**1. Introduction**

Solar flares are prominent eruptive phenomenon happening in the solar atmosphere [1–3], where the matters have high temperature and hence in plasma state [4]. The energy of solar flares comes from the magnetic field in the solar atmosphere [1]. Major flares usually originate from solar active regions (ARs). In solar ARs, strong and concentrated bipolar magnetic field exists and manifests as dark sunspots in photosphere [2, 5].

The photospheric magnetic field acts as the bottom boundary of corona system and confines the magnetic structure of the corona [4, 5]. Because in the corona the plasmas are very tenuous, the magnetic force plays the dominant role, and other forces can be neglected. Thus, the plasmas in the corona are distributed along field lines and satisfy force-free condition (i.e., the Lorentz force being zero) for steady corona [6]. For complex ARs, the coronal magnetic field generally contains electric current around the magnetic polarity inversion lines (PILs), which corresponds to the nonpotential magnetic field and manifests as twisted field lines [7, 8]. The coronal magnetic field structure evolves as the response to the variations

of the photospheric magnetic field. This coronal evolution can be quasi-steady and approximated by the force-free condition [9, 10].

In some situations, the variations of photospheric magnetic field may cause sudden changes of topological structure of coronal magnetic field at certain sites in the corona. The plasmas at these sites lost equilibrium and are ejected from their original positions. This process is accompanied with magnetic reconnection and leads to the release of magnetic energy in the corona [1, 3, 11]. Part of the released magnetic energy is converted to the electromagnetic emission which manifests as sudden brightening across a broad range of electromagnetic wave spectrum, and hence the flare phenomenon is initiated [2]. The typical electromagnetic emissions include white-light flare in photosphere, optical flare in chromosphere, and soft X-ray flare in the corona [2, 4]. Other released magnetic energy is converted to the mechanical energy of the erupted plasmoid and is also carried off by the highenergy particle radiation [2–4], which might lead to the coronal mass ejections and the solar energetic particles associated with solar flares [12–14].

An overview on the relations between the variation of coronal magnetic field and the solar flare eruption is given in this chapter. In Section 2, the main observational properties of the solar flares are presented. In Section 3, the nonpotentiality of the coronal magnetic field associated with the solar flares is discussed. The process of the flare initiation caused by the variation of coronal magnetic field is described in Section 4. Section 5 provides the summary and conclusion.

#### **2. Solar flare observations**

The energy of solar flares comes from the magnetic field in the solar atmosphere. It is natural that almost all major flares were found to be located in solar ARs which possess strong and concentrated bipolar magnetic field and manifests as dark sunspots in photosphere [1–5].

The electromagnetic emissions of solar flares can be observed in the corona, chromosphere, and photosphere of the Sun [2, 4]. In the standard model of solar flare eruption [3, 4], the magnetic reconnection associated with a flare takes place in the corona, just above the AR PIL and beneath the erupting plasmoid. The heat produced in the space of magnetic reconnection is transmitted to the chromosphere along the field lines. At the foot points of the field lines, the matters in chromosphere are heated up to extremely high temperature (about 107 K) and manifest as two bright ribbons located at the two sides of the PIL in the filtergrams observed through the chromospheric spectral lines (such as Hα, Ca II H and K, etc.). The flare brightening in chromosphere is traditionally called optical flare since it can be observed via an optical device equipped with a band filter of the selected chromospheric spectral line (see **Figure 1** for an example of flare image in chromosphere). The heated chromospheric materials subsequently fill up the arcade system of field lines over the PIL, which manifests as bright flare loop arcade in the corona in the images observed in extreme ultraviolet (EUV) or soft X-ray band [2, 4] (see **Figure 2**).

The energetic electrons produced by the magnetic reconnections also transmit downward along the field lines and can reach as low as upper photosphere level and cause flare brightening in white-light band [2, 4]. In fact, the first observed major flare event by Carrington in 1859 is white-light flare [15].

Because the photosphere of the Sun is very bright, the white-light flares cannot be observed very easily and frequently [16], whereas the soft X-ray flares originate from the thermal radiation in the corona and have much low background radiation, thus, the solar soft X-ray flux is widely adopted as the basis for standard flare

**195**

**Figure 2.**

*SOHO spacecraft.*

**Figure 1.**

*spectral line by the Hinode satellite.*

*Variation of Coronal Magnetic Field and Solar Flare Eruption*

magnitude classification (i.e., A, B, C, M, X-class series of flare classification; see https://www.swpc.noaa.gov/products/goes-x-ray-flux) [14]. Other bands of electromagnetic spectrum, such as radio, ultraviolet (UV), hard X-ray, and γ-ray,

*Coronal image of the flare on 13 December 2006. The image was observed through the 195 Å EUV band by the* 

*Chromospheric image of a major flare event on 13 December 2006. The image was observed through the Ca II H* 

Since the magnetic reconnection associated with solar flare eruptions takes place in the corona, the coronal magnetic field distribution is crucial for understanding the physical process of flares [1, 3, 4]. In fact, the photospheric magnetic field acts

are also commonly used for solar flare observations and studies [2, 4].

**3. Nonpotentiality of coronal magnetic field**

**3.1 Force-free magnetic field of steady corona**

*DOI: http://dx.doi.org/10.5772/intechopen.86168*

*Variation of Coronal Magnetic Field and Solar Flare Eruption DOI: http://dx.doi.org/10.5772/intechopen.86168*

#### **Figure 1.**

*Nanofluid Flow in Porous Media*

**2. Solar flare observations**

sunspots in photosphere [1–5].

soft X-ray band [2, 4] (see **Figure 2**).

flare event by Carrington in 1859 is white-light flare [15].

approximated by the force-free condition [9, 10].

the solar energetic particles associated with solar flares [12–14].

described in Section 4. Section 5 provides the summary and conclusion.

of the photospheric magnetic field. This coronal evolution can be quasi-steady and

In some situations, the variations of photospheric magnetic field may cause sudden changes of topological structure of coronal magnetic field at certain sites in the corona. The plasmas at these sites lost equilibrium and are ejected from their original positions. This process is accompanied with magnetic reconnection and leads to the release of magnetic energy in the corona [1, 3, 11]. Part of the released magnetic energy is converted to the electromagnetic emission which manifests as sudden brightening across a broad range of electromagnetic wave spectrum, and hence the flare phenomenon is initiated [2]. The typical electromagnetic emissions include white-light flare in photosphere, optical flare in chromosphere, and soft X-ray flare in the corona [2, 4]. Other released magnetic energy is converted to the mechanical energy of the erupted plasmoid and is also carried off by the highenergy particle radiation [2–4], which might lead to the coronal mass ejections and

An overview on the relations between the variation of coronal magnetic field and the solar flare eruption is given in this chapter. In Section 2, the main observational properties of the solar flares are presented. In Section 3, the nonpotentiality of the coronal magnetic field associated with the solar flares is discussed. The process of the flare initiation caused by the variation of coronal magnetic field is

The energy of solar flares comes from the magnetic field in the solar atmosphere. It is natural that almost all major flares were found to be located in solar ARs which possess strong and concentrated bipolar magnetic field and manifests as dark

The electromagnetic emissions of solar flares can be observed in the corona, chromosphere, and photosphere of the Sun [2, 4]. In the standard model of solar flare eruption [3, 4], the magnetic reconnection associated with a flare takes place in the corona, just above the AR PIL and beneath the erupting plasmoid. The heat produced in the space of magnetic reconnection is transmitted to the chromosphere along the field lines. At the foot points of the field lines, the matters in chromosphere are heated up to extremely high temperature (about

 K) and manifest as two bright ribbons located at the two sides of the PIL in the filtergrams observed through the chromospheric spectral lines (such as Hα, Ca II H and K, etc.). The flare brightening in chromosphere is traditionally called optical flare since it can be observed via an optical device equipped with a band filter of the selected chromospheric spectral line (see **Figure 1** for an example of flare image in chromosphere). The heated chromospheric materials subsequently fill up the arcade system of field lines over the PIL, which manifests as bright flare loop arcade in the corona in the images observed in extreme ultraviolet (EUV) or

The energetic electrons produced by the magnetic reconnections also transmit downward along the field lines and can reach as low as upper photosphere level and cause flare brightening in white-light band [2, 4]. In fact, the first observed major

Because the photosphere of the Sun is very bright, the white-light flares cannot be observed very easily and frequently [16], whereas the soft X-ray flares originate from the thermal radiation in the corona and have much low background radiation, thus, the solar soft X-ray flux is widely adopted as the basis for standard flare

**194**

107

*Chromospheric image of a major flare event on 13 December 2006. The image was observed through the Ca II H spectral line by the Hinode satellite.*

#### **Figure 2.**

*Coronal image of the flare on 13 December 2006. The image was observed through the 195 Å EUV band by the SOHO spacecraft.*

magnitude classification (i.e., A, B, C, M, X-class series of flare classification; see https://www.swpc.noaa.gov/products/goes-x-ray-flux) [14]. Other bands of electromagnetic spectrum, such as radio, ultraviolet (UV), hard X-ray, and γ-ray, are also commonly used for solar flare observations and studies [2, 4].
