet is often consid-ered to be simple (for example, with a single shearing layer such as often considered Harrissheets). As such, since we are mostly interested in the large-scale property of the magneticfield in the region surrounding the plasmoid, taking a simple model for the coronal field suchas Aschwanden’s one should still be a valid approximation.Furthermore, when the gas pressure inside a plasmoid balances with the gas pressureand the magnetic pressure outside of the plasmoid, the following relationship is satisfied,2 n in ( h ) k B T in = 2 n out ( h ) k B T out + B cor ( h )8 π (5)This equation is rewritten as follows, n in ( h ) = n out ( h ) T out T in + B cor ( h )8 π k B T in (6)Here we neglected the term of magnetic pressure, i.e. the guide field, inside a plasmoid forsimplicity. If the guide field inside a plasmoid is not negligible, n in is overestimated and givesthe upper limit. By inserting the equations above (2)-(4) to this pressure balance equation(6), we get the following equation, n in ( h ) = n (cid:0) h h (cid:1) p T out T in + B π k B T in (cid:16) hh D (cid:17) − ( h ≤ h ) n Q exp (cid:16) − hλ T (cid:17) T out T in + B π k B T in (cid:16) hh D (cid:17) − ( h ≥ h ) (7)Here the temperatures in the corona and surrounding the plasmoid, and in the plasmoiditself, are supposed to be constant. These assumptions can be made since the time scaleof the thermal conduction t cond is much shorter than the typical time scale τ . Referringto Ohyama & Shibata (1998) and Nishizuka et al. (2010), we set the coronal temperature T cor =1.5 × K, and the plasmoid temperature T in =1.0 × K.From equation (6), we have obtained a direct relation between the density inside theplasmoid, n in , and the height of the DPS emission. By using f max and f min , deduced fromthe observations at the start of the DPS event, we can calculate the related n max and n min with equation (2), and deduce the heights h min and h max that give the size of the plasmoid W pla = h max - h min (Fig. 10). Here we assume that the plasmoid is of a similar extent in widthas in height. In the following, we also define the average height of the plasmoid at the starttime h start = ( h max + h min )/2 as well as h end for the end of the event. 22 –Then, the other plasmoid properties can be computed as follows. The plasmoid ejectionvelocity is given as the difference during ∆ t of the average heights of the plasmoid, v pla = ∆ h ∆ t = h end − h start t end − t start (8)The Alfv´en speed and the plasma β , the ratio between thermal and magnetic pressures, arecalculated from the outside coronal magnetic field and density, v A ( h ) = B cor ( h )4 πm p n out ( h ) (9) β = 2 n out ( h ) k B T out B cor ( h ) / π (10)Assuming an incompressible plasma in the reconnection region (such as Sweet-Parker recon-nection model), the reconnection rate M A is expressed by the mass conservation equation be-tween the inflow and the outflow: v in L in = v pla W pla (equation (1); see also Shibata & Tanuma2001). Then, the reconnection rate, calculated with the normalized inflow velocity, as wellas the energy release rate, are given as follows, M A = v in v A = W pla L in · v pla v A (11) dEdt = 2 B cor ( h ) π v in L in (12)In the following, we assume that L in is similar to the height of the DPS emission at thestart of the event, h start (Fig. 10). This is acceptable, when the length of a current sheetis much larger than the height of the loop-top ( L in = h start - h loop − top - W pla ∼ h start ). On thebasis of our calculation result (Fig. 11 in the next section), it is true that the estimatedheight of the plasmoid is (2-4) × cm, which is larger than the typical loop-height ( ∼ cm). Some EUV observations of plasmoid ejection show that the current sheet can extendmuch further above the flare loops (e.g. Lin & Forbes 2000; Webb et al. 2003; Savage et al.2010; Reeves & Golub 2011). However, in cases considered here with DPS events associatedwith HXR peaks and therefore occurring in the impulsive phase at the start of the flare, thecurrent sheet is expected much shorter than several R sun what Savage et al. (2010) findseveral hours after the loss of equilibrium. At the time of the DPS, the flare loops couldaccount for 50% of the calculated plasmoid height. L in also includes the added radius of theplasmoid at the top of the current sheet. The uncertainties of this L in propagate through tothe determination of the reconnection rate M A in the following equation; | ∆ M A | M A = | ∆ W pla | W pla + | ∆ L in | L in + | ∆ v pla | v pla + | ∆ v A | v A (13)Therefore, the uncertainty of M A is also 50-90% from the determination and measurementerrors of L in , in addition to the errors from the other parameters. 23 –Fig. 10.— Cartoon of a flare eruption with the plasmoid ejection velocity v pla , the width ofa plasmoid W pla , the length of the inflow region L in and the inflow velocity v in . 24 – Figure 11 shows histograms of the distribution of the velocity, the width, the heightof ejected plasmoid and the reconnection rate, which are calculated from the DPS eventsof cases (I)+(II) and (III). We consider cases (I) and (II) together as they have a similardefinition (events with constant frequency drifts) and as to allow direct comparison with themore numerous DPSs of case (III). We also do not show the histograms for case (IV)-DPSs, asthese events are rather complicated with multiple events with non-constant frequency driftshappening at the same time: the histogram would be biased by how we would separate eachindividual event.Interpreting DPSs as signatures of plasmoids, most of the cases (I)+(II)-events showupward motions of plasmoids, while the case (III)-events contain both upward and downwardplasmoid events. The case (III)-events show acceleration or deceleration of plasmoids andvelocity change in time. The two phases before and after acceleration/deceleration arecounted twice in case (III) and events with n-times velocity changes are counted (n+1)times, similar to B´arta et al. (2008). The velocity of plasmoids is mainly in the range of0-5 × cm s − (Fig. 11(a)). The 60-70% of case (III) are upward events, while 30-40% aredownward events. The distributions of upward and downward events are almost the same.The width of a plasmoid is typically (0.3-1.1) × cm, and the height of the plasmoid, i.e.the length of a current sheet attached below the plasmoid, is typically (1.8-3.6) × cm(see Figs. 11(b)-11(c)). This is the first paper to estimate the width of the plasmoid and thelength of a current sheet (W pla and L in ) from DPS events, and the original histograms of theinstantaneous bandwidth and the starting frequency are in almost the same range of B´artaet al. (2008). The typical duration of DPSs is 0-60 s (Fig. 11(d)). The reconnection ratederived from the DPS events of cases (I)+(II) and (III) is typically less than 0.04 (Fig. 11(e)and 11(f)). This is comparable to the ones found in previous studies (M A =0.001-0.1, e.g.Tsuneta et al. 1997; Ohyama & Shibata 1997; Yokoyama et al. 2001; Isobe et al. 2002;Asai et al. 2004; Narukage & Shibata 2006; Takasao et al. 2012).Then what determines and/or controls the reconnection rate? The dependence of thereconnection rate on the plasmoid velocity, the width (size), the plasma beta, and the aspectratio of a current sheet attached below a plasmoid is shown in Figures 12(a)-12(e) for cases(I)+(II) and (III). The reconnection rate has a good correlation with the plasmoid velocity.This tendency is retained even after normalizing the plasmoid velocity by the Alfv´en velocity.On the other hand, the width and the aspect ratio of plasmoids are weakly correlated with thereconnection rate (Figs. 12(c) and 12(d)). The plasma beta is mainly distributed in the lowbeta regime (0.02-0.04), and it seems that the distribution of the reconnection rate is broader 25 –with smaller plasma beta. Furthermore, the relationship between the ejection velocity andthe width of plasmoids is shown in Figure 12(f). For larger plasmoid with W pla > cm,the plasmoid velocity tends to become smaller as the size becomes larger. This is probablybecause the larger plasmoids are heavier and are consequently more decelerated by thegravity force than smaller plasmoids. This result is consistent with B´arta et al. (2008). Onthe other hand, for smaller plasmoids with W pla < × cm, the plasmoid velocity tendsto increase as the width of the plasmoid increases. This may indicate that larger plasmoidinduces stronger inflow, enhancing the reconnection rate and accelerating itself by the fasterreconnection outflow. Next we compared DPS events with imaging observations in EUV emissions taken bythe Atmospheric Imaging Assembly (AIA) on board SDO, to identify a possible correlationbetween DPSs and plasmoids seen in the EUV corona. Since the temporal resolution of AIAis limited to 12 s, only long-duration DPS events ( > × cm s − . In this event, thereare no RHESSI data, but the steepest slope of the GOES SXR flux was observed at thebeginning of the outward motion. In the 211 ˚A images small plasma blobs are seen to movein the trailing region of the outward-moving loops. We found a downward motion blob during12:50:33-12:51:09 UT, and then two small plasma blob ejections between 12:51:57-12:52:33UT. The radio spectrograph data during the same period is shown in Figure 13(b). Thereare three periods of DPS: a downward-in-height (upward-in-frequency) DPS (12:50:00 UT),a constant frequency DPS (12:50:40 UT), and an upward-in-height (downward-in-frequency)DPS (12:52:30 UT). The upward motion of the DPS after 12:52:30 UT corresponds to thetiming of the outward moving coronal loops observed in 94 ˚A and the upward velocity ofthe DPS is 2 × cm s − , which is much larger than the apparent velocity (2 × cm s − ).The downward motion of the DPS after 12:50 UT has no clear corresponding features in 94˚A images, but small scale blobs in 211 ˚A images may be candidates to explain the observedDPSs.Figure 14(a) shows a flare event on 2012 May 8, which shows footpoint brighteningsfollowed by multiple plasma ejections and a loop expansion: the initial ejection at 13:05:26 26 –Fig. 11.— Histograms of the distributions of (a) the ejection velocity, (b) the width and(c) the height of plasmoids, (d) the duration and (e)-(f) the reconnection rate during theupward/ downward-in-height plasmoid ejections, which are derived from the DPS events ofcases (I)+(II) and (III) during 2002-2012. 27 –Fig. 12.— (a)-(e) Correlation study for cases (I)+(II) and (III), showing the dependenceof the reconnection rate on the original plasmoid velocity, the plasmoid velocity normalizedby the local Alfv´en velocity, the plasmoid width, the aspect ratio of the reconnection region(i.e. the ratio of the width and the length of a current sheet formed below a plasmoid) andthe plasma beta. (f) The relationship between the velocity and the width of plasmoids. 28 –UT, the second one at 13:06:02 UT, the loop expansion during 13:07-13:08 UT and the thirdejection at 13:08:02 UT. The radio spectrum of DPSs is shown in Figure 14(i), in whichthree DPSs are observed: a slow rising-in-height DPS (13:04:50 UT), a downward-in-heightDPS (13:07:00 UT) and another slow rising-in-height DPS (13:07:20 UT). The first upward-in-height DPS occurred at the beginning of the first and the second eruptions in 94 ˚A and193 ˚A images, the second downward-in-height DPS is during the loop expansion above theactive region but there seems to be no clear corresponding moving feature, and the thirdDPS is at the beginning of the double plasma ejection.Figure 15(a) shows an east-limb flare event on 2012 July 6. In 304 ˚A images, a coolprominence upward motion (marked by an arrow) was observed around 13:28-13:30 UT,which was located below a cavity observed in 94 ˚A images and at the footpoint of the darkopen field lines in the 131 ˚A images. In the 304 ˚A snapshot images, small scale intermittentplasma movements are also observed inside the loop structure, apart from the previousprominence. On the other hand, an upward(-in-height) DPS occurred at 13:29:22 UT (Fig.15(b)), when the cool prominence in 304 ˚A showed upward motion and when the slope ofthe GOES SXR flux became the steepest. The apparent upward velocity is 1 × cm s − which is the vertical velocity on the limb, while the upward velocity estimated from the DPSis 1 × cm s − . The later radio burst after 13:30:25 UT may be related to the inner plasmaflow inside the coronal loop structure.Here we note that, in the paper by B´arta et al. (2008) and also in the present study,we found that the DPS with larger instantaneous bandwidth usually drifts slower than thatwith smaller bandwidth. It means that larger plasmoids move slower than smaller ones. It ishighly probable that in the current sheet there are several plasmoids with different sizes. InEUV we recognize only the largest plasmoid and this EUV plasmoid need not be the sameas the plasmoid, where the DPS is generated. It may explain the difference in the velocityof the EUV plasmoid and that derived from the DPS on 2012 July 6. It is true that thesize (width) of the observed EUV plasmoids is in the range of 5”-40”, i.e. (0.4-3.6) × cm. This is comparable to but a little larger than the typical width of the DPS plasmoids(0.3-1.1) × cm. 29 –Fig. 13.— (a)-(f) Snapshot images of a flare event on 2012 June 13, taken by 94 and 211 ˚Afilters of AIA/SDO. In (b) and (c), the front of a plasma ejecta is shown by a solid line. (e)(f)are zoom-up images of (d) taken by 211 ˚A whose field-of-view is shown by a square line in(d). Arrows show small plasma blobs moving in the coronal loops. (g) A radio spectrum ofDPSs on 2012 June 13, taken by the radiospectrograph telescope in Ondˇrejov observatroy. 30 –Fig. 14.— (a)-(h) Snapshot images of a flare event on 2012 May 8, taken by 94 and 193 ˚Afilters of AIA/SDO. The event shows two ribbon structure and plasma ejections marked byarrows. (i) A spectrum of DPSs on 2012 May 8, taken by the radiospectrograph telescopein Ondˇrejov observatory. 31 –Fig. 15.— (a)-(c) Snapshot images of a flare event on 2012 July 6, taken by 304, 131 and 94˚A filters of AIA/SDO at almost the same time. Arrows in (a) show moving cool plasma incoronal loops (above) and an eruption of a cool plasma (below). In (b)(c), a cavity is shownby an arrow, which is located at the footpoint of the cool plasma ejection observed in 304˚A images. 32 –
5. Summary and Discussion
We statistically analyzed 106 DPS events in the frequency range of 0.8-4.5 GHz, observedwith radiospectrographs in Ondˇrejov observatory between 2002 and 2012. The number ofDPSs increases with the solar activity, and it peaked at around 2002 and 2012. The DPSswere classified into 4 groups: (I) single events with a constant frequency drift [12 events], (II)multiple events occurring in the same flare with constant frequency drifts [11 events], (III)single or multiple events with increasing or decreasing frequency drift rates [52 events], and(IV) complex events containing multiple events occurring at the same time in the differentfrequency range [31 events]. Most of the DPS events show an increase or a decrease in theirfrequency drifts. 70% of DPSs drifted toward lower frequency, while 30% drifted towardlarger frequency. In other words, interpreting DPSs as plasmoids, most plasmoid ejectionsare accelerated or decelerated, and 70% of plasmoids are ejected upward and 30% downward.Of the DPS events with simultaneous RHESSI observations, 90% of events occurred inassociation with HXR bursts, mainly in the energy range of 15-25 keV, and they occurredat the beginning or at the peak time of HXR burst. 90% of DPSs were associated with thepeak of the GOES SXR gradient and/or RHESSI HXR burst. With the exception of thelarge flares, HXR photons with energy 25 keV is typically produced by nonthermal electrons,whereas the origin for the HXR in the energy range of 15-25 keV is a mixture of thermaland nonthermal electrons. This is why our result indicates that most of the events areassociated with particle acceleration and partially plasma heating. 5 events were observedwith radio bursts known as the broadband continuum (type IV burst), and they occurred atthe beginning of the radio bursts in the higher frequency range, except for one event. Whenthe duration of the HXR burst was long, multiple DPSs occurred.Interpreting DPSs as signatures of plasmoids, we measured the ejection velocity, thewidth and the height of a plasmoid, from which we estimated the inflow velocity and thereconnection rate by considering the mass conservation of incompressible plasma: the velocity0-5 × cm s − , the width (0.3-1.1) × cm, the height (= the current sheet length) (1.8-3.6) × cm, the duration 0-60 s, and the reconnection rate 0-0.04. The width is smaller thanthe height of the plasmoid, but they are comparable to each other (consistent with B´artaet al. (2008)). This means that DPS plasmoids are observed in the lower corona, just afterthe formation and the ejection. This is different from other events of larger X-ray plasmoidejection (e.g. Glesener et al. 2013). There is a positive correlation between the reconnectionrate and the ejection velocity, while the aspect ratio of a current sheet has no clear correlationwith the reconnection rate. For larger plasmoid (W pla > cm), the plasmoid velocity tendsto decrease as the size becomes larger, whereas for smaller plasmoids (W pla < × cm),the plasmoid velocity tends to increase as the width of the plasmoid increases. This is 33 –probably because the larger plasmoids are heavier and are consequently more decelerated bythe gravity force than smaller plasmoids. When plasmoids are small, the gravity force is toosmall to affect the plasmoid dynamics, rather the plasmoid velocity increases as the width ofthe plasmoid increases, probably because larger plasmoids induces more inflow, enhancingthe reconnection rate and additionally accelerates themselves by fasten reconnection outflow.Some of the DPSs show plasmoid counterparts in AIA images, i.e. plasma ejections orblobs, but others are not clear. This is probably because the emission mechanisms of DPSsand EUVs are different and because the time scale of DPSs is too short compared with theAIA time cadence. DPSs are always associated with HXR in 15-25 keV, but not always in25-100 keV. Power-law indices of HXR spectra are soft. This indicates that the DPS emissionmechanism is not determined by the energy of particles but rather by the condition of thebump-in-tail distribution in electron velocity ( dF ( v ) /dv > v > F ( v ) being the velocitydistribution function), which produces the instability for which a wave-particle interactionoccurs.In laboratory experiments, the reconnection electric field is enhanced when a plasmoidis ejected out of a current sheet (Ono et al. 2011; Hayashi et al. 2012). This enables a moreefficient particle acceleration and a reconnection rate enhancement, which is consistent withour results. It is also noted that a larger plasmoid ejection leads to a larger enhancementof the electric field and thus a larger reconnection rate in laboratory experiments. However,in our analysis as well as that of B´arta et al. (2008), smaller plasmoids induce a largerreconnection rate. This is probably because larger plasmoids in the solar atmosphere aredecelerated by the gravity force, which does not play a strong effect in a laboratory confinedplasma configuration. This can explain the differences between laboratory experiments andthe solar atmosphere.The intensity of HXR emission can be described by using Neupert effect as follows; I HXR ∝ dI SXR dt ∝ dEthdt ∼ dEkindt = ddt (cid:18) mv pl (cid:19) = mv pl · dv pl dt (14)Here we assumed equipartition of released energy to thermal and kinetic energies. Thisindicates a positive correlation between the HXR intensity and the plasmoid velocity andacceleration. Since the HXR intensity is empirically believed to be proportional to thereconnection rate (Asai et al. 2004), the plasmoid velocity is also proportional to the re-connection rate, as well as equation (1) proposed in plasmoid-induced reconnection model(Shibata & Tanuma 2001).We classified 106 DPSs into 4 cases and mainly analyzed cases (I)-(III). Case (IV)shows multiple DPSs at the same time individually moving upward and downward. Some 34 –DPSs in case (IV) show merging and separation processes, which may indicate that thecoalescence and split of plasmoids take place. With recent numerical simulations, multipleplasmoid forming at different scales in a current sheet and particle accelerations in associationwith plasmoid dynamics have been intensively studied. The comparison between the eventsoccurring in the corona and simulations may give us further understandings of energy releaseby magnetic reconnection and particle acceleration, and the onset of flares, eruptions andradio bursts.We first acknowledge an anonymous referee for his/her useful comments and sugges-tions. This work was supported in part by JSPS KAKENHI Grant Number 24740132 andin part by the JSPS Core-to-Core Program 22001. MK and MB acknowledge the supportby grant P209/12/0103 (GA CR). REFERENCES
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