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Author name code: gudiksen
ADS astronomy entries on 2022-09-14
author:"Gudiksen, Boris V." 

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Title: Chromospheric emission from nanoflare heating in RADYN
    simulations
Authors: Bakke, H.; Carlsson, M.; Rouppe van der Voort, L.; Gudiksen,
   B. V.; Polito, V.; Testa, P.; De Pontieu, B.
2022A&A...659A.186B    Altcode: 2022arXiv220111961B
  Context. Heating signatures from small-scale magnetic reconnection
  events in the solar atmosphere have proven to be difficult to
  detect through observations. Numerical models that reproduce flaring
  conditions are essential in understanding how nanoflares may act as a
  heating mechanism of the corona. <BR /> Aims: We study the effects of
  non-thermal electrons in synthetic spectra from 1D hydrodynamic RADYN
  simulations of nanoflare heated loops to investigate the diagnostic
  potential of chromospheric emission from small-scale events. <BR />
  Methods: The Mg II h and k, Ca II H and K, Ca II 854.2 nm, and Hα and
  Hβ chromospheric lines were synthesised from various RADYN models of
  coronal loops subject to electron beams of nanoflare energies. The
  contribution function to the line intensity was computed to better
  understand how the atmospheric response to the non-thermal electrons
  affects the formation of spectral lines and the detailed shape of
  their spectral profiles. <BR /> Results: The spectral line signatures
  arising from the electron beams highly depend on the density of the
  loop and the lower cutoff energy of the electrons. Low-energy (5 keV)
  electrons deposit their energy in the corona and transition region,
  producing strong plasma flows that cause both redshifts and blueshifts
  of the chromospheric spectra. Higher-energy (10 and 15 keV) electrons
  deposit their energy in the lower transition region and chromosphere,
  resulting in increased emission from local heating. Our results indicate
  that effects from small-scale events can be observed with ground-based
  telescopes, expanding the list of possible diagnostics for the presence
  and properties of nanoflares.

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Title: Accelerated particle beams in a 3D simulation of the quiet Sun
Authors: Frogner, L.; Gudiksen, B. V.; Bakke, H.
2020A&A...643A..27F    Altcode: 2020arXiv200514483F
  Context. Observational and theoretical evidence suggest that beams
  of accelerated particles are produced in flaring events of all sizes
  in the solar atmosphere, from X-class flares to nanoflares. Current
  models of these types of particles in flaring loops assume an
  isolated 1D atmosphere. <BR /> Aims: A more realistic environment
  for modelling accelerated particles can be provided by 3D radiative
  magnetohydrodynamics codes. Here, we present a simple model for particle
  acceleration and propagation in the context of a 3D simulation of
  the quiet solar atmosphere, spanning from the convection zone to the
  corona. We then examine the additional transport of energy introduced
  by the particle beams. <BR /> Methods: The locations of particle
  acceleration associated with magnetic reconnection were identified by
  detecting changes in magnetic topology. At each location, the parameters
  of the accelerated particle distribution were estimated from local
  conditions. The particle distributions were then propagated along the
  magnetic field, and the energy deposition due to Coulomb collisions
  with the ambient plasma was computed. <BR /> Results: We find that
  particle beams originate in extended acceleration regions that are
  distributed across the corona. Upon reaching the transition region,
  they converge and produce strands of intense heating that penetrate the
  chromosphere. Within these strands, beam heating consistently dominates
  conductive heating below the bottom of the transition region. This
  indicates that particle beams qualitatively alter the energy transport
  even outside of active regions.

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Title: A comprehensive three-dimensional radiative magnetohydrodynamic
    simulation of a solar flare
Authors: Cheung, M. C. M.; Rempel, M.; Chintzoglou, G.; Chen, F.;
   Testa, P.; Martínez-Sykora, J.; Sainz Dalda, A.; DeRosa, M. L.;
   Malanushenko, A.; Hansteen, V.; De Pontieu, B.; Carlsson, M.; Gudiksen,
   B.; McIntosh, S. W.
2019NatAs...3..160C    Altcode: 2018NatAs...3..160C
  Solar and stellar flares are the most intense emitters of X-rays and
  extreme ultraviolet radiation in planetary systems<SUP>1,2</SUP>. On
  the Sun, strong flares are usually found in newly emerging sunspot
  regions<SUP>3</SUP>. The emergence of these magnetic sunspot groups
  leads to the accumulation of magnetic energy in the corona. When
  the magnetic field undergoes abrupt relaxation, the energy released
  powers coronal mass ejections as well as heating plasma to temperatures
  beyond tens of millions of kelvins. While recent work has shed light
  on how magnetic energy and twist accumulate in the corona<SUP>4</SUP>
  and on how three-dimensional magnetic reconnection allows for rapid
  energy release<SUP>5,6</SUP>, a self-consistent model capturing how
  such magnetic changes translate into observable diagnostics has remained
  elusive. Here, we present a comprehensive radiative magnetohydrodynamics
  simulation of a solar flare capturing the process from emergence to
  eruption. The simulation has sufficient realism for the synthesis of
  remote sensing measurements to compare with observations at visible,
  ultraviolet and X-ray wavelengths. This unifying model allows us to
  explain a number of well-known features of solar flares<SUP>7</SUP>,
  including the time profile of the X-ray flux during flares, origin
  and temporal evolution of chromospheric evaporation and condensation,
  and sweeping of flare ribbons in the lower atmosphere. Furthermore,
  the model reproduces the apparent non-thermal shape of coronal X-ray
  spectra, which is the result of the superposition of multi-component
  super-hot plasmas<SUP>8</SUP> up to and beyond 100 million K.

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Title: Radiative MHD Simulation of a Solar Flare
Authors: Cheung, Mark; Rempel, Matthias D.; Chintzoglou, Georgios;
   Chen, Feng; Testa, Paola; Martinez-Sykora, Juan; Sainz Dalda, Alberto;
   DeRosa, Marc L.; Malanushenko, Anna; Hansteen, Viggo; Carlsson, Mats;
   De Pontieu, Bart; Gudiksen, Boris; McIntosh, Scott W.
2019AAS...23431005C    Altcode:
  We present a radiative MHD simulation of a solar flare. The
  computational domain captures the near-surface layers of the convection
  zone and overlying atmosphere. Inspired by the observed evolution of
  NOAA Active Region (AR) 12017, a parasitic bipolar region is imposed
  to emerge in the vicinity of a pre-existing sunspot. The emergence of
  twisted magnetic flux generates shear flows that create a pre-existing
  flux rope underneath the canopy field of the sunspot. Following erosion
  of the overlying bootstrapping field, the flux rope erupts. Rapid
  release of magnetic energy results in multi-wavelength synthetic
  observables (including X-ray spectra, narrowband EUV images, Doppler
  shifts of EUV lines) that are consistent with flare observations. This
  works suggests the super-position of multi-thermal, superhot (up
  to 100 MK) plasma may be partially responsible for the apparent
  non-thermal shape of coronal X-ray sources in flares. Implications
  for remote sensing observations of other astrophysical objects is also
  discussed. This work is an important stepping stone toward high-fidelity
  data-driven MHD models.

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Title: On the Origin of the Magnetic Energy in the Quiet Solar
    Chromosphere
Authors: Martínez-Sykora, Juan; Hansteen, Viggo H.; Gudiksen, Boris;
   Carlsson, Mats; De Pontieu, Bart; Gošić, Milan
2019ApJ...878...40M    Altcode: 2019arXiv190404464M
  The presence of magnetic field is crucial in the transport of energy
  through the solar atmosphere. Recent ground-based and space-borne
  observations of the quiet Sun have revealed that magnetic field
  accumulates at photospheric heights, via a local dynamo or from
  small-scale flux emergence events. However, most of this small-scale
  magnetic field may not expand into the chromosphere due to the entropy
  drop with height at the photosphere. Here we present a study that uses
  a high-resolution 3D radiative MHD simulation of the solar atmosphere
  with non-gray and non-LTE radiative transfer and thermal conduction
  along the magnetic field to reveal that (1) the net magnetic flux
  from the simulated quiet photosphere is not sufficient to maintain a
  chromospheric magnetic field (on average), (2) processes in the lower
  chromosphere, in the region dominated by magnetoacoustic shocks,
  are able to convert kinetic energy into magnetic energy, (3) the
  magnetic energy in the chromosphere increases linearly in time until
  the rms of the magnetic field strength saturates at roughly 4-30 G
  (horizontal average) due to conversion from kinetic energy, (4) and
  that the magnetic features formed in the chromosphere are localized
  to this region.

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Title: Emission of Joule heating events in simulations of the
    solar corona
Authors: Kanella, Charalambos; Gudiksen, Boris V.
2019A&A...621A..95K    Altcode:
  Context. Nanoscale events in cooperation with steady heating from a
  slow heating mechanism, such as slow-burning current-sheets, could be
  able to heat the corona; however, their observational traces are hard
  to detect via current instrumentation. After we locate heating events
  in magnetohydrodynamic (MHD) simulations and synthesise observational
  data, we extract observational signatures of small-scale events. <BR
  /> Aims: Our mission is threefold. The first goal is to observe
  the manifestation of small-scale events via three observational
  tools: intensity maps of three extreme ultraviolet (EUV) filters in
  the Atmospheric Imaging Assembly (AIA) instrument with resolution
  better than that in AIA images, emission measure (EM) analysis, and
  time-lag maps. The second goal is to identify the reason why we cannot
  quantify the energy release from observed events. The third goal is
  to study the differences between the radiation from isolated heating
  events and that from the whole corona. <BR /> Methods: We employed a
  three-dimensional magnetohydrodynamic (3D-MHD) simulation using the
  Bifrost code. We simulated the atmosphere of a network embedded in the
  quiet Sun (QS), and we identified 3D heating events in the corona in
  several time-steps. Then we synthesised the three observational tools
  for two cases. First, we considered information from the total column
  mass in the corona, and then we considered only regions that exhibit
  heating events. <BR /> Results: We report on the differences between
  the two regions of investigation, which also consist of the evidence
  to justify why observers cannot identify small-scale heating events
  in observations. We found that the combination of multiple heating
  events at different cooling phases along the line of sight gives the
  impression of thin elongated threads of events. For this reason, the
  EM as a function of temperature has a multi-thermal distribution. Both
  the radiation and the emission measure of the isolated heating events
  have values at least ten times lower than the signal calculated from
  the total corona. We also found that heating events move together
  with diffuse emission from the slow heating mechanism, and for
  this reason we cannot differentiate between the two. In addition,
  we find that the frequency of heating events and their intensity
  affect the EM distribution as a function of temperature. We also
  find that the filter's intensity, EM, and time-lag maps of heating
  events are different to those incorporating information from the
  total column mass of the corona. However, the two regions have,
  on average, comparable values, which are slightly smaller than the
  analytical cooling timescales calculated for an optically thin and
  radiation-dominated atmosphere.

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Title: Non-thermal electrons from solar nanoflares
Authors: Bakke, Helle; Frogner, Lars; Gudiksen, Boris Vilhelm
2018arXiv181112404B    Altcode:
  Context. We introduce a model for including accelerated particles
  in pure magnetohydrodynamics (MHD) simulations of the solar
  atmosphere. Aims. We show that the method is viable and produces
  results that enhance the realism of MHD simulations of the solar
  atmosphere. Methods. The acceleration of high-energy electrons in
  solar flares is an accepted fact, but is not included in the most
  advanced 3D simulations of the solar atmosphere. The effect of the
  acceleration is not known, and here we introduce a simple method to
  account for the ability of the accelerated electrons to move energy
  from the reconnection sites and into the dense transition zone and
  chromosphere. Results. The method was only run for a short time and with
  low reconnection energies, but this showed that the reconnection process
  itself changes, and that there is a clear effect on the observables
  at the impact sites of the accelerated electrons. Further work will
  investigate the effect on the reconnection sites and the impact sites
  in detail.

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Title: Non-thermal electrons from solar nanoflares. In a 3D radiative
    MHD simulation
Authors: Bakke, H.; Frogner, L.; Gudiksen, B. V.
2018A&A...620L...5B    Altcode:
  Context. We introduce a model for including accelerated particles in
  pure magnetohydrodynamics (MHD) simulations of the solar atmosphere. <BR
  /> Aims: We show that the method is viable and produces results that
  enhance the realism of MHD simulations of the solar atmosphere. <BR />
  Methods: The acceleration of high-energy electrons in solar flares is an
  accepted fact, but is not included in the most advanced 3D simulations
  of the solar atmosphere. The effect of the acceleration is not known,
  and here we introduce a simple method to account for the ability of
  the accelerated electrons to move energy from the reconnection sites
  and into the dense transition zone and chromosphere. <BR /> Results:
  The method was only run for a short time and with low reconnection
  energies, but this showed that the reconnection process itself changes,
  and that there is a clear effect on the observables at the impact sites
  of the accelerated electrons. Further work will investigate the effect
  on the reconnection sites and the impact sites in detail.

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Title: Investigating 4D coronal heating events in magnetohydrodynamic
    simulations
Authors: Kanella, Charalambos; Gudiksen, Boris V.
2018A&A...617A..50K    Altcode: 2018arXiv180604495K
  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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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.

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Title: Disentangling flows in the solar transition region
Authors: Zacharias, P.; Hansteen, V. H.; Leenaarts, J.; Carlsson,
   M.; Gudiksen, B. V.
2018A&A...614A.110Z    Altcode: 2018arXiv180407513Z
  Context. The measured average velocities in solar and stellar spectral
  lines formed at transition region temperatures have been difficult
  to interpret. The dominant redshifts observed in the lower transition
  region naturally leads to the question of how the upper layers of the
  solar (and stellar) atmosphere can be maintained. Likewise, no ready
  explanation has been made for the average blueshifts often found in
  upper transition region lines. However, realistic three-dimensional
  radiation magnetohydrodynamics (3D rMHD) models of the solar atmosphere
  are able to reproduce the observed dominant line shifts and may thus
  hold the key to resolve these issues. <BR /> Aims: These new 3D rMHD
  simulations aim to shed light on how mass flows between the chromosphere
  and corona and on how the coronal mass is maintained. These simulations
  give new insights into the coupling of various atmospheric layers
  and the origin of Doppler shifts in the solar transition region and
  corona. <BR /> Methods: The passive tracer particles, so-called corks,
  allow the tracking of parcels of plasma over time and thus the study of
  changes in plasma temperature and velocity not only locally, but also
  in a co-moving frame. By following the trajectories of the corks, we
  can investigate mass and energy flows and understand the composition
  of the observed velocities. <BR /> Results: Our findings show that
  most of the transition region mass is cooling. The preponderance of
  transition region redshifts in the model can be explained by the higher
  percentage of downflowing mass in the lower and middle transition
  region. The average upflows in the upper transition region can be
  explained by a combination of both stronger upflows than downflows
  and a higher percentage of upflowing mass. The most common combination
  at lower and middle transition region temperatures are corks that are
  cooling and traveling downward. For these corks, a strong correlation
  between the pressure gradient along the magnetic field line and the
  velocity along the magnetic field line has been observed, indicating a
  formation mechanism that is related to downward propagating pressure
  disturbances. Corks at upper transition region temperatures are
  subject to a rather slow and highly variable but continuous heating
  process. <BR /> Conclusions: Corks are shown to be an essential tool
  in 3D rMHD models in order to study mass and energy flows. We have
  shown that most transition region plasma is cooling after having been
  heated slowly to upper transition region temperatures several minutes
  before. Downward propagating pressure disturbances are identified as
  one of the main mechanisms responsible for the observed redshifts at
  transition region temperatures. <P />The movie associated to Fig. 3
  is available at <A href="https://www.aanda.org">http://www.aanda.org</A>

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Title: Two-dimensional Radiative Magnetohydrodynamic Simulations of
    Partial Ionization in the Chromosphere. II. Dynamics and Energetics
    of the Low Solar Atmosphere
Authors: Martínez-Sykora, Juan; De Pontieu, Bart; Carlsson, Mats;
   Hansteen, Viggo H.; Nóbrega-Siverio, Daniel; Gudiksen, Boris V.
2017ApJ...847...36M    Altcode: 2017arXiv170806781M
  We investigate the effects of interactions between ions and
  neutrals on the chromosphere and overlying corona using 2.5D
  radiative MHD simulations with the Bifrost code. We have extended
  the code capabilities implementing ion-neutral interaction effects
  using the generalized Ohm’s law, I.e., we include the Hall term
  and the ambipolar diffusion (Pedersen dissipation) in the induction
  equation. Our models span from the upper convection zone to the corona,
  with the photosphere, chromosphere, and transition region partially
  ionized. Our simulations reveal that the interactions between ionized
  particles and neutral particles have important consequences for the
  magnetothermodynamics of these modeled layers: (1) ambipolar diffusion
  increases the temperature in the chromosphere; (2) sporadically the
  horizontal magnetic field in the photosphere is diffused into the
  chromosphere, due to the large ambipolar diffusion; (3) ambipolar
  diffusion concentrates electrical currents, leading to more violent
  jets and reconnection processes, resulting in (3a) the formation of
  longer and faster spicules, (3b) heating of plasma during the spicule
  evolution, and (3c) decoupling of the plasma and magnetic field in
  spicules. Our results indicate that ambipolar diffusion is a critical
  ingredient for understanding the magnetothermodynamic properties in the
  chromosphere and transition region. The numerical simulations have been
  made publicly available, similar to previous Bifrost simulations. This
  will allow the community to study realistic numerical simulations with
  a wider range of magnetic field configurations and physics modules
  than previously possible.

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Title: Realistic radiative MHD simulation of a solar flare
Authors: Rempel, Matthias D.; Cheung, Mark; Chintzoglou, Georgios;
   Chen, Feng; Testa, Paola; Martinez-Sykora, Juan; Sainz Dalda, Alberto;
   DeRosa, Marc L.; Viktorovna Malanushenko, Anna; Hansteen, Viggo H.;
   De Pontieu, Bart; Carlsson, Mats; Gudiksen, Boris; McIntosh, Scott W.
2017SPD....4840001R    Altcode:
  We present a recently developed version of the MURaM radiative
  MHD code that includes coronal physics in terms of optically thin
  radiative loss and field aligned heat conduction. The code employs
  the "Boris correction" (semi-relativistic MHD with a reduced speed
  of light) and a hyperbolic treatment of heat conduction, which allow
  for efficient simulations of the photosphere/corona system by avoiding
  the severe time-step constraints arising from Alfven wave propagation
  and heat conduction. We demonstrate that this approach can be used
  even in dynamic phases such as a flare. We consider a setup in which
  a flare is triggered by flux emergence into a pre-existing bipolar
  active region. After the coronal energy release, efficient transport
  of energy along field lines leads to the formation of flare ribbons
  within seconds. In the flare ribbons we find downflows for temperatures
  lower than ~5 MK and upflows at higher temperatures. The resulting
  soft X-ray emission shows a fast rise and slow decay, reaching a peak
  corresponding to a mid C-class flare. The post reconnection energy
  release in the corona leads to average particle energies reaching 50
  keV (500 MK under the assumption of a thermal plasma). We show that
  hard X-ray emission from the corona computed under the assumption of
  thermal bremsstrahlung can produce a power-law spectrum due to the
  multi-thermal nature of the plasma. The electron energy flux into the
  flare ribbons (classic heat conduction with free streaming limit) is
  highly inhomogeneous and reaches peak values of about 3x10<SUP>11</SUP>
  erg/cm<SUP>2</SUP>/s in a small fraction of the ribbons, indicating
  regions that could potentially produce hard X-ray footpoint sources. We
  demonstrate that these findings are robust by comparing simulations
  computed with different values of the saturation heat flux as well as
  the "reduced speed of light".

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Title: Identification of coronal heating events in 3D simulations
Authors: Kanella, Charalambos; Gudiksen, Boris V.
2017A&A...603A..83K    Altcode: 2017arXiv170302808K
  Context. The solar coronal heating problem has been an open question
  in the science community since 1939. One of the proposed models
  for the transport and release of mechanical energy generated
  in the sub-photospheric layers and photosphere is the magnetic
  reconnection model that incorporates Ohmic heating, which
  releases a part of the energy stored in the magnetic field. In
  this model many unresolved flaring events occur in the solar
  corona, releasing enough energy to heat the corona. <BR /> Aims:
  The problem with the verification and quantification of this model
  is that we cannot resolve small scale events due to limitations
  of the current observational instrumentation. Flaring events have
  scaling behavior extending from large X-class flares down to the so
  far unobserved nanoflares. Histograms of observable characteristics
  of flares show powerlaw behavior for energy release rate, size, and
  total energy. Depending on the powerlaw index of the energy release,
  nanoflares might be an important candidate for coronal heating; we seek
  to find that index. <BR /> Methods: In this paper we employ a numerical
  three-dimensional (3D)-magnetohydrodynamic (MHD) simulation produced
  by the numerical code Bifrost, which enables us to look into smaller
  structures, and a new technique to identify the 3D heating events at
  a specific instant. The quantity we explore is the Joule heating, a
  term calculated directly by the code, which is explicitly correlated
  with the magnetic reconnection because it depends on the curl of the
  magnetic field. <BR /> Results: We are able to identify 4136 events
  in a volume 24 × 24 × 9.5 Mm<SUP>3</SUP> (I.e., 768 × 786 × 331
  grid cells) of a specific snapshot. We find a powerlaw slope of the
  released energy per second equal to α<SUB>P</SUB> = 1.5 ± 0.02, and
  two powerlaw slopes of the identified volume equal to α<SUB>V</SUB>
  = 1.53 ± 0.03 and α<SUB>V</SUB> = 2.53 ± 0.22. The identified
  energy events do not represent all the released energy, but of the
  identified events, the total energy of the largest events dominate
  the energy release. Most of the energy release happens in the lower
  corona, while heating drops with height. We find that with a specific
  identification method large events can be resolved into smaller ones,
  but at the expense of the total identified energy releases. The
  energy release that cannot be identified as an event favors a low
  energy release mechanism. <BR /> Conclusions: This is the first step
  to quantitatively identify magnetic reconnection sites and measure
  the energy released by current sheet formation.

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Title: Chromospheric and Coronal Wave Generation in a Magnetic
    Flux Sheath
Authors: Kato, Yoshiaki; Steiner, Oskar; Hansteen, Viggo; Gudiksen,
   Boris; Wedemeyer, Sven; Carlsson, Mats
2016ApJ...827....7K    Altcode: 2016arXiv160608826K
  Using radiation magnetohydrodynamic simulations of the solar
  atmospheric layers from the upper convection zone to the lower corona,
  we investigate the self-consistent excitation of slow magneto-acoustic
  body waves (slow modes) in a magnetic flux concentration. We
  find that the convective downdrafts in the close surroundings of
  a two-dimensional flux slab “pump” the plasma inside it in
  the downward direction. This action produces a downflow inside the
  flux slab, which encompasses ever higher layers, causing an upwardly
  propagating rarefaction wave. The slow mode, excited by the adiabatic
  compression of the downflow near the optical surface, travels along the
  magnetic field in the upward direction at the tube speed. It develops
  into a shock wave at chromospheric heights, where it dissipates,
  lifts the transition region, and produces an offspring in the form
  of a compressive wave that propagates further into the corona. In the
  wake of downflows and propagating shock waves, the atmosphere inside
  the flux slab in the chromosphere and higher tends to oscillate with a
  period of ν ≈ 4 mHz. We conclude that this process of “magnetic
  pumping” is a most plausible mechanism for the direct generation
  of longitudinal chromospheric and coronal compressive waves within
  magnetic flux concentrations, and it may provide an important heat
  source in the chromosphere. It may also be responsible for certain
  types of dynamic fibrils.

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Title: Physics &amp; Diagnostics of the Drivers of Solar Eruptions
Authors: Cheung, Mark; Rempel, Matthias D.; Martinez-Sykora, Juan;
   Testa, Paola; Hansteen, Viggo H.; Viktorovna Malanushenko, Anna;
   Sainz Dalda, Alberto; DeRosa, Marc L.; De Pontieu, Bart; Carlsson,
   Mats; Chen, Feng; McIntosh, Scott W.; Gudiksen, Boris
2016SPD....47.0607C    Altcode:
  We provide an update on our NASA Heliophysics Grand Challenges Research
  (HGCR) project on the ‘Physics &amp; Diagnostics of the Drivers of
  Solar Eruptions’. This presentation will focus on results from a
  data-inspired, 3D radiative MHD model of a solar flare. The model
  flare results from the interaction of newly emerging flux with a
  pre-existing active region. Synthetic observables from the model
  reproduce observational features compatible with actual flares. These
  include signatures of coronal magnetic reconnection, chromospheric
  evaporation, EUV flare arcades, sweeping motion of flare ribbons
  and sunquakes.

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Title: Structures in the Outer Solar Atmosphere
Authors: Fletcher, L.; Cargill, P. J.; Antiochos, S. K.; Gudiksen,
   B. V.
2016mssf.book..231F    Altcode:
  No abstract at ADS

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Title: A publicly available simulation of an enhanced network region
    of the Sun
Authors: Carlsson, Mats; Hansteen, Viggo H.; Gudiksen, Boris V.;
   Leenaarts, Jorrit; De Pontieu, Bart
2016A&A...585A...4C    Altcode: 2015arXiv151007581C
  Context. The solar chromosphere is the interface between the
  solar surface and the solar corona. Modelling of this region is
  difficult because it represents the transition from optically
  thick to thin radiation escape, from gas-pressure domination to
  magnetic-pressure domination, from a neutral to an ionised state,
  from MHD to plasma physics, and from near-equilibrium (LTE) to
  non-equilibrium conditions. <BR /> Aims: Our aim is to provide the
  community with realistic simulations of the magnetic solar outer
  atmosphere. This will enable detailed comparison of existing and
  upcoming observations with synthetic observables from the simulations,
  thereby elucidating the complex interactions of magnetic fields and
  plasma that are crucial for our understanding of the dynamic outer
  atmosphere. <BR /> Methods: We used the radiation magnetohydrodynamics
  code Bifrost to perform simulations of a computational volume
  with a magnetic field topology similar to an enhanced network
  area on the Sun. <BR /> Results: The full simulation cubes are
  made available from the Hinode Science Data Centre Europe. The
  general properties of the simulation are discussed, and limitations
  are discussed. <P />The Hinode Science Data Centre Europe (<A
  href="http://www.sdc.uio.no/search/simulations">http://www.sdc.uio.no/search/simulations</A>).

---------------------------------------------------------
Title: Time Dependent Nonequilibrium Ionization of Transition Region
    Lines Observed with IRIS
Authors: Martínez-Sykora, Juan; De Pontieu, Bart; Hansteen, Viggo H.;
   Gudiksen, Boris
2016ApJ...817...46M    Altcode: 2015arXiv151200865M
  The properties of nonstatistical equilibrium ionization of silicon
  and oxygen ions are analyzed in this work. We focus on five solar
  targets (quiet Sun; coronal hole; plage; quiescent active region,
  AR; and flaring AR) as observed with the Interface Region Imaging
  Spectrograph (IRIS). IRIS is best suited for this work owing to the
  high cadence (up to 0.5 s), high spatial resolution (up to 0.″32),
  and high signal-to-noise ratios for O IV λ1401 and Si IV λ1402. We
  find that the observed intensity ratio between lines of three times
  ionized silicon and oxygen ions depends on their total intensity
  and that this correlation varies depending on the region observed
  (quiet Sun, coronal holes, plage, or active regions) and on the
  specific observational objects present (spicules, dynamic loops, jets,
  microflares, or umbra). In order to interpret the observations, we
  compare them with synthetic profiles taken from 2D self-consistent
  radiative MHD simulations of the solar atmosphere, where the
  statistical equilibrium or nonequilibrium treatment of silicon and
  oxygen is applied. These synthetic observations show vaguely similar
  correlations to those in the observations, I.e., between the intensity
  ratios and their intensities, but only in the nonequilibrium case do
  we find that (some of) the observations can be reproduced. We conclude
  that these lines are formed out of statistical equilibrium. We use
  our time-dependent nonequilibrium ionization simulations to describe
  the physical mechanisms behind these observed properties.

---------------------------------------------------------
Title: Numerical Modeling of the Solar Chromosphere and Corona:
    What Has Been Done? What Should Be Done?
Authors: Hansteen, V.; Carlsson, M.; Gudiksen, B.
2015ASPC..498..141H    Altcode:
  A number of increasingly sophisticated numerical simulations spanning
  the solar atmosphere from below the photosphere in the convection
  zone to far above in the corona have shed considerable insight into
  the role of the magnetic field in the structure and energetics of the
  Sun's outer layers. This development is strengthened by the wealth of
  observational data now coming on-line from both ground and space based
  observatories. In this talk we will concentrate on the successes and
  failures of the modeling effort thus far and discuss the inclusion of
  various effects not traditionally considered in the MHD description
  such as time dependent ionization, non-LTE radiative transfer, and
  generalized Ohm's law.

---------------------------------------------------------
Title: IRIS observations and 3D `realistic' MHD models of the solar
    chromosphere
Authors: Hansteen, V.; Carlsson, M.; Gudiksen, B.
2015hsa8.conf...19H    Altcode:
  The Interface Region Imaging Spectrograph (IRIS) is a NASA “Small
  Explorer” mission. It was launched in late June 2013 and since then
  it has obtained spectra and images from the outer solar atmosphere at
  unprecedented spatial and temporal resolution. Its primary goal is to
  probe the photosphere-corona interface: the source region of outer
  atmosphere heating and dynamics and a region that has an extremely
  complicated interplay between plasma, radiation and magnetic field. The
  scientific justification for IRIS hinges on the capabilities of 3D
  magnetohydrodynamic models to allow the confident interpretation of
  observed data. The interplay between observations and modeling is
  discussed, illustrated with examples from recent IRIS observations.

---------------------------------------------------------
Title: Structures in the Outer Solar Atmosphere
Authors: Fletcher, L.; Cargill, P. J.; Antiochos, S. K.; Gudiksen,
   B. V.
2015SSRv..188..211F    Altcode: 2014SSRv..tmp...52F; 2014arXiv1412.7378F
  The structure and dynamics of the outer solar atmosphere are reviewed
  with emphasis on the role played by the magnetic field. Contemporary
  observations that focus on high resolution imaging over a range
  of temperatures, as well as UV, EUV and hard X-ray spectroscopy,
  demonstrate the presence of a vast range of temporal and spatial scales,
  mass motions, and particle energies present. By focusing on recent
  developments in the chromosphere, corona and solar wind, it is shown
  that small scale processes, in particular magnetic reconnection, play
  a central role in determining the large-scale structure and properties
  of all regions. This coupling of scales is central to understanding
  the atmosphere, yet poses formidable challenges for theoretical models.

---------------------------------------------------------
Title: Synthesized Spectra of Optically Thin Emission Lines
Authors: Olluri, K.; Gudiksen, B. V.; Hansteen, V. H.; De Pontieu, B.
2015ApJ...802....5O    Altcode:
  In recent years realistic 3D numerical models of the solar atmosphere
  have become available. The models attempt to recreate the solar
  atmosphere and mimic observations in the best way, in order to make it
  possible to couple complicated observations with physical properties
  such as the temperatures, densities, velocities, and magnetic fields. We
  here present a study of synthetic spectra created using the Bifrost code
  in order to assess how well they fit with previously taken solar data. A
  study of the synthetic intensity, nonthermal line widths, Doppler
  shifts, and correlations between any two of these three components of
  the spectra first assuming statistical equilibrium is made, followed by
  a report on some of the effects nonequilibrium ionization will have on
  the synthesized spectra. We find that the synthetic intensities compare
  well with the observations. The synthetic observations depend on the
  assumed resolution and point-spread function (PSF) of the instrument,
  and we find a large effect on the results, especially for intensity
  and nonthermal line width. The Doppler shifts produce the reported
  persistent redshifts for the transition region (TR) lines and blueshifts
  for the upper TR and corona lines. The nonthermal line widths reproduce
  the well-known turnoff point around (2-3) × 10<SUP>5</SUP> K, but
  with much lower values than those observed. The nonthermal line widths
  tend to increase with decreasing assumed instrumental resolution, also
  when nonequilibrium ionization is included. Correlations between the
  nonthermal line width of any two TR line studies as reported by Chae et
  al. are reproduced, while the correlations of intensity to line width
  are reproduced only after applying a PSF to the data. Doppler shift
  correlations reported by Doschek for the TR lines and correlations of
  Doppler shift to nonthermal line width of the Fe xii <SUB>19.5</SUB>
  line reported by Doschek et al. are reproduced.

---------------------------------------------------------
Title: Non-equilibrium Ionization Effects on the Density Line Ratio
    Diagnostics of O IV
Authors: Olluri, K.; Gudiksen, B. V.; Hansteen, V. H.
2013ApJ...767...43O    Altcode:
  The dynamic timescales in the solar atmosphere are shorter than the
  ionization and recombination times of many ions used for line ratio
  diagnostics of the transition region and corona. The long ionization
  and recombination times for these ions imply that they can be found far
  from their equilibrium temperatures, and spectroscopic investigations
  require more care before being trusted in giving correct information
  on local quantities, such as density and temperature. By solving
  the full time-dependent rate equations for an oxygen model atom
  in the three-dimensional numerical model of the solar atmosphere
  generated by the Bifrost code, we are able to construct synthetic
  intensity maps and study the emergent emission. We investigate the
  method of electron density diagnostics through line ratio analysis
  of the O IV 140.1 nm to the 140.4 nm ratio, the assumptions made
  in carrying out the diagnostics, and the different interpretations
  of the electron density. The results show big discrepancies between
  emission in statistical equilibrium and emission where non-equilibrium
  (NEQ) ionization is treated. Deduced electron densities are up to an
  order of magnitude higher when NEQ effects are accounted for. The
  inferred electron density is found to be a weighted mean average
  electron density along the line of sight and has no relation to the
  temperature of emission. This study shows that numerical modeling is
  essential for electron density diagnostics and is a valuable tool when
  the ions used for such studies are expected to be out of ionization
  equilibrium. Though this study has been performed on the O IV ion,
  similar results are also expected for other transition region ions.

---------------------------------------------------------
Title: Non-equilibrium Ionization in the Bifrost Stellar Atmosphere
    Code
Authors: Olluri, K.; Gudiksen, B. V.; Hansteen, V. H.
2013AJ....145...72O    Altcode:
  The chromosphere and transition region have for the last 20 years been
  known to be quite dynamic layers of the solar atmosphere, characterized
  by timescales shorter than the ionization equilibrium timescales of
  many of the ions dominating emission in these regions. Due to the
  fast changes in the properties of the atmosphere, long ionization and
  recombination times can lead these ions to being found far from their
  equilibrium temperatures. A number of the spectral lines that we observe
  can therefore not be expected a priori to reflect information about
  local quantities such as the density or temperature, and interpreting
  observations requires numerical modeling. Modeling the ionization
  balance is computationally expensive and has earlier only been done
  in one dimension. However, one-dimensional models can primarily be
  used to investigate the possible importance of a physical effect, but
  cannot verify or disprove the importance of that effect in the fully
  three-dimensional solar atmosphere. Here, using the atomic database
  package DIPER, we extend one-dimensional methods and implement a solver
  for the rate equations of the full three-dimensional problem, using
  the numerical code Bifrost. We present our implementation and report
  on a few test cases. We also report on studies of the important C IV
  and Fe XII ions in a semi-realistic two-dimensional solar atmosphere
  model, focusing on differences between statistical equilibrium and
  non-equilibrium ionization results.

---------------------------------------------------------
Title: Non-equilibrium ionization in 3D numerical models
Authors: Olluri, Kosovare; Gudiksen, Boris; Hansteen, Viggo
2012decs.confE.118O    Altcode:
  The dynamic timescales in the chromosphere and transition region have
  been observed to be much smaller then the ionization equilibration
  timescales of many ions found in the region. Due to the fast changes in
  the properties of the atmosphere, long ionization- and recombination
  times may lead to ions being found far from their equilibrium
  temperatures. Spectroscopic investigations therefore needs to be
  interpreted with the help of numerical modeling in order to produce
  reliable results. By solving the rate equations within a realistic MHD
  simulation of the solar atmosphere, we are able to follow the ionization
  balance, and study the non equilibrium effects of the emitting gas. Due
  top lack of computation power, this has previously been done in simple
  1D, but because of the many free parameters in these models, their
  conclusions are not free of uncertainties. The resent development in
  computing technology and atmospheric modeling makes it possible to
  study the full 3D effect of non equilibrium ionization. With the solar
  atmosphere model Bifrost, we have a 3D platform for calculating and
  following the ionization degree of important atoms of high abundances
  in the solar atmosphere. We will present our implementation, and a
  study of the carbon IV 1549 Å , Iron XII 195 Å, Oxygen IV 1399 Å
  and 1401 Å lines in 2D.

---------------------------------------------------------
Title: State of the art single fluid MHD numerical modeling of the
    coupled solar atmosphere
Authors: Gudiksen, Boris
2012decs.confE.115G    Altcode:
  Modeling the solar atmosphere has for a long time been known to be a
  very complex problem. The wealth of observational features identified in
  solar observations have multiplied with increasing spatial, temporal
  and spectral resolution. To explain the high quality of space and
  ground based observations, models must be very sophisticated and be
  able to treat a number of physical regimes, where the dominating terms
  in the equations change drastically. Numerical simulations are now able
  to explain some, but certainly not all of the observed features. The
  numerical complexity of solving the equations governing the physics of
  the solar atmosphere is very high, and a number of different numerical
  techniques must be used in order to create a coherent picture of the
  connected solar atmosphere. We are now at a level where simulations
  have to include a much larger range in vertical extend than has been
  previously done. The wealth of numerical problems arising when doing so
  has lead to a number of numerical codes that are specialized to deal
  with a specific problem, and which now are being augmented to handle
  a larger range of problems. Hopefully with time we will have a number
  of numerical codes that are sophisticated enough to deal reliably with
  the whole solar atmosphere. I will give a review of some the codes that
  have been able to produce results from a fully connected solar model.

---------------------------------------------------------
Title: Non-equilibrium ionization in 3D numerical models
Authors: Olluri, Kosovare; Gudiksen, Boris; Hansteen, Viggoh
2012decs.confE.117O    Altcode:
  The dynamic timescales in the chromosphere and transition region have
  been observed to be much smaller then the ionization equilibration
  timescales of many ions found in the region. Due to the fast changes in
  the properties of the atmosphere, long ionization- and recombination
  times may lead to ions being found far from their equilibrium
  temperatures. Spectroscopic investigations therefore needs to be
  interpreted with the help of numerical modeling in order to produce
  reliable results. By solving the rate equations within a realistic MHD
  simulation of the solar atmosphere, we are able to follow the ionization
  balance, and study the non equilibrium effects of the emitting gas. Due
  top lack of computation power, this has previously been done in simple
  1D, but because of the many free parameters in these models, their
  conclusions are not free of uncertainties. The resent development in
  computing technology and atmospheric modeling makes it possible to
  study the full 3D effect of non equilibrium ionization. With the solar
  atmosphere model Bifrost, we have a 3D platform for calculating and
  following the ionization degree of important atoms of high abundances
  in the solar atmosphere. We will present our implementation, and a
  study of the carbon IV 1549 Å , Iron XII 195 Å, Oxygen IV 1399 Å
  and 1401 Å lines in 2D.

---------------------------------------------------------
Title: The stellar atmosphere simulation code Bifrost. Code
    description and validation
Authors: Gudiksen, B. V.; Carlsson, M.; Hansteen, V. H.; Hayek, W.;
   Leenaarts, J.; Martínez-Sykora, J.
2011A&A...531A.154G    Altcode: 2011arXiv1105.6306G
  Context. Numerical simulations of stellar convection and photospheres
  have been developed to the point where detailed shapes of observed
  spectral lines can be explained. Stellar atmospheres are very complex,
  and very different physical regimes are present in the convection zone,
  photosphere, chromosphere, transition region and corona. To understand
  the details of the atmosphere it is necessary to simulate the whole
  atmosphere since the different layers interact strongly. These physical
  regimes are very diverse and it takes a highly efficient massively
  parallel numerical code to solve the associated equations. <BR /> Aims:
  The design, implementation and validation of the massively parallel
  numerical code Bifrost for simulating stellar atmospheres from the
  convection zone to the corona. <BR /> Methods: The code is subjected
  to a number of validation tests, among them the Sod shock tube test,
  the Orzag-Tang colliding shock test, boundary condition tests and
  tests of how the code treats magnetic field advection, chromospheric
  radiation, radiative transfer in an isothermal scattering atmosphere,
  hydrogen ionization and thermal conduction. Results.Bifrost completes
  the tests with good results and shows near linear efficiency scaling
  to thousands of computing cores.

---------------------------------------------------------
Title: On the minimum temperature of the quiet solar chromosphere
Authors: Leenaarts, J.; Carlsson, M.; Hansteen, V.; Gudiksen, B. V.
2011A&A...530A.124L    Altcode: 2011arXiv1104.5081L
  <BR /> Aims: We aim to provide an estimate of the minimum temperature
  of the quiet solar chromosphere. <BR /> Methods: We perform a 2D
  radiation-MHD simulation spanning the upper convection zone to the
  lower corona. The simulation includes non-LTE radiative transfer
  and an equation-of-state that includes non-equilibrium ionization
  of hydrogen and non-equilibrium H<SUB>2</SUB> molecule formation. We
  analyze the reliability of the various assumptions made in our model
  in order to assess the realism of the simulation. <BR /> Results:
  Our simulation contains pockets of cool gas with down to 1660 K from
  1 Mm up to 3.2 Mm height. It overestimates the radiative heating,
  and contains non-physical heating below 1660 K. Therefore we conclude
  that cool pockets in the quiet solar chromosphere might have even
  lower temperatures than in the simulation, provided that there exist
  areas in the chromosphere without significant magnetic heating. We
  suggest off-limb molecular spectroscopy to look for such cool pockets
  and 3D simulations including a local dynamo and a magnetic carpet to
  investigate Joule heating in the quiet chromosphere.

---------------------------------------------------------
Title: Three-dimensional surface convection simulations of metal-poor
    stars. The effect of scattering on the photospheric temperature
    stratification
Authors: Collet, R.; Hayek, W.; Asplund, M.; Nordlund, Å.; Trampedach,
   R.; Gudiksen, B.
2011A&A...528A..32C    Altcode: 2011arXiv1101.3265C
  Context. Three-dimensional (3D) radiative hydrodynamic model atmospheres
  of metal-poor late-type stars are characterized by cooler upper
  photospheric layers than their one-dimensional counterparts. This
  property of 3D model atmospheres can dramatically affect the
  determination of elemental abundances from temperature-sensitive
  spectral features, with profound consequences on galactic chemical
  evolution studies. <BR /> Aims: We investigate whether the cool surface
  temperatures predicted by 3D model atmospheres of metal-poor stars
  can be ascribed to approximations in the treatment of scattering
  during the modelling phase. <BR /> Methods: We use the Bifrost
  code to construct 3D model atmospheres of metal-poor stars and test
  three different ways to handle scattering in the radiative transfer
  equation. As a first approach, we solve iteratively the radiative
  transfer equation for the general case of a source function with
  a coherent scattering term, treating scattering in a correct and
  consistent way. As a second approach, we solve the radiative transfer
  equation in local thermodynamic equilibrium approximation, neglecting
  altogether the contribution of continuum scattering to extinction in the
  optically thin layers; this has been the default mode in our previous
  3D modelling as well as in present Stagger-Code models. As our third
  and final approach, we treat continuum scattering as pure absorption
  everywhere, which is the standard case in the 3D modelling by the
  CO<SUP>5</SUP>BOLD collaboration. <BR /> Results: For all simulations,
  we find that the second approach produces temperature structures
  with cool upper photospheric layers very similar to the case in which
  scattering is treated correctly. In contrast, treating scattering as
  pure absorption leads instead to significantly hotter and shallower
  temperature stratifications. The main differences in temperature
  structure between our published models computed with the Stagger-
  and Bifrost codes and those generated with the CO<SUP>5</SUP>BOLD
  code can be traced to the different treatments of scattering. <BR />
  Conclusions: Neglecting the contribution of continuum scattering to
  extinction in optically thin layers provides a good approximation
  to the full, iterative solution of the radiative transfer equation
  in metal-poor stellar surface convection simulations, and at a much
  lower computational cost. Our results also demonstrate that the cool
  temperature stratifications predicted for metal-poor late-type stars
  by previous models by our collaboration are not an artifact of the
  approximated treatment of scattering.

---------------------------------------------------------
Title: Radiative transfer with scattering for domain-decomposed 3D
    MHD simulations of cool stellar atmospheres. Numerical methods and
    application to the quiet, non-magnetic, surface of a solar-type star
Authors: Hayek, W.; Asplund, M.; Carlsson, M.; Trampedach, R.; Collet,
   R.; Gudiksen, B. V.; Hansteen, V. H.; Leenaarts, J.
2010A&A...517A..49H    Altcode: 2010arXiv1007.2760H
  <BR /> Aims: We present the implementation of a radiative
  transfer solver with coherent scattering in the new BIFROST
  code for radiative magneto-hydrodynamical (MHD) simulations of
  stellar surface convection. The code is fully parallelized using
  MPI domain decomposition, which allows for large grid sizes and
  improved resolution of hydrodynamical structures. We apply the code
  to simulate the surface granulation in a solar-type star, ignoring
  magnetic fields, and investigate the importance of coherent scattering
  for the atmospheric structure. <BR /> Methods: A scattering term
  is added to the radiative transfer equation, requiring an iterative
  computation of the radiation field. We use a short-characteristics-based
  Gauss-Seidel acceleration scheme to compute radiative flux divergences
  for the energy equation. The effects of coherent scattering are
  tested by comparing the temperature stratification of three 3D
  time-dependent hydrodynamical atmosphere models of a solar-type star:
  without scattering, with continuum scattering only, and with both
  continuum and line scattering. <BR /> Results: We show that continuum
  scattering does not have a significant impact on the photospheric
  temperature structure for a star like the Sun. Including scattering in
  line-blanketing, however, leads to a decrease of temperatures by about
  350 K below log<SUB>10</SUB> τ<SUB>5000</SUB> ⪉ -4. The effect is
  opposite to that of 1D hydrostatic models in radiative equilibrium,
  where scattering reduces the cooling effect of strong LTE lines in
  the higher layers of the photosphere. Coherent line scattering also
  changes the temperature distribution in the high atmosphere, where
  we observe stronger fluctuations compared to a treatment of lines as
  true absorbers.

---------------------------------------------------------
Title: On the nature of coronal loops above the quiet sun network
Authors: Bingert, S.; Zacharias, P.; Peter, H.; Gudiksen, B. V.
2010AdSpR..45..310B    Altcode:
  The structure and dynamics of a box in a stellar corona can be
  modeled employing a 3D MHD model for different levels of magnetic
  activity. Depending on the magnetic flux through the surface the
  nature of the resulting coronal structures can be quite different. We
  investigate a model of an active region for two sunspots surrounded by
  magnetic field patches comparable in magnetic flux to the sunspots. The
  model results in emission from the model corona being concentrated in
  loop structures. In Gudiksen and Nordlund (2005) the loops seen in EUV
  and X-ray emission outline the magnetic field, following the general
  paradigm. However, in our model, where the magnetic field is far from
  a force-free state, the loops seen in X-ray emission do not follow
  the magnetic field lines. This result is of interest especially for
  loops as found in areas where the magnetic field emerging from active
  regions interacts with the surrounding network.

---------------------------------------------------------
Title: Chromospheric heating and structure as determined from high
    resolution 3D simulations .
Authors: Carlsson, M.; Hansteen, V. H.; Gudiksen, B. V.
2010MmSAI..81..582C    Altcode: 2010arXiv1001.1546C
  We have performed 3D radiation MHD simulations extending from the
  convection zone to the corona covering a box 16 Mm<SUP>3</SUP> at 32
  km spatial resolution. The simulations show very fine structure in
  the chromosphere with acoustic shocks interacting with the magnetic
  field. Magnetic flux concentrations have a temperature lower than the
  surroundings in the photosphere but higher in the low chromosphere. The
  heating is there mostly through ohmic dissipation preferentially at
  the edges of the flux concentrations. The magnetic field is often
  wound up around the flux concentrations. When acoustic waves travel
  up along the field this topology leads to swirling motions seen in
  chromospheric diagnostic lines such as the calcium infrared triplet.

---------------------------------------------------------
Title: Photospheric Motions and Their Effects on the Corona: A
    Numerical Approach
Authors: Gomes de Jesus, Leandro Filipe; Gudiksen, Boris Vilhelm
2009ApJ...704..705G    Altcode: 2009arXiv0908.4174G; 2009ApJ...704..705F
  We perform a number of numerical simulations of the solar corona with
  the aim of understanding how it responds to different conditions in
  the photosphere. By changing parameters which govern the motion of
  the plasma at the photosphere, we study the behavior of the corona,
  in particular, the effects on the current density generated. A
  magnetohydrodynamics code is used to run simulations, using a 20 × 20
  × 20 Mm<SUP>3</SUP> box with timespans ranging from one hundred to
  several hundreds of minutes. All the experiments show a fast initial
  increase of the current density, followed by a stabilization around an
  asymptotic value which depends on the photospheric conditions. These
  asymptotic average current densities as well as the turnover points
  are discussed.

---------------------------------------------------------
Title: Coronal dynamics and heating theories
Authors: Gudiksen, Boris V.
2009AdSpR..43..108G    Altcode:
  A large number of coronal heating theories have been proposed and
  most of them can be labeled as AC or DC heating theories. Here a short
  description of these two main theories is given, and the results of a
  DC heating model simulation is explained in more detail. As a result of
  that model, arguments are given for putting emphasis on launching a very
  fast spectrograph, ideally a imaging spectrograph as soon as possible.

---------------------------------------------------------
Title: On the Nature of Coronal Loops
Authors: Bingert, S.; Zacharias, P.; Peter, H.; Gudiksen, B.
2008ESPM...12.3.29B    Altcode:
  The structure and dynamics of a box in a stellar corona can be
  modeled employing a 3D MHD model for different levels of magnetic
  activity. <P />Depending on the magnetic flux through the surface the
  nature of the resulting coronal structures can be quite different. <P
  />We will compare two different models of an active region, one for
  two basically isolated sunspots, and another one for two sunspots
  surrounded by magnetic field patches similar to the chromospheric
  network. <P />The current paradigm is that these loops follow magnetic
  field lines as pearls on a string, and thus the majority of present
  corona models describe structures following the field lines. <P />Our
  study challenges this paradigm by showing through a three-dimensional
  model that coronal structures in complex magnetic field geometries might
  appear loop-like while they are not aligned with the magnetic field. <P
  />Using a forward model approach, both models result in emission from
  the corona being concentrated in loop structures. <P />In the first case
  the loops seen in EUV and X-ray emission are following the magnetic
  field. <P />However, in the second case, where the magnetic field is
  far from a force-free state, the loops seen in X-ray emission do not
  follow the magnetic field, but are more related to the current sheets
  formed in response to the footpoint motions of the magnetic field. <P
  />This result is of interest especially for loops as found in areas
  where the magnetic field emerging from active regions interacts with
  the surrounding network or in the complex magnetic structures within
  chromospheric network patches.

---------------------------------------------------------
Title: On the nature of coronal loops
Authors: Peter, H.; Bingert, S.; Gudiksen, B. V.
2008AGUSMSP41C..05P    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Topological Dissipation &amp; The Solar Corona
Authors: Gudiksen, B. V.
2007ASPC..369..269G    Altcode:
  Reconnection in the solar corona has to take place, as was convincingly
  shown by tet{Parker72}, the question remains if it is sufficient
  to heat the corona. One of the major problems in coronal physics,
  is modeling reconnection. Reconnection is the basis of most heating
  models, in spite the fact that we really don't know how reconnection
  works. Simulating reconnection with realistic parameters is highly
  problematic and the solar corona has a parameter space not well
  explored. Here I try to give a hint of what conclusions one can reach
  about reconnection from large scale simulations of the solar corona. A
  model of the solar corona with a numerical diffusion reproduces a
  number of observables, and seem to reproduce the corona well, only
  using minimal assumptions. The overall well reproduced corona, means
  that it is highly likely that reconnection does not differ much from the
  diffusion scheme of the numerical code. That means that reconnection in
  the solar corona transfers most of the liberated magnetic energy into
  heat locally and mechanisms such as waves and high energy particles can
  not carry the a significant part of the energy released in reconnection.

---------------------------------------------------------
Title: 3D Numerical Models of the Chromosphere, Transition Region,
    and Corona
Authors: Hansteen, V. H.; Carlsson, M.; Gudiksen, B.
2007ASPC..368..107H    Altcode: 2007arXiv0704.1511H
  A major goal in solar physics has during the last five decades
  been to find how energy flux generated in the solar convection zone
  is transported and dissipated in the outer solar layers. Progress
  in this field has been slow and painstaking. However, advances in
  computer hardware and numerical methods, vastly increased observational
  capabilities and growing physical insight seem finally to be leading
  towards understanding. Here we present exploratory numerical MHD models
  that span the entire solar atmosphere from the upper convection zone
  to the lower corona. These models include non-grey, non-LTE radiative
  transport in the photosphere and chromosphere, optically thin radiative
  losses as well as magnetic field-aligned heat conduction in the
  transition region and corona.

---------------------------------------------------------
Title: Heating the solar corona.
Authors: Gudiksen, B. V.
2007MmSAI..78..293G    Altcode:
  The heating mechanism at work in the solar corona has been unknown
  since the temperature of the corona was discovered in the late nineteen
  thirties. Here I will present results from a model which we believe
  is the first model which allows forward modeling of observational
  signatures, and can fit several observational features of the solar
  corona. If this model proves to be a correct representation of the
  solar corona, the question of the coronal heating mechanism will
  finally be solved.

---------------------------------------------------------
Title: Connections: Photosphere -- Chromosphere - Corona
Authors: Gudiksen, B. V.
2006ASPC..354..331G    Altcode:
  The chromosphere is not only the region where the atmosphere goes from
  being optically thick to optically thin, but also the region where
  the dynamics changes from being controlled by the plasma to being
  controlled by the magnetic field. The magnetic field changes from
  being concentrated in small regions to being space filling. This
  expansion has traditionally been modeled by the magnetic funnel
  or wine-glass picture. For several reasons it is hard to gain any
  information about the magnetic field in this region, so this model
  remains unconfirmed. Three recent methods to acquire magnetic field
  information from this interesting region will be reviewed, and I will
  argue that the results from such investigations will require that we
  heavily revise the simplistic magnetic funnel picture.

---------------------------------------------------------
Title: Forward Modeling of the Corona of the Sun and Solar-like Stars:
    From a Three-dimensional Magnetohydrodynamic Model to Synthetic
    Extreme-Ultraviolet Spectra
Authors: Peter, Hardi; Gudiksen, Boris V.; Nordlund, Åke
2006ApJ...638.1086P    Altcode: 2005astro.ph..3342P
  A forward model is described in which we synthesize spectra from an ab
  initio three-dimensional MHD simulation of an outer stellar atmosphere,
  where the coronal heating is based on braiding of magnetic flux due to
  photospheric footpoint motions. We discuss the validity of assumptions
  such as ionization equilibrium and investigate the applicability of
  diagnostics like the differential emission measure inversion. We find
  that the general appearance of the synthesized corona is similar to
  the solar corona and that, on a statistical basis, integral quantities
  such as average Doppler shifts or differential emission measures are
  reproduced remarkably well. The persistent redshifts in the transition
  region, which have puzzled theorists since their discovery, are
  explained by this model as caused by the flows induced by the heating
  through braiding of magnetic flux. While the model corona is only
  slowly evolving in intensity, as is observed, the amount of structure
  and variability in Doppler shift is very large. This emphasizes the need
  for fast coronal spectroscopic observations, as the dynamical response
  of the corona to the heating process manifests itself in a comparably
  slow evolving coronal intensity but rapid changes in Doppler shift.

---------------------------------------------------------
Title: Coronal dynamics and heating theories
Authors: Gudiksen, B. V.; Nordlund, Aa.
2006cosp...36.3545G    Altcode: 2006cosp.meet.3545G
  The solar corona has been modeled as a collection of single hydrostatic
  loops and as a hydrostatic plane parallel atmosphere but these models
  have had serious problems reproducing the observations made of the
  solar corona The favored coronal heating models rely on large gradients
  in wave speed for AC models and gradients in the magnetic field for
  DC models and both provide an energy release that has no reason to
  be uniform across the magnetic field and so the heating function at
  play in the solar corona is most likely intermittent in both space and
  time and we must therefore embrace a dynamic model of the corona This
  conclusion is supported by high cadence high resolution observations
  of the chromosphere and transition region which show a very dynamic
  atmosphere I will concentrate on a 3D MHD simulation of the solar
  atmosphere from the photosphere to the low corona and will show
  that even for a quiescent active region and even though the observed
  intensity of the loops is close to constant the loops are not in a
  static equilibrium The corona is very dynamic and images made from
  the simulation of doppler shifts show much more time dependence and
  intermittency than does images showing only intensity

---------------------------------------------------------
Title: Coronal Heating Through Braiding of Magnetic Field Lines
    Synthesized Coronal EUV Emission and Magnetic Structure
Authors: Peter, H.; Gudiksen, B. V.; Nordlund, A.
2005ESASP.596E..14P    Altcode: 2005ccmf.confE..14P
  No abstract at ADS

---------------------------------------------------------
Title: EUV Emission from a 3D MHD Coronal Model: Temporal Variability
    in a Synthesized Corona
Authors: Peter, H.; Gudiksen, B. V.; Nordlund, Å.
2005ESASP.592..527P    Altcode: 2005soho...16E..98P; 2005ESASP.592E..98P
  No abstract at ADS

---------------------------------------------------------
Title: The Structure of the Base of the Corona
Authors: Bingert, S.; Peter, H.; Gudiksen, B.; Nordlund, Ake
2005ESASP.592..471B    Altcode: 2005ESASP.592E..84B; 2005soho...16E..84B
  No abstract at ADS

---------------------------------------------------------
Title: 3D Numerical Models of Quiet Sun Coronal Heating
Authors: Hansteen, V. H.; Gudiksen, B.
2005ESASP.592..483H    Altcode: 2005soho...16E..87H; 2005ESASP.592E..87H
  No abstract at ADS

---------------------------------------------------------
Title: DC Heating - Is it Enough? (Invited)
Authors: Gudiksen, B. V.
2005ESASP.592..165G    Altcode: 2005soho...16E..25G; 2005ESASP.592E..25G
  No abstract at ADS

---------------------------------------------------------
Title: Erratum: “An AB Initio Approach to Solar Coronal Loops”
    (<A href="/abs/2005ApJ...618.1031G">ApJ, 618, 1031 [2005]</A>)
Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke
2005ApJ...623..597G    Altcode:
  Because of an error at the Press, incorrect versions of Figures 4 (top
  and bottom panels), 5, 7, and 9 were published. In all these figures, a
  dotted or dash-dotted line appeared as a solid line. The correct figures
  appear below. Figures 4 (middle panel), 6, 8, and 10 are also reproduced
  here for comparison purposes. The Press sincerely regrets these errors.

---------------------------------------------------------
Title: Erratum: “An AB Initio Approach to the Solar Coronal
    Heating Problem” (<A href="/abs/2005ApJ...618.1020G">ApJ, 618, 1020
    [2005]</A>)
Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke
2005ApJ...623..600G    Altcode:
  Because of an error at the Press, an incorrect version of Figure 5
  was published, in which what should be a dash-dotted line (showing
  convective flux) appears as a solid line. The correct version appears
  below. The Press sincerely regrets the error.

---------------------------------------------------------
Title: Tackling the coronal heating problem using 3D MHD coronal
    simulations with spectral synthesis
Authors: Peter, H.; Gudiksen, B. V.; Nordlund, A.
2005ESASP.560...59P    Altcode: 2005csss...13...59P
  No abstract at ADS

---------------------------------------------------------
Title: Dynamo action in M-dwarfs
Authors: Dorch, S. B. F.; Gudiksen, B. V.; Ludwig, H. -G.
2005ESASP.560..515D    Altcode: 2005csss...13..515D; 2004astro.ph..9219D
  Magnetic activity in M-dwarfs present enigmatic questions: On the
  one hand they have higher field strengths and larger filling factors
  than the magnetic field on the Sun, on the other hand, they are fully
  convective and their atmospheres are more neutral, hence they do not
  have an undershoot layer for magnetic flux storage and as we show here,
  cannot have small-scale dynamo action in their photospheres either. We
  present a discussion of these facts and propose a new numerical model
  to investigate M-dwarf magnetism.

---------------------------------------------------------
Title: An AB Initio Approach to Solar Coronal Loops
Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke
2005ApJ...618.1031G    Altcode: 2004astro.ph..7267G
  Data from recent numerical simulations of the solar corona and
  transition region are analyzed, and the magnetic field connections
  between the low corona and the photosphere are found to be close to
  those of a potential field. The field line-to-field line displacements
  follow a power-law distribution with typical displacements of just a
  few Mm. Three loops visible in simulated TRACE filters are analyzed
  in detail and found to have significantly different heating rates
  and distributions thereof, one of them showing a small-scale heating
  event. The dynamical structure is complicated, even though all the
  loops are visible in a single filter along most of their lengths. The
  loops are nonstatic and are in the process of evolving into loops with
  very different characteristics. Differential emission measure (DEM)
  curves along one of the loops illustrate that DEM curves have to be
  treated carefully if physical characteristics are to be extracted.

---------------------------------------------------------
Title: An Ab Initio Approach to the Solar Coronal Heating Problem
Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke
2005ApJ...618.1020G    Altcode: 2004astro.ph..7266G
  We present an ab initio approach to the solar coronal heating problem by
  modeling a small part of the solar corona in a computational box using
  a three-dimensional MHD code including realistic physics. The observed
  solar granular velocity pattern and its amplitude and vorticity power
  spectra, as reproduced by a weighted Voronoi tessellation method,
  are used as a boundary condition that generates a Poynting flux in
  the presence of a magnetic field. The initial magnetic field is a
  potential extrapolation of a SOHO/MDI high-resolution magnetogram,
  and a standard stratified atmosphere is used as a thermal initial
  condition. Except for the chromospheric temperature structure, which
  is kept nearly fixed, the initial conditions are quickly forgotten
  because the included Spitzer conductivity and radiative cooling
  function have typical timescales much shorter than the time span of the
  simulation. After a short initial start-up period, the magnetic field is
  able to dissipate (3-4)×10<SUP>6</SUP>ergscm<SUP>-2</SUP>s<SUP>-1</SUP>
  in a highly intermittent corona, maintaining an average temperature
  of ~10<SUP>6</SUP> K, at coronal density values for which simulated
  images of the TRACE 171 and 195 Å passbands reproduce observed photon
  count rates.

---------------------------------------------------------
Title: Analysis of Synthetic EUV Spectra from 3d Models of the Corona
Authors: Bingert, S.; Peter, H.; Gudiksen, B.; Nordlund, A.; Dobler, W.
2004ESASP.575..348B    Altcode: 2004soho...15..348B
  No abstract at ADS

---------------------------------------------------------
Title: Synthetic EUV Spectra from 3D MHD Coronal Simulations:
    Coronal Heating Through Magnetic Braiding
Authors: Peter, H.; Gudiksen, B. V.; Nordlund, Å.
2004ESASP.575...50P    Altcode: 2004soho...15...50P
  No abstract at ADS

---------------------------------------------------------
Title: Coronal Heating through Braiding of Magnetic Field Lines
Authors: Peter, Hardi; Gudiksen, Boris V.; Nordlund, Åke
2004ApJ...617L..85P    Altcode: 2004astro.ph..9504P
  Cool stars such as our Sun are surrounded by a million degree hot outer
  atmosphere, the corona. For more than 60 years, the physical nature
  of the processes heating the corona to temperatures well in excess of
  those on the stellar surface have remained puzzling. Recent progress in
  observational techniques and numerical modeling now opens a new window
  to approach this problem. We present the first coronal emission-line
  spectra synthesized from three-dimensional numerical models describing
  the evolution of the dynamics and energetics as well as of the magnetic
  field in the corona. In these models the corona is heated through
  motions on the stellar surface that lead to a braiding of magnetic
  field lines inducing currents that are finally dissipated. These
  forward models enable us to synthesize observed properties such as
  (average) emission-line Doppler shifts or emission measures in the outer
  atmosphere, which until now have not been understood theoretically,
  even though many suggestions have been made in the past. As our model
  passes these observational tests, we conclude that the flux braiding
  mechanism is a prime candidate for being the dominant heating process
  of the magnetically closed corona of the Sun and solar-like stars.

---------------------------------------------------------
Title: Self-Regulating Supernova Heating in Interstellar Medium
    Simulations
Authors: Sarson, Graeme R.; Shukurov, Anvar; Nordlund, Åke; Gudiksen,
   Boris; Brandenburg, Axel
2004Ap&SS.292..267S    Altcode: 2003astro.ph..7013S
  Numerical simulations of the multi-phase interstellar medium have been
  carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box
  model, with random motions driven by supernova explosions. These
  calculations incorporate the effects of magnetic fields and rotation
  in 3D; these play important dynamical roles in the galaxy, but are
  neglected in many other simulations. The supernovae driving the motions
  are not arbitrarily imposed, but occur where gas accumulates into cold,
  dense clouds; their implementation uses a physically motivated model
  for the evolution of such clouds. The process is self-regulating, and
  produces mean supernova rates as part of the solution. Simulations with
  differing mean density show a power law relation between the supernova
  rate and density, with exponent 1.7; this value is within the range
  suggested from observations (taking star formation rate as a proxy for
  supernova rate). The global structure of the supernova driven medium
  is strongly affected by the presence of magnetic fields; e.g. for one
  solution the filling factor of hot gas is found to vary from 0.19 (with
  no field) to 0.12 (with initial mid-plane field B <SUB>0</SUB>= 6 μG).

---------------------------------------------------------
Title: The effects of spiral arms on the multi-phase ISM
Authors: Shukurov, Anvar; Sarson, Graeme R.; Nordlund, Åke; Gudiksen,
   Boris; Brandenburg, Axel
2004Ap&SS.289..319S    Altcode: 2002astro.ph.12260S
  Statistical parameters of the ISM driven by thermal energy
  injectionsfrom supernova explosions have been obtained from 3D,
  nonlinear,magnetohydrodynamic, shearing-box simulations for spiral
  arm andinterarm regions. The density scale height obtained for the
  interarm regionsis 50% larger than within the spiral arms because
  of thehigher gas temperature. The filling factorof the hot gas is
  also significantly larger between the armsand depends sensitively on
  magnetic field strength.

---------------------------------------------------------
Title: An Ab Initio Approach to the Solar Coronal Heating Problem
Authors: Gudiksen, B. V.; Nordlund, Å.
2004IAUS..219..488G    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: The coronal heating problem
Authors: Gudiksen, Boris V.
2004PhDT.......169G    Altcode:
  The heating of the solar corona has been investigated during four
  of decades and several mechanisms able to produce heating have been
  proposed. It has until now not been possible to produce quantitative
  estimates that would establish any of these heating mechanism as the
  most important in the solar corona. In order to investigate which
  heating mechanism is the most important, a more detailed approach
  is needed. <P />In this thesis, the heating problem is approached
  "ab initio";, using well observed facts and including realistic
  physics in a 3D magneto-hydrodynamic simulation of a small part
  of the solar atmosphere. The "engine" of the heating mechanism is
  the solar photospheric velocity field, that braids the magnetic
  field into a configuration where energy has to be dissipated. The
  initial magnetic field is taken from an observation of a typical
  magnetic active region scaled down to fit inside the computational
  domain. The driving velocity field is generated by an algorithm that
  reproduces the statistical and geometrical fingerprints of solar
  granulation. Using a standard model atmosphere as the thermal initial
  condition, the simulation goes through a short startup phase, where
  the initial thermal stratification is quickly forgotten, after which
  the simulation stabilizes in statistical equilibrium. In this state,
  the magnetic field is able to dissipate the same amount of energy as
  is estimated to be lost through radiation, which is the main energy
  loss mechanism in the solar corona. <P />The simulation produces
  heating that is intermittent on the smallest resolved scales and
  hot loops similar to those observed through narrow band filters in
  the ultra violet. Other observed characteristics of the heating are
  reproduced, as well as a coronal temperature of roughly one million
  K. Because of the ab initio approach, the amount of heating produced
  in these simulations represents a lower limit to coronal heating and
  the conclusion is that such heating of the corona is unavoidable.

---------------------------------------------------------
Title: Dark cores in sunspot penumbral filaments
Authors: Scharmer, Göran B.; Gudiksen, Boris V.; Kiselman, Dan;
   Löfdahl, Mats G.; Rouppe van der Voort, Luc H. M.
2002Natur.420..151S    Altcode:
  Sunspot umbrae-the dark central regions of the spots-are surrounded
  by brighter filamentary penumbrae, the existence of which remains
  largely inexplicable. The penumbral filaments contain magnetic fields
  with varying inclinations and are associated with flowing gas, but
  discriminating between theoretical models has been difficult because
  the structure of the filaments has not hitherto been resolved. Here
  we report observations of penumbral filaments that reveal dark cores
  inside them. We cannot determine the nature of these dark cores,
  but their very existence provides a crucial test for any model of
  penumbrae. Our images also reveal other very small structures, in line
  with the view that many of the fundamental physical processes in the
  solar photosphere occur on scales smaller than 100km.

---------------------------------------------------------
Title: Bulk Heating and Slender Magnetic Loops in the Solar Corona
Authors: Gudiksen, Boris Vilhelm; Nordlund, Åke
2002ApJ...572L.113G    Altcode:
  The heating of the solar corona and the puzzle of the slender high
  reaching magnetic loops seen in observations from the Transition
  Region and Coronal Explorer (TRACE) has been investigated through
  three-dimensional numerical simulations and found to be caused by
  the well-observed plasma flows in the photosphere displacing the
  footpoints of magnetic loops in a nearly potential configuration. It
  is found that even the small convective displacements cause magnetic
  dissipation sufficient to heat the corona to temperatures of the
  order of a million K. The heating is intermittent in both space and
  time-at any one height and time it spans several orders of magnitude,
  and localized heating causes transonic flows along field lines, which
  explains the observed nonhydrostatic stratification of loops that are
  bright in emission measure.

---------------------------------------------------------
Title: Bright loops in the solar corona
Authors: Gudiksen, Boris V.; Nordlund, Aake
2002astro.ph..3167G    Altcode:
  The heating of the solar corona and the puzzle of the slender high
  reaching magnetic loops seen in observations from the Transition
  Region And Coronal Explorer(TRACE) has been investigated through 3D
  numerical simulations, and found to be caused by the well observed
  plasma flows in the photosphere displacing the footpoints of magnetic
  loops in a nearly potential configuration. It is found that even the
  small convective displacements cause magnetic dissipation sufficient to
  heat the corona to temperatures of the order of a million Kelvin. The
  heating is intermittent in both space and time - at any one height
  and time it spans several orders of magnitude, and localized heating
  causes transonic flows along field lines, which explains the observed
  non-hydrostatic equilibrium of loops that are bright in emission
  measure.

---------------------------------------------------------
Title: Bulk and Loop Heating of the Solar Corona
Authors: Gudiksen, Boris
2002smra.progE...7G    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Flux-loss of buoyant ropes interacting with convective flows
Authors: Dorch, S. B. F.; Gudiksen, B. V.; Abbett, W. P.; Nordlund, Å.
2001A&A...380..734D    Altcode: 2001astro.ph.10205D
  We present 3-d numerical magneto-hydrodynamic simulations of a buoyant,
  twisted magnetic flux rope embedded in a stratified, solar-like model
  convection zone. The flux rope is given an initial twist such that it
  neither kinks nor fragments during its ascent. Moreover, its magnetic
  energy content with respect to convection is chosen so that the flux
  rope retains its basic geometry while being deflected from a purely
  vertical ascent by convective flows. The simulations show that magnetic
  flux is advected away from the core of the flux rope as it interacts
  with the convection. The results thus support the idea that the amount
  of toroidal flux stored at or near the bottom of the solar convection
  zone may currently be underestimated.