# The Influence of Magnetic Turbulence on the Energetic Particle Transport Upstream of Shock Waves

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## Abstract

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## 1. Introduction

## 2. Shock Crossings by ACE

## 3. The Role of Magnetic Field Intermittency on the Parallel Particle Transport

## 4. Particle Scattering Times

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Two satellite shock crossings in quasi–parallel (

**left panels**) and in quasi–perpendicular configuration (

**right panels**). From top to bottom: the magnetic field intensity from the ACE/MAG instrument at a resolution of 1 vec/s; the radial component of the solar wind bulk speed and the plasma temperature from the ACE/SWEPAM experiment at 64 s resolution; and the ion fluxes in four energy channels (as indicated in the legend in the right bottom panel) from the ACE/EPAM instrument at a resolution of 12 s, as a function of the distance from the shock time (vertical dashed lines). Notice that far downstream of the 11 February 2011 event (at about 200 min from the shock), a hot (and low density) portion of the solar wind plasma occurs, also associated to larger fluctuations in $\left|B\right|$, though this is not actually related to the shock itself.

**Figure 2.**Plot in log–log axes of the ion energy fluxes in four different channels (as indicated in the figure legend) as a function of the distance from the shock time. For the quasi-parallel shock of the 17 June 2011 (

**left panel**) the far upstream decay is well fitted by an exponential function $J\left(t\right)\propto exp(-t/T)$, while in the quasi-perpendicular shock on 11 February 2011 (

**right panel**), the ion fluxes decay as a power-law in the upstream region suggesting superdiffusive transport. The exponential and power−law best fits are reported in the panels together with their best fit parameters.

**Figure 3.**Kurtosis as a function of the time scale $\tau $ in the quasi-parallel shock crossing of the 17 June 2011 (

**left panel**) and in the quasi-perpendicular shock crossing on 11 February 2011 (

**right panel**). The Gaussian level of 3 is indicated by the horizontal dashed line and the time scale corresponding to the Larmor radius of energetic protons of 100 keV is shown by the vertical solid line. Error bars are also reported.

**Figure 4.**Probability density functions of the 100 keV energetic particles’ scattering times computed upstream of shock crossings with different levels of $\delta B/{B}_{0}$ and similar intermittency (

**left panel**) and with different intermittency values but a similar $\delta B/{B}_{0}$ (

**right panel**).

**Table 1.**Parameters of the ACE shock crossings analyzed: date of the events; time of the shock in UT; shock geometry; Alfvénic Mach number; the exponent of superdiffusion; the maximum value of the kurtosis at the Larmor scale of 100 keV protons; the fluctuation amplitude calculated at the scale of 100 keV protons; and the flux of the 100 keV protons at the shock.

Date | Time (UT) | ${\mathit{\theta}}_{\mathbf{Bn}}$ (${}^{\circ}$) | ${\mathit{M}}_{\mathit{A}}$ | $\mathit{\alpha}$ | ${\mathit{K}}_{\mathbf{max}}\left(\mathit{\tau}\right)$ | $\mathit{\delta}\mathit{B}/{\mathit{B}}_{0}$ | J*(cm${}^{-2}$/s*MeV*sr) |
---|---|---|---|---|---|---|---|

27 January 2000 | 14:00 | $23\pm 15$ | $1.6\pm 0.4$ | ND | $8.0\pm 0.7$ | $0.04\pm 0.02$ | $171.6$ |

11 February 2011 | 23:18 | $85.4\pm 8.8$ | $3.6\pm 0.5$ | $1.69\pm 0.01$ | $15.0\pm 0.9$ | $0.09\pm 0.03$ | $4.9\times {10}^{5}$ |

23 June 2000 | 12:27 | $88.7\pm 4.5$ | $3.5\pm 0.2$ | $1.60\pm 0.01$ | $5.3\pm 1.3$ | $0.09\pm 0.04$ | $4.4\times {10}^{5}$ |

17 August 2001 | 10:16 | $68.1\pm 5.4$ | $2.7\pm 0.8$ | $1.62\pm 0.01$ | $6.7\pm 1.3$ | $0.11\pm 0.05$ | $4.1\times {10}^{5}$ |

17 July 2002 | 15:26 | $4.3\pm 8.0$ | $4.4\pm 0.4$ | ND | $11.6\pm 1.2$ | $0.23\pm 0.09$ | $3.8\times {10}^{5}$ |

11 November 2004 | 16:43 | $151.6\pm 7.7$ | $1.43\pm 0.46$ | ND | $4.4\pm 0.7$ | $0.05\pm 0.02$ | $2.1\times {10}^{4}$ |

28 May 2010 | 01:53 | $6.0\pm 5.1$ | $2.76\pm 0.1$ | ND | $4.8\pm 0.8$ | $0.2\pm 0.1$ | 423 |

23 August 2010 | 16:55 | $124\pm 12$ | $3.9\pm 1.1$ | $1.77\pm 0.01$ | $5.3\pm 0.8$ | $0.15\pm 0.05$ | ${10}^{5}$ |

17 June 2011 | 02:01 | $40\pm 3$ | $2.7\pm 0.{1}^{2}$ | ND | $4.2\pm 1.0$ | $0.12\pm 0.04$ | $2.8\times {10}^{4}$ |

12 September 2014 | 15:26 | $99.4\pm 3.8$ | $2.8\pm 0.4$ | $1.797\pm 0.003$ | $5.3\pm 1.5$ | $0.15\pm 0.05$ | $6.5\times {10}^{4}$ |

2 as measured from WIND data. |

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**MDPI and ACS Style**

Perri, S.; Prete, G.; Malara, F.; Pucci, F.; Zimbardo, G.
The Influence of Magnetic Turbulence on the Energetic Particle Transport Upstream of Shock Waves. *Atmosphere* **2021**, *12*, 508.
https://doi.org/10.3390/atmos12040508

**AMA Style**

Perri S, Prete G, Malara F, Pucci F, Zimbardo G.
The Influence of Magnetic Turbulence on the Energetic Particle Transport Upstream of Shock Waves. *Atmosphere*. 2021; 12(4):508.
https://doi.org/10.3390/atmos12040508

**Chicago/Turabian Style**

Perri, Silvia, Giuseppe Prete, Francesco Malara, Francesco Pucci, and Gaetano Zimbardo.
2021. "The Influence of Magnetic Turbulence on the Energetic Particle Transport Upstream of Shock Waves" *Atmosphere* 12, no. 4: 508.
https://doi.org/10.3390/atmos12040508