Nina Tureson

Marc Marteau

Thierry Cabioch

Ngo Van Nong

Jens Jensen

Jun Lu

Grzegorz Greczynski

Daniele Fournier

Niraj Singh

Ajay Soni

Laurent Belliard

Arnaud Le Febvrier
email: arnaud.le.febvrier@liu.se

Effect of ion-implantation-induced defects and Mg dopants on thermoelectric properties of ScN

For applications in energy harvesting, environmentally friendly cooling, and as power sources in remote or portable applications, it is desired to enhance the efficiency of thermoelectric materials. One strategy consists of reducing the thermal conductivity while increasing or retaining the thermoelectric power factor. An approach to achieve this is doping to enhance the Seebeck coefficient and electrical conductivity, while simultaneously introducing defects in the materials to increase phonon scattering. Here, we use Mg ion implantation to induce defects in epitaxial ScN (111) films. The films were implanted with Mg + ions with different concentration profiles along the thickness of the film, incorporating 0.35 to 2.2 at.% of Mg in ScN. Implantation at high temperature (600 ˚C), with few defects due to the temperature, does not substantially affect the thermal conductivity compared to a reference ScN. Samples implanted at room temperature, in contrast, exhibited a reduction of the thermal conductivity by a factor of three. The sample doped with 2.2 at.% Mg also showed an increased power factor after implantation. This study thus shows the effect of ioninduced defects on thermal conductivity of ScN films. High-temperature implantation allows the defects to be annealed out during implantation, while the defects are retained for roomtemperature implanted samples, allowing for a drastic reduction in thermal conductivity.

Introduction

Thermoelectric materials and devices are applied for energy harvesting, converting waste heat (temperature gradients) into useful electricity, as power sources in remote or portable applications using Seebeck effect, and for environmentally friendly cooling using the Peltier effect [1]. The efficiency of a thermoelectric material is connected to the dimensionless thermoelectric figure of merit (ZT=S 2 σT/κ), which consists of the Seebeck coefficient (S), the electrical conductivity (σ), the thermal conductivity (κ), and the absolute temperature (T). To enhance the figure of merit of a material, and thus the efficiency, strategic optimizations are required since all parameters (S,  and ) are highly interrelated [2,3].

Different approaches are used for improving ZT, including strategies to increase the power factor and reducing the thermal conductivity. Maximizing the power factor includes the search of new materials or optimization of existing ones using approaches such as doping, alloying and/or nanoscale effects (e.g., quantum confinement) [4]. Minimizing the thermal conductivity can be achieved by alloying, forming composites, use of naturally poor thermal conductors such as some layered materials, with soft phonon modes, and nanostructuring of the materials [2,3,[5][6][7][8][9][10]. For nanoscale materials, quantum size effects can affect the density of state at the Fermi level (E F ) and thus increase the power factor [5,11]. From bulk (3D) to thin film (2D), the thermal conductivity can be reduced by boundary scattering without reducing the electrical conductivity or power factor. With thin films, similar approaches are used as for bulk materials, and further approaches include superlattices and multilayers [12][13][14][15].

In the present study, we investigate an approach to enhance the power factor of thin films by doping in combination with reduction of the thermal conductivity by the creation of defects (point defects and nanoscale line defects). For doping, we use ion implantation instead of directly introducing the dopants while depositing the material. Ion implantation is a commonly used technique for doping of silicon in the semiconductor industry and is suitable for doping thin films or the surface of bulk materials. It is a method known for precise dose control and good reproducibility as well as full range possible implanted elements. Depending on the energy and mass of the implanted ions, different degrees of damage will be induced in the implanted material. Typical collision cascade effects will so create point defects (vacancies, interstitials, vacancy-interstitial pairs, and antisites) and possibly extended defects (dislocations, vacancy clusters, …) which can progressively evolve or disappear during annealing. These evolutions are strongly materials dependent [16]. In contrast to semiconductor industry, these defects and imperfections can be an advantage for thermoelectric materials and increase phonon scattering, leading to a reduced thermal conductivity.

As a possible model system to demonstrate this general idea of reducing the thermal conductivity as well as doping by ion implantation, we choose ScN. Several of the semiconducting transition metal nitrides, in particular ScN-and CrN-based materials have recently emerged as promising thermoelectric materials [13,[17][18][19][20][21][22]. ScN has favorable properties such as high carrier mobility (10-180 cm 2 V -1 s -1 ), carrier concentration in the range 10 18 -10 22 cm -3 [23], low electrical resistivity (~300 µΩ cm) [19] and a narrow indirect band gap of around 0.9 eV [23,24]. In comparison with established thermoelectric materials like PbTe and Bi 2 Te 3 [2], the power factor of ScN (2.5-3.3 W m -1 K -2 ) [19,25] is in the same order of magnitude [19,[25][26][27][28][29]. However, the thermal conductivity is relatively high (10-12 W m -1 K -1 ) [25,30] and needs to be minimized for thermoelectric application. Previous studies have shown different approaches for reducing the thermal conductivity of ScN [27,[30][31][32]. For example, the thermal conductivity of ScN was reduced by a factor of five using Nb alloying, but the power factor was degraded, leading to an overall thermoelectric figure of merit similar to that of ScN [27].

The nature of dopants used in the ScN system has to be chosen wisely. More than creating defects in the ScN matrix, the dopant may play an important role on the electronic and/or optical properties of ScN. Kerdsongpanya et al. theoretically demonstrated the influence of introduction of impurities in ScN on either N or Sc sites on the density of states around E F [33]. The desired effect for maximizing the Seebeck coefficient of thermoelectric materials is to have a steep slope of the transport distribution function close to E F . This can be achieved with the presence of impurities or vacancies in the ScN matrix which creates a peak close to E F [2,34]. Kerdsongpanya et. al. proposed magnesium doping in ScN to achieve a peak shift towards E F [33]. According to first-principles calculations a few percent of Mg doping is enough to induce these effects [33]. Mg contents above 3 at.% shift E F into the valence band, rendering the material p type, as experimentally demonstrated by Saha et al. [28,35]. Furthermore, contaminants such as oxygen and fluorine can act as donors in ScN, also leading to a shift of E F [25,33].

In the present work, epitaxial ScN thin films were grown using DC reactive magnetron sputtering and then implanted with Mg + ions. Different implantation conditions were tested in order to analyze the influence on the thermoelectric properties of the concentration of dopants but also of the defects created by implantation. A series of samples implanted at room temperature with different doses from 0 to 2.2 at.%, was used for a complete study with the evolution of the thermoelectric properties with the concentration of dopants implanted with defects. The samples implanted at room temperature with an average concentration of 2.2 at.% of Mg exhibited a large decrease in thermal conductivity by 70 % and an increased absolute value of the Seebeck coefficient by 60 %. One of the samples was implanted at high temperature with 2.2 at.% Mg in order to isolate the effect of magnesium doping since a large fraction of the implantation-induced defects might be annealed during the implantation process at high temperature. The same implantation (2.2 at. % Mg) performed at room temperature on a ScN film was used for comparison and for evaluating the effect of irradiation-induced defects on the thermoelectric properties.

Experimental details

ScN thin films were deposited using DC reactive magnetron sputtering in an ultra-high vacuum chamber (base pressure 10 -6 Pa) with Sc (50-mm diameter, MaTek: Sc 99.5%). The sputtering targets were operated with 125 W under a pressure of 0.27 Pa (2 mTorr) in an Ar/N 2 (flow ratio 75 % Ar / 25 % N 2 ) sputtering-gas mixture. 10 mm x 10 mm one side-polished substrates of Al 2 O 3 (c-cut) (Alineason Materials & Technology) were used.

The sapphire substrates were kept at a temperature of 800 ˚C and under constant rotation during the deposition. Prior to deposition, the substrates were cleaned first for 10 min in acetone in an ultrasonic bath, then in ethanol, and blown dry with a N 2 -gun. One sample was selected as a reference (labelled REF), the other six samples were implanted with Mg + ions.

The SRIM 2013 software [START_REF] Ziegler | SRIM Software ver[END_REF] was used to simulate and determinate the appropriate ion energies and respective doses needed to obtain the desired Mg concentration in the ScN film (density of 4.26 g/cm 3 (calculated from the ICDD data 032-0656286)). Two different profiles for the Mg concentration were applied: one flat by using five different energies for Mg + ions and one with a Gaussian-like profile along the thickness of the film by using only one energy for implanted ions. The implanted dose of Mg was adjusted for each energy by controlling the duration of the implantation while maintaining a current beam density not exceeding 5 A cm -2 to avoid a temperature increase of the ScN films during the implantation process. Table 1 summarizes the conditions of implantation for the different samples. The first series of samples were implanted at room temperature with different average concentrations of Mg (Mg/(Sc+N+Mg)) from 0.35 at.% to a maximum of 2.2 at.% (labelled RT as Room Temperature). Another film was also implanted to obtain 2.2 at.% of Mg at a temperature of 600 ˚C (labeled HT as High Temperature). Finally, a sample was implanted at room temperature but using only one energy of 150 keV for implanted Mg + (labelled SE as Single-Energy) with a total dose selected to obtain an average of 2.2 at.% of Mg in ScN, but with a Gaussian-like profile. For every implantation, the samples were tilted with an angle of 2-5˚ to prevent channeling of the implanted Mg ions into the epitaxial ScN thin films.

Table 1. List of the samples with their labels and different conditions of Mg implantation. The thickness of each film is also listed. The average concentration of magnesium is the one deduced from depth XPS profile measurement performed on the sample 2.2RT and extrapolated to the other samples according the ToF SIMS measurement. (HT = High Temperature, SE = Single-Energy, RT = Room Temperature.) X-ray diffraction (XRD) measurements were performed with an X'Pert PRO from PANalytical apparatus for -2θ scans using a Cu K α radiation with a nickel filter. Philips Compositional depth profiles were obtained by recording core level spectra after each sputtering step consisting of 3 minutes-long bombardment with 4 keV Ar+ ions followed by 10 min. irradiation at the reduced energy of 0.5 keV to minimize the surface damage and avoid forward implantation of surface species [START_REF] Greczynski | [END_REF]. The Ar+ ion beam was incident at the 20° angle from the surface and rastered over the area of 3×3 mm 2 . All spectra were collected from the area of 0.3×0. gold/substrate and on a gold/film/substrate sample. Finally, the amplitude and phase experimental data were fitted according to a standard Fourier diffusion law to extract the thermal conductivity of the ScN films [38][39][40][41]. A full explanation of the thermal conductivity measurement, fitting and model used is reported in the Supplemental Material.

The in-plane Seebeck coefficient and the electrical resistivity were measured simultaneously from room temperature to 500C under a low-pressure helium atmosphere (∼ 9×10 4 Pa, purity 99.999% with <0.5 ppm residual oxygen) using ULVAC-RIKO ZEM3 with a special design for thin films. The substrate contribution to the Seebeck coefficient and electrical resistivity is negligible, and the instrumental error is within 7%. The roomtemperature Hall effect measurements up to 5 T magnetic field were performed employing physical property measurement system (PPMS Dynacool). A depth-profile composition analysis of the sample 2.2 RT by x-ray photoelectron spectroscopy gave an average concentration (Mg/(Mg+Sc+N)) around 2.2 at.% at a plateau (50-300 nm depth) plus a presence of oxygen at 9 at.% (see Supplemental Material, figure S6). Even with a base pressure of 610 -8 torr, oxygen incorporation at several at.% level in ScN occurs due to the high reactivity of Sc with oxygen from residual water during deposition [18,32,33,[43][44][45][46][47]. Gregoire et. al. demonstrated an occupancy of oxygen on the nitrogen site possible from 2 at.% to 6 at.% which correspond at a maximum to Sc 0.94  0.06 N 0.94 O 0.06 [32]. A higher presence of oxygen in the film leads to the accumulation of oxygen at the grain boundaries and defects [18]. In the present study, the most probable case is an incorporation of oxygen at few at.% level in the Sc 1-x Mg x N 1-y O y (0 < y < 0.06) and Sc 2 O 3 at the grain boundaries/defects at a few percent ( 2 mol.%) (More details can be found in the Supplemental Material, figure S7). This sample with an average of 2.2 at.% of Mg was used as reference in order to calculate the percentage of magnesium in each film from the Mg + signal intensity detected by TOF-SIMS. It is important to note that the oxygen content does not affect the purpose of the present work, as these oxygen contaminations only marginally affect the thermal conductivity [48]. However, oxygen doping acts as donor doping and leads to a shift E F towards the conduction band [25,33]. Thus, we do not obtain ptype Mg-doped ScN, as in the work of Saha et al. [28,35].

From the SRIM simulations, a depth profile of the implanted Mg ions in ScN thin films can be calculated (Figures 3a and4b). Figure 3a shows how several implantation energies have been used to obtain an approximately constant concentration of magnesium in the ScN film. Figure 3b gives the Mg profile from only one implantation energy (150 keV), with a total dose of Mg equivalent as for the 2.2 RT sample. A maximum of around 3 at.% was expected at 200 nm from the surface of the sample (figure 3b). The Mg profiles measured with TOF-SIMS are presented in Figure 3c and 3d. Since the thin films have slightly different thicknesses, the film depths were normalized according to film/substrate interface in order to facilitate comparison. The intensities were also normalized to the substrate signal (Al + ). The ScN reference sample had no detectable Mg + signal. The Mg + signal measured on the flat-profile-implanted samples is slightly lower at the surface of the film, but then almost flat until it drops close to the substrate interface. The intensity of the Mg + signal is consistent with a higher concentration of magnesium in the film. We note that the sample implanted at high temperature (2.2 HT) and at room temperature (2.2 RT) have the same elemental depth profile features (profile and intensity). A variation of the concentration of Mg is observed along the thickness with a maximum observed at half of the thickness (200 nm) and, almost symmetrically, a decrease of Mg concentration up to the surface and the film/substrate interface. The profiles throughout the film appear relatively similar for all samples and match the profiles from the SRIM simulations. The small increase of the Mg + signal appearing at the interface between film and substrate is due to different Mg + yield in ScN and Al 2 O 3 .

Figure 4 shows HAADF-HRSTEM images of the ScN reference sample, the 2.2

RT sample and 2.2 HT sample where two columnar grains and the grain boundary between them can be observed for both samples. Local Fast Fourier Transforms (FFT) were performed on the different zones marked in the corresponding micrograph. Very similar comments can be addressed for the reference sample (before implantation) (figure 4a) and the hightemperature-implanted sample (2.2 HT) (figure 4c). They both present a high level of ordering and homogeneity inside the grains with sharp spots on local FFT. In other words, these observations did not allow for identification of defects inside the grains which could have formed during the growth process or during the Mg implantation at 600°C. In the case of the room-temperature-implanted sample, the high degree of ordering of the atoms is visible in some parts of the columnar grains and this is confirmed by the sharp spots on the local FFT (see areas #1 and #2 on figure 4b). Blurry and likely defect-rich areas, with a typical size of ten nanometers, are distinguishable as well as a broadening of the spot on their local FFT (area #3). The HRSTEM analysis illustrates the difference between the room-temperature implantation and high-temperature implantation of ScN. By implanting the magnesium at 600C, the thermal energy during implantation appears to be sufficient to anneal out most of the defects induced by implantation. In contrast, at room temperature, the defects and local misalignment of atoms exists within the grains.

Figure 5a Figure 6 shows the thermal conductivity of the Mg-implanted ScN films. The value of the thermal conductivity of the ScN reference sample is similar to earlier reported values for ScN thin films (10-12 W m -1 K -1 ) [25,27,30,48]. The sample implanted at high temperature exhibits a thermal conductivity similar to the value of the reference sample ScN.

With a temperature high enough to anneal out the defects, the difference is within the error bars and can thus be considered negligible in this case. The smaller or negligible effect of Mg dopants on thermal conductivity compare to the one observed in previous study with Nb doping can be explain by a lower difference of atomic mass between Sc (44.95 u) and Mg (24.31 u) than Sc and Nb (92.20 u) [27].

For room-temperature implantation, a trend of decreasing thermal conductivity for higher amount of implanted Mg is clear. A large drop between the ScN reference (10.5 W m -1 K -1 ) and the sample implanted with 0.37 at.% of Mg (4.2 W m -1 K -1 ) can be seen. The other implanted samples at room temperature and using multi-energy implantation have similarly low values of the thermal conductivity as the 0.37 RT sample. A minimum is observed for 0.75 at.% of Mg in ScN with a thermal conductivity of 3.2 Wm -1 K -1 . The sample implanted using a single beam-energy also has a similar thermal conductivity, comparable to the lowest observed with a flat Mg concentration-profile.

This large decrease in thermal conductivity (2.5 times lower) for ScN when implanting a small amount of Mg may be explained by the increased level of phonon scattering due to the presence of defects induced by ion implantation. The single-energy implanted sample did not show a substantially different thermal conductivity in comparison to the multi-energy implanted samples. Thus, the Mg concentration-profile along the thickness of the film does not substantially affect the thermal conductivity of the film. In summary, these results indicate that room temperature Mg implantation is preferred if a lower thermal conductivity is desired, to avoid annealing out the defects and retaining the corresponding phonon scattering.

The results of simultaneous measurements of the Seebeck coefficient and the electrical resistivity together with their corresponding power factor are shown in figure 7. Fig. The ScN reference film is also plotted showing the lowest absolute value of the Seebeck coefficient (-41 µV/K at 775 K). The film implanted at high temperature (5% HT), considered here as "defect-free", e hi ited an a solute value of the See ec coefficient slightly higher than the ScN reference sample mentioned above (-56 µV/K at 775 K). The trend of increasing the Seebeck coefficient predicted from DFT calculations [33] exhibited a temperature dependence of the electrical resistivity ((T)) similar to the ScN reference, ut with higher values (~750 µΩ cm). Similar to the Seebeck coefficient, no differences are observed between the multi-energy and the single-energy implanted films. For all the samples implanted at room temperature, a trend of starting with almost constant resistivity values can be observed, but then a decrease after around 450 K. This change of resistivity may be due to recombination of some point defects (such as Frenkel defects). These point defects can recombine at low temperature (a few hundreds of kelvin) and can lead to the creation of extended defects in the materials (line defects such as dislocations or twins). The removal of defects after implantation differs between materials. In the case of silicon, the most studied material for ion implantation, a complete removal of the extended defects can be achieved only at high temperature such as 1100-1300 K [START_REF] Rimini | Ion Implantation: Basics to Device Fabrication[END_REF]. In our case, one can propose that the measurement temperature is insufficient too to anneal the extended defects present before the measurement and/or created by point-defect recombination during the measurements. The temperature dependent resistivity from 70K to room temperature is presented in supplemental material (figure S8) where differences between the reference sample and the 2.2 RT can be observed due to the mobility of charge carrier which is affected by the defects induced during implantation. The resistivity values differ slightly with the concentration of Mg. In the temperature range of measurement, the sample with 0.75 at.% of Mg exhibited the highest values of electrical resistivity and the 2.2 at.% implanted at room temperature the lowest. The increase of the electrical resistivity can be due to a small contribution of Mg insertion into ScN film observed on 2.2 HT sample and an important contribution from the defects created by ion bombardment [START_REF] Ziman | Electrons and phonons : the theory of transport phenomena in solids[END_REF].

The combination of the Seebeck coefficient and the electrical conductivity for ScN reference sample gives the power factor ~ 0.5510 -3 W m -1 K 2 at 775 K. The sample implanted at high temperature exhibited a lower power factor than the ScN reference sample as well as the samples implanted with a low amount of magnesium (0.35 to 1.1 at.%). The samples with 2.2 at.% implanted using a single-energy and multi-energies exhibited the highest power factor 0.6410 -3 W m -1 K 2 (at 775 K).

The lower (absolute) value of the Seebeck coefficient for ScN compared to earlier reported ScN films, is most likely due to the higher amount of oxygen contamination present in the film, especially the presence of oxide at grain boundaries and/or defects [18,19,32,47]. A presence of oxide at grain boundaries/defects affected the thermoelectric properties with a reduced Seebeck and electrical conductivity resulting to a low power factor [18,27].

Saha et al reported on the electrical, carrier concentration and Seebeck coefficient of Sc 1-x Mg x N films grown by dc-magnetron co-sputtering [28,35]. They reported an increase of electrical resistivity, a decrease of the mobility and room temperature Seebeck values between -50 to -100V/K when doping with Mg. They also reported a switch from n-type to p-type behavior for film with x > 0.028. In the present study, the film contained a higher amount of oxygen and, within the doping range of the study, only n-type behavior was observed. As previously mentioned, the doping by magnesium in ScN shifts E F towards the valence band, but oxygen doping ScN leads to a shift towards the conduction band [25,33].

The higher oxygen contamination in the present work than in the work of Saha et al. thus explains why the n-type behavior is retained also for higher concentration of magnesium in ScN.

Mg doping in ScN with low amount of defects, achieved by high temperature ion implantation, yielded a similar thermal conductivity as the ScN reference and lower power factor due to a higher electrical resistivity. However, implantation of magnesium at room temperature with a constant or Gaussian-like distribution of Mg along the thickness led to samples exhibiting different physical properties. Implantation at room temperature will create point defects and extended defects which play an important role on the conduction of phonons and charge carriers (electrons or holes). Three features can be emphasized here after implantation of Mg: a decrease of the thermal conductivity, an increase of the absolute value of Seebeck coefficient, an increase of the resistivity and a different (T).

Conclusions

Ion implantation was used to implant Mg in order to induce doping and defects in epitaxial ScN (111) films grown on sapphire substrates using reactive DC magnetron sputtering. Mg + ions were implanted with different concentration profiles along the thickness of the film. The ion implantations of 0.3 to 2.2 at.% of Mg in ScN did not affect the rock-salt ScN crystal structure nor morphology of the films. A high temperature of implantation tends to anneal the defects, while doping did not alter the thermal conductivity in comparison to a ScN reference ( 10 W m -1 K -1 ). In contrast, the room-temperature-implanted samples exhibited large reduction in thermal conductivity to values close to 3.2 W m -1 K -1 and an increase of the power factor is also observed for the sample with 2.2 at. % Mg compared to the ScN reference samples. Thus, this study showed the importance of ion-induced defects in the material on the thermal conductivity, in that high temperature implantation allows the defects to be annealed out during implantation, while the defects are retained for roomtemperature implanted samples, allowing for a drastic reduction in thermal conductivity.

X

  'Pert-MRD with Cu K α radiation was used for the rocking curves and φ-scans. Surface and cross sections of the films were e amined y scanning electron microscopy (S M, O emini 550, eiss). igh Resolution Scanning ransmission lectron Microscopy ( RS M) images were ac uired with the in ping double C s -corrected FEI Titan 3 60-300 operated at 300 kV using the High Angle Annular Dark Field (HAADF) detector. Time-of-flight Secondary Ion Mass Spectrometry (TOF-SIMS) using a TOF-SIMS V instrument (ION-TOF GmbH, Germany) was used for measuring the Mg distribution in the implanted films. Dual-beam depth profiling, by alternately applying an analysis beam and a sputter beam (non-interlace), was done in positive mode. This allows selected positive secondary ion species to be monitored as a function of sputter time. A low-energy electron flood gun was applied for charge-compensation during profiling. A quasi-continuous 2.0 keV O 2 + beam with a current of 670 nA and scanned over 350 x 350 m 2 , was used as sputter beam. A pulsed 30 keV Bi + beam, cycle time 40 s, was used as analysis beam, with a target current of 3.8 pA and an analysis field of view of 80 x 80 m 2 at the centre of the sputter craters. Ion mass spectra were acquired, with an extraction voltage of 2000 V between the sputter sequences, in the so-called spectroscopy mode (bunched 6.5 ns Bi + ion beam pulse width). SurfaceLab 6 software (v. 6.5, ION-TOF GmbH) was used for spectra recording and data processing. XPS was performed with an Axis Ultra DLD instrument from Kratos Analytical (UK). The system base pressure during spectra acquisition was 1.1×10 -9 Torr (1.5×10 -7 Pa). A monochromatic Al Kα radiation (h = 1486.6 eV) from the source powered to 150 W was used.

  7 mm 2 and at normal emission angle. The analyzer pass energy was set to 20 eV which results in the full width at half maximum of 0.55 eV for the Ag 3d 5/2 peak. Elemental compositions were determined based on Sc 2p, N 1s, O 1s, and Mg 2s peak areas using Casa XPS software (version 2.3.16), and elemental sensitivity factors supplied by Kratos Analytical Ltd.Thermal conductivity of the films was obtained at room temperature using modulated thermoreflectance microscopy (MTRM). In this setup, a pump beam at 532 nm delivered by a Cobolt MLD laser, intensity modulated by an acousto-optical modulator at a frequency f, is focused on the surface of the sample with an objective lens (N.A. = 0.5). Then, thermal waves were excited in the sample and monitored by the reflectivity surface change recorded around the pump location by another focused laser beam. The specification of the setup is the spatial measurement around the pump beam. We use a 488 nm Oxxius laser to maximize the probe sensitivity to the thermal field on a gold surface. A photodiode and a lock-in amplifier record the AC reflectivity component, in a frequency range between 1 kHz and 1 MHz. The measurement of the reflectivity of the probe on the surface is performed along a x axe from -10 m to + 10 m around the pump beam area. The figure S1 represents typical curve of the amplitude and the phase part of the reflectivity signal measured on a

3

  Results and discussionXRD -2 scans of as-deposited and Mg-implanted ScN thin films are presented in figure1a. The observation of only one diffraction peak from the film demonstrated strong (111) texture of the ScN thin films. The inset shows the ScN (111) peaks in magnified view around 34.34 . From here, it is evident that no peak shift is observed after the Mg implantation. The corresponding lattice parameter 4.52 Å is close to earlier reported values (4.50 Å, ICDD PDF 00-045-0978 (ScN)). Figure1bshows the evolution of the Full Width at Half Maximum (FWHM) of the Rocking curve performed on the 111 reflection of the film. FWHM Values vary between 2.4  and 1.9  showing that no degradation of the macroscopic view of the crystal quality of the film was noticeable by XRD. The inset shows ascan of ScN reference sample (=70.5, ScN (111)). The six peaks appear due to twin domain symmetry of ScN grown on sapphire substrates[19,27]. Thus, the films are composed of single phase epitaxial cubic ScN with an out-of-plane [111] orientation. Due to the low quantity of implantation and the small difference of the ionic radius between Sc 3+ (VI) and Mg 2+ (VI), it is not possible to discuss a potential substitution of Mg for Sc by these XRD results.In figure2, the optical image and the surface morphology from the SEM of the films are shown. No noticeable change of the morphology of the surface of the film has been observed by SEM after implantation of Mg ions The non-implanted ScN sample has a yellowish color characteristic of ScN material[42], but the Mg-implanted samples are brown/black. This drastic change of color indicates changes in the bandgap with insertion of states or doping[33].

  7 a-c presents the results from the 2.2 at.% Mg sample with three different conditions (room temperature RT, high temperature HT and single-energy SE) plus the as deposited ScN reference sample. In Fig. 7 d-f, the results from the samples with different Mg concentrations are presented. The Seebeck coefficient, the electrical resistivity, and the power factor at certain fixed temperatures as a function of Mg concentration and type of implantation are presented in figure S9 of Supplemental Material.

Figure 1 Figure 1 .

 11 Figure 1

Figure 2 Figure 2 .

 22 Figure 2

Figure 3 Figure 3 .

 33 Figure 3

Figure 4 Figure 4 .

 44 Figure 4

Figure 5 Figure 5 .

 55 Figure 5

Figure 6 Figure 6 .

 66 Figure 6

Figure 7 Figure 7 .

 77 Figure 7

Table 2 :

 2 is a closer comparison of the TOF-SIMS analysis of the 2.2 RT and 2.2 SE samples. Both samples had a similar substrate/film interface up to 100-150 nm thickness. At a distance between 150 nm and 300 nm, the 2.2 SE had a higher at.% of Mg (3 at.% locally) than the 2.2 RT . Close to the surface, the 2.2 SE had a lower at.% of Mg than 2.2 RT down to a negligible amount of Mg at the top surface of the film. Figure5brepresents The different characteristics of the sample after ion implantations: concentration of dopant and induced defects with their depth profile and average displacement per atom (dpa).

		Dopants		Defects
	Sample label	Average conc. of Mg (at.%)	Depth profile	Temperature of implantation	Point and/or extended defects	Average dpa along the film
	2.2 HT	2.2	"flat"	600 C	-	-
	2.2 SE	2.2	Gaussian-like peak	room temperature	yes	20
	2.2 RT	2.2				19
	1.1 RT 0.73 RT	1.1 0.75	"flat"	room temperature	yes	9.5 6.6
	0.39 RT	0.35				3.3
	REF	0	-	-	-	-

the evolution of total atom displacement (recoil expressed in displacement per atom, dpa) of Sc and N simulated by SRIM in a case of multi-energy and a single-energy implantation aiming for a total dose of 43 10 15 ions/cm 2 . The two simulated curves show a similar quantity and distribution of displacement per atom (~20-30 dpa) and thus defects induced by the implantation. In terms of composition, the 2.2 RT and 2.2 SE samples differed with different profiles of Mg along the thickness. Nevertheless, in terms of total displacement per atom and total induced defects, the 2.2 RT and 2.2 SE films were essentially identical with an average displacement per atom evaluated at 19 dpa for the sample 2.2 RT and 20 dpa for the 2.2 SE. The different results from TOF-SIMS, HRSTEM, and SRIM simulation are summarized in Table

2

.

  is corroborated by the results obtained from these experiments. Implantation at room temperature led to samples exhibiting higher absolute values of the Seebeck coefficient up to around -67 µV/K (775 K). The Mg concentration profile does not seem to affect the Seebeck coefficient with similar behavior with the temperature for the 2.2 SE. The evolution of the Seebeck coefficient values with the concentration of dopants is low with a maximum absolute values obtained for the sample with 0.75 at.% of Mg (-69 µV/K at 775 K). The results from the Seebeck coefficient measurements show at first an effect of the magnesium doping with an increase of the Seebeck values and secondly combining with the creation of defect (point and/or extended defects) another increase of the Seebeck coefficient values. The lowest electrical resistivity value is observed for the ScN reference sample (~250 µΩ cm). This sample exhibited almost a constant electrical resistivity values over the whole measured temperature range. The sample implanted at high temperature (2.2 HT)

Acknowledgments

The authors acknowledge the funding from the European Research Council under the uropean Community's Seventh Framewor Programme (FP7=2007-2013) ERC Grant Agreement No. 335383, the Swedish Foundation for Strategic Research (SSF) through the Future Research Leaders 5 program, the Swedish Research Council (VR) under Project No. 2016-03365, the Knut and Alice Wallenberg Foundation through the Wallenberg Academy Fellows program, and the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). AS would like to acknowledge DAE-BRNS (37(3)/14/02/2015/BRNS) and IIT Mandi for research facilities.


P Vemareddy

P Demóulin

STUDY OF THREE-DIMENSIONAL MAGNETIC STRUCTURE AND THE SUCCESSIVE ERUPTIVE NATURE OF ACTIVE REGION 12371

Keywords: Sun, reconnection-Sun, flares -Sun, coronal mass ejection -Sun, magnetic fields-Sun, sigmoid -Sun, evolution

We study the magnetic structure of successively erupting sigmoid in active region 12371 by modeling the quasi-static coronal field evolution with non-linear force-free field (NLFFF) equilibria. HMI/SDO vector magnetograms are used as input to the NLFFF model. In all eruption events, the modeled structure resembles the observed pre-eruptive coronal sigmoid and the NLFFF core-field is a combination of double inverse J-shaped and inverse-S field-lines with dips touching the photosphere. Such field-lines are formed by flux-cancellation reconnection of opposite-J field-lines at bald-patch locations. It implies the formation of a weakly twisted flux-rope from large scale sheared arcade field lines. Later on, this flux-rope undergo coronal tether-cutting reconnection until a CME is triggered. The modeled structure captured these major features of sigmoid-to-arcade-to-sigmoid transformation, that is being recurrent under continuous photospheric flux motions. Calculations of the field-line twist reveal a fractional increase followed by a decrease of the number of pixels having a range of twist. This traces the buildup process of a twisted core-field by slow photospheric motions and the relaxation after eruption, respectively. Our study infers that the large eruptivity of this AR is due to a steep decrease of the background coronal field meeting the torus instability criteria at low height (≈ 40 Mm) in contrast to non-eruptive ARs.

INTRODUCTION

It is now accepted that the source of energy for all solar activity is from magnetic fields. Active regions (ARs) are higher concentrations of magnetic field regions often associated with violent activity like jets, flares, coronal mass ejections (CMEs) etc. In X-rays and EUV observations, these regions are sometimes seen with a sigmoid structure (Rust & Kumar 1996;Gibson et al. 2002) situated over the central polarity inversion line (PIL). The sigmoid structure is either forward or inverse S-shaped. Several CMEs are seen to be launched from these sigmoidal ARs and hence sigmoid is one of the most important pre-cursor structure for solar eruptions (Manoharan et al. 1996;Hudson et al. 1998;Canfield et al. 1999Canfield et al. , 2007)). Two types of sigmoids were reported: transient and long lived sigmoids. Transient sigmoids are sharp and bright and they usually become clearly noticeable only for a short time before eruption, while long-lived ones appear more diffuse and can survive for several hours, even days (Pevtsov 2002;McKenzie & Canfield 2008).

The magnetic structure of sigmoids was described as sheared arcade and flux rope (FR) topology (Moore et al. 2001). In the sheared arcade model, the two magnetic elbows are sheared field lines which are located nearby on both sides of the PIL in the central part of the configuration. In the FR scenario, a magnetic FR is embedded in a stabilizing potential envelope field (Moore & Roumeliotis 1992;Hood & Priest 1979;Titov & Démoulin 1999). How these sigmoids turn to be eruptive? Magnetic reconnection (resistive instability) plays the prime role in the vemareddy@iiap.res.in sheared arcade model as opposed to ideal MHD instability in the FR model in triggering the eruption (Moore et al. 2001;Antiochos et al. 1999;Amari et al. 2003;Török & Kliem 2005;Gibson et al. 2006). The interface separating a coronal FR from its ambient field usually forms a sigmoidal shape when observed from above and FRs are naturally invoked in different models of sigmoids (Titov & Démoulin 1999;Gibson et al. 2006;Bobra et al. 2008;Savcheva & van Ballegooijen 2009). Sigmoids are considered to result from enhanced current dissipation in thin sheets which accumulate hot plasma along corresponding shaped field lines (Gibson et al. 2002;Janvier 2017) .

During the evolution of an AR, magnetic energy is built up (during several hours or even days) in the corona due to flux emergence and photospheric motions (Schrijver 2009). The energy is stored in a non-potential field associated to large scale electric currents (Priest & Forbes 2002;Aulanier et al. 2010).

Topological analysis of magnetic structures constructed from analytic configurations predicts that the current sheets form along magnetic interface layers called separatrices, as well along their generalization called quasi-separatrix layers [START_REF] Priest | Magnetic reconnection : MHD theory and applications Priest[END_REF][START_REF] Priest | Magnetic reconnection : MHD theory and applications Priest[END_REF]Aulanier et al. 2005). The connectivity of field lines is discontinuous for separatrices, while it changes drastically along QSLs (Demoulin et al. 1996). In an analytical force-free FR model embedded in an arcade field, Titov & Démoulin (1999) showed that in the process of the FR emerging rigidly into the corona, a separatrix surface, touching the photosphere at a so called bald-patch (BP, B • ∇B z | P IL > 0), is present along the PIL section during the earlier phase of emergence. The BP separatrix surface has a generic S-shape when viewed from top, similar to sigmoid shape. In the later phase of emergence, the S-shaped BP separatrix is transformed into a double J-shaped QSL. The topological analysis of the FR eruptions found co-spatial flare ribbons with hook-shaped QSLs (Démoulin et al. 1996;Williams et al. 2005;Janvier et al. 2014;Zhao et al. 2016), leading to extension of 2D version of standard model to 3D (Janvier et al. 2015).

In decaying ARs, the sigmoids were reported to be formed by flux cancellation induced by converging motions of magnetic elements towards PIL (Green & Kliem 2009;Tripathi et al. 2009;Vemareddy & Mishra 2015). Helical field lines are formed by reconnection of the sheared field lines (Pneuman 1983;van Ballegooijen & Martens 1989). Indeed, numerical simulations had shown the FR formation under cancelling magnetic flux scenario (e.g., Amari et al. 2003). On the other hand, numerical models producing FRs also relied on magnetic flux emergence of twisted FRs originating from the convection zone and rising through the photosphere (Magara 2001;Fan & Gibson 2004;Gibson et al. 2004;Archontis et al. 2009;Hood et al. 2012). In these models, as the FR emerges a filamentary current sheet forms, reconnection occurs and a new coronal FR is formed. When integrated along the local vertical, the current sheet appears as sigmoid.

Observationally studying the 3D magnetic structure of AR is presently not possible. Therefore, one relies on models based on field measurements at the photosphere as the lower boundary condition. A non-linear force-free field (NLFFF) model is typically used to reconstruct pre-eruptive coronal field (Valori et al. 2005;Savcheva & van Ballegooijen 2009;Wiegelmann 2008;De Rosa et al. 2009;Jiang & Feng 2012). This is justified by the low-β coronal condition. However, this is not realised at the photospheric level and a pre-processing procedure is applied to drive the lower boundary towards force-free condition (Wiegelmann et al. 2006). Moreover, the photospheric flow speed is very slow, typically well below 1 km s -1 (Vemareddy et al. 2012) , compared to the coronal field relaxing speed to equilibrium, which is several hundred km s -1 . Therefore, the coronal field evolution, driven by slow photospheric motion, can be approximated as a quasi-static evolution and it is modelled by time sequence of successive static force-free equilibria. It enables to study the build-up of pre-eruptive 3D structure like sigmoid, then to find hints on the most appropriate configurations leading to eruptions (e.g., Sun et al. 2012Sun et al. , 2013;;Savcheva et al. 2012a;Jiang et al. 2014;Vemareddy & Wiegelmann 2014;Vemareddy et al. 2016).

In present article, we construct 3D magnetic structure of sigmoidal AR by NLFFF model and study the preeruptive configuration of observed CMEs. For tis purpose, we employ vector magnetic field measurements at the photospheric level obtained from Helioseismic and Magnetic Imager (HMI; Schou et al. 2012) on board Solar Dynamic Observatory (SDO; Pesnell et al. 2012). We study below the AR 12371 which was producing successive fast CMEs during its disk transit. In EUV observations, the pre-eruptive configuration of all CMEs is a sigmoid. Being CME productive, we study how the sigmoid developed repeatedly and how it was brought eventually to instability. This case is in contrast with most previous studies of decaying ARs where only one single sigmoid eruption was present during the observation window (Démoulin et al. 2002;Green & Kliem 2009;Green et al. 2011;Vemareddy & Mishra 2015). Based on the time sequence of this static NLFFF extrapolations, we focus on studying 1) the sigmoid build up in the preeruptive configuration, 2) the build up of the coronal electric currents and their dissipation during eruption, 3) the magnetic energy, 4) the evolution of field line twist distribution and, 5) the role of the background field in driving the eruptions. We outline the observations during CME onset in Section 2. Results of the above studies are described in Section 3. Summary with a discussion of the results is given in Section 4.

OUTLINE OF OBSERVATIONS AND CONTEXT

OF THE STUDY AR 12371 is an AR formed before its appearance at the eastern limb. It produced successive fast CMEs in a span of its disk transit (18-25 June, 2015). Recent study of this AR by Vemareddy (2017) presented a detailed analysis of the magnetic evolution in relation with the initiating mechanism of the successive CMEs. Here we give a brief outline of earlier results in the context of this study. Observations at the Sun register the initiation times of four eruptions as 15:05 UT on 18 (SOL2015-06-18T15:05, CME1), 00:45 UT on 21 (SOL2015-06-21T00:45, CME2), 16:15 UT on 22 (SOL2015-06-22T16:15, CME3), and 07:30 UT on 25 (SOL2015-06-25T07:30, CME4) of June 2015, respectively, by the commencement of enhancing EUV brightening associated to fast structural changes. Subsequently, the disk integrated GOES X-ray light curve (Figure 1) delineates that the CMEs are associated with long duration M-class flares starting from 18/16:25 UT, 21T02:00 UT, 22T17:39 UT, 25T08:02 UT respectively.

These CMEs emerged the C2 fieldof-view at 18/17:24 UT, 21T02:36 UT, 22T18:36 UT, 25T08:00 UT, respectively. All four CMEs are fast (> 1000 km s -1 ) in LASCO field-of-view.

In Figure 2, we show simultaneous multi-wavelength observations, taken from different instruments, of the AR Fourth row: AIA 131 Å observations before eruptions. In particular they show the coronal loop sets as magnetic elbows and are traced with dashed curves L1 and L2 by inspecting time series of images. In these observations, the pre-cursor brightening related to slow tether-cutting reconnection is seen with L1. Fifth row: Composite images of coronal observations in AIA 94 Å (red), 335 Å (green), and 193 Å (blue) passbands. The loop set L3 (outlined with an orange curve) is understood as the dynamic reconnection product of L1 and L2. See Section 2 for more details.

during the onset phase of CMEs. Different wavelength snapshots at different times are selected to best show the observed structures. All image panels are aligned accounting spatial scales. In the first row, we plot line of sight magnetograms obtained from HMI. The AR successive passage reveals presence of leading negative flux (N1) with a following bipole with negative (N2, N3) and positive (P1, P2) flux regions. The inner bipole (N2, N3) is seen with large shear and converging motions (see Figure 6 of Vemareddy 2017) with respect to (P1, P2), forming sheared polarity inversion line (PIL) indicated with a blue curve. The field distribution of (N2, N3) be-comes diffused and disintegrated in successive days while the leader polarity is increasingly separated from the following polarity.

In the second row of Figure 2, we plot GONG-Hα images. They show the presence of a dark filament between leading and following sunspots before the eruptions. In tandem, 304 Å observations from the Atmospheric Imaging Assembly (AIA, Lemen et al. 2012) are well in support with H α , showing co-spatial existence of continuous filament channel. A filament is present on the PIL portion southward of the AR. It could only be related to the faint magnetic field observed southward of the AR and be irrelevant to the eruption, since no apparent change of the filament can be recognized after the commencement of EUV brightening from the time sequences associated to Figure 2. The 131 Å channel of AIA (fourth row panels) evidences sheared loop morphology comparable to those previously reported in other ARs (e.g. Moore et al. 2001). They consist of two opposite J-shaped loops outlined by L1 and L2 (dashed orange curves) identified from sequence of images. We call them magnetic elbows. The inner ends of these loops are nearby and crossed each other with a sharp interface low over the PIL. Finally, the composite images prepared from the hot AIA channels are shown in the bottom row of Figure 2. They provide the evidence for continuous sigmoidal structure (labeled L3) during the initiation of all four CMEs.

The configuration outlined by L1 and L2, especially in the three last events, is typically found in models having a sheared core (e.g. Antiochos et al. 1994;Aulanier et al. 2010). In the tether-cutting scenario, magnetic reconnection is initiated at the interface of L1 and L2 closest legs when converging motions push the legs against each other. The large-scale reconnected field lines have a shape comparable to L3. This reconnection progressively transforms sheared field lines, such as observed with L1 and L2, to twisted field lines, as outlined with L3. As reconnection proceeds further, the FR bulges and rises in height. In numerical simulations (Aulanier et al. 2010), once the FR is at a too large height, the configuration becomes unstable and the FR escapes the coronal closed field environment into the outer corona as a CME. The AIA composite images (fifth row panels in Figure 2) evidence this flux-rope (labelled as L3) during initiation of CMEs.

The study of magnetic field evolution (please refer to Figure 7 in Vemareddy ( 2017)) implies decreasing magnetic flux in both AR polarities, which is an indication of magnetic flux cancellation. Velocity field of flux motions derived from DAVE4VM (Schuck 2008) show the shear and converging motions, which are in support of above tether cutting reconnection, within the inner bipolar regions (Figure 3). These motions were suggested to be prime factors to the flux cancellation and the net flux decrease (Chae et al. 2002(Chae et al. , 2004)). Under this flux evolution, the net current and α av (mean twist parameter of magnetic field) show increasing trend till June 22. This is an indication of build up of non-potentiality (Martin 1998;Wang & Muglach 2007). Further, with these observational findings of magnetic evolution, Vemareddy (2017) described that the repeated sigmoid formation and its eruption by successive CMEs is a result of energy storage and release by persistent shearing and con-verging motions. With monotonous injection of negative helicity, the corona over-accumulates helicity and expels excess helicity by CME. Predominant influx of helicity of either sign over time is the key for the formation of coronal sigmoid or FR, which would be initiated to ejection by ideal or non-ideal instability (Moore et al. 2001;Török & Kliem 2005). Using vector magnetic field observations at the photosphere, in the present article, we study the different aspects in magnetic structure of the pre-eruptive sigmoid with NLFFF models.

RESULTS

Non-linear Force-free Modelling of the AR Field

The AR magnetic structure is reconstructed by performing nonlinear force-free field (NLFFF) extrapolation of the observed photospheric vector magnetic field (Bobra et al. 2014;Hoeksema et al. 2014). The procedure minimizes a volume integral including a linear combination of the Lorentz force and of the magnetic field divergence (Wiegelmann 2004;Wiegelmann & Inhester 2010). The field of view of the boundary field covers the full AR such that flux is nearly balanced over the entire time interval. During all four CME events, the flux imbalance is less than 8%. To further satisfy the force-free conditions, the magnetic field components are subjected to a preprocessing procedure (Wiegelmann et al. 2006). Next, we rebinned the observations to 1 arc-second per pixel. In order to weaken the effects of the lateral boundaries, the observed boundary is inserted in an extended field of view and computations are performed on a uniformly spaced computational grid of 512 × 512 × 256 representing physical dimensions of 373 × 373 × 186 Mm 3 . To reduce the effect of pseudo top and side boundaries on the evolving interior field, a boundary wall (of width 64 grid points) of cosine weighting function is used in the function which is minimized.

The NLFFF code is initiated with a 3D potential field constructed from the vertical field component of the observed field (Gary 1989). After introducing the photospheric vector magnetic field at the lower boundary, the magnetic field is relaxed the most possible to decrease both the Lorentz force and the divergence of the magnetic field. Typically, the observed photospheric field, even after processing, is not compatible with the NLFFF state, but it can be relaxed to a state with an average angle typically around 9 degrees between the electric current and magnetic field vectors in the computational volume.

A typical vector magnetogram used in the NLFFF reconstruction is shown in Figure 3a. The rectangular box covers the inner bipolar region. Horizontal velocity field, derived from DAVE4VM method, indicate a large scale converging and shear motions of opposite polarities in the inner bipolar region as displayed in panel b). Under these motions, the field vectors are sheared where the angle between potential transverse field and the observed transverse field is non zero. We measured the shear angle defined as the angle between the potential transverse field and the observed transverse field. In panels c-f), these shear angle maps are displayed at different epochs of evolution. Both the positive and negative polarities have sheared locations greater than 45 • . Especially, the negative polarity region is more sheared than positive polarity. The magnetic shear is in particular im- In all panels, the axis units are in pixels of 0.5 arcsec.

portant around the PIL in between (N2, N3) and (P1, P2) (See Figure 2 for polarity identification). Tracked magnetograms infer a southward motion of the negative polarity with respect to the positive polarity. This is the main origin of this shear region (Vemareddy 2017).

As pointed by Moore et al. (2001), two likely factors for the eruption are the flux content of the sheared core field relative to the envelope field and the height at which the reconnection begins. The greater the reconnection height, the smaller the fraction of the core field that can be released as the eruption proceeds. We compute the shear angle in the inner bipolar region (rectangular box in Figure 3a) for the vector magnetograms recorded just before all three eruptions. In this bipolar region, we found that 20%, 30%, 30% of pixels have greater than 45 • shear angle, while the pixels with shear angle greater than 25 • are 58%, 45%, 48% respectively for the last three events. Alternatively, the numbers meet the Moore et al's first criteria of excess flux content of sheared core field with shear angle above 25 • .

In Figure 4, we show the NLFFF magnetic structure just before the CMEs. Being located at E50 • , the CME1 is excluded for further analysis due to severe projection effects. The field lines are selected according to the total current density (|J| = 1 µ0 (∇ × B)) and the horizontal field component (B h = B 2 x + B 2 y ), i.e., the seed points are biased with large |J|, B h in a subvolume covering the inner bipolar region. This will ensure to select field lines that outline most of the observed coronal loops (Figure 2). A color scheme according to Bh strength is applied for the field lines. The bottom plane is B z in first column panels. Field lines connecting the peripheral regions of P1 and N2 form one J-section loop set, and those connecting N1 and P2 form another J-section loop set. These two bundles of J-shaped field lines are formed by highly sheared arcades.

Owing to line-tied shearing motions of the foot points, the field lines near the PIL, in the AR center, are strongly sheared. They are enveloping field lines over the middle of the sigmoid. This sheared magnetic configuration, as shown in Figure 2, being further driven by converging motions, of two opposite J-sections is expected to favor the formation of FR by tether-cutting reconnection (Titov & Démoulin 1999;Jiang et al. 2012;Savcheva et al. 2012a).

To compare this modeled magnetic structure to coronal observations, the same field lines are over plotted on EUV observations of corona in 171 Å and 94 Å passbands the NLFFF sheared core. The sheared core is less compact for the last event on June 25 compared to others. This indicates a relaxed configuration after a sequence of eruptions and quasi-static evolution in between two events.

We point that the projection effects in the corona are greater than for the photosphere. Notedly, being away from disk center, projection effects introduce some departures with large scale loops especially for 25 June (located at 40 • west). However, the low lying core structure is nearly reproduced because disk transformation from local to observer frames mostly take into account these projection effects.

In a study of sigmoid eruption from another AR (AR 11283) Jiang et al. (2014) reported the FR formation by reconnection which was attached to photosphere at the bald patch (BP) until eruption. Following their analysis, we further discuss the eruption cases in AR 12371 as follows. In Figure 5, we examine the core field topology of the NLFFF structure. Field lines anchoring away from the PIL correspond to two J-sections with their arms farther apart from the PIL. For the events on June 21 and 22, the field lines anchored near the PIL are inverse S-shaped and graze the PIL. Indeed, we note little difference in the observed EUV morphology with the core field. The northern sigmoid elbow in all the cases could

21T00:48UT a2) b2) b3) c2) c3) 22T17:24UT 25T07:36UT a3)
Event#2@21T00:48UT

Event#3@22T17:24UT

Event#4@25T07:36UT a1) b1) c1) BP separatrix is a common topological feature in sheared bipolar regions, where the buildup of FR begins with the appearance of BP (Titov & Démoulin 1999;Aulanier et al. 2010). In Figure 6, the field lines along the PIL are displayed in a close view for BP topology. The structure for the event on June 21 clearly show BP separatrix field lines. Field lines surrounding the BP separatrix are combination of inverse-J and S shaped field lines. A prominent dip touching tangentially the magnetogram level is displayed in the perspective view in the top right panel of Figure 6 for event 2. A similar topology is evident for event 3 and 4. In the case of event 4, the field line dips are not touching the magnetogram level (z dip 0.2 Mm above this level) so in this case a BP region is not present at the photospheric level. Still, the inverse S-shape for the field lines is clear. Notedly, these BP/dip locations moves southward in time.

As is the case in AR 12371, flux cancellation is a process transforming double J-shaped field lines to an Sshaped FR (van Ballegooijen & Martens 1989;Feynman & Hundhausen 1994) and is associated with the formation of BP with field lines tangential to the magnetogram level. This process is also expected to occur in our studied cases. Converging motions toward PIL drive the flux cancellation reconnection resulting in long FR field line and evidently the field lines of NLFFF along PIL include crossed inverse-J and S. Finally, we notice that the BP locations evolve along the PIL before CMEs (not shown) so that magnetic reconnection, building the FR, is expected to occur at intermittent positions along the PIL.

BP separatrices are preferential sites of thin current sheets due to persistent photospheric shearing motions. The reconnection of field lines in these current sheets produces high temperature emission visible in hot AIA passbands. As reconnection progresses dynamically, the FR builds by added flux. In this phase, it has been shown by MHD numerical simulations that the BP bifurcates resulting in the transformation of a BP separatrix to a QSL (Aulanier et al. 2010). Then the standard coronal tether-cutting reconnection sets in below the FR elevating its main body. Later on, the FR becomes unstable leading to the flare onset (Aulanier et al. 2010;Savcheva et al. 2012a,b). The snapshot of NLFFF model only captures static structure indicating BP topology i.e., the global magnetic topology evolution but not the dynamic reconnection.

Moreover, the precursor brightening (4th row panels in Figure 2) is co-spatial with the twisted core field (Figure 5). The brightening commences around an hour before the main eruption with the appearance of an hot inverse-S trace in the core, commencing the bright ribbons in the flare phase. Then, the forming FR by flux cancellation detaches the photosphere earlier on, favoring coronal tether-cutting reconnection, as in the numerical simulations reported above.

Coronal Current Distribution

Owing to time evolution of coronal magnetic field by persistent slow photospheric shearing motions, we see a transition of potential-like arcade in the post eruption phase of previous eruption to double inverse J-shaped sheared arcade (this transition is analyzed in Section 3.4). This process naturally builds coronal volume currents in the stressed configuration. To have more insights on the coronal current distribution, we examine direct volume rendering of |J| (not shown). Near the magnetic field concentrations, |J| is stronger since |J| is proportional to |B| along a field line in a force-free field. Especially, intense |J| are present above the inner bipolar region corresponding to the sheared/twisted field structure.

Further, we vertically integrated |J| in the coronal volume and the resulting 2D maps are shown in first column panels of Figure 7. The overall morphology of this current distribution is similar to the sigmoid observed in EUV (Figure 2). For the event 4 of June 25, the |J| distribution in the core is somewhat less intense than for the two previous events. This is associated with difference in compactness and twist of the field structure seen in panel (C2) of Figure 5.

Corresponding to before and after the eruption, in the second and third column panels of Figure 7 the distributed coronal current on either side of the PIL, whereas above the PIL the intense current concentration corresponds to twisted core field.

The smaller height of coronal current in June 25 panel likely indicates less stressed field owing to less compact sheared core as seen in Figure 5 (bottom row). These results delineate that the pre-eruption configuration comprises a sheared/twisted core with intense coronal electric currents above the PIL. For events 2 and 3 (top and middle rows) the electric current is more concentrated before than after the eruption. After the eruption, in the last column panels, the coronal current is less dense due to expansion of the core field.

Field Line Twist Maps

Given 3D field distribution, one can calculate the twist number for each field line [START_REF] Bateman | MHD instabilities[END_REF]Inoue et al. 2011;Liu et al. 2016)

T w = L µ 0 J || 4πB dl = L ∇ × B B 4πB 2 dl (1)
Here the twist is related to the parallel electric current given by J || = J B |B| and the line integral is along the selected magnetic field line of length L. If the magnetic field is force free, ∇×B = αB, then

T w = 1 4π L α dl = αL 4π
since α is constant for each individual field line. A 4π factor in the denominator includes a factor that converts radians into turns and a factor (2) relating local twist (radians per unit length) with α (Longcope et al. 1998).

In the extrapolation, the magnetic field is not exactly force-free so we rather perform the integration with ∇×B within the integral. B and ∇ × B are computed at any point in the volume by tri-linear interpolation. Then, the line integral is carried out by a five-point Newton-Cotes formula using the procedure int tabulated.pro available in IDL. For a finer structure of T w distribution, the field line integration is performed on a grid of spatial resolution double that of extrapolation grid. The field lines, that reach one lateral or top boundary, are assumed to be open, and they are set with zero value of T w . The resultant T w maps at the times before the onset of CMEs are displayed in left column panels of Figure 8. We find that the field line twist magnitude does not exceeds 1.1 turns across the maps at different times. Therefore, we scale the maps within ±1.1 turns on a blue-red color map. The central core has always negative values of T w ranging from -1.0 to -0.4 turns. In all the cases, a highlytwisted core, surrounded by T w values with opposite sign, is observed.

For a more quantitative analysis, we choose a smaller rectangular region surrounding the core of the sigmoid for the three events (its extension is shown in the central left panel of Figure 8), and perform an histogram analysis of T w at pixels with |B z | > 120G. Within this region, the fraction of pixels having more than one turn is 1.4%, 1.2%, 1.46% respectively before these successive CMEs. Similarly, the fraction of pixels with 0.5 < |T w | < 1 turn is still small since it is limited to 11.8%, 15%, 12% respectively of the total number of pixels with |T w | > 0 within the selected rectangular region.

We compare the above results with the ones obtained for another AR where twisting motions were analyzed (AR 10930 Inoue et al. 2011). The fraction of pixels in the above two intervals of twist is 5% and 40%, respectively. Therefore, it appears that rotational flux motions are more efficient in injecting twist and helicity than shear and converging motions, as expected. Further, according to Török et al. (2004), the critical twist to destabilize the ideal MHD kink modes in an anchored magnetic loop is about 1.75. Therefore, the observed low twist distribution in the studied AR suggests that the kink instability is not a relevant process to trigger these eruptions.

The right column panels of Figure 8 show histograms of T w , where each panel shows variation of T w distribution during the CME eruption. To show how T w vary, we compute T w at two epochs before eruption and one epoch after eruption and plotted in different colors (blue color histogram is after eruption). Note that the asymmetric distribution is a signature of dominant negative twist in rectangular region corresponding to core flux. In all cases, the occurrences in the histogram wings is lower than that before the CME. To quantify this decrease of twist owing to magnetic energy release, we count the pixels with |T w | above and below 0.3 turns and express in terms of percentage change from higher values (> 0.3) to lower values during pre-to-post eruption evolution. At the epochs before CME eruption, the percentage of pixels above 0.3 turns is 28%, 31%, 32% respectively, suggest-ing increasing twisted flux from first to last event. For the three CME cases on 21, 22 and 25 June, we found that the above percent of pixels decrease to 26%, 29%, 16% (so a decrease of 2%, 2%, 16%) respectively. The corresponding effect is seen with the histograms, where the histogram wings in the post eruption shrink below that for pre-eruption.

3.4. Buildup of a Sheared/Twisted Core Field As AR magnetic structure evolves, the formation of a twisted core field from an initial arcade configuration is expected under the effect of shearing and converging motions. To show this, the NLFFF reconstruction is applied at different times in the post eruption evolution of CME1 on June 18. In Figure 9, we show magnetic structure of the AR at three instances. The first snapshot is in the relaxing phase present after the CME1. The core field has a remnant shear besides elbow field lines. In the course of further evolution driven by slow shearing/converging motions, the core field becomes twisted gradually. In particular, in the later two snapshots (pointed by white color arrow), the core field appears more like a bundle of twisted field lines (FR). In addition, the elbow field lines appear more compact than earlier on. This buildup of twisted core is a key process of energy storage in the sigmoid structure which occurs to reform the FR from the pre-eruption arcade. This leads to the launch of the CME2 at 02:00 UT on June 21.

This development of a twisted core is further studied quantitatively by utilizing the twist T w maps derived from the NLFFF extrapolations. Similar to earlier section, in the last panel of Figure 9 we display histograms of T w maps at four times in the aftermath evolution of the CME1. This time evolution of histograms delineate the transfer of pixels about the center (with |T w | < 0.5) toward the wings (|T w | > 0.5). The fraction of pixels with |T w | > 1 turn shows a slight increase from 0.4% to 1.2% from first instance to the last. However, corresponding to the buildup of the sheared core, the fraction of pixels with 0.5 < |T w | < 1 is significant and growing from 6.1% to 11.3%, so almost by a factor 2. If we rather select the interval 0.3 < |T w | < 1, the fractional increase is lower as it grows from 21.2% to 29.7% from first instance to the last one, so increasing only by a factor ≈ 1.4. magnetic field energy (E t ). To study the height variation of the magnetic free energy, we compute the surface integral of free energy as (e.g., Mackay et al. 2011;Vemareddy et al. 2016)

E f,s (z) = S B 2 2µ 0 dx dy - S B 2 p 2µ 0 dx dy (2)
from the NLFFF and potential fields of the AR. For this purpose, we consider the time frames before and after the eruption. Specifically, we choose the pre-flare snapshot just before the first observed brightenings and the post eruption snapshot at the end of the flare decay phase ensuring the field relaxation gets captured in the vector magnetograms.

We caution that our computations of free energy estimation is subjected to errors due to projection effects, ex-trapolation model, and noise/bias in input observations. Moreover, implicit smoothing in preprocessing procedure also contributes underestimating the actual coronal free energy content.

During the three CME cases the plots in Figure 10 delineate that most of the coronal free energy is contained below 20 Mm and E f,s is maximum a low height, below 5 Mm. This energy is related to the coronal electric current distribution depicted in Figure 7. E f,s decrease for event 2 is small, while for events 3 and 4 the decrease of E f,s is significant in the range 10-30 Mm. Only in event 3 an increase of E f,s is present at low height.

In Table 1, the global energies for all three CME events are reported. In each case the time is considered just before and after the flares as above. E p and E t are of the order of 10 33 erg, which is the typical energy content of large ARs (e.g., AR12192 Jiang et al. 2016b). From event 2 through 3, E p drops gradually. This is consistent with the photospheric magnetic flux which is decreasing both by dispersion and by cancellation at the PIL. A decreasing E p with reducing AR flux content is also observed in AR 11283 in the study by Jiang et al. (2014). In all events the potential energy is almost the same before and after (Table 1) as expected because of the small observed evolution during the events of the vertical field component at the photospheric level. The magnetic energy available for an event, which is converted e.g. as kinetic, thermal and radiative energies, is mostly the difference of coronal magnetic energy between after and before the event since eruptions are involving the ejection of closed magnetic structures and since the energy input by photospheric shearing motion is small compare to the energy accumulated between two events (with a constant flux rate, this ratio is the ratio of the durations, so of the order of 2/24 ≈ 0.1).

The magnetic free energy drop for the three events is 0.05, 0.17, 0.46 in units of 10 32 ergs, respectively, accounting for 2.3%, 6.4%, 32% of the pre-eruption free energy. These small values are qualitatively consistent with the estimates of twist number variation in Section 3.3, where only a small number of field lines (upto 16%) show a variation of twist number corresponding to field reconfiguration.

In summary, our analysis suggests that magnetic energy is being pre-stored in the magnetic structure by gradual shearing motions around the PIL, then it is released by intermittent eruptions.

Torus Instability

To reveal the role of background field, we also compute the decay index n(z) = -d log(B h )/d log z, where B h is the horizontal component of the background field and z is the height above the photosphere. Since the vertical magnetic-field component does not contributes to the inward confining force, the decay index is computed only with the horizontal components of the field. This background field strength decides the torus instability (TI) criteria. Török & Kliem (2005) proposed the value of 1.5 as a critical decay index. In fact, the critical value of n depends on a number of factors, but is expected to be in the range 1.1 ≤ n crit ≤ 2 [START_REF] Bateman | MHD instabilities[END_REF]Kliem & Török 2006;Démoulin & Aulanier 2010).

In the present study, B h (z) is obtained at different spatial points located along the PIL in the inner bipolar 2), in horizontal planes as a function of height (z, in Mm). Blue (red) curve represents E f,s before (after) eruption (Table 1). Most of the free energy is located below 20 Mm. On average, the post eruption curves are below pre-eruption curves, indicating that, as expected, E f,s drops through the CME eruption.

region. Then an average value of n(z) is derived corresponding to B h (z) at those points in both potential field and NLFFF (grey and black curves in Figure 11).

The theory separates the FR magnetic field from the background field and n(z) is only computed from the background field. This separation is trivial because analyzed analytical models are constructed by the superposition of these two fields. However, with magnetic extrapolations there is no precise way to separate the FR field, or its associated electric currents, from the background. Then, we consider two extreme limits: all the currents are associated with the FR, so the background field is potential, and at the opposite the FR has a negli- -Decay index (n) of the background field (ordinate) as a function of vertical height (abscissa, in Mm). Black (gray) continuous curve represents the mean decay index obtained from the potential (NLFFF) field, respectively. The horizontal field strength (B h [G]) is also plotted at the same spatial locations with dashed lines within a range between 0 and 500 G (see the scale located on the right side of panels). Dotted horizontal line indicates the critical value of n crit = 1.5. For all three events, this critical value of n corresponds to a height just below or ≈ 40 Mm. gible fraction of electric currents, so the background field is the full NLFFF. These are clearly very extreme cases but we show below that the results are comparable so that we do not need to define what is the field associated to the FR for this study of the decay index.

In Figure 11, we plot n(z) above z=0 plane. B h is also plotted (in units of Gauss) with its scale reported on the right of each panel. In all three cases, the n(z) for potential field and NLFFF follows each other except short scale spikes in NLFFF arising due to differentiation of a more structured field. For all three cases, the characteristic curve n(z) approaches the critical value, set to n crit = 1.5, at a height between 20 and 50 Mm, indicating a favorable magnetic environment for the destabilization of the FR, then the launch of a CME when the magnetic evolution brings the FR axis to such height.

There is some height difference for n crit (up to 10 Mm) for NLFFF and potential field, but the average critical height is around 40 Mm.

The TI domain in AR 12371 is comparable to other eruptive ARs, for instance, the flare-CME productive ARs 11158, 11429 have TI critical height of 42, 34 Mm respectively (Sun et al. 2015). Notedly, the horizontal field at 42 Mm in these eruptive cases is (∼ 50 G), so smaller by a factor of four than in confined AR 12192 (230 G). ARs with failed eruptions have a distinct TI height range compared to ARs with successful eruptions. Recent observations found that the critical height for TI can be as high as 236 Mm (Wang et al. 2017). For a confined eruption studied by (Guo et al. 2010), n crit is always above 100 Mm suggesting a stronger restraining field over the FR. Similarly, the CME less AR 12192 is found to have stronger overlying field with a TI critical height up to 77 Mm (Sun et al. 2015). Indeed, the super AR 12192, producing large flares without CMEs, is found to have more closed field flux above than in the sheared core field surrounding the PIL (Sun et al. 2015;Jiang et al. 2016b).

SUMMARY AND DISCUSSION

We study the magnetic structure of AR 12371, by modeling the coronal field with the photospheric vector magnetic field measurements, in relation to the erupting sigmoid observed successively over days. The AR coronal magnetic field is mainly driven by continued shear motions at the photospheric level, which inject helicity flux of dominant negative sign (See Figure 8 in Vemareddy 2017). Being co-spatial with the sigmoid, the injected helicity flux is mostly included in the sheared/twisted field of the sigmoid. As the coronal field can not accommodate indefinite an accumulation of magnetic helicity, a CME is inevitable (Low 1994), then the stored helicity is partly ejected with the FR.

In the present study of the three events, the model field structure of pre-eruptive sigmoid has a low-lying twisted core and an overlying arcade resembling the sigmoid morphology observed in coronal EUV images. The NLFFF core is dominantly embedded in a large scale sheared arcade with the inner part along the PIL having opposite J-shaped field lines with crossed legs. Closer and above the PIL inverse-S field lines with dips touching tangentially the photosphere are present (Figure 6). This kind of topology is a manifestation of BP-separatrix field lines formed by photospheric reconnection of opposite-J field lines and indicates the formation of weakly twisted FR at the inner core of the sigmoid embedded in the large scale sheared arcade (Antiochos et al. 1999). As shown in previous simulations (see Section 1), a larger FR is progressively build up by reconnection at the photospheric level, then in the corona below the FR. At some point of the evolution the FR become unstable which leads to a CME.

Moreover, the NLFFF modeled structure captured major features of energy storage and release mechanism, viz., sigmoid-to-arcade-to-sigmoid transformation, that is being recurrent under continuous photospheric flux motions. Calculations of the field line twist reveal an increase of pixels (≈ 7% averaging over the events) having a range of field line twist (0.3 < T w < 1), indicating the quasi-static buildup process of twisted core field by slow shearing and converging motions around the PIL. Similarly, we observed a decrease of pixels within the same range of twist, consistent with the decrease of free energy corresponding to the field reconfiguration from sigmoid to potential like arcade during the eruption.

The magnetic evolution in this AR is in contrast to the confined AR 12192 which has a larger helicity flux but a much weaker (by a factor of 10) normalized coronal helicity content (H/Φ 2 ). As inferred by Vemareddy (2017), a small value of H/Φ 2 implies a large flux content unrelated to sheared/twisted part. This flux is present as an overlying flux to stabilize the FR. This is complemented by the results of n(z) in the AR field. The critical height in eruptive AR 12371 is around 40 Mm while in confined AR 12192, it is at larger height (77 Mm, Sun et al. 2015).

The ejective nature of AR 12371 differs in some global magnetic properties with respect to those of confined eruptive ARs. The super AR 12192 is an interesting example being not producing any CME even in association with X-class flares and therefore is a non-eruptive counterpart of AR 12371. Data driven modeling of AR 12192, performed by Jiang et al. (2016b), have shown that the AR field structure remained in the sheared arcade configuration without forming two-J shape like and escaping FR unlike the AR case studied here.

Our analysis of observations are based on static mod-eling of NLFFF of AR magnetic structure. More insights on dynamic aspects of FR formation, its lift off can be gained from data driven MHD modeling of the AR (e.g., Jiang et al. 2012Jiang et al. , 2016a) ) and would be worth of further investigation.

Fig. 1 .

 1 Fig. 1.-Disk integrated GOES X-ray flux (1-8 Å) during June 18-25, 2015. Vertical dotted lines mark initial times of CMEassociated M-class flares from AR 12371.

Fig. 2 .

 2 Fig. 2.-Multi-wavelength observations of the AR 12371 during the initiation of four CMEs shown in the four columns. Each panel of the same event have the same field of view. First row: HMI line-of-sight magnetic field maps with labeled polarity regions. Blue curve is the main PIL. Second row: GONG Hα observations showing traces of chromospheric filaments and sunspots (related to HMI magnetic polarities). Third row: AIA 304 Å observations showing the presence of filament (pointed by blue arrow) before the onset of CME eruption. Fourth row: AIA 131 Å observations before eruptions. In particular they show the coronal loop sets as magnetic elbows and are traced with dashed curves L1 and L2 by inspecting time series of images. In these observations, the pre-cursor brightening related to slow tether-cutting reconnection is seen with L1. Fifth row: Composite images of coronal observations in AIA 94 Å (red), 335 Å (green), and 193 Å (blue) passbands. The loop set L3 (outlined with an orange curve) is understood as the dynamic reconnection product of L1 and L2. See Section 2 for more details.

Fig

  Fig. 3.-a) HMI Vector magnetogram of AR 12371 on June 20. Blue/red arrows represent horizontal field. Background is vertical field image with contours at ±150 G. b) Tracked horizontal velocity field on vertical field map. Field-of-view covers the inner bipolar region as shown with rectangle box in panel a). Careful inspection implies a slow shear and converging motion between the opposite polarity regions. c-f) Maps of shear angle in the inner bipolar region covered by rectangle box in a) (see the side color bar). Contours (red/blue) of Bz at ±150 are overlaid. In the vicinity of the PIL, both the positive and negative polarities have sheared locations greater than 45 • . Finally, as a result of flux cancellation along the PIL and dispersion of the photospheric field, the polarity regions decayed in area from June 18 to 25.In all panels, the axis units are in pixels of 0.5 arcsec.

Fig

  Fig. 4.-NLFFF magnetic structure of AR 12371 during the three eruption events. First column: Field lines plotted on top of the photospheric magnetogram (Bz) with labeled polarity regions. The global structure is a sigmoid with two opposite J-shaped sections and an inner sheared core. Second column: Same field lines on AIA 171 Å images. Color scale is chosen in contrast to background images. Third column: Same field lines on AIA 94 Å images. Hot plasma emission is mainly co-spatial with the strongly sheared core. Note that for event 4 (bottom rows) the projection effects tend to deviate the model structure, especially long field lines from the observed 171 Å loops indicated by arrow. Field lines are color coded (blue (red): ∼1200 (2)G) with the horizontal field strength in height in column 1 and 3.

Fig. 5 .

 5 Fig. 5.-Field line shapes in the core and EUV observations (organized by rows). First column: Field lines on EUV-94 images, showing twisted field embedded in large-scale sheared arcade. The twisted field is co-spatial with EUV emission, whereas emission from the northern elbow comes from high lying potential field. (see also Figure 4) Second column: Top view of the core field line structure. The photospheric Bz distribution observed at the same times is shown with gray levels in the background for all panels. Third column: Perspective view of the same field lines showing the coronal extent of the sheared arcade be related to high lying potential-like arcade. The southern elbow seem to constitute by a continuity of field lines belonging to both low lying core field and high lying arcade to the leading polarity.BP separatrix is a common topological feature in sheared bipolar regions, where the buildup of FR begins with the appearance of BP(Titov & Démoulin 1999;Aulanier et al. 2010). In Figure6, the field lines along the PIL are displayed in a close view for BP topology. The structure for the event on June 21 clearly show BP separatrix field lines. Field lines surrounding the BP separatrix are combination of inverse-J and S shaped field lines. A prominent dip touching tangentially the magnetogram level is displayed in the perspective view in the top right panel of Figure6for event 2. A similar topology is evident for event 3 and 4. In the case of event 4, the field line dips are not touching the magnetogram level (z dip 0.2 Mm above this level) so in this case a

  Fig.6.-NLFFF structure in the inner core evidencing the BP separatrix topology. Left column: Top view of field lines plotted on Bz maps. These field lines are combination of double inverse-J and S shape along the PIL. Right column: Perspective view of the same field lines having prominent dips touching tangentially the photosphere. Arrows point to the field line dips near to the surface (z = 0). This kind of topology is suited for flux cancellation reconnection of inverse J-shape field lines to form inverse-S shape field lines and the FR.

  Fig. 7.-Current distribution just before and after three CME events. First column: Vertically integrated maps of |J| scaled within the interval [0,800]A m -2 (see the top color bar). They are mimicking the sigmoid observed in EUV (Figure 2). The position of the vertical slice SL, used in the right panels, is shown by a blue line. Second and third columns: Electric current density, |J|, in the vertical slice before and after eruption. Contours (white curves) of the vertical component Bz at ±80 G are over-plotted in each panel. |J| is scaled within the interval [0, 50] mA m -2 (see top color bar). The strong |J| region corresponds to the sheared core field and it is surrounded by weaker currents present in the arms of the two elbow magnetic structures (Figure 5). The height scale is indicated in the panels of the middle column.

  Fig. 8.-Spatial distributions and histograms of the field line twist (see Equation (1)). Left column: Tw distribution of AR 12371 about half an hour before the onset of CME events. Red (blue) color pixels refer to positive (negative) twist. Maps are scaled within ±1.1 turns as shown by the blue-red color scale. Field lines with foot points around the PIL have higher negative twist. They are surrounded by positive twisted field. A smaller rectangular region, as show in the 22T17:24 UT (second) panel, is chosen for the histogram analysis. Right column: Histograms of Tw before and after the onset of each CME. The asymmetry in the distributions is due to a dominant negative Tw in the rectangular region. The histograms shrink slightly in width over time owing to relaxation of the field during CME eruption.

  Fig. 9.-Development of twisted core field by shearing motions over two days of quasi-static evolution after CME1. Image panels: NLFFF field lines are over-plotted on magnetograms in the post eruption evolution of first CME (starting at 17:24UT on June 18) and before the second CME (starting at 02:30UT on June 21). The first time is just after CME1 and the next ones are separated by about one day. Arrows point to the buildup of the twisted core field. Field lines are color coded (blue (red): ∼1200 (2)G) with the horizontal field strength in height. Bottom right panel: Histograms of Tw (Equation (1)) at four different times. It shows increasing wings corresponding to the development of a twisted core field.

Fig. 10 .

 10 Fig. 10.-Free energy E f,s , Equation (2), in horizontal planes as a function of height (z, in Mm). Blue (red) curve represents E f,s before (after) eruption (Table1). Most of the free energy is located below 20 Mm. On average, the post eruption curves are below pre-eruption curves, indicating that, as expected, E f,s drops through the CME eruption.

  Fig. 11.-Decay index (n) of the background field (ordinate) as a function of vertical height (abscissa, in Mm). Black (gray) continuous curve represents the mean decay index obtained from the potential (NLFFF) field, respectively. The horizontal field strength (B h[G]) is also plotted at the same spatial locations with dashed lines within a range between 0 and 500 G (see the scale located on the right side of panels). Dotted horizontal line indicates the critical value of n crit = 1.5. For all three events, this critical value of n corresponds to a height just below or ≈ 40 Mm.

TABLE 1

 1 Magnetic energy in units of 10 32 ergs before and after each CME eruption in AR 12371. Ep, Et and E f are respectively the potential, total, and free magnetic energy (E f = Et -Ep). Magnetic Energy Magnetic free energy (E f ) is a measure for excess energy available for the eruptive flares. It is estimated by subtracting the potential field energy (E p ) from total

	event (time)	Ep	Et	E f
	CME2(2015-06-21T00:48 UT) 26.25 28.39 2.14
	CME2(2015-06-21T04:00 UT) 25.97 28.64 2.09
	CME3(2015-06-22T17:24 UT) 21.54 24.19 2.64
	CME3(2015-06-22T19:24 UT) 21.75 24.23 2.47
	CME4(2015-06-25T07:36 UT) 22.58 24.03 1.44
	CME4(2015-06-25T09:00 UT) 22.81 23.80 0.98
	3.5.

SDO is a mission of NASA's Living With a Star Program. This work utilizes data obtained by the Global Oscillation Network Group (GONG) Program, managed by the National Solar Observatory, which is operated by AURA, Inc., under a cooperative agreement with the National Science Foundation. We are grateful to the referee's detailed constructive comments and suggestions which improved the scientific presentation of the results. P.V. is supported by an INSPIRE grant of AORC scheme under the Department of Science and Technology. The NLFFF code is developed by Dr. T. Wiegelmann of Max Planck Institute for Solar System. We thank Jun Chen and Rui Liu of University of Science and Technology of China for a useful discussion on field line twist computation. 3D rendering is due to VAPOR (www.vapor.ucar.edu) software. We acknowledge an extensive usage of the multi-node, multi-processor high performance computing facility at Indian Institute of Astrophysics.