# Multiscale Features of Magnetic Field Fluctuations and Field-Aligned Currents in the Polar Ionosphere: A Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

## 3. Data Description and Methods

## 4. Results

## 5. Discussion

- (i)
- circular polarization exhibits a complex multiscale structure especially in regions where FACs flow;
- (ii)
- there is a plane where the magnetic field fluctuations are circularly polarized, that is mainly perpendicular to the local main geomagnetic field direction;
- (iii)
- magnetic fluctuations in the plane perpendicular to the main geomagnetic field consist of multiscale bundles of fluctuations characterized by a positive and negative polarization (helicity ${\u03f5}_{\Vert}$).

## 6. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

2D | Two-dimensional |

AE | Auroral Electojet index |

ESA | European Space Agency |

FAC | Field-Aligned Current |

MHD | Magnetohydrodynamics |

NEC | North-East-Center |

Probabilty Density Function | |

PSD | Power Spectral Density |

PVI | Partial Variance of Increments |

RMHD | Reduced Magnetohydrodynamics |

UT | Universal Time |

## References

- Kintner, P.M.; Franz, J.; Schuck, P.; Klatt, E. Interferometric coherency determination of wavelength or what are broadband ELF waves? J. Geophys. Res.
**2000**, 105, 21237–21250. [Google Scholar] [CrossRef] [Green Version] - Chang, T. Colloid-like Behavior and Topological Phase Transitions in Space Plasmas: Intermittent Low Frequency Turbulence in the Auroral Zone. Phys. Scr. Vol. T
**2001**, 89, 80–83. [Google Scholar] [CrossRef] - Biskamp, D. Magnetohydrodynamic Turbulence; Cambridge University Press: Cambridge, UK, 2003. [Google Scholar]
- Chang, T.; Tam, S.W.Y.; Wu, C.C. Complexity induced anisotropic bimodal intermittent turbulence in space plasmas. Phys. Plasmas
**2004**, 11, 1287–1299. [Google Scholar] [CrossRef] [Green Version] - Tam, S.W.Y.; Chang, T.; Kintner, P.M.; Klatt, E. Intermittency analyses on the SIERRA measurements of the electric field fluctuations in the auroral zone. Geophys. Res. Lett.
**2005**, 32, L05109. [Google Scholar] [CrossRef] [Green Version] - Consolini, G.; De Michelis, P.; Alberti, T.; Giannattasio, F.; Coco, I.; Tozzi, R.; Chang, T.T.S. On the multifractal features of low-frequency magnetic field fluctuations in the field-aligned current ionospheric polar regions: Swarm observations. J. Geophys. Res. Space Phys.
**2020**, 125, e2019JA027429. [Google Scholar] [CrossRef] - Moffatt, H.K. Magnetic Field Generation in Electrically Conducting Fluids; Cambridge University Press: Cambridge, UK, 1978. [Google Scholar]
- Matthaeus, W.H.; Goldstein, M.L. Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind. J. Geophys. Res.
**1982**, 87, 6011–6028. [Google Scholar] [CrossRef] - Smith, C.W. Magnetic helicity in the solar wind. Adv. Space Res.
**2003**, 32, 1971–1980. [Google Scholar] [CrossRef] - Stribling, T.; Matthaeus, W.H.; Oughton, S. Magnetic helicity in magnetohydrodynamic turbulence with a mean magnetic field. Phys. Plasmas
**1995**, 2, 1437–1452. [Google Scholar] [CrossRef] [Green Version] - Matthaeus, W.H.; Smith, C. Structure of correlation tensors in homogeneous anisotropic turbulence. Phys. Rev. A
**1981**, 24, 2135–2144. [Google Scholar] [CrossRef] [Green Version] - Gedalin, M.; Russel, C.T. Application of wavelets to the analysis of multiscale structures. In Physics of Space Plasmas (1998): Proceedings of the 1998 Cambridge Symposium/Workshop in Geospace Physics on Multiscale Phenomena in Space Plasmas II; Chang, T., Jasperse, J.R., Eds.; MIT Center for Theoretical Geo/Cosmo Plasma Physics: Cambridge, MA, USA, 1998; Volume 15, p. 103108. [Google Scholar]
- Telloni, D.; Bruno, R.; D’Amicis, R.; Pietropaolo, E.; Carbone, V. Wavelet Analysis as a Tool to Localize Magnetic and Cross-helicity Events in the Solar Wind. Astrophys. J.
**2012**, 751, 19. [Google Scholar] [CrossRef] - Ritter, P.; Lühr, H.; Rauberg, J. Determining field-aligned currents with the Swarm constellation mission. Earth Planets Space
**2013**, 65, 1285–1294. [Google Scholar] [CrossRef] [Green Version] - Finlay, C.C.; Olsen, N.; Tøffner-Clausen, L. DTU candidate field models for IGRF-12 and the CHAOS-5 geomagnetic field model. Earth Planets Space
**2015**, 67, 114. [Google Scholar] [CrossRef] [Green Version] - Mininni, P.D.; Pouquet, A. Finite dissipation and intermittency in magnetohydrodynamics. Phys. Rev. E
**2009**, 80, 25401. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Müller, W.C.; Malapaka, S.K.; Busse, A. Inverse cascade of magnetic helicity in magnetohydrodynamic turbulence. Phys. Rev. E
**2012**, 85, 15302. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Müller, W.C.; Malapaka, S.K. Role of helicities for the dynamics of turbulent magnetic fields. Geophys. Astrophys. Fluid Dyn.
**2013**, 107, 93–100. [Google Scholar] [CrossRef] [Green Version] - Kintner, P.M.; Seyler, C.E. The status of observations and theory of high latitude ionospheric and magnetospheric plasma turbulence. Space Sci. Rev.
**1985**, 41, 1572–9672. [Google Scholar] [CrossRef] - Mounir, H.; Berthelier, A.; Cerisier, J.C.; Lagoutte, D.; Beghin, C. The small-scale turbulent structure of the high latitude ionosphere—Arcad-Aureol-3 observations. Ann. Geophys.
**1991**, 9, 725–737. [Google Scholar] - Golovchanskaya, I.V.; Ostapenko, A.A.; Kozelov, B.V. Relationship between the high-latitude electric and magnetic turbulence and the Birkeland field-aligned currents. J. Geophys. Res. (Space Phys.)
**2006**, 111, A12301. [Google Scholar] [CrossRef] - Wu, C.C.; Chang, T. 2D MHD simulation of the emergence and merging of coherent structures. Geophys. Res. Lett.
**2000**, 27, 863–866. [Google Scholar] [CrossRef] - Greco, A.; Servidio, S.; Matthaeus, W.H.; Dmitruk, P. Intermittent structures and magnetic discontinuities on small scales in MHD simulations and solar wind. Planet. Space Sci.
**2010**, 58, 1895–1899. [Google Scholar] [CrossRef] - Franci, L.; Landi, S.; Verdini, A.; Matteini, L.; Hellinger, P. Solar Wind Turbulent Cascade from MHD to Sub-ion Scales: Large-size 3D Hybrid Particle-in-cell Simulations. Astrophys. J.
**2018**, 853, 26. [Google Scholar] [CrossRef] - Papini, E.; Franci, L.; Landi, S.; Verdini, A.; Matteini, L.; Hellinger, P. Can Hall Magnetohydrodynamics Explain Plasma Turbulence at Sub-ion Scales? Astrophys. J.
**2019**, 870, 52. [Google Scholar] [CrossRef] [Green Version] - Franci, L.; Stawarz, J.E.; Papini, E.; Hellinger, P.; Nakamura, T.; Burgess, D.; Landi, S.; Verdini, A.; Matteini, L.; Ergun, R.; et al. Modeling MMS Observations at the Earth’s Magnetopause with Hybrid Simulations of Alfvénic Turbulence. Astrophys. J.
**2020**, 898, 175. [Google Scholar] [CrossRef] - Papini, E.; Cicone, A.; Piersanti, M.; Franci, L.; Hellinger, P.; Landi, S.; Verdini, A. Multidimensional Iterative Filtering: A new approach for investigating plasma turbulence in numerical simulations. J. Plasma Phys.
**2020**, 86, 871860501. [Google Scholar] [CrossRef] - Consolini, G.; De Michelis, P.; Coco, I.; Alberti, T.; Marcucci, M.F.; Giannattasio, F.; Tozzi, R. Sign-Singularity Analysis of Field-Aligned Currents in the Ionosphere. Atmosphere
**2021**, 12, 708. [Google Scholar] [CrossRef] - Valentini, F.; Perrone, D.; Stabile, S.; Pezzi, O.; Servidio, S.; De Marco, R.; Marcucci, F.; Bruno, R.; Lavraud, B.; De Keyser, J.; et al. Differential kinetic dynamics and heating of ions in the turbulent solar wind. New J. Phys.
**2016**, 18, 125001. [Google Scholar] [CrossRef] [Green Version] - Tetreault, D. Turbulent relaxation of magnetic fields 1: Coarse-grained dissipation and reconnection. J. Geophys. Res.
**1992**, 97, 8531–8540. [Google Scholar] [CrossRef] - Tetreault, D. Turbulent relaxation of magnetic fields 2. Self-organization and intermittency. J. Geophys. Res.
**1992**, 97, 8541–8547. [Google Scholar] [CrossRef] - Hulot, G.; Léger, J.M.; Vigneron, P.; Jager, T.; Bertrand, F.; Coïsson, P.; Deram, P.; Boness, A.; Tomasini, L.; Faure, B. Nanosatellite high-precision magnetic missions enabled by advances in a stand-alone scalar/vector absolute magnetometer. In Proceedings of the IGARSS 2018 IEEE International Geoscience and Remote Sensing Symposium, Valencia, Spain, 22–27 July 2018; pp. 6320–6323. [Google Scholar] [CrossRef]

**Figure 1.**A schematic picture of the orientation of the vector $\mathbf{X}$ and the propagation direction in the case of a plane wave.

**Figure 2.**The external magnetic field components in the NEC reference frame and parallel (${b}_{\Vert}$) and perpendicular (${b}_{\perp i}$) to the local main geomagnetic field. Data refer to measurements recorded on October 25, 2016 from 17:50 UT to 18:08 UT.

**Figure 3.**

**Upper panel**: Magnetic field components, ${b}_{\perp}^{1}$ and ${b}_{\perp}^{2}$, perpendicular to the local main magnetic field direction.

**Lower panel**: The scalogram relative to the circular polarization, ${P}_{c}^{w}(t,\tau )$, with ${\tau}_{0}=0.02$ s.

**Figure 4.**

**Upper panel**: the wavelet energy scalogram ${E}_{n}(t,\tau )={\mathbf{W}}^{*}\mathbf{W}$.

**Lower panel**: the FAC density, ${j}_{FAC}$.

**Figure 5.**The average $\langle {P}_{c}^{w}\left(\delta r\right)\rangle $ as a function of the spatial scale $\delta r={v}_{s}\tau $. Red and blue lines refer to the overall interval and to the two selected FAC intervals, respectively.

**Figure 6.**

**Upper panel**: The component ${n}_{\Vert}$ of the propagation direction $\widehat{\mathbf{n}}$ parallel to the local main geomagnetic field.

**Lower panel**: the FAC density, ${j}_{FAC}$.

**Figure 7.**The probability density function (PDF), $p\left({n}_{\Vert}\right)$, for a selected number of spatial scales, $\delta r={v}_{s}\tau $.

**Figure 8.**

**Upper panel**: The polarization scalogram, ${\u03f5}_{\Vert}(t,\tau )$, in the plane perpendicular to the local main geomagnetic field.

**Lower panel**: the FAC density, ${j}_{FAC}$.

**Figure 9.**

**Upper panel**: The scalogram, of $|{p}_{\perp}^{(1,2)}(t,\tau )|$, in the plane perpendicular to the local main geomagnetic field. Unit is $({\mathrm{nT}}^{2}\xb7\mathrm{s})$.

**Lower panel**: the FAC density, ${j}_{FAC}$.

**Figure 10.**The average spectra of $|{p}_{\perp}^{(1,2)}|$ for the regions where FACs flow and in the polar cap.

**Figure 11.**

**Upper panel**: The scalogram, of positive-hand polarization energy, ${p}_{\perp}^{(+)}$, in the plane perpendicular to the main geomagnetic field.

**Mid panel**: The scalogram, of negative-hand polarization energy, ${p}_{\perp}^{(-)}$, in the plane perpendicular to the local main geomagnetic field.

**Lower panel**: the FAC density, ${j}_{FAC}$. Polarization energy unit is $({\mathrm{nT}}^{2}\xb7\mathrm{s})$.

**Figure 12.**A schematic picture of the two possible scenarios. Panel (

**a**): a complex current structures consisting of multiscale upward and downward current filaments. Panel (

**b**), a complex multiscale structure of coherent magnetic flux tubes aligned to the main geomagnetic field ${\mathbf{B}}_{0}$.

**Figure 13.**Comparison between the $PV{I}_{{\tau}_{0}}$ computed at the smallest available timescale ${\tau}_{0}=0.02$ s and the FAC intensity for the selected time interval.

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**MDPI and ACS Style**

Consolini, G.; De Michelis, P.; Alberti, T.; Coco, I.; Giannattasio, F.; Pezzopane, M.; Tozzi, R.
Multiscale Features of Magnetic Field Fluctuations and Field-Aligned Currents in the Polar Ionosphere: A Case Study. *Universe* **2022**, *8*, 610.
https://doi.org/10.3390/universe8120610

**AMA Style**

Consolini G, De Michelis P, Alberti T, Coco I, Giannattasio F, Pezzopane M, Tozzi R.
Multiscale Features of Magnetic Field Fluctuations and Field-Aligned Currents in the Polar Ionosphere: A Case Study. *Universe*. 2022; 8(12):610.
https://doi.org/10.3390/universe8120610

**Chicago/Turabian Style**

Consolini, Giuseppe, Paola De Michelis, Tommaso Alberti, Igino Coco, Fabio Giannattasio, Michael Pezzopane, and Roberta Tozzi.
2022. "Multiscale Features of Magnetic Field Fluctuations and Field-Aligned Currents in the Polar Ionosphere: A Case Study" *Universe* 8, no. 12: 610.
https://doi.org/10.3390/universe8120610