Impulsive Heating Research Articles

Direct Imaging of a Prolonged Plasma/Current Sheet and Quasiperiodic Magnetic Reconnection on the Sun

Magnetic reconnection is widely believed to be the fundamental process in the solar atmosphere that underlies magnetic energy release and particle acceleration. This process is responsible for the onset of solar flares, coronal mass ejections, and other explosive events (e.g., jets). Here, we report direct imaging of a prolonged plasma/current sheet along with quasiperiodic magnetic reconnection in the solar corona using ultra-high-resolution observations from the 1.6 m Goode Solar Telescope at the Big Bear Solar Observatory and the Solar Dynamics Observatory/Atmospheric Imaging Assembly. The current sheet appeared near a null point in the fan–spine topology and persisted over an extended period (≈20 hr). The length and apparent width of the current sheet were about 6″ and 2″, respectively, and the plasma temperature was ≈10–20 MK. We observed quasiperiodic plasma inflows and outflows (bidirectional jets with plasmoids) at the reconnection site/current sheet. Furthermore, quasiperiodic reconnection at the long-lasting current sheet produced recurrent eruptions (small flares and jets) and contributed significantly to the recurrent impulsive heating of the active region. Direct imaging of a plasma/current sheet and recurrent null-point reconnection for such an extended period has not been reported previously. These unprecedented observations provide compelling evidence that supports the universal model for solar eruptions (i.e., the breakout model) and have implications for impulsive heating of active regions by recurrent reconnection near null points. The prolonged and sustained reconnection for about 20 hr at the breakout current sheet provides new insights into the dynamics and energy release processes in the solar corona.

Cylindrical compression of thin wires by irradiation with a Joule-class short-pulse laser

Equation of state measurements at Jovian or stellar conditions are currently conducted by dynamic shock compression driven by multi-kilojoule multi-beam nanosecond-duration lasers. These experiments require precise design of the target and specific tailoring of the spatial and temporal laser profiles to reach the highest pressures. At the same time, the studies are limited by the low repetition rate of the lasers. Here, we show that by the irradiation of a thin wire with single-beam Joule-class short-pulse laser, a converging cylindrical shock is generated compressing the wire material to conditions relevant to the above applications. The shockwave was observed using Phase Contrast Imaging employing a hard X-ray Free Electron Laser with unprecedented temporal and spatial sensitivity. The data collected for Cu wires is in agreement with hydrodynamic simulations of an ablative shock launched by highly impulsive and transient resistive heating of the wire surface. The subsequent cylindrical shockwave travels toward the wire axis and is predicted to reach a compression factor of 9 and pressures above 800 Mbar. Simulations for astrophysical relevant materials underline the potential of this compression technique as a new tool for high energy density studies at high repetition rates.

Coronal energy release by MHD avalanches

Context. Magnetohydrodynamic (MHD) instabilities, such as the kink instability, can trigger the chaotic fragmentation of a twisted magnetic flux tube into small-scale current sheets that dissipate as aperiodic impulsive heating events. In turn, the instability could propagate as an avalanche to nearby flux tubes and lead to a nanoflare storm. Our previous work was devoted to related 3D MHD numerical modeling, which included a stratified atmosphere from the solar chromosphere to the corona, tapering magnetic field, and solar gravity for curved loops with the thermal structure modelled by plasma thermal conduction, along with optically thin radiation and anomalous resistivity for 50 Mm flux tubes. Aims. Using 3D MHD modeling, this work addresses predictions for the extreme-ultraviolet (EUV) imaging spectroscopy of such structure and evolution of a loop, with an average temperature of 2–2.5 MK in the solar corona. We set a particular focus on the forthcoming MUSE mission, as derived from the 3D MHD modeling. Methods. From the output of the numerical simulations, we synthesized the intensities, Doppler shifts, and non-thermal line broadening in 3 EUV spectral lines in the MUSE passbands: Fe IX 171 Å, Fe XV 284 Å, and Fe XIX 108 Å, emitted by ∼1 MK, ∼2 MK, and ∼10 MK plasma, respectively. These data were detectable by MUSE, according to the MUSE expected pixel size, temporal resolution, and temperature response functions. We provide maps showing different view angles (front and top) and realistic spectra. Finally, we discuss the relevant evolutionary processes from the perspective of possible observations. Reults. We find that the MUSE observations might be able to detect the fine structure determined by tube fragmentation. In particular, the Fe IX line is mostly emitted at the loop footpoints, where we might be able to track the motions that drive the magnetic stressing and detect the upward motion of evaporating plasma from the chromosphere. In Fe XV, we might see the bulk of the loop with increasing intensity, with alternating filamentary Doppler and non-thermal components in the front view, along with more defined spots in the topward view. The Fe XIX line is very faint within the chosen simulation parameters; thus, any transient brightening around the loop apex may possibly be emphasized by the folding of sheet-like structures, mainly at the boundary of unstable tubes. Conclusions. In conclusion, we show that coronal loop observations with MUSE can pinpoint some crucial features of MHD-modeled ignition processes, such as the related dynamics, helping to identify the heating processes.

Ion heating/transport characteristics of the merging startup plasma scenario in the TS-6 spherical tokamak

Here we report the ion heating/transport characteristics of the merging startup scenario in the TS-6 spherical tokamak. In addition to the previously investigated impulsive heating process during magnetic reconnection, here we also focus on a longer time scale response of the ion temperature profile both during and after merging, including the semi-steady plasma confinement phase. During magnetic reconnection, (i) the ion temperature profile forms a poloidally asymmetric profile around the X-point in the initiation phase and (ii) radially asymmetric higher deposition is obtained at the high field side. After merging, (iii) the radially asymmetric double-peak structure is affected by parallel heat conduction and is aligned with field lines, but it does not simply become a flux function on a microsecond time scale—inboard/outboard asymmetry lasts even in the semi-steady confinement phase. (iv) Under the influence of the low-aspect-ratio configuration, there is a two to three times higher toroidal field on the high-field side on the same closed flux surface: characteristic asymmetry of inboard/outboard ion temperature has been found experimentally for the first time.

Modeling Transition Region Hot Loops on the Sun: The Necessity of Rapid, Complex Spatiotemporal Heating and Nonequilibrium Ionization

The study examines the heating profile of hot solar transition region loops, particularly focusing on transient brightenings observed in IRIS 1400 Å slit-jaw images. The findings challenge the adequacy of simplistic, singular heating mechanisms, revealing that the heating is temporally impulsive and requires a spatially complex profile with multiple heating scales. A forward-modeling code is utilized to generate synthetic Interface Region Imaging Spectrograph (IRIS) emission spectra of these loops based on HYDRAD model output, confirming that emitting ions are out of equilibrium. The modeling further indicates that density-dependent dielectronic recombination rates must be included to reproduce the observed line ratios. Collectively, this evidence substantiates that the loops are subject to impulsive heating and that the components of the transiently brightened plasma are driven far from thermal equilibrium. Heating events such as these are ubiquitous in the transition region, and the analysis described above provides a robust observational diagnostic tool for characterizing the plasma.

Mass Flows in Expanding Coronal Loops

An expansion of the cross-sectional area directly impacts the mass flow along a coronal loop and significantly alters the radiative and hydrodynamic evolution of that loop as a result. Previous studies have found that an area expansion from the chromosphere to the corona significantly lengthens the cooling time of the corona and appears to suppress draining from the corona. In this work, we examine the fluid dynamics to understand how the mass flow rate, the energy balance, and the cooling and draining timescales are affected by a nonuniform area. We find that in loops with moderate or large expansion (cross-sectional area expansion factors of 2, 3, 10, 30, 100 from the photosphere to the apex), impulsive heating, for either direct thermal heating or electron beam heating, induces a steady flow into the corona, so that the coronal density continues to rise during the cooling phase, whereas a uniform loop drains during the cooling phase. The induced upflow carries energy into the corona, balancing the losses from thermal conduction, and continues until thermal conduction weakens enough so that it can no longer support the radiative losses of the transition region. As a result, the plasma cools primarily radiatively until the onset of catastrophic collapse. The speed and duration of the induced upflow both increase in proportion to the rate of area expansion. We argue that observations of blueshifted spectral lines, therefore, could place a constraint on a loop’s area expansion.

Modeling of Condensations in Coronal Loops Produced by Impulsive Heating with Variable Frequencies and Locations

We present the results of models of impulsively heated coronal loops using the 1D hydrodynamic Adaptively Refined Godunov Solver code. The impulsive heating events (which we refer to as nanoflares) are modeled by discrete pulses of energy along the loop. We explore the occurrence of cold condensations due to the effective equivalent of thermal nonequilibrium in loops with steady heating, and examine its dependence on nanoflare timing and intensity and also nanoflare location along the loop, including randomized distributions of nanoflares. We find that randomizing the distribution of nanoflares, both in time/intensity and location, diminishes the likelihood of condensation occurring as compared to distributions with regularly occurring nanoflares with the same average properties. The usual criteria that condensation is favored for heating near loop footpoints and with high cadences are more strict for randomized (as opposed to regular) nanoflare distributions, and for randomized distributions the condensations stay in the loop for a shorter amount of time. That said, condensation can sometimes occur in cases where the average values of parameters (frequency or location) are beyond the critical limits above which condensation does not occur for corresponding steady, non-randomized values of those parameters. These properties of condensation occurring due to randomized heating can be used in the future to investigate the diagnostics of coronal heating mechanisms.

A Possible Mechanism for the “Late Phase” in Stellar White-light Flares

M dwarf flares observed by the Transiting Exoplanet Survey Satellite (TESS) sometimes exhibit a peak-bump light-curve morphology, characterized by a secondary, gradual peak well after the main, impulsive peak. A similar late phase is frequently detected in solar flares observed in the extreme ultraviolet from longer hot coronal loops distinct from the impulsive flare structures. White-light emission has also been observed in off-limb solar flare loops. Here, we perform a suite of one-dimensional hydrodynamic loop simulations for M dwarf flares inspired by these solar examples. Our results suggest that coronal plasma condensation following impulsive flare heating can yield high electron number density in the loop, allowing it to contribute significantly to the optical light curves via free-bound and free–free emission mechanisms. Our simulation results qualitatively agree with TESS observations: the longer evolutionary timescale of coronal loops produces a distinct, secondary emission peak; its intensity increases with the injected flare energy. We argue that coronal plasma condensation is a possible mechanism for the TESS late-phase flares.

Spectro-polarimetric Properties of Sunquake Sources in X1.5 Flare and Evidence for Electron and Proton Beam Impacts

The first significant sunquake event of Solar Cycle 25 was observed during the X1.5 flare of 2022 May 10, by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory. We perform a detailed spectro-polarimetric analysis of the sunquake photospheric sources, using the Stokes profiles of the Fe i 6173 Å line, reconstructed from the HMI linear and circular polarized filtergrams. The results show fast variations of the continuum emission with rapid growth and slower decay lasting 3–4 minutes, coinciding in time with the hard X-ray impulses observed by the Konus instrument on board the Wind spacecraft. The variations in the line core appeared slightly ahead of the variations in the line wings, showing that the heating started in the higher atmospheric layers and propagated downward. The most significant feature of the line profile variations is the transient emission in the line core in three of the four sources, indicating intense, impulsive heating in the lower chromosphere and photosphere. In addition, the observed variations of the Stokes profiles reflect transient and permanent changes in the magnetic field strength and geometry in the sunquake sources. Comparison with the radiative hydrodynamics models shows that the physical processes in the impulsive flare phase are substantially more complex than those predicted by proton and electron beam flare models currently presented in the literature.

Winking filaments due to cyclic evaporation-condensation

Context. Observations have shown that some filaments appear and disappear in the Hα line wing images periodically. There have been no attempts to model these “winking filaments” thus far. Aims. The evaporation-condensation mechanism is widely used to explain the formation of solar filaments. Here, we demonstrate, for the first time, how multi-dimensional evaporation-condensation in an arcade setup invariably causes a stretching of the magnetic topology. We aim to check whether this magnetic stretching during cyclic evaporation-condensation could reproduce a winking filament. Methods. We used our open-source code MPI-AMRVAC to carry out 2D magnetohydrodynamic simulations based on a quadrupolar configuration. A periodic localized heating, which modulates the evaporation-condensation process, was imposed before, during, and after the formation of the filament. Synthetic Hα and 304 Å images were produced to compare the results with observations. Results. For the first time, we noticed the winking filament phenomenon in a simulation of the formation of on-disk solar filaments, which was in good agreement with observations. Typically, the period of the winking is different from the period of the impulsive heating. A forced oscillator model explains this difference and fits the results well. A parameter survey is also done to look into details of the magnetic stretching phenomenon. We found that the stronger the heating or the higher the layer where the heating occurs, the more significant the winking effect appears.

Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

Center-to-limb Variation of Transition-region Doppler Shifts in Active Regions

Studying Doppler shifts provides deep insights into the flow of mass and energy in the solar atmosphere. We perform a comprehensive measurement of Doppler shifts in the transition region and its center-to-limb variation (CLV) in the strong-field regions (∣ B ∣ ≥ 50 G) of 50 active regions (ARs), using the Si iv 1394 Å line recorded by the Interface Region Imaging Spectrometer. To locate the ARs and identify strong-field regions, we have used the magnetograms obtained by the Helioseismic and Magnetic Imager (HMI). We find that in strong-field regions, on average, all the ARs show a mean redshift ranging between 4 and 11 km s−1, which varies with ARs. These flows show a mild CLV, with sizable magnitudes at the limb and substantial scatter in the mid-longitude range. Our observations do not support the idea that redshifts in the lower transition region (T ≲ 0.1 MK) are produced by field-aligned downflows as a result of impulsive heating and they warrant an alternative interpretation, such as a downflow of type-II spicules in the presence of a chromospheric wall created by cooler type-I spicules.

Nanoflare Heating of the Solar Corona Observed in X-Rays

The existence of the million-degree corona above the cooler photosphere is an unsolved problem in astrophysics. Detailed study of the quiescent corona that exists regardless of the phase of the solar cycle may provide fruitful hints toward resolving this conundrum. However, the properties of heating mechanisms can be obtained only statistically in these regions due to their unresolved nature. Here, we develop a two-step inversion scheme based on the machine-learning scheme of Upendran & Tripathi (2021a) for the empirical impulsive heating model of Pauluhn & Solanki (2007), and apply it to disk integrated flux measurements of the quiet corona as measured by the X-ray solar monitor on board Chandrayaan-2. We use data in three energy passbands, viz, 1–1.3, 1.3–2.3, and 1–2.3 keV, and estimate the typical impulsive event frequencies, timescales, amplitudes, and the distribution of amplitudes. We find that the impulsive events occur at a frequency of ≈25 events per minute with a typical lifetime of ≈10 minutes. They are characterized by a power-law distribution with a slope α ≤ 2.0. The typical amplitudes of these events lie in an energy range of 1021–1024 erg, with a typical radiative loss of about ≈103 erg cm−2 s−1 in the energy range of 1–2.3 keV. These results provide further constraints on the properties of subpixel impulsive events in maintaining the quiet solar corona.

Solar coronal heating from small-scale magnetic braids

Relaxation of braided coronal magnetic fields through reconnection is thought to be a source of energy to heat plasma in active region coronal loops. However, observations of active region coronal heating associated with an untangling of magnetic braids remain sparse. One reason for this paucity could be the lack of coronal observations with a sufficiently high spatial and temporal resolution to capture this process in action. Using new observations with high spatial resolution (250−270 km on the Sun) and high cadence (3−10 s) from the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter, we observed the untangling of small-scale coronal braids in different active regions. The untangling is associated with impulsive heating of the gas in these braided loops. We assess that coronal magnetic braids overlying cooler chromospheric filamentary structures are perhaps more common. Furthermore, our observations show signatures of spatially coherent and intermittent coronal heating during the relaxation of the magnetic braids. Our study reveals the operation of gentle and impulsive modes of magnetic reconnection in the solar corona.

Geometric Assumptions in Hydrodynamic Modeling of Coronal and Flaring Loops

In coronal loop modeling, it is commonly assumed that the loops are semicircular with a uniform cross-sectional area. However, observed loops are rarely semicircular, and extrapolations of the magnetic field show that the field strength decreases with height, implying that the cross-sectional area expands with height. We examine these two assumptions directly, to understand how they affect the hydrodynamic and radiative response of short, hot loops to strong, impulsive electron beam heating events. Both the magnitude and rate of area expansion impact the dynamics directly, and an expanding cross section significantly lengthens the time for a loop to cool and drain, increases upflow durations, and suppresses sound waves. The standard T ∼ n 2 relation for radiative cooling does not hold with expanding loops, which cool with relatively little draining. An increase in the eccentricity of loops, on the other hand, only increases the draining timescale, and is a minor effect in general. Spectral line intensities are also strongly impacted by the variation in the cross-sectional area because they depend on both the volume of the emitting region as well as the density and ionization state. With a larger expansion, the density is reduced, so the lines at all heights are relatively reduced in intensity, and because of the increase of cooling times, the hottest lines remain bright for significantly longer. Area expansion is critical to accurate modeling of the hydrodynamics and radiation, and observations are needed to constrain the magnitude, rate, and location of the expansion—or lack thereof.

Enthalpy-based modeling of tomographically reconstructed quiet-Sun coronal loops

The structure of the solar corona is made of magnetic flux tubes or loops. Due to the lack of contrast with their environment, observing and studying coronal loops in the quiet Sun is extremely difficult. In this work we use a differential emission measure tomographic (DEMT) technique to reconstruct, from a series of EUV images covering an entire solar rotation, the average 3D distribution of the thermal properties of the coronal plasma. By combining the DEMT products with extrapolations of the global coronal magnetic field, we reconstruct coronal loops and obtain the energy input required to keep them at the typical million-degree temperatures of the corona. We statistically study a large number of reconstructed loops for Carrington rotation (CR) 2082 obtaining a series of typical average loops of different lengths. We look for relations between the thermal properties and the lengths of the constructed typical loops and find similar results to those found in a previous work (Mac Cormack et al., 2020).. We also analyze the typical loop properties by comparing them with the zero-dimensional (0D) hydrodynamic model Enthalpy-Based Thermal Evolution of Loops (EBTEL, Klimchuk et al., 2008). We explore two heating scenarios. In the first one, we apply a constant heating rate assuming that typical loops are in quasi-static equilibrium. In the second scenario we heat the plasma in the loops using short impulsive events. We find that the reconstructed typical loops are overdense with respect to quasi-static equilibrium solutions of the hydrodynamic model. Impulsive heating, on the other hand, reproduces better the observed densities and temperatures for the shorter and approximately semicircular loops. The thermal properties of longer loops cannot be correctly reproduced with the EBTEL model. We suggest that to properly assess the physical characteristics of the analyzed loops in future works, it would be necessary to use a more sophisticated 1D model, with which to study the loop temperature and density profiles and test localized heating at different locations along the loops.

On the Formation of Solar Wind and Switchbacks, and Quiet Sun Heating

Abstract The solar coronal heating in quiet Sun (QS) and coronal holes (CHs), including solar wind formation, are intimately tied by magnetic field dynamics. Thus, a detailed comparative study of these regions is needed to understand the underlying physical processes. CHs are known to have subdued intensity and larger blueshifts in the corona. This work investigates the similarities and differences between CHs and QS in the chromosphere using the Mg ii h and k, C ii line, and transition region using Si iv line, for regions with identical absolute magnetic flux density (∣B∣). We find CHs to have subdued intensity in all of the lines, with the difference increasing with line formation height and ∣B∣. The chromospheric lines show excess upflows and downflows in CH, while Si iv shows excess upflows (downflows) in CHs (QS), where the flows increase with ∣B∣. We further demonstrate that the upflows (downflows) in Si iv are correlated with both upflows and downflows (only downflows) in the chromospheric lines. CHs (QS) show larger Si IV upflows (downflows) for similar flows in the chromosphere, suggesting a common origin to these flows. These observations may be explained due to impulsive heating via interchange (closed-loop) reconnection in CHs (QS), resulting in bidirectional flows at different heights, due to differences in magnetic field topologies. Finally, the kinked field lines from interchange reconnection may be carried away as magnetic field rotations and observed as switchbacks. Thus, our results suggest a unified picture of solar wind emergence, coronal heating, and near-Sun switchback formation.

Particle heating and acceleration by reconnecting and nonreconnecting current sheets

In this article, we study the physics of charged particle energization inside a strongly turbulent plasma, where current sheets naturally appear in evolving large-scale magnetic topologies, but they are split into two populations of fractally distributed reconnecting and nonreconnecting current sheets (CS). In particular, we implemented a Monte Carlo simulation to analyze the effects of the fractality and we study how the synergy of energization at reconnecting CSs and at nonreconnecting CSs affects the heating, the power-law high energy tail, the escape time, and the acceleration time of electrons and ions. The reconnecting current sheets systematically accelerate particles and play a key role in the formation of the power-law tail in energy distributions. On the other hand, the stochastic energization of particles through their interaction with nonreconnecting CSs can account for the heating of the solar corona and the impulsive heating during solar flares. The combination of the two acceleration mechanisms (stochastic and systematic), commonly present in many explosive events of various sizes, influences the steady-state energy distribution, as well as the transport properties of the particles in position- and energy-space. Our results also suggest that the heating and acceleration characteristics of ions and electrons are similar, the only difference being the time scales required to reach a steady state.

Capturing transient plasma flows and jets in the solar corona

Intensity bursts in ultraviolet (UV) to X-ray wavelengths and plasma jets are typical signatures of magnetic reconnection and the associated impulsive heating of the solar atmospheric plasma. To gain new insights into the process, high-cadence observations are required to capture the rapid response of plasma to magnetic reconnection as well as the highly dynamic evolution of jets. Here, we report the first 2 s cadence extreme-UV observations recorded by the 174 Å High Resolution Imager of the Extreme Ultraviolet Imager on board the Solar Orbiter mission. These observations, covering a quiet-Sun coronal region, reveal the onset signatures of magnetic reconnection as localized heating events. These localized sources then exhibit repeated plasma eruptions or jet activity. Our observations show that this spatial morphological change from localized sources to jet activity could occur rapidly on timescales of about 20 s. The jets themselves are intermittent and are produced from the source region on timescales of about 20 s. In the initial phases of these events, plasma jets are observed to exhibit speeds, as inferred from propagating intensity disturbances, in the range of 100 km s−1 to 150 km s−1. These jets then propagate to lengths of about 5 Mm. We discuss examples of bidirectional and unidirectional jet activity observed to have been initiated from the initially localized bursts in the corona. The transient nature of coronal bursts and the associated plasma flows or jets along with their dynamics could provide a benchmark for magnetic reconnection models of coronal bursts and jets.

Signatures of Type III Solar Radio Bursts from Nanoflares: Modeling

Abstract There is a wide consensus that the ubiquitous presence of magnetic reconnection events and the associated impulsive heating (nanoflares) are strong candidates for solving the solar coronal heating problem. Whether nanoflares accelerate particles to high energies like full-sized flares is unknown. We investigate this question by studying the type III radio bursts that the nanoflares may produce on closed loops. The characteristic frequency drifts that type III bursts exhibit can be detected using a novel application of the time-lag technique developed by Viall & Klimchuk (2012) even when there are multiple overlapping events. We present a simple numerical model that simulates the expected radio emission from nanoflares in an active region, which we use to test and calibrate the technique. We find that in the case of closed loops the frequency spectrum of type III bursts is expected to be extremely steep such that significant emission is produced at a given frequency only for a rather narrow range of loop lengths. We also find that the signature of bursts in the time-lag signal diminishes as: (1) the variety of participating loops within that range increases; (2) the occurrence rate of bursts increases; (3) the duration of bursts increases; and (4) the brightness of bursts decreases relative to noise. In addition, our model suggests a possible origin of type I bursts as a natural consequence of type III emission in a closed-loop geometry.