Dissipation Of Current Sheets Research Articles

Chromospheric and coronal heating in an active region plage by dissipation of currents from braiding

AbstractThe question of what heats the outer solar atmosphere remains one of the longstanding mysteries in astrophysics. Statistical studies of Sun-like stars reveal a correlation between global chromospheric and coronal emissions, constraining theoretical models of potential heating mechanisms. However, spatially resolved observations of the Sun have surprisingly failed to show a similar correlation on small spatial scales. Here we use unique coordinated observations of the chromosphere (from the IRIS satellite) and the low corona (from the Hi-C 2.1 sounding rocket), and machine-learning-based inversion techniques, to show a strong correlation on spatial scales of a few hundred kilometres between heating in the chromosphere and emission in the upper transition region in strong magnetic field regions (‘plage’). Our observations are compatible with an advanced three-dimensional magnetohydrodynamic simulation in which the dissipation of current sheets caused by magnetic field braiding is responsible for heating the plasma simultaneously to chromospheric and coronal temperatures. Our results provide deep insight into the nature of the heating mechanism in solar active regions.

Spatio-temporal analysis of chromospheric heating in a plage region

Context. Our knowledge of the heating mechanisms that are at work in the chromosphere of plage regions remains highly unconstrained from observational studies. While many heating candidates have been proposed in theoretical studies, the exact contribution from each of them is still unknown. The problem is rather difficult because there is no direct way of estimating the heating terms from chromospheric observations. Aims. The purpose of our study is to estimate the chromospheric heating terms from a multi-line high-spatial-resolution plage dataset, characterize their spatio-temporal distribution and set constraints on the heating processes that are at work in the chromosphere. Methods. We used nonlocal thermodynamical equilibrium inversions in order to infer a model of the photosphere and chromosphere of a plage dataset acquired with the Swedish 1-m Solar Telescope (SST). We used this model atmosphere to calculate the chromospheric radiative losses from the main chromospheric cooler from H I, Ca II, and Mg II atoms. In this study, we approximate the chromospheric heating terms by the net radiative losses predicted by the inverted model. In order to make the analysis of time-series over a large field of view computationally tractable, we made use of a neural network which is trained from the inverted models of two non-consecutive time-steps. We have divided the chromosphere in three regions (lower, middle, and upper) and analyzed how the distribution of the radiative losses is correlated with the physical parameters of the model. Results. In the lower chromosphere, the contribution from the Ca II lines is dominant and predominantly located in the surroundings of the photospheric footpoints. In the upper chromosphere, the H I contribution is dominant. Radiative losses in the upper chromosphere form a relatively homogeneous patch that covers the entire plage region. The Mg II also peaks in the upper chromosphere. Our time analysis shows that in all pixels, the net radiative losses can be split in a periodic component with an average amplitude of amp̅Q = 7.6 kW m−2 and a static (or very slowly evolving) component with a mean value of −26.1 kW m−2. The period of the modulation present in the net radiative losses matches that of the line-of-sight velocity of the model. Conclusions. Our interpretation is that in the lower chromosphere, the radiative losses are tracing the sharp lower edge of the hot magnetic canopy that is formed above the photosphere, where the electric current is expected to be large. Therefore, Ohmic current dissipation could explain the observed distribution. In the upper chromosphere, both the magnetic field and the distribution of net radiative losses are room-filling and relatively smooth, whereas the amplitude of the periodic component is largest. Our results suggest that acoustic wave heating may be responsible for one-third of the energy deposition in the upper chromosphere, whereas other heating mechanisms must be responsible for the rest: turbulent Alfvén wave dissipation or ambipolar diffusion could be among them. Given the smooth nature of the magnetic field in the upper chromosphere, we are inclined to rule out Ohmic dissipation of current sheets in the upper chromosphere.

Особенности развития длительных потоков высокоэнергичного гамма-излучения на разных стадиях солнечных вспышек

We have studied properties of sustained gamma fluxes having quantum energies of >100 MeV at different stages of flares with 1-min temporal resolution (Fermi/LAT). 
 The most probable process of emergence of high-energy gamma-quanta during the impulsive phase of flares (6 events) has been confirmed. Acceleration of particles, produced by flare energy release (at dissipation of current sheet), occurs when they interact with a shock front of a coronal mass ejection (CME), which develops in the same active region at the same time. Nuclear interactions of accelerated protons (>500 MeV) with plasma ions lead further to the emergence of high-energy gamma-quanta. We have established that the interaction between a flare flux and a high-speed CME during the flare impulsive phase occurs within fairly limited periods — from 2 to 16 min. In the events considered, we have found a direct connection between maximum gamma flux F max (γ > 100 MeV) and CME velocity.
 High maximum values of gamma fluxes are typical of the flare impulsive phase: 3.5·10⁻⁴ cm⁻²s⁻¹ ≤ F max (γ > 100 MeV) ≤ 1.3·10⁻² cm⁻² s⁻¹. At the same time, the value F max (γ > 100 MeV) = 0.013 cm⁻²s⁻¹ was the highest for the events observed by Fermi/LAT from 2008 to 2017.
 During the development of CMEs moving with a supersonic speed, shock waves are formed which are the major power source of accelerated particles during the main phase of gradual flares. In some cases, however, the impact of shock waves on particle acceleration is the greatest in the short impulsive phase.
 To reveal parameters most effectively influencing the generation of high-energy gamma-ray emission, we have compared 17 flare events. The most significant parameter proved to be the time interval of joint action of flare process and CME shocks.
 We have established that during simultaneous development of flare process and CME attendant on the flare, the most efficient particle acceleration occurs which gives rise to maximum fluxes of high-energy gamma-quanta.

Features of development of sustained fluxes of high-energy gamma-ray emission at different stages of solar flares

We have studied properties of sustained gamma fluxes having quantum energies of >100 MeV at different stages of flares with 1-min temporal resolution (Fermi/LAT). 
 The most probable process of emergence of high-energy gamma-quanta during the impulsive phase of flares (6 events) has been confirmed. Acceleration of particles, produced by flare energy release (at dissipation of current sheet), occurs when they interact with a shock front of a coronal mass ejection (CME), which develops in the same active region at the same time. Nuclear interactions of accelerated protons (>500 MeV) with plasma ions lead further to the emergence of high-energy gamma-quanta. We have established that the interaction between a flare flux and a high-speed CME during the flare impulsive phase occurs within fairly limited periods — from 2 to 16 min. In the events considered, we have found a direct connection between maximum gamma flux F max (γ > 100 MeV) and CME velocity.
 High maximum values of gamma fluxes are typical of the flare impulsive phase: 3.5·10⁻⁴ cm⁻²s⁻¹ ≤ F max (γ > 100 MeV) ≤ 1.3·10⁻² cm⁻² s⁻¹. At the same time, the value F max (γ > 100 MeV) = 0.013 cm⁻²s⁻¹ was the highest for the events observed by Fermi/LAT from 2008 to 2017.
 During the development of CMEs moving with a supersonic speed, shock waves are formed which are the major power source of accelerated particles during the main phase of gradual flares. In some cases, however, the impact of shock waves on particle acceleration is the greatest in the short impulsive phase.
 To reveal parameters most effectively influencing the generation of high-energy gamma-ray emission, we have compared 17 flare events. The most significant parameter proved to be the time interval of joint action of flare process and CME shocks.
 We have established that during simultaneous development of flare process and CME attendant on the flare, the most efficient particle acceleration occurs which gives rise to maximum fluxes of high-energy gamma-quanta.

The Formation and Dissipation of Current Sheets and Shocks due to Compressive Waves in a Stratified Atmosphere Containing a Magnetic Null

We study the propagation and dissipation of magnetohydrodynamic waves in a set of numerical models that each include a solar--like stratified atmosphere and a magnetic field with a null point. All simulations have the same magnetic field configuration but different transition region heights. Compressive wave packets introduced in the photospheric portion of the simulations refract towards the null and collapse it into a current sheet, which then undergoes reconnection. The collapsed null forms a current sheet due to a strong magnetic pressure gradient caused by the inability of magnetic perturbations to cross the null. Although the null current sheet undergoes multiple reconnection episodes due to repeated reflections off the lower boundary, we find no evidence of oscillatory reconnection arising from the dynamics of the null itself. Wave mode conversion around the null generates a series of slow mode shocks localized near each separatrix. The shock strength is asymmetric across each separatrix, and subsequent shock damping therefore creates a tangential discontinuity across each separatrix, with long--lived current densities. A parameter study of the injected wave energy to reach the null confirms our previous WKB estimates. Finally, using current estimates of the photospheric acoustic power, we estimate that the shock and Ohmic heating we describe may account for $\approx1-10\%$ of the radiative losses from coronal bright points with similar topologies, and are similarly insufficient to account for losses from larger structures such as ephemeral regions. At the same time, the dynamics are comparable to proposed mechanisms for generating type--II spicules.

Investigating 4D coronal heating events in magnetohydrodynamic simulations

Context. One candidate model for heating the solar corona is magnetic reconnection that embodies Ohmic dissipation of current sheets. When numerous small-scale magnetic reconnection events occur, then it is possible to heat the corona; if ever observed, these events would have been the speculated nanoflares. Aims. Because of the limitations of current instrumentation, nanoflares cannot be resolved. But their importance is evaluated via statistics by finding the power-law index of energy distribution. This method is however biased for technical and physical reasons. We aim to overcome limitations imposed by observations and statistical analysis. This way, we identify, and study these small-scale impulsive events. Methods. We employed a three-dimensional magnetohydrodynamic (3D MHD) simulation using the Bifrost code. We also employed a new technique to identify the evolution of 3D joule heating events in the corona. Then, we derived parameters describing the heating events in these locations, studied their geometrical properties and where they occurred with respect to the magnetic field. Results. We report on the identification of heating events. We obtain the distribution of duration, released energy, and volume. We also find weak power-law correlation between these parameters. In addition, we extract information about geometrical parameters of 2D slices of 3D events, and about the evolution of resolved joule heating compared to the total joule heating and magnetic energy in the corona. Furthermore, we identify relations between the location of heating events and the magnetic field. Conclusions. Even though the energy power index is less than 2, when classifying the energy release into three categories with respect to the energy release (pico-, nano-, and micro-events), we find that nano-events release 82% of the resolved energy. This percentage corresponds to an energy flux larger than that needed to heat the corona. Although no direct conclusions can be drawn, it seems that the most popular population among small-scale events is the one that contains nano-scale energetic events that are short lived with small spatial extend. Generally, the locations and size of heating events are affected by the magnitude of the magnetic field.

CURRENT SHEETS AND COLLISIONLESS DAMPING IN KINETIC PLASMA TURBULENCE

We present the first study of the formation and dissipation of current sheets at electron scales in a wave-driven, weakly collisional, 3D kinetic turbulence simulation. We investigate the relative importance of dissipation associated with collisionless damping via resonant wave-particle interactions versus dissipation in small-scale current sheets in weakly collisional plasma turbulence. Current sheets form self-consistently from the wave-driven turbulence, and their filling fraction is well correlated to the electron heating rate. However, the weakly collisional nature of the simulation necessarily implies that the current sheets are not significantly dissipated via Ohmic dissipation. Rather, collisionless damping via the Landau resonance with the electrons is sufficient to account for the measured heating as a function of scale in the simulation, without the need for significant Ohmic dissipation. This finding suggests the possibility that the dissipation of the current sheets is governed by resonant wave-particle interactions and that the locations of current sheets correspond spatially to regions of enhanced heating.

THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. III. RECONNECTED FIELD TOPOLOGY PRODUCED BY CURRENT-SHEET DISSIPATION

In this paper, the third in a series of papers on topological changes of magnetic fields, we study how the dissipation of an initial current sheet (CS) in a closed three-dimensional (3D) field affects the field topology. The initial field is everywhere potential except at the location of the CS which is in macroscopic equilibrium under the condition of perfect conductivity. In the physical world of extremely high, but finite, conductivity, the CS dissipates and the field seeks a new equilibrium state in the form of an everywhere potential field since the initial field is everywhere untwisted. Our semi-analytical study indicates that the dissipation of the single initial CS must induce formation of additional CSs in extensive parts of the magnetic volume. The subsequent dissipation of these other sheets brings about topological changes by magnetic reconnection in order for the global field to become potential. In 2D fields, the magnetic reconnection due to the dissipation of a CS is limited to the magnetic vicinity of the dissipating sheet. Thus, the consequence of CS dissipation is physically and topologically quite different in 2D and 3D fields. A discussion of this result is given in general relation to the Parker theory of spontaneous CSs and heating in the solar corona and solar flares.

THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. II. THE RECLOSING OF AN OPENED FIELD

This is a study of the spontaneous formation of current sheets responding to the closing of an opened magnetic field by resistive reconnection in an electrically, highly conducting atmosphere outside a unit sphere. Pairs of initial-final equilibrium states are calculated explicitly, taking the field to be composed of three systems of untwisted flux in both states. In the initial state, two of the three flux systems are closed potential fields whereas the third system contains an equilibrium current sheet that keeps the potential fields on its two sides globally open. The final state is an everywhere potential field, with all three flux systems closed, produced by the resistive dissipation of the current sheet in the initial state. The unit sphere is taken to be a rigid, perfectly conducting wall during reconnection, so that the normal flux distribution is unchanged on the unit sphere. Field solutions subject to this unchanging boundary condition are obtained with and without the assumption of axisymmetry. The mathematical model has been designed to show that the topological changes produced by the current-sheet dissipation are simple under axisymmetry but radically different in the absence of axisymmetry, a fundamental point established in the first paper of this series. In the general case, the topological changes imply that other current sheets must have formed. Some of these current sheets form on the separatrix flux surfaces of the multipolar field. Others form throughout the closed-flux systems induced by volumetric changes. The opening and reclosing of magnetic fields during a solar coronal mass ejection may produce a multitude of current sheets not previously anticipated in the current understanding of this phenomenon. Basic to this study is a general topological property of magnetic flux tubes treated separately in the Appendix.

Potential Magnetic Field around a Helical Flux Rope Current Structure in the Solar Corona

We consider the potential magnetic field associated with a helical electric line current flow, idealizing the near-potential coronal field within which a highly localized twisted current structure is embedded. It is found that this field has a significant axial component off the helical magnetic axis where there is no current flow, such that the flux winds around the axis. The helical line current field, in including the effects of flux rope writhe, is therefore more topologically complex than straight line and ring current fields sometimes used in solar flux rope models. The axial flux in magnetic fields around confined current structures may be affected by the writhe of these current structures such that the field twists preferentially with the same handedness as the writhe. This property of fields around confined current structures with writhe may be relevant to classes of coronal magnetic flux rope, including structures observed to have sigmoidal forms in soft X-rays and prominence magnetic fields. For example, ``bald patches'' and the associated heating by Parker current sheet dissipation seem likely. Thus some measurements of flux rope magnetic helicities may derive from external, near-potential fields. The predicted hemispheric preference for positive and negative magnetic helicities is consistent with observational results for prominences and sigmoids and past theoretical results for flux rope internal fields.

Substorms and Their Solar Wind Causes

Consequences of the solar wind input observed as large scale magnetotail dynamics during substorms are reviewed, highlighting results from statistical studies as well as global magnetosphere/ionosphere observations. Among the different solar wind input parameters, the most essential one to initiate reconnection relatively close to the Earth is a southward IMF or a solar wind dawn-to-dusk electric field. Larger substorms are associated with such reconnection events closer to the Earth and the magnetotail can accumulate larger amounts of energy before its onset. Yet, how and to what extent the magnetotail configuration before substorm onset differs for different solar wind driver is still to be understood. A strong solar wind dawn-to-dusk electric field is, however, only a necessary condition for a strong substorm, but not a sufficient one. That is, there are intervals when the solar wind input is processed in the magnetotail without the usual substorm cycle, suggesting different modes of flux transport. Furthermore, recent global observations suggest that the magnetotail response during the substorm expansion phase can be also controlled by plasma sheet density, which is coupled to the solar wind on larger time-scales than the substorm cycle. To explain the substorm dynamics it is therefore important to understand the different modes of energy, momentum, and mass transport within the magnetosphere as a consequence of different types of solar wind-magnetosphere interaction with different time-scales that control the overall magnetotail configuration, in addition to the internal current sheet instabilities leading to large scale tail current sheet dissipation.

Filamentary Loop Systems and Spontaneous Current Sheets in the Solar Corona

The solar coronal plasma is too hot and too highly conducting thermally to be static in the absence of powerful inward forces. Sufficiently strong and closed magnetic field configurations do, however, contain the plasma in the low corona in spite of its high temperature. Very many of these closed loop structures, with greatly varying physical characteristics, coexist in quasi-static mutual equilibrium in the corona. We model three-dimensional (3D) loop systems by horizontally stacking many diverse loops into a 3D equilibrium solution, where individual loops are separated from each other by tangential discontinuities. Simulated narrowband filter images of this solution reproduce the filamentary appearance of loop systems familiar from observations. A simple 3D time-dependent model of horizontal shearing motions is also presented. We then investigate the dissipation and field reconnection across these tangential discontinuities that must form spontaneously in coronal magnetic fields. The postdiffusion dynamics are dictated by the outward cross-field gas pressure gradient forces, which are increasing functions of pressure and temperature. Thus, in isothermal systems a net plasma outflow results from each field diffusion, while in nonisothermal systems relatively hot loops tend to expand as a result of field diffusion processes, which may allow hot plasma ultimately to escape into the solar wind. Accompanying cool downflows predicted by the calculations may be identified with observed persistent mass downflows in active region loops in cool coronal lines. In addition, current sheet dissipation in a sheared loop system may create field-aligned counterflow patterns in neighboring loops, a phenomenon that has also been observed.

Filamentation Instability of Thin Current Sheets in Low-β Plasmas

An analytic theory is presented for the collisionless filamentation instability of thin current sheets in the frequency domain of lower-hybrid waves in low-β plasmas. In a configuration with a strong guide field, the plasma dynamics is studied in a fluid description, accounting for the effects of electron polarization and finite Larmor radii, as well as of the motion of unmagnetized ions in the presence of perpendicular electric fields. In the linear phase, two types of unstable perturbations of a thin current sheet with steep edges are identified that correspond to its filamentation or tearing and bending. Using a surface-wave formalism for the modes whose wavelength is larger than the current sheet thickness, the corresponding growth rates are calculated as the contributions of singularities in the dispersion function of surface waves. These are governed by the electron inertia and by linear coupling with local plasma modes propagating in the perpendicular direction that are subjected to the Buneman instability. This new linear instability provides a suitable channel for the dissipation of current sheets that evolve during the collisionless magnetic reconnection in shear- and kinetic-Alfvén regimes, and for the creation of anomaluos resistivity.

Effects of Complexity on the Flux-Tube Tectonics Model

The quiet-Sun magnetic field emerges through the solar photosphere in a multitude of mixed-polarity magnetic concentrations and is subsequently tangled up into intricate regions of interconnecting flux. Moreover, since these discrete concentrations are likely to be extremely small in size, with fluxes of around only 1017 Mx, the number of such flux sources in, say, a supergranule, will be extremely large. The flux-tube tectonics model of Priest, Heyvaerts, and Title (2002) demonstrated how the formation and dissipation of current sheets along the separatrices that separate the regions of different connectivity are likely to make an important contribution to coronal heating. Since the full complexity of the magnetic field is below present observable scales, this study examines the effect of having the magnetic flux emerge through configurations structured on smaller and smaller scales. It is found that, by fixing the amount of flux emerging into a given 2D region, the main factors influencing the current build-up along the separatrices are the number of sources through which the flux emerges and the spatial distribution of the sources on the photosphere. The free energy (i.e., that above potential) is stored lower and lower in the atmosphere as the complexity of the system increases. A simple comparison is then made between coronal heating by separator currents and by separatrix currents. It is found that both result in comparable amounts of energy release, with separatrix heating being the more dominant.

Theory of 3D reconnection and coronal heating heating

Magnetic reconnection is a prime candidate for heating coronae. We here summarise recent developments in the theory of 31) reconnection and the different ways in which it is thought to heat the solar corona. At 3D null points reconnection may occur by either spine, fan or separator reconnection. In absence of null points, reconnection of two flux tubes is completely different from 21) reconnection, since in general in 3D a flux-conserving velocity w does not exist. Instead two flux tubes split into four parts, which ‘flip’ via ‘virtual flux tubes’ to form four flux tubes. Heating in the corona has been proposed to occur by: driven reconnection at X-ray bright points; binary reconnection due to the coronal interaction of a pair of opposite-polarity magnetic sources; separator reconnection due to a higher-order interaction; braiding; and coronal tectonics due to the formation and dissipation of current sheets at myriads of separatix surfaces that thread the corona and separate the flux coming from the many different sources in the photosphere.

A Flux‐Tube Tectonics Model for Solar Coronal Heating Driven by the Magnetic Carpet

We explore some of the consequences of the magnetic carpet for coronal heating. Observations show that most of the magnetic flux in the quiet Sun emerges as ephemeral regions and then quickly migrates to supergranule boundaries. The original ephemeral concentrations fragment, merge, and cancel over a time period of 10-40 hr. Since the network photospheric flux is likely to be concentrated in units of 1017 Mx or smaller, there will be myriads of coronal separatrix surfaces caused by the highly fragmented photospheric magnetic configuration in the quiet network. We suggest that the formation and dissipation of current sheets along these separatrices are an important contribution to coronal heating. The dissipation of energy along sharp boundaries we call, by analogy with geophysical plate tectonics, the tectonics model of coronal heating. Similar to the case on Earth, the relative motions of the photospheric sources will drive the formation and dissipation of current sheets along a hierarchy of such separatrix surfaces at internal dislocations in the corona. In our preliminary assessment of such dissipation we find that the heating is fairly uniform along the separatrices, so that each elementary coronal flux tube is heated uniformly. However, 95% of the photospheric flux closes low down in the magnetic carpet and the remaining 5% forms large-scale connections, so the magnetic carpet will be heated more effectively than the large-scale corona. This suggests that unresolved observations of coronal loops should exhibit enhanced heating near their feet in the carpet, while the upper parts of large-scale loops should be heated rather uniformly but less strongly.

Observations and Models of Coronal Heating

Energy release in the solar Corona is characterized by a sequence of space and time localized events, whose intensity follows power-law distributions. In quiet Sun regions, small energy events, possibly under the detection threshold, dominate, thus supporting the “nanoflare” scenario of coronal heating. Two complementar models of heating are discussed, in connection with the above observational features. The first model is based on Alfvénic wavepackets dissipation in 3D force-free magnetic fields; the presence of regions of chaoticity of magnetic lines allows for a fast wave dissipation, within a fraction of a solar radius. The second model describes a MHD turbulence in low-β plasma, in which magnetic energy is continuously furnished by slow photospheric motions. Energy release events corresponds dissipation of current sheets, often associated with magnetic reconnection. The resulting distribution of dissipated power follows a power law, similar to observations.

Fast magnetic reconnection with anomalous ion heating and its application

Magnetic reconnection of two toroidal plasmas with the third field component Bx parallel to the X-lines revealed a clear dependence of sheet-current resistivity and ion heating energy on the sheet-width normalized by the ion gyroradius. Initially, the effective resistivity of sheet-current stayed constant, but it increased significantly when the sheet was compressed shorter than the ion-gyroradius. The anomalous current-sheet dissipation was followed by large increase in ion outflow velocity and ion temperature. This anomalous effect caused both the reconnection speed and the ion heating energy to increase with external compression force and inversely with the Bx component. These properties of reconnection lead us to a new controlled plasma heating for various fusion plasmas and other industrial plasmas.

Numerical Simulation of a Coronal Streamer

This paper focuses on a single fluid, two-dimensional, axisymmetric, time-dependent, magnetohydrodynamic numerical simulation of the formation and evolution of a coronal streamer in a current sheet.Two types of evolution are described: (a) the disruption of the streamer in a CME and (b) the dissolution of the streamer probably caused by the current sheet dissipation in the solar atmosphere. In the first case, the ejected plasmoid density reaches 21 × 109 cm-3 at 8 solar radii from the Sun; in the second case, the maximum density attained is about 5 × 109 cm-3. The temperature does not exceed 5 × 106 K. These plasma parameters fit well the observations.

Observability of coronal heating processes

The mechanisms that could possibly heat the corona are briefly reviewed with emphasis on their observability. Observing enhanced wave flux at footpoints of active regions would confirm wave heating. Observation of nonthermal electrons in tiny coronal events (nanoflares) would confirm dissipation of current sheets. Presence of large scale flows in coronal arcades would underline the importance of turbulent resistivity for coronal heating. A comparison of HeI absorption in quiet and active regions demonstrates the difficulty of interpreting data that connect chromospheric dynamics with coronal heating. Finally, the implications of the search for observations of coronal heating processes are mentioned.