Features of Magnetic Field Fluctuations in the Ionosphere at Swarm altitude

The magnetosphere-ionosphere system is recognized as a complex and active element affected by space weather and as a region where important scientific questions related to space weather impacts need to be answered. In this framework, there is a high priority on the understanding of how local, regional, and global-scale phenomena couple to produce observed responses across various scales. Turbulence provides one pathway by which energy cascades across scales from large to small ones where energy can be dissipated in the form of heating. The Swarm mission, that is a true multi-point and multi-purpose constellation, represents a unique opportunity to address some of these scientific questions. In detail, it gives us a chance of investigating the nature and the scaling features of magnetic field fluctuations for different geomagnetic activity levels, and unveiling the role played by turbulence of ionospheric plasma medium on the magnetic field fluctuations. Recently, using Swarm magnetic field data at high-latitude in the Northern Hemisphere, the local scaling indices of the 1st and 2nd order structure functions of the magnetic field fluctuations have been evaluated, showing their capability both to give new insights about the ionosphere-magnetosphere coupling and to provide information on the ionospheric turbulence. Here, we improve and extend the analysis by investigating the scaling features of the geomagnetic field fluctuations of external origin, recorded by Swarm A satellite during a period of 2 years (April 2014–March 2016). Maps of the local Hurst exponent values, which allow us to study scaling properties of the geomagnetic field’s spatial fluctuations are shown, both at high-latitudes (in the Northern and Southern Hemisphere) and at lowand midlatitudes (±60°) according to two different geomagnetic activity conditions. The aim is to capture the essential features of the spatial fluctuations of the geomagnetic field and understand their origins.


Introduction
There is a growing body of literature that recognises the importance of the turbulence and intermittent phenomena in the ionospheric environment. Fluctuations of plasma density, electrostatic potential and magnetic and electric fields have confirmed the existence of a turbulent state in the ionosphere. This state, which can be detected at different spatial scales, is mainly the result of the various phenomena characterising the different magnetospheric regions coupled to the ionosphere via the geomagnetic field lines.
It has been shown that the turbulent character of the ionospheric plasma density plays an important role in the formation and dynamics of ionospheric inhomogenities, which can have a great impact, for example, on the propagation of electromagnetic waves. These inhomogenities, indeed, may affect the Global Navigation Satellite System (GNSS) performance, being responsible for different problems: from a simple signal delay to its total loss in case of scintillation events up to the production of misleading information due to strong ionospheric gradients. That is the reason why it has been recognized that plasma density plays a key role in the ionospheric processes.
Actually, other physical quantities, often underestimated, can play a crucial role in this framework and provide interesting information on the features of turbulence in the ionospheric environment. Since the work of Kinter and Seyler (1985), the turbulent properties of electric and magnetic fluctuations observed by rockets and spacecraft at different altitudes have been addressed in several papers. Great attention was especially paid to the analysis of turbulent properties of the high-latitude electric fluctuations trying to understand the nature of the phenomenon and to clarify its driving mechanisms. Many interesting features of electric field fluctuations were obtained using both data from low-altitude polar-orbiting Dynamic Explorer 2 (DE2) spacecraft during its several crossings of the auroral zone and polar cap under different interplanetary magnetic field orientations Golovchanskaya and Kozelov, 2010) and data based on ground-based stations and rockets measurements. These works suggested that small-scale electric and magnetic fields in the auroral zone are due to intermittent ionospheric turbulence, which develops in the regions of large-scale field-aligned currents (see, e.g., Kintner, 1976;Weimer et al., 1985;Basu et al., 1988;Tam et al., 2005;Golovchanskaya et al., 2006;Kozelov and Golovchanskaya, 2006;Kozelov et al., 2008). Some theories associated the observed ionospheric turbulence with structures of magnetospheric origin (e.g., Golovchanskaya et al., 2006) driven, for example, by shear flow instabilities. Other studies related the ionospheric turbulence directly to turbulence in the solar wind (e.g., Parkinson, 2006;Abel et al., 2009). Ionospheric turbulence in the form of spatial and temporal fluctuations of 3 plasma density has often been observed also at mid and low latitudes (Le et al., 2003;Molchanov et al., 2004). The irregularities, resulting from a variety of plasma instabilities associated with perturbations in the complex arrangement of electric and magnetic field, were observed by ground-based coherent and incoherent scatter radars, sounding rockets and satellites. For example, Jahn and LaBelle (1998) presented one of the first rocket measurements of equatorial spread F irregularities at altitudes above 600 km, showing how power spectra of the electron density fluctuations were characterised by dual-power law behaviour. Based on plasma density data from the Cosmos-900 satellite Molchanov et al. (2004) analysed the spatial distribution of the ionospheric turbulence (in the spatial range between 15 and 300 km) at the satellite height h=450-500 km and found a power density spectrum in the case of both the plasma and the electric field in the analysed regions. Bhattacharyya (1990) studied the chaotic behaviour of ionospheric density fluctuations, using amplitude and phase scintillation data, and found the existence of low-dimensional chaos. The same chaotic behaviour of ionospheric turbulence was also investigated by Wernik and Yeh (1994) using scintillation data and numerical modelling of scintillation at high-latitude. A unified picture of plasma irregularities in equatorial spread F was developed from the analysis of satellite, sounding rocket, and coherent scatter radar observations by Hysell (2000) in his interesting overview of equatorial ionospheric turbulent conditions.
It is important to notice that the spatial features of plasma density irregularities have a wide range of scale sizes, spanning from centimeters to hundreds or perhaps thousands of kilometers.
This observed broad range of irregularity scale sizes, which is indicative of nonlinear modecoupling, exhibits a power-law scaling, with variable spectral indices. During recent years, large variations of the spectral index, used to describe the ionospheric turbulence, were registered to be dependent on the different geomagnetic conditions of observations. The European Space Agency minisatellite constellation mission, called Swarm, can be extremely useful in this context. Indeed, thanks to both the inclination of the orbits and the precession of their planes, Swarm satellites ensure a global coverage in a few months (Friis-Christensen et al., 2006). Data recorded by these satellites can be consequently used to statistically analyse the features of magnetic field fluctuations across the globe.
In this framework, we characterise the features of magnetic field fluctuations in the F-region of the ionosphere using measurements recorded by the Swarm A satellite during a period of two years (April 2014 -March 2016). The fluctuations are described under the assumption that, according to previous findings, they obey a power-law distribution. Under this assumption, we consider the horizontal magnetic field intensity of magnetospheric and ionospheric origin and analyse the changes in the scaling properties of its spatial/temporal fluctuations, which are valid 4 for a certain range of scales. To do this, we evaluate the local Hurst exponent, that characterises the time fluctuations observed in a signal defining their degree of persistence or anti-persistence, and discuss the changes in the Hurst exponent values in relation to the most important ionospheric and magnetospheric current systems, which could reveal the nature of the magnetic field fluctuations.
The paper is organised as follows. At first, the data sources are discussed, and then, a brief summary of the method of analysis is presented. Following this, the analysis is applied on the selected data in three different latitudinal regions: Northern high latitudes, middle and low latitudes and Southern high latitudes. Finally, the implications of findings are discussed.

Data
This study is based on in situ observations of the geomagnetic field recorded on Swarm A, one We use the CHAOS-6 geomagnetic field model (Finlay et al., 2016) to remove from the observed magnetic data the main field and its secular variation. CHAOS-6 is a high-resolution geomagnetic model, which spans a period between 1997 and 2016, and it is obtained from satellite magnetic data (Swarm, CHAMP, and Ørsted) along with ground observatory data (Finlay et al., 2015). Thus, from the original data we remove the contribution coming from the internal field modelled by CHAOS-6 to obtain the external magnetic field of magnetospheric and ionospheric origin along the three magnetic field components. From the BX (Northward) and BY (Eastward) components of the geomagnetic field of external origin in the NEC (North-East-Centre) frame of reference we evaluate the intensity of the horizontal magnetic field component BH = (B 2 X + B 2 Y) 1 ⁄ 2 , which is analysed in three different latitudinal regions: Northern high latitudes (magnetic latitude > 50° N), mid-and low-latitudes (within ± 60° magnetic latitude) and Southern high latitudes (>50° S) and according to two different geomagnetic 5 activity levels. The Auroral Electrojet index (AE) and SYM-H index are used to discriminate between quiet and active periods. The AE index is used to monitor the level of geomagnetic disturbance resulting from the auroral electrojets, being a proxy of the total currents in the auroral zone, while the SYM-H index gives information about the strength of the ring current around the Earth, which increases during disturbed periods. To select geomagnetically quiet periods we consider the following simultaneous conditions: AE<60 nT and -5 nT <SYM-H<5 nT. In this way the chosen time periods are supposed to be devoid of the magnetic perturbations introduced by the occurrence of storm and substorm events. On the other hand, to select active periods we consider the following simultaneous conditions: AE>100 nT and SYM-H<-30 nT.
In this case, the chosen time periods can be reasonably considered to capture the external perturbations induced by magnetic storm events. The geomagnetic storms are primarily responsible for geomagnetic variations at low and mid-latitudes, while the geomagnetic substorms, which usually influence the geomagnetic field at high latitudes, can also contaminate the magnetic observations at lower latitudes due to the equatorward expansion of the auroral ovals during intense events. These choices of geomagnetic activity levels, which differ from previous works (e.g. De Michelis et al, 2015), are chosen to ensure a manageable data set since the simultaneous use of constrains on AE and SYM-H strongly reduces the amount of available data for each level. The AE and SYM-H data with one minute cadence can be downloaded from the OMNI website (www.cdaweb.gsfc.nasa.gov/istp-public/). Data are presented in terms of a quasi-dipole (QD) coordinate system, which is an apex system, introduced by Richmond (1995), and organized with respect to the Sun position introducing the magnetic local time (MLT), which is evaluated using the common definition given by Baker and Wing (1989). It has been shown, indeed, that this coordinate representation of the data in the QD coordinate system is most appropriate when analysing data in terms of ionospheric currents, which are fixed with respect to the Sun (Laundal and Gjerloev, 2014).

Method of analysis
To investigate the magnetic spatial fluctuation features we adopt the same method used in our previous studies (De Michelis et al., 2015Michelis et al., , 2016Michelis et al., , 2017) that is based on structure function analysis, a methodology that is widely used in different fields where turbulence phenomena and scale-invariant features play a fundamental role (Frisch, 1995). In detail, we evaluate the firstorder structure function S1 defined according to the following equation: where BH(t) is the time series to be analysed, < > denotes an ensemble average of the increments of the variable taken over all pairs of points separated by a scale τ that quantifies the scale of interest, and T is the time interval over which the average is calculated. In the case of a scaleinvariant signal, the first-order structure function, ! , depends on the scale τ by a power-law,

Figure 2. Local Hurst exponent values during both quiet (top panel) and active (bottom panel) geomagnetic conditions at low and middle QD magnetic latitudes (±60°) as function of MLT.
Thus, the persistent character of the magnetic field fluctuations seems to correspond with those regions where the intensity of the horizontal component of the magnetic field changes as a consequence of different ionospheric current systems. These current systems develop over spatial scale larger than 300 km and consequently they may be responsible, at the lower spatial scales that we are examining (8-300 km), for the persistent character of the fluctuations that will tend to cluster in a direction.
When the geomagnetic activity level increases passing from a quiet period to an active one, the Also in this case, the observed difference in the character of magnetic field fluctuations reflects the morphology and dynamics of that part of the ionosphere, which is crossed by the satellite. At high-latitude the ionosphere differs significantly from its mid-latitude counterpart. The highlatitude ionosphere is characterised by a strong coupling between the magnetosphere and ionosphere through electric fields and currents as well as particle flows, which make the description of this ionospheric region difficult. It is known that this region is more directly modified by magnetospheric processes that are largely controlled by the interaction between the solar wind and the Earth's magnetosphere. Indeed, at these latitudes the ionospheric currents are joined with currents flowing along geomagnetic field lines into the magnetosphere and their electrodynamics is dominated by the influences of magnetospheric processes.   One feature of a self-affine time series, which means of a time series whose rescaled version of a small part has the same statistical distribution as the larger part, is that its power-spectral density is defined as a power-law function of the frequency, whose exponent, β, is directly linked to the The conclusions derived from the Northern high latitude analysis seem to be supported by the analysis reported in this work, where the Southern high latitudes and the mid and low latitude regions have also been considered. Ionospheric and magnetospheric current systems and plasma convection processes in the equatorial region, at mid latitudes, and at high latitudes determine the scaling features (persistence or anti-persistence) of magnetic fluctuations at small spatial scales (8-300 km). The primary mechanisms that seem to control these scaling features are probably the shear motions in the plasma flow or the current-convective processes.