Energetic ion scattering by solar wind discontinuities

Authors

Affiliation

Zijin Zhang

University of California, Los Angeles

Anton Artemyev

University of California, Los Angeles

Abstract

Because solar wind plasma flow transports the entire spectrum of magnetic field fluctuations (from low-frequency inertial range to electron kinetic range), it is a natural laboratory for plasma turbulence investigation. Among the various wave modes and coherent plasma structures that contribute to this spectrum, one of the most important solar wind elements is ion-scale solar wind discontinuities. These structures, which carry very intense current, have been considered as a free energy source for plasma instabilities that contribute to solar wind heating. Investigations of such discontinuities have been mostly focused on their magnetic field signatures; much less is known about their role in scattering of energetic ions. In this studay, we consider observational-based model of ion dynamics and scattering in force-free rotational magnetic discontinuities. Focusing on quantification of the scattering effect, we demonstrate that background sheared magnetic field plays an important role in determining the efficiency of pitch angle scattering. We provide a model included statistical properties of solar wind discontinuities and providing estimates of ion scattering rate.

Introduction

The transport of energetic particles within the heliosphere is significantly influenced by the turbulent magnetic field present in the solar wind. However, this turbulence should not be regarded merely as a collection of random magnetic field fluctuations. Instead, the nonlinear energy cascade process results in the formation of coherent structures. These coherent structures have been shown to act as efficient particle scatterers in non-collisional plasmas (Artemyev et al. 2020).

We investigated the interaction of ions with rotational discontinuities by employing a simplified analytical model for the magnetic field configuration. Our study aimed to examine how the particle pitch angle is influenced by the parameters of the magnetic field configuration and the initial conditions of the particles.

Test particle simulations of ion scattering by solar wind discontinuities

We assume the following expression:

$$\mathbf{B}=B_0(\cos \theta e_z+\sin \theta (\sin \phi (z)e_z+\cos \phi (z)e_y))$$

with $\phi (z)=\beta \tanh (z)$,

We normalize the magnetic field $\mathbf{B}$ to the background magnetic field magnitude $B_0$, the position $\mathbf{r}$ to the thickness of the discontinuity $L$, time $t$ to $1/{\Omega }_0$, with ${\Omega }_0=q{B}_0/m_p$, and the velocity $v$ to characteristic velocity $v_0={\Omega }_{0}L$. And the dimensionless form of the motion equation can be written as follows:

$$\frac{d(\gamma \mathbf{v})}{dt}=\mathbf{v}\times \mathbf{B},\frac{d\mathbf{r}}{dt}=\mathbf{v}$$

And therefore, the parameters important for our investigation of the ion scattering is $\theta$, $\beta$, and $v_0$.

Using data from the Wind mission, we compiled a dataset of 100,000 discontinuities, with their orientations determined via the minimum variance analysis of the magnetic field (MVAB) method. The orientation of these discontinuities is critical for accurately determining both their thickness ($L$) and the in-plane magnetic field rotation (${\omega }_{in}$), which are key factors in the ion scattering process. To ensure the robustness of the analysis, we utilized a filtered dataset that includes only discontinuities where $\Delta |B|/|B|>0.05$ or $\omega >60°$. As noted by Liu et al. (2023), the MVAB method yields acceptable accuracy for B_N when these conditions are met. Importantly, these two parameters, thickness and rotation, do not depend on the discontinuity normal and can be directly calculated from the magnetic field data.

The most probable values in the 3D distribution are a characteristic velocity ($v_0$) of approximately 250 km/s, a in-plane rotation angle (${\omega }_{in}$) about 90 degrees, and an azimuthal angle ($\theta$) of around 85 degrees.

Results

Scan the parameter with angle difference by 10 degree and velocity by …

Transition matrix for different particle energies

Examples of transition matrix

θ = 85°, β = 60°

Figure 1: Transition matrix for 100 keV particles.

$$\begin{array}{r}{M}_1(n)={\sum }_i({\alpha }_i^n-{\alpha }_i^0)/{\sum }_i\\ M_2(n)={\sum }_i({\alpha }_i^n-{\alpha }_i^0{)}^2-M_1^2/{\sum }_i\end{array}$$

Figure 2: Examples of ion pitch angle scattering by solar wind discontinuities for different energies.

Mixing rates

:::

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Notations

• $B_0$: background magnetic field

• $\alpha$: pitch angle, $w=\cos (\alpha )$ is the pitch angle cosine

• $\psi$: gryo phase

• θ : azimuthal angle, angle between $B_0$ and $B_N=B_0\cos (\theta )$

• φ : polar angle

• β : half of in plnae rotation angle ${\omega }_{in}$

TODO

The independence of the parameters from discontinuities observations

multivariate discrete non-parametric distribution

References

• F. Malara et al. (2023)
• Francesco Malara, Perri, and Zimbardo (2021)
• Artemyev et al. (2020)

References

Artemyev, A. V., A. I. Neishtadt, A. A. Vasiliev, V. Angelopoulos, A. A. Vinogradov, and L. M. Zelenyi. 2020. “Superfast Ion Scattering by Solar Wind Discontinuities.” Physical Review E 102 (3): 033201. https://doi.org/10.1103/PhysRevE.102.033201.

Liu, Y. Y., J. B. Cao, H. S. Fu, Z. Wang, Z. Z. Guo, and R. J. He. 2023. “Failures of Minimum Variance Analysis in Diagnosing Planar Structures in Space.” The Astrophysical Journal Supplement Series 267 (1): 13. https://doi.org/10.3847/1538-4365/acdd58.

Malara, F., S. Perri, J. Giacalone, and G. Zimbardo. 2023. “Energetic Particle Dynamics in a Simplified Model of a Solar Wind Magnetic Switchback.” Astronomy & Astrophysics 677 (September): A69. https://doi.org/10.1051/0004-6361/202346990.

Malara, Francesco, Silvia Perri, and Gaetano Zimbardo. 2021. “Charged-Particle Chaotic Dynamics in Rotational Discontinuities.” Physical Review E 104 (2): 025208. https://doi.org/10.1103/PhysRevE.104.025208.