The Effect of External Magnetic Field on Electron Scale Kelvin–Helmholtz Instability

We use particle-in-cell,fully electromagnetic,plasma kinetic simulation to study the effect of external magnetic field on electron scale Kelvin–Helmholtz instability(ESKHI).The results are applicable to collisionless plasmas when,e.g.,solar wind interacts with planetary magnetospheres or a magnetic field is generated in AGN jets.We find that as in the case of magnetohydrodynamic(MHD)KHI,in the kinetic regime,the presence of an external magnetic field reduces the growth rate of the instability.In the MHD case,there is a known threshold magnetic field for KHI stabilization,while for ESKHI this is to be analytically determined.Without a kinetic analytical expression,we use several numerical simulation runs to establish an empirical dependence of ESKHI growth rate,Γ(B_(0))ω_(pe),on the strength of the applied external magnetic field.We find the best fit is hyperbolic,Γ(B_(0))ω_(pe)=Γ_(0)ω_(pe)/(A+BB_(0)),where Γ_(0) is the ESKHI growth rate without an external magnetic field and B_(0)=B_(0)/B_(MHD)is the ratio of external and two-fluid MHD stability threshold magnetic field,derived here.An analytical theory to back up this growth rate dependence on the external magnetic field is needed.The results suggest that in astrophysical settings where a strong magnetic field pre-exists,the generation of an additional magnetic field by the ESKHI is suppressed,which implies that nature provides a“safety valve”—natural protection not to“over-generate”magnetic field by the ESKHI mechanism.Remarkably,we find that our two-fluid MHD threshold magnetic field is the same(up to a factor √γ_(0))as the DC saturation magnetic field,previously predicted by fully kinetic theory.

Physics-informed Neural Network for Force-free Magnetic Field Extrapolation

In this paper,we propose a physics-informed neural network extrapolation method that leverages machine learning techniques to reconstruct coronal magnetic fields.We enhance the classical neural network structure by introducing the concept of a quasi-output layer to address the challenge of preserving physical constraints during the neural network extrapolation process.Furthermore,we employ second-order optimization methods for training the neural network,which are more efficient compared to the first-order optimization methods commonly used in classical machine learning.Our approach is evaluated on the widely recognized semi-analytical model proposed by Low and Lou.The results demonstrate that the deep learning method achieves high accuracy in reconstructing the semianalytical model across multiple evaluation metrics.In addition,we validate the effectiveness of our method on the observed magnetogram of active region.

A study of the relation between intensity oscillations and magnetic field parameters in a sunspot: Hinode observations

We present properties of intensity oscillations of a sunspot in the photo- sphere and chromosphere using G band and Ca u H filtergrams from Hinode. Intensity power maps as function of magnetic field strength and frequency reveal reduction of power in the G band with an increase in photospheric magnetic field strength at all frequencies. In Ca II H, however, stronger fields exhibit more power at high frequen- cies, particularly in the 4.5-8.0 mHz band. Power distributions in different locations of the active region show that the oscillations in Ca II H exhibit more power compared to that of the G band. We also relate the power in intensity oscillations with differ- ent components of the photospheric vector magnetic field using near simultaneous spectro-polarimetric observations of the sunspot from the Hinode spectropolarime- ter. The photospheric umbral power is strongly anti-correlated with the magnetic field strength and its line-of-sight component but there is a good correlation with the trans- verse component. A reversal of this trend is observed in the chromosphere except at low frequencies （V≤ 1.5 mHz）. The power in sunspot penumbrae is anti-correlated with the magnetic field parameters at all frequencies （1.0 ≤ v ≤ 8.0 mHz） in both the photosphere and chromosphere, except that the chromospheric power shows a strong correlation in the frequency range 3-3.5 mHz.

Determination of the Topology Skeleton of Magnetic Fields in a Solar Active Region

Magnetic topology has been a key to the understanding of magnetic energy release mechanism. Based on observed vector magnetograms, we have determined the threedimensional （3D） topology skeleton of the magnetic fields in the active region NOAA 10720. The skeleton consists of six 3D magnetic nulls and a network of corresponding spines, fans, and null-null lines. For the first time, we have identified a spiral magnetic null in Sun＇s corona. The magnetic lines of force twisted around the spine of the null, forming a ＇magnetic wreath＇ with excess of free magnetic energy and resembling observed brightening structures at extraultraviolet （EUV） wavebands. We found clear evidence of topology eruptions which are referred to as catastrophic changes of topology skeleton associated with a coronal mass ejection （CME） and an explosive X-ray flare. These results shed new lights on the structural complexity and its role in explosive magnetic activity. The concept of flux rope has been widely used in modelling explosive magnetic activity, although their observational identity is rather obscure or, at least, lacking of necessary details up to date. We suggest that the magnetic wreath associated with the 3D spiral null is likely an important class of the physical entity of flux ropes.

A Statistical Study of Magnetic Flux Emergence in Solar Active Regions Prior to Strongest Flares

Using the data on magnetic field maps and continuum intensity for Solar Cycles 23 and 24,we explored 100 active regions(ARs)that produced M5.0 or stronger flares.We focus on the presence/absence of the emergence of magnetic flux in these ARs 2-3 days before the strong flare onset.We found that 29 ARs in the sample emerged monotonically amidst quiet-Sun.A major emergence of a new magnetic flux within a pre-existing AR yielding the formation of a complex flare-productive configuration was observed in another 24 cases.For 30 ARs,an insignificant(in terms of the total magnetic flux of pre-existing AR)emergence of a new magnetic flux within the pre-existing magnetic configuration was observed;for some of them the emergence resulted in a formation of a configuration with a small δ-sunspot;11 out of 100 ARs exhibited no signatures of magnetic flux emergence during the entire interval of observation.In six cases the emergence was in progress when the AR appeared on the Eastern limb,so that the classification and timing of emergence were not possible.We conclude that the recent flux emergence is not a necessary and/or sufficient condition for strong flaring of an AR.The flux emergence rate of flare-productive ARs analyzed here was compared with that of flare-quiet ARs analyzed in our previous studies.We revealed that the flare-productive ARs tend to display faster emergence than the flare-quiet ones do.

Lossless Compression Method for the Magnetic and Helioseismic Imager(MHI)Payload

The Solar Polar-orbit Observatory(SPO),proposed by Chinese scientists,is designed to observe the solar polar regions in an unprecedented way with a spacecraft traveling in a large solar inclination angle and a small ellipticity.However,one of the most significant challenges lies in ultra-long-distance data transmission,particularly for the Magnetic and Helioseismic Imager(MHI),which is the most important payload and generates the largest volume of data in SPO.In this paper,we propose a tailored lossless data compression method based on the measurement mode and characteristics of MHI data.The background out of the solar disk is removed to decrease the pixel number of an image under compression.Multiple predictive coding methods are combined to eliminate the redundancy utilizing the correlation(space,spectrum,and polarization)in data set,improving the compression ratio.Experimental results demonstrate that our method achieves an average compression ratio of 3.67.The compression time is also less than the general observation period.The method exhibits strong feasibility and can be easily adapted to MHI.

Analysis of sudden variations in photospheric magnetic fields during a large flare and their influences in the solar atmosphere

The solar active region NOAA 11719 produced a large two-ribbon flare on 2013 April 11. We have investigated sudden variations in the photospheric magnetic fields in this active region during the flare by employing magnetograms obtained in the spectral line Fe I 6173 A acquired by the Helioseismic and Magnetic Imager （HMI） onboard the Solar Dynamics Observatory （SDO） spacecraft. The analysis of the line-of-sight magnetograms from HMI show sudden and persistent magnetic field changes at different locations of the active region before the onset of the flare and during the flare. The vector magnetic field observations available from HMI also show coincident variations in the total magnetic field strength and its inclination angle at these locations. Using the simultaneous Dopplergrams obtained from HMI, we observe perturbations in the photospheric Doppler signals following the sudden changes in the magnetic fields in the aforementioned locations. The power spectrum analysis of these velocity signals shows enhanced acoustic power in these affected locations during the flare as compared to the pre-flare condition. Accompanying these observations, we have also used nearly simultaneous chromospheric observations obtained in the spectral line Ha 6562.8 A by the Global Oscillation Network Group （GONG） to study the evolution of flare- ribbons and intensity oscillations in this active region. The Ha intensity oscillations also show enhanced oscillatory power during the flare in the aforementioned locations. These results indicate that the transient Lorentz force associated with sudden changes in the magnetic fields could drive localized photospheric and chromospheric oscillations, like the flare-induced oscillations in the solar atmosphere.

Case studies of EUV cyclones and their associated magnetic fields

EUV cyclones are rotating structures in the solar corona, and they are usually rooted in the underlying rotating network magnetic fields in the photosphere. However, their connection with the surrounding magnetic fields remains unknown. Here we report an observational study of four typical cyclones which are rooted in different kinds of magnetic fields. We use Solar Dynamics Observatory^Atmospheric Imaging Assembly data to investigate the rotation of EUV features in cyclones and Helioseismic and Magnetic Imager data to study the associated magnetic fields. The results show that, （1） an EUV cyclone rooted in a sunspot rotates with the photo- spheric magnetic field; （2） two EUV cyclones in two faculae of an active region are connected to the same sunspot of the active region but rotate oppositely; （3） an EUV cyclone is rooted in a coronal hole with weak open magnetic fields; （4） a pair of con- jugated cyclones is rooted in magnetic fields that have opposite polarity with opposite directions of rotation. The differences in the spatial extent of a cyclone, characteristics of its rotation and underlying fields indicate that cyclones are ubiquitous over the solar atmosphere and that the magnetic structures relevant to the cyclones are more complicated than expected.

Evaluation of Coronal and Interplanetary Magnetic Field Extrapolation Using PSP Solar Wind Observation

Using solar wind observation near PSP perihelions as constraints,we have investigated the parameters in various PFSS model methods.It is found that the interplanetary magnetic field extrapolation with source surface height R_(SS)=2 Rs is better than that with R_(SS)=2.5 Rs.HMI and GONG magnetograms show similar performances in the simulation of magnetic field variation,but the former appears to have a slight advantage in reconstruction of intensity while the latter is more adaptable to sparser grids.The finite-difference method of constructing eigenvalue problems for potential fields can achieve similar accuracy as the analytic method and greatly improve the computational efficiency.MHD modeling performs relatively less well in magnetic field prediction,but it is able to provide rich information about solar-terrestrial space.

Distribution of Helical Properties of Solar Magnetic Fields

We summarize studies of helical properties of solar magnetic fields such as current helicity and twist of magnetic fields in solar active regions (ARs), that are observational tracers of the alpha-effect in the solar convective zone (SCZ). Information on their spatial distribution is obtained by analysis of systematic magnetographic observations of active regions taken at Huairou Solar Observing Station of National Astronomical Observatories of Chinese Academy of Sciences. The main property is that the tracers of the alpha-effect are antisymmetric about the solar equator. Identifying longitudinal migration of active regions with their individual rotation rates and taking into account the internal differential rotation law within the SCZ known from helioseismology, we deduce the distribution of the effect over depth. We have found evidence that the alpha-effect changes its value and sign near the bottom of the SCZ, and this is in accord with the theoretical studies and numerical simulations. We discuss other regularities which can be revealed by further analysis such as possible dependence on longitude, time, and magnetic field strength, etc.

A New Method of Identifying 3D Null Points in Solar Vector Magnetic Fields

Employing the Poincar6 index of isolated null-points in a vector field, we worked out a mathematical method of searching for 3D null-points in coronal magnetic fields. After introducing the relevant differential topology, we test the method by using the analytical model of Brown ＆ Priest. The location of nullpoint identified by our method coincides precisely with the analytical solution. Finally we apply the method to the 3D coronal magnetic fields reconstructed from an observed MDI magnetogram of a super-active region （NOAA 10488）. We find that the 3D null-point seems to be a key element in the magnetic topology associated with flare occurrence.

On the Relation Between Coronal Green Line Brightness and Magnetic Fields Intensity

Two-dimensional(2 D) solar coronal magnetogram is difficult to be measured directly until now.From the previous knowledge,a general relation has been noticed that the brighter green-line brightness for corona,the higher coronal magnetic field intensity may correspond to.To try to further reveal the relationship between coronal green line brightness and magnetic field intensity,we use the 2 D coronal images observed by Yunnan Observatories Greenline Imaging System(YOGIS) of the 10 cm Lijiang coronagraph and the coronal magnetic field maps calculated from the current-free extrapolations with the photospheric magnetograms taken by Helioseismic and Magnetic Imager(HMI) on board the Solar Dynamics Observatory(SDO) spacecraft.In our analysis,we identified the coronal loop structures and construct two-dimensional maps of the corresponding magnetic field intensity in the plane of the sky(POS) above the limb.We derive the correlation coefficients between the coronal brightness and the magnetic field intensity for different heights of coronal layers.We further use a linear combination of a Gaussian and a quadratic profile to fit the correlation coefficients distribution,finding a largest correlation coefficient of 0.82 near 1.1 R(solar radii) where is almost the top of the closed loop system.For the small closed loop system identified,the correlation coefficient distributions crossing and covering the loop are calculated.We also investigate the correlation with extended heliocentric latitude zones and long period of one whole Carrington Rotation,finding again that the maximum correlation coefficient occurs at the same height.It is the first time for us to find that the correlation coefficients are high(all are larger than 0.8) at the loop-tops and showing poor correlation coefficients with some fluctuations near the feet of the coronal loops.Our findings indicate that,for the heating of the low-latitude closed loops,both DC(dissipation of currents) and AC(dissipation of Alfvén and magnetosonic waves) mechanisms should act simultaneously on the whole closed loop system while the DC mechanisms dominate in the loop-top regions.Therefore,in the distributions of the correlation coefficients with different heights of coronal layers,for both large-and small-scale latitude ranges,the coefficients can reach their maximum values at the same coronal height of 1.1 R,which may indicate the particular importance of the height of closed loops for studying the coupling of the local emission mechanism and the coronal magnetic fields,which maybe helpful for studying the origin of the low-speed solar wind.

Coronal Flux Rope Equilibria in Closed Magnetic Fields

Using a 2.5-dimensional ideal MHD model in Cartesian coordinates, weinvestigate the equilibrium properties of coronal magnetic flux ropes in background magnetic fieldsthat are completely closed. The background fields are produced by a dipole, a quadrupole, and anoctapole, respectively, located below the photosphere at the same depth. A magnetic flux rope isthen launched from below the photosphere, and its magnetic properties, i.e., the annular magneticflux Φ_p and the axial magnetic flux Φ_z, are controlled by a single emergence parameter. Thewhole system eventually evolves into equilibrium, and the resultant flux rope is characterized bythree geometrical parameters: the height of the rope axis, the half-width of the rope, and thelength of the vertical current sheet below the rope. It is found that the geometrical parametersincrease monotonically and continuously with increasing Φ_p and Φ_z: no catastrophe occurs.Moreover, there exists a steep segment in the profiles of the geometrical parameters versus eitherΦ_p or Φ_z, and the faster the background field decays with height, the larger both the gradientand the growth amplitude within the steep segment will be.

Diagnostic Functions of Solar Coronal Magnetic Fields from Radio Observations

In solar physics,it is a big challenge to measure the magnetic fields directly from observations in the upper solar atmosphere,including the chromosphere and corona.Radio observations are regarded as the most feasible approach to diagnose the magnetic field in solar chromosphere and corona.However,because of the complexity and diversity of the emission mechanisms,the previous studies have only presented the implicit diagnostic functions of the magnetic field for specific mechanism from solar radio observations.This work collected and sorted out all methods for diagnosing coronal magnetic field from solar radio observations,which are expressed as a set of explicit diagnostic functions.In particular,this work supplemented some important diagnostic methods missed in other reviews.This set of diagnostic functions can completely cover all regions of the solar chromosphere and corona,including the quiet region,active region and flaring source regions.At the same time,it also includes incoherent radiation such as bremsstrahlung emission of thermal plasma above the quiet region,cyclotron and gyro-synchrotron emissions of magnetized hot plasma and mildly relativistic nonthermal electrons above the active regions,as well as coherently plasma emission around flaring source regions.Using this set of diagnostic functions and the related broadband spectral solar radio imaging observations,we can derive the magnetic fields of almost all regions in the solar atmosphere,which may help us to make full use of the spectral imaging observations of the new generation solar radio telescopes(such as MUSER,EVOSA and the future FASR,etc.) to study the solar activities,and provide a reliable basis for the prediction of disastrous space weather events.

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be so small (β = 10-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magnetic energy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magnetic energy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of the corresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as to whether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope. This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed to be detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.

Structure and evolution of magnetic fields associated with solar eruptions

This paper reviews the studies of solar photospheric magnetic field evo- lution in active regions and its relationship to solar flares. It is divided into two top- ics, the magnetic structure and evolution leading to solar eruptions and rapid changes in the photospheric magnetic field associated with eruptions. For the first topic, we describe the magnetic complexity, new flux emergence, flux cancelation, shear mo- tions, sunspot rotation and magnetic helicity injection, which may all contribute to the storage and buildup of energy that trigger solar eruptions. For the second topic, we concentrate on the observations of rapid and irreversible changes of the photospheric magnetic field associated with flares, and the implication on the restructuring of the three-dimensional magnetic field. In particular, we emphasize the recent advances in observations of the photospheric magnetic field, as state-of-the-art observing facilities （such as Hinode and Solar Dynamics Observatory） have become available. The link- ages between observations, theories and future prospectives in this research area are also discussed.

Effects of Magnetic Fields on Neutrino-dominated Accretion Model for Gamma-ray Bursts

Many models of gamma-ray bursts suggest a common central engine; a black hole of several solar masses accreting matter from a disk at an accretion rate from 0.01 to 10 M⊙s^-1, the inner region of the disk is cooled by neutrino emission and large amounts of its binding energy are liberated, which could trigger the fireball. We improve the neutrino- dominated accreting flows by including the effects of magnetic fields. We find that more than half of the liberated energy can be extracted directly by the large-scale magnetic fields in the disk, and it turns out that the temperature of the disk is a bit lower than the neutrino-dominated accreting flows without magnetic field. Therefore, the outflows are magnetically-dominated rather than neutrino dominated. In our model, the neutrino mechanism can fuel some GRBs （not the brightest ones）, but cannot fuel X-ray flares. The magnetic processes （both BZ and electromagnetic luminosity from a disk） are viable mechanisms for most of GRBs and their following X-ray flares.

Long-term evolution of magnetic fields in flaring Active Region NOAA 12673

During the lifetime of AR 12673,its magnetic field evolved drastically and produced numerous large flares.In this study,using full maps of the Sun observed by the Solar Dynamics Observatory and the Solar Terrestrial Relations Observatory,we identified that AR 12673 emerged in decayed AR 12665,which had survived for two solar rotations.Although both ARs emerged at the same location,they possessed different characteristics and different flare productivities.Therefore,it is important to study the long-term magnetic evolution of both ARs to identify the distinguishing characteristics of an AR that can produce large solar flares.We used the Space-weather Helioseismic and Magnetic Imager Active Region Patch data to investigate the evolution of the photospheric magnetic field and other physical properties of the recurring ARs during five Carrington rotations.All these investigated parameters dynamically evolved through a series of solar rotations.We compared the long-term evolution of AR 12665 and AR 12673 to understand the differences in their flare-producing properties.We also studied the relation of the long-term evolution of these ARs with the presence of active longitude.We found that the magnetic flux and complexity of AR12673 developed much faster than those of AR 12665.Our results confirmed that a strong emerging flux that emerged in the pre-existing AR near the active longitude created a very strong and complex AR that produced large flares.

Systematic investigation of mid-term periodicity of the solar full-disk magnetic fields

The Magnetic Plage Strength Index(MPSI) and the Mount Wilson Sunspot Index(MWSI), which have been measured at Mount Wilson Observatory(MWO) since the 1970 s and which indicate weak and strong magnetic field activity on the solar full disk, respectively, are used to systematically investigate midterm periodicities in the solar full-disk magnetic fields. Multitudinous mid-term periodicities are detected in MPSI and MWSI on timescales of 0.3 to 4.5 yr, and these periodicities are found to fluctuate around several typical periodicities within a small amplitude in different solar cycles or phases. The periodicity of 3.44 yr is found in MPSI, and the periodicities of 3.85 and 3.00 yr are detected in MWSI. Our analysis indicates that they reflect the true oscillating signals of solar magnetic field activity. The typical periodicities are 2.8,2.3 and 1.8 yr in MPSI and MWSI, and possible mechanisms for these periodicities are discussed. A 1.3 yr periodicity is only detected in MPSI, and should be related to meridional flows on the solar surface. The typical annual periodicity of MPSI and MWSI is 1.07 yr, which is not derived from the annual variation of Earth’s heliolatitude. Several periodicities shorter than 1 yr found in MPSI and MWSI are considered to be Rieger-type periodicities.

Some issues in diagnostics of solar chromospheric magnetic fields with the Mg b_2 line

Up to now, exact measurements of chromospheric magnetic fields have not been as successful as those done in the photosphere. We are currently engaging in diagnostics of chromospheric magnetic fields with the Mg b2 line by employing the Multi-Channel Solar Telescope at Huairou Solar Observing Station. Therefore, how to improve accuracy in the measurement is the main issue of our present study. To this end, we first study linear calibration coefficients for longitudinal and transverse components of chromospheric fields, which vary with wavelength, in the case of a weak field assumption. Then the polarization crosstalk introduced by instruments is analyzed in detail with two numerical simulation methods. Comparisons of the po- larization signals between cases with and without correction are presented. The result indicates that polarization accuracy is greatly improved after crosstalk correction.