PARTICLE ACCELERATION IN PLASMOID EJECTIONS DERIVED FROM RADIO DRIFTING PULSATING STRUCTURES

DPSs are ensembles of type III-like bursts, i.e., emissions from high-energy electron beams via wave–particle interactions. In DPSs, electrons are trapped in plasmoids. Therefore these 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, there are electrons accelerated simultaneously in the same reconnection region, which are not trapped in the plasmoids. These can then generate HXRs in deep and dense layers of the Sun's atmosphere. Therefore, some association of DPSs and HXR bursts can be expected (Karlický et al. 2004). This association can be further influenced by the fact that any beam of superthermal electrons generates the X-rays in dense layers, but the radio emission of the beam can be reduced due to an inappropriate beam distribution function, reduced wave conversion, and absorption effects. On the other hand, if the magnetic field structure associated with many interacting plasmoids becomes complicated, all accelerated electrons are trapped in this structure and do not reach the dense layers of the solar atmosphere. In this case we can observe DPSs without corresponding HXRs. Since a DPS (a series of acceleration episodes) lasts much longer than a single type III burst (one acceleration episode), we study here the mean association of DPSs with HXR peaks, i.e., not for individual acceleration episodes 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 presented above, and 51% of all the events (54 DPSs) turned out to be simultaneously observed with RHESSI. For these events, we drew light curves integrated on-disk in three different energy ranges, 15–25 keV, 25–50 keV, and 50–100 keV. For one DPS event not correlated with any RHESSI data, we used data taken by the Czech-made Hard X-Ray Spectrometer (HXRS; Fárník et al. 2001) on board the U.S. Department of Energy Multispectral Thermal Imager satellite. HXRS has three energy bands: HXRS-S1 for 19–29 keV, HXRS-S2 for 44–67 keV, and HXRS-S3 for 100–147 keV, with a time cadence of 200 ms. For the other events with neither RHESSI nor HXRS data, we calculated the time derivative of SXR light curves taken by GOES, whose peak is believed to be well correlated with HXR peaks, as known from the Neupert (1968) effect. The criterion used to distinguish whether or not there is an HXR component is an evident increase of HXR emission up to over 40 counts with 4 s cadence (above the background level) in a short timescale, at least in an energy band of 15–25 keV, 25–50 keV, or 50–100 keV. As for the events without RHESSI HXR data, we picked up all the events with positive GOES SXR gradients occurring at the same time as DPSs.

We find that 49 DPSs events (90%) with RHESSI are associated with HXR peaks, and 5 events (10%) are not (Table 2). When considering all the events with RHESSI, HXRS, or GOES we found that 95 events (90%) are correlated with HXR peaks and/or SXR peak gradients, and 11 events (10%) are not (Table 3). We summarize the results also in the Figure 4 pie graphs, which indicate that most of the DPS events are related to HXR emissions and are 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 HXR events. In other words, not all of the DPS events are associated with HXR events. In particular, case (IV) is less correlated with HXR peaks. Considering the Neupert (1968) effect, it can be rewritten that not all of the DPS events are associated with SXR flares.

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Actually, we confirmed that not all of the DPS events are correlated with GOES SXR flares over C class. The majority of DPSs occurred with HXR and SXR flares, but some DPSs with SXR flares and no HXRs (indicating soft flares), some (seven DPS events, marked with daggers in Table 1) with HXRs but without SXRs (because the count of HXRs is so small, e.g., 40–200, that the SXR component is covered in the SXR background), and others (five DPS events with asterisks in Table 1) with neither HXRs nor SXRs (but these were also in active regions). For the last 12 events without SXR flares, 7 of them are interpreted to be independent events from SXR because the time difference between DPSs and SXR peaks is so large. Two of them occurred in the decay phase of the GOES flares without any enhancement of SXR. One is in the quiet SXR activity. Three of them are neglected because of the small increase of SXR, e.g., from GOES C5.0 to C5.4. These are probably because the magnetic structure in case (IV) is complex, which in some cases can trap all accelerated electrons, and thus no accelerated electrons reach dense layers of the solar atmosphere, and then much reduced X-ray emission is produced.

Figures 5–7 show typical DPS events associated with HXR bursts. The radiospectra of the DPSs are attached with HXR light curves taken by RHESSI, denoted by a solid line (15–25 keV), a dotted line (25–50 keV), and a dashed line (50–100 keV). Every event shows an evident emission in the 15–25 keV energy band, but only a small number of events show very weak ones in higher energy bands. This indicates that DPSs are more related to particles/plasmas in the energy range of 15–25 keV, rather than in the higher energy range of 25–100 keV. The occurrence ratio of different HXRs energy events is summarized in Table 4. All the DPSs associated with HXR peaks taken by RHESSI are accompanied by an enhancement in the 15–25 keV band. HXRs in the 25–100 keV bands are observed in less than 25% of all the events that were associated with HXRs in the 15–25 keV range. Case (I) shows the largest occurrence ratio of 50–100 keV events to 15–25 keV events, case (IV) shows the second, case (II) shows the third, and case (III) shows the smallest.

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HXR light curves sometimes show a small hump before the main peak in time, which is well correlated with a DPS event. It is also noted that HXRs in different energy bands show a time difference between their peaks, i.e., higher energy peaks are reached earlier than lower energy peaks, and DPSs are in general more closely correlated with the higher energy peaks, in terms of the timing, only when there is an HXR peak in higher energy bands. This can be explained as higher energy particles can precipitate to the chromosphere faster than lower energy ones, so the timing of higher energy particles is closer to the timing of particle acceleration in the corona near DPS-emitting plasmoids.

DPS events (with HXR peaks) can be classified by their relationship to these peaks. Figure 5 shows events that precede HXR peaks. Figures 6(a) and (b) shows DPSs whose acceleration or deceleration occurs at the same time as HXR peaks, and Figures 6(c) and (d) shows events that occur after HXR peaks. Here we determine the peak time of the HXR (15–25 keV), t_HXR, and the start time of the corresponding DPSs, t_DPS. The time difference between the two times (Δt = t_DPS-t_HXR) is illustrated in Figure 8. A positive Δt corresponds to a delay of DPSs relative to HXRs, while a negative Δt indicates the occurrence of DPSs before the onset or during the rising phase of HXR bursts. In Figure 9, most of the events are distributed in the range of −60 s<Δt <30 s, which can be fitted with a Gaussian function centered at the null value for Δt, and with its negative-side tail enhanced (or double Gaussian functions are also suitable). This means that DPSs mainly occur in the flare ascending phase just after the onset 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 |Δt| > 60 s, but these may be independent from the HXR activity. Furthermore, there is no tendency for the events with larger/smaller Δt to be associated with larger/shorter duration HXR peaks, i.e., when Δt is small the events are not always impulsive.

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As explained above, the association of DPSs with HXRs can be influenced by the radio emission mechanism and by the trapping in the complex magnetic fields resulting from the formation, and possibly the interaction, of multiple plasmoids. The acceleration regions in the current sheet higher in the corona can get magnetically connected and/or disconnected multiple times, as the magnetic topology evolves in the layers below (see, e.g., Bárta et al. 2011). Namely, new plasmoid formation and coalescence, taking place below the acceleration region, influences the evolution of the magnetic connectivity of this acceleration region all the way down to the chromosphere/photosphere. Therefore, defining a clear correspondence between the radio DPS emissions and HXRs remains difficult. Here we propose looking at the general tendencies for this connection that can be deduced from observations. We interpret cases of positive Δt when the radio emission takes more time, for the radiation process to take place, e.g., a specific velocity distribution, compared to HXRs. Cases with negative Δt may indicate that the trapping in a complex magnetic field or complex magnetic connectivity domain leads to particles necessitating more time to precipitate to the chromosphere due to the trapping in the magnetic topology, or that very few high-energy particles first escaped to the lower dense layers, leading to weak HXRs, while the bulk of high-energy particles emitting HXRs escaped with a slight delay.

The enhancement of HXRs during the acceleration of a plasmoid is only evident for one event. Rather, during multiple plasmoid acceleration events or multiple DPS events, initially enhanced HXR emission gradually decreases (28 events, e.g., Figure 5(c)) or reaches the background level (5 events, e.g., Figure 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., Figures 5(d) and 6(d)).

Figure 7 shows DPS events with additional radio bursts, which are called broadband continua or type IV bursts. Of the 48 DPS events with RHESSI HXR peaks, 6 events are accompanied by radio bursts in the frequency range of 0.8–4.5 GHz. One event occurred during the main phase of the radio burst, while five events occurred before or at the initial phase of the radio burst. We also note that one DPS during the main phase is observed in the higher frequency of a radio burst, while five DPSs before radio bursts are in the lower frequency. Tan et al. (2008) reported that 88% of DPSs took place at the initial phase of radio bursts (0.6–7.6 GHz) in their analysis. In our analysis, DPSs with radio bursts known as broadband continua (type IV bursts) only represent 13% of all the cases, and five out of six (=83%) of the events occurred at the initial phase of the radio bursts. Fárník et al. (2001) also reported that the GHz broadband radio pulses taken by the 3 GHz Ondřejov radiometer are delayed by 2–14 s relative to the HXR emission peaks. If DPSs are synchronized with HXR peaks, DPSs should be observed 2–14 s prior to the radio bursts.

It has long been established that fast-drifting radio bursts (type III and reverse-drift bursts) in the decimetric frequency range are caused by radiation from plasma oscillations excited 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 quickly drifting features have been proposed to be 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 the observed radio frequency equal to the fundamental electron plasma frequency f_p,

$$\begin{equation} f_p = 8980 \sqrt{n_e}, \end{equation} \tag{ 2 }$$

with n_e the electron density (in cgs units). Implicitly it is assumed that the observed decimetric radio emission is related to the fundamental plasma emission. If some bursts were emitted at the harmonic level of the plasma frequency, the inferred density would be a factor of four lower.

Here we link the atmospheric density with the magnetic field strength, the height of the DPS event, etc. First, the plasma density in the environment surrounding the plasmoid, denoted hereafter as n_out, is given by models from Alvarez & Haddock (1973) and Aschwanden & Benz (1997; see also Equation (176) in Aschwanden 2002):

$$\begin{eqnarray} n_{{\rm out}}(h)= \left\lbrace\begin{array}{@{}ll}n_1 \left(\frac{h_1}{h} \right)^p & (h \le h_1),\\ n_Q \exp \left(-\frac{h}{\lambda _T} \right) & (h \ge h_1),\\ \end{array}\right. \end{eqnarray} \tag{ 3 }$$

where h₁ = 1.6 × 10¹⁰ cm is the transition height between the lower and the higher corona, n₁ = 4.6 × 10⁷, cm⁻³, n_Q = 4.6 × 10⁸ cm⁻³ is the base density, λ_T = RT/g = 6.9 × 10⁹ cm is the thermal spatial scale of density, and the power-law index is p = 2.38. We can estimate the coronal magnetic field by considering the Sun as a magnetic spherical dipole, as suggested in Aschwanden et al. (1999),

$$\begin{equation} B_{{\rm cor}}(h)= B_0 \left(1+\frac{h}{h_D} \right)^{-3}, \end{equation} \tag{ 4 }$$

where B₀ = 100 G and h_D = 7.5 × 10⁹ cm. We note here that, for the purpose of our study, we need some simple formula approximating the dependence of the magnetic field on heights in the corona. In the review book of Aschwanden (2004, pp. 19–20), there are two such approximations: Dulk and McLean's formula, which is valid above 1.02R_sun (Dulk & McLean 1978) and Aschwanden's approximation. Both approximations were derived from observations. We used Aschwanden's approximation because it is a commonly used approximation of the magnetic field in the low corona. It is true that the current layer where the plasmoids are formed is quite a complex region, however, even in simulations of plasmoid formation, the ambient magnetic field around the current sheet is often considered to be simple (for example, with a single shearing layer such as the often-considered Harris sheets). As such, since we are mostly interested in the large-scale property of the magnetic field in the region surrounding the plasmoid, taking a simple model for the coronal field such as Aschwanden's should still be a valid approximation.

Furthermore, when the gas pressure inside a plasmoid balances with the gas pressure and the magnetic pressure outside a plasmoid, the following relationship is satisfied:

$$\begin{equation} 2n_{{\rm in}}(h) k_B T_{{\rm in}} = 2n_{{\rm out}}(h) k_B T_{{\rm out}} + \frac{B_{{\rm cor}}^2(h)}{8\pi }. \end{equation} \tag{ 5 }$$

This equation is rewritten as follows:

$$\begin{equation} n_{{\rm in}}(h)= n_{{\rm out}}(h) \frac{T_{{\rm out}}}{T_{{\rm in}}} +\frac{B_{{\rm cor}}^2(h)}{8\pi }\frac{1}{2k_B T_{{\rm in}}}. \end{equation} \tag{ 6 }$$

Here we neglected the term of magnetic pressure, i.e., the guide field, inside a plasmoid for simplicity. If the guide field inside a plasmoid is not negligible, n_in is overestimated and gives the upper limit. By inserting the above Equations (2)–(4) into this pressure balance Equation (6), we get the following equation:

$$\begin{eqnarray} &&n_{{\rm in}}(h)\nonumber\\ &&= \left\lbrace \begin{array}{@{}ll} \displaystyle n_1 \left(\frac{h_1}{h} \right)^p \frac{T_{{\rm out}}}{T_{{\rm in}}}+ \frac{B_0^2}{8\pi 2k_B T_{{\rm in}}}\left(1+\frac{h}{h_D} \right)^{-6} & (h \le h_1)\\ \displaystyle n_Q \exp \left(-\frac{h}{\lambda _T} \right) \frac{T_{{\rm out}}}{T_{{\rm in}}} +\frac{B_0^2}{8\pi 2k_B T_{{\rm in}}} \left(1+\frac{h}{h_D} \right)^{-6} & (h \ge h_1)\\ \end{array}\right..\nonumber\\ \end{eqnarray} \tag{ 7 }$$

Here the temperatures in the corona and surrounding the plasmoid, and in the plasmoid itself, are supposed to be constant. These assumptions can be made since the timescale of the thermal conduction t_cond is much shorter than the typical timescale τ. Referring to Ohyama & Shibata (1997) and Nishizuka et al. (2010), we set the coronal temperature T_cor = 1.5 × 10⁶ K, and the plasmoid temperature T_in = 1.0 × 10⁷ K.

From Equation (6), we have obtained a direct relation between the density inside the plasmoid, n_in, and the height of the DPS emission. By using f_max and f_min, deduced from the 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 (Figure 10). Here we assume that the plasmoid is of a similar extent in width as in height. In the following, we also define the average height of the plasmoid at the start time h_start = (h_max+h_min)/2 as well as h_end for the end of the event.

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Then the other plasmoid properties can be computed as follows. The plasmoid ejection velocity is given as the difference during Δt of the average heights of the plasmoid,

$$\begin{equation} v_{{\rm pla}}= \frac{\Delta h}{\Delta t} = \frac{h_{{\rm end}}-h_{{\rm start}}}{t_{{\rm end}}-t_{{\rm start}}}. \end{equation} \tag{ 8 }$$

The Alfvén speed and the plasma β, the ratio between thermal and magnetic pressures, are calculated from the outside coronal magnetic field and density,

$$\begin{eqnarray} &&v_A(h)=\frac{B_{{\rm cor}}(h)}{4\pi m_p n_{{\rm out}}(h)} \end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray} &&\beta = \frac{2n_{{\rm out}}(h)k_B T_{{\rm out}}}{B_{{\rm cor}}^2(h)/8\pi }. \end{eqnarray} \tag{ 10 }$$

Assuming an incompressible plasma in the reconnection region (such as in the Sweet–Parker reconnection model), the reconnection rate M_A is expressed by the mass conservation equation between the inflow and the outflow: v_inL_in = v_plaW_pla (Equation (1); see also Shibata & Tanuma 2001). Then, the reconnection rate, calculated with the normalized inflow velocity, as well as the energy release rate, are given as follows:

$$\begin{eqnarray} &&M_A = \frac{v_{{\rm in}}}{v_A} = \frac{W_{{\rm pla}}}{L_{{\rm in}}} \cdot \frac{v_{{\rm pla}}}{v_A} \end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray} &&\frac{dE}{dt} = 2\frac{B_{{\rm cor}}(h)^2}{4\pi } v_{{\rm in}}L_{{\rm in}}^2. \end{eqnarray} \tag{ 12 }$$

In the following, we assume that L_in is similar to the height of the DPS emission at the start of the event, h_start (Figure 10). This is acceptable, when the length of a current sheet is much larger than the height of the loop-top (L_in = h_start-h_loop-top-W_pla/2 ∼ h_start). On the basis of our calculation result (Figure 11 in the next section), it is true that the estimated height of the plasmoid is (2–4) × 10⁹ cm, which is larger than the typical loop-height (∼10⁹ cm). Some EUV observations of plasmoid ejections show that the current sheet can extend much further above the flare loops (e.g., Lin & Forbes 2000; Webb et al. 2003; Savage et al. 2010; Reeves & Golub 2011). However, in the cases considered here with DPS events associated with HXR peaks and therefore occurring in the impulsive phase at the start of the flare, the current sheet is expected to be much shorter than several R_sun, what Savage et al. (2010) find several hours after the loss of equilibrium. At the time of the DPS, the flare loops could account for 50% of the calculated plasmoid height. L_in also includes the added radius of the plasmoid at the top of the current sheet. The uncertainties of this L_in propagate through to the determination of the reconnection rate M_A in the following equation:

$$\begin{equation} \frac{|\Delta M_A|}{M_A} = \frac{|\Delta W_{{\rm pla}}|}{W_{{\rm pla}}} + \frac{|\Delta L_{{\rm in}}|}{L_{{\rm in}}} + \frac{|\Delta v_{{\rm pla}}|}{v_{{\rm pla}}} + \frac{|\Delta v_A|}{v_A}. \end{equation} \tag{ 13 }$$

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Therefore, the uncertainty of M_A is also 50%–90% from the determination and measurement errors of L_in, in addition to the errors from the other parameters.

Figure 11 shows histograms of the distribution of the velocity, width, and height of ejected plasmoids, and the reconnection rate, which are calculated from the DPS events of cases (I)+(II) and (III). We consider cases (I) and (II) together as they have a similar definition (events with constant frequency drifts) and to allow direct comparison with the more numerous DPSs of case (III). We also do not show the histograms for case (IV) DPSs, as these events are rather complicated with multiple events with non-constant frequency drifts happening at the same time: the histogram would be biased by how we would separate each individual event.

Interpreting DPSs as signatures of plasmoids, most of the case (I)+(II) events show upward motions of plasmoids, while the case (III) events contain both upward and downward plasmoid events. The case (III) events show acceleration or deceleration of plasmoids and velocity change in time. The two phases before and after acceleration/deceleration are counted twice in case (III) and events with n times velocity changes are counted (n+1) times, similar to Bárta et al. (2008). The velocity of plasmoids is mainly in the range of 0–5 × 10⁷ cm s⁻¹ (Figure 11(a)). 60%–70% of case (III)s are upward events, while 30%–40% are downward events. The distributions of upward and downward events are almost the same. The width of a plasmoid is typically (0.3–1.1) × 10⁹ 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) × 10⁹ cm (see Figures 11(b)–(c)). This is the first paper to estimate the width of the plasmoid and the length of a current sheet (W_pla and L_in) from DPS events, and the original histograms of the instantaneous bandwidth and the starting frequency are in almost the same range of Bárta et al. (2008). The typical duration of DPSs is 0–60 s (Figure 11(d)). The reconnection rate derived from the DPS events of cases (I)+(II) and (III) is typically less than 0.04 (Figures 11(e) and (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).

What, then, determines and/or controls the reconnection rate? The dependence of the reconnection rate on the plasmoid velocity, width (size), plasma beta, and aspect ratio of a current sheet attached below a plasmoid is shown in Figure 12(a)–(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 Alfvén velocity. On the other hand, the width and the aspect ratio of plasmoids are weakly correlated with the reconnection rate (Figures 12(c) and (d)). The plasma beta is mainly distributed in the low beta regime (0.02–0.04), and it seems that the distribution of the reconnection rate is broader with smaller plasma beta. Furthermore, the relationship between the ejection velocity and the width of plasmoids is shown in Figure 12(f). For larger plasmoid with W_pla > 10⁹ cm, the plasmoid velocity tends to become smaller as the size becomes larger. This is probably because the larger plasmoids are heavier and are consequently more decelerated by the gravity force than smaller plasmoids. This result is consistent with Bárta et al. (2008). On the other hand, for smaller plasmoids with W_pla < 6 × 10⁸ cm, the plasmoid velocity tends to increase as the width of the plasmoid increases. This may indicate that a larger plasmoid induces stronger inflow, enhancing the reconnection rate and accelerating itself by the faster reconnection outflow.

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Next we compared DPS events with imaging observations in EUV emissions taken by the Atmospheric Imaging Assembly (AIA) on board SDO, to identify a possible correlation between DPSs and plasmoids seen in the EUV corona. Since the temporal resolution of AIA is limited to 12 s, only long-duration DPS events (>1 minutes) observed after the SDO launch are used for analysis.

Figures 13(a)–(c) shows snapshot images of a flare event on 2012 June 13 taken with the AIA 94 Å filter. The event shows a plasma ejection in the southeast direction between 12:32 and 13:17 UT. The loops are gradually moving outward around 12:32 UT and the motion accelerates at 12:53 UT up to an apparent velocity of 2 × 10⁶ cm s⁻¹. In this event, there are no RHESSI data, but the steepest slope of the GOES SXR flux was observed at the beginning of the outward motion. In the 211 Å images small plasma blobs are seen to move in the trailing region of the outward-moving loops. We found a downward-motion blob during 12:50:33–12:51:09 UT, and then two small plasma blob ejections between 12:51:57 and 12:52:33 UT. The radio spectrograph data during the same period is shown in Figure 13(b). There are three periods of DPSs: 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 the timing of the outward-moving coronal loops observed in 94 Å and the upward velocity of the DPS is 2 × 10⁷ cm s⁻¹, which is much larger than the apparent velocity (2 × 10⁶ cm s⁻¹). The downward motion of the DPS after 12:50 UT has no clear corresponding features in 94 Å images, but small-scale blobs in 211 Å images may be candidates for explaining the observed DPSs.

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Figure 14(a) shows a flare event on 2012 May 8, which shows footpoint brightenings followed by multiple plasma ejections and a loop expansion: the initial ejection at 13:05:26 UT, the second one at 13:06:02 UT, the loop expansion during 13:07-13:08 UT, and the third ejection at 13:08:02 UT. The radio spectrum of DPSs is shown in Figure 14(i), in which three DPSs are observed: a slow rising-in-height DPS (13:04:50 UT), a downward-in-height DPS (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 Å and 193 Å images, the second downward-in-height DPS is during the loop expansion above the active region but there seems to be no clear corresponding moving feature, and the third DPS is at the beginning of the double plasma ejection.

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Figure 15(a) shows an east limb flare event on 2012 July 6. In 304 Å images, a cool prominence upward motion (marked by an arrow) was observed around 13:28–13:30 UT, which was located below a cavity observed in 94 Å images and at the footpoint of the dark open field lines in the 131 Å images. In the 304 Å snapshot images, small-scale intermittent plasma movements are also observed inside the loop structure, apart from the previous prominence. On the other hand, an upward(in height) DPS occurred at 13:29:22 UT (Figure 15(b)), when the cool prominence in 304 Å showed upward motion and when the slope of the GOES SXR flux became the steepest. The apparent upward velocity is 1 × 10⁶ cm s⁻¹, which is the vertical velocity on the limb, while the upward velocity estimated from the DPS is 1 × 10⁷ cm s⁻¹. The later radio burst after 13:30:25 UT may be related to the inner plasma flow inside the coronal loop structure.

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Here we note that, in the paper by Bárta et al. (2008) and also in the present study, we found that the DPS with larger instantaneous bandwidth usually drifts slower than that with smaller bandwidth. This means that larger plasmoids move slower than smaller ones. It is highly probable that in the current sheet there are several plasmoids with different sizes. In EUV, we recognize only the largest plasmoid and this EUV plasmoid need not be the same as the plasmoid, where the DPS is generated. It may explain the difference in the velocity of the EUV plasmoid and that derived from the DPS on 2012 July 6. It is true that the size (width) of the observed EUV plasmoids is in the range of 5''–40'', i.e., (0.4–3.6) × 10⁹ cm. This is comparable to but a little larger than the typical width of the DPS plasmoids (0.3–1.1) × 10⁹ cm.