# Influence of the Magnetic Field Topology in the Evolution of Small-Scale Two-Fluid Jets in the Solar Atmosphere

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## Abstract

**:**

## 1. Introduction

## 2. Model and Methods

#### 2.1. The System of Two-Fluid Equations

#### 2.2. Model of the Solar Atmosphere

#### 2.3. Magnetic Field Configurations

**B**for a two-dimensional Cartesian system, one gets $\nabla \times \mathbf{B}=-(\partial {B}_{x}/\partial y)$ $\widehat{z}$, thus

#### 2.4. Perturbations

#### 2.5. Numerical Methods

## 3. Results of the Numerical Simulations

#### 3.1. Uniform Magnetic Field

#### 3.2. Flux Tube-Type Configuration

## 4. Discussion

#### 4.1. Maximum Height of the Jets

#### 4.2. Temperature of the Jets

#### 4.3. Collisions between Ions and Neutrals

## 5. Conclusions

- The Jets1,2,3 generated within the uniform magnetic field (Section 3.1) with ${A}_{v}=100$ km/s showed a relationship in their maximum heights as follows, ${y}_{\mathrm{max}}\left(\mathrm{Jet}3\right)<{y}_{\mathrm{max}}\left(\mathrm{Jet}2\right)\left(\mathrm{Jet}1\right)$, and the same was seen for the case with the flux tube (Section 3.2). This behavior had already been reported in Ref. [30], a velocity pulse with ${A}_{v}=40$ km/s was used. One observes such a behaviour because the jets that arise from zones closer to the photosphere have a more significant amount of plasma that can be dragged by the pulse that perturbs the hydrostatic equilibrium. In this collective behaviour of the plasma and under the solar conditions that were taken into account here, it was not possible to observe any hint of what was predicted by the theory in Section 3.2. It is important to emphasize that the jets generated in the uniform magnetic field, reached a higher height, with a $\Delta {y}_{(i,n)\mathrm{max}}=0.75,1.2,\mathrm{and}\phantom{\rule{0.166667em}{0ex}}1.15$ Mm, concerning their counterparts in the flux tube. This result reveals a kind of braking due to the constriction of the magnetic lines in $0\le y\le 5$ Mm. Jet1 reached heights that have been reported for macrospicules [14], while Jet2 and Jet3 reached heights typical of Type I and Type II spicules [13], respectively. The three jets do not show similarities with surges since they are greater, less frequent, and more explosive than spicules. However, this requires a broader study to be able to determine if the ${y}_{0}$, at which these jets are generated can be a crucial factor in categorizing the spicules reported in Refs. [13,55,56], or if the nature of these jets creation, such as magnetic reconnection or another phenomenon, is the one that best categorizes the jets within the family of spicules already described with current observations.
- The characteristic times of collision between particles were $\tau =[1.3,3.4]$ ms, for the core and peripheries of the jet, respectively, which guaranteed from $t>0$ the coupling between ions and neutrals during the entire lifetime of the jets (${t}_{f}=600$ s), such that a joint dynamic between the fluids is observed.
- From Figure 3 and Figure 4, one can see that the jets created in the constant magnetic field are somewhat thinner than those found in the flux tube field configuration. The densities inside the jets remained within a value of ${\rho}_{i}\approx 4\times {10}^{-12}$ kg/m${}^{3}$ and ${\rho}_{n}\approx 5.4\times {10}^{-5}$ kg/m${}^{3}$ during the evolution time.
- The velocity drifts between particles were measured at the tips of the jets when they reached their maximum heights, being negligible (0–4.72 $\times {10}^{-3}$ km/s for any heat contribution that the friction between fluids could add to the coronal region. The filamentary regions above the jets with temperatures ${T}_{i,n}>6.5\times {10}^{5}$ K were generated by the shock wave that propagated towards the corona with velocities $V>100$ km/s. The temperature of the peripheries of the jets exceeded $3.62\times {10}^{5}$ K, arising entirely from friction due to the collisional interaction between the coronal plasma and the jet particles.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**

**Left**to

**right**: The $log{\rho}_{i}$, $log{\rho}_{n}$, ion-to-neutral densities ratio, ${\rho}_{i}/{\rho}_{n}$, for the solar atmosphere model at the initial time, $t=0$, and $log{T}_{i}=log{T}_{n}$.

**Figure 2.**

**Upper**: magnetic field lines for the vertical straight magnetic field configuration (

**left**) and for the flux tube configuration (

**right**) at the initial time, $t=0$. The color bar represents the magnitude of the magnetic field $\left|\mathbf{B}\right|$.

**Lower**: The plasma-$\beta $ corresponding to the vertical straight magnetic field (

**left**) and the flux tube (

**right**) at the initial time, $t=0$.

**Figure 3.**Uniform magnetic field case.

**Left**: maximum heights reached by the jets generated at ${y}_{0}=1.3$ (Jet1), 1.5 (Jet2), and 1.8 Mm (Jet3), at t = 300 s, t = 270 s, and t = 210 s, respectively (left to right). Temporal evolution of $log{\rho}_{i,n}(x,y)$ is shown for ion (

**upper**) and neutral (

**lower**) densities.

**Right**: temperatures reached by the jets Jet1, Jet2, and Jet3 generated at t = 300 s, t = 270 s, and t = 210 s, respectively (left to right). Temporal evolution is shown for $log{T}_{i,n}(x,y)$ for ions (

**upper**) and neutrals (

**lower**).

**Figure 4.**Flux tube case.

**Left**: maximum heights reached by the jets generated at at ${y}_{0}=1.3$ (Jet1), 1.5 (Jet2), and 1.8 Mm (Jet3), at t = 300 s, t = 250 s, and t = 190 s, respectively (left to right). Temporal evolution of $log{\rho}_{i,n}(x,y)$ is shown for ion (

**upper**) and neutral (

**lower**) densities.

**Right**: temperatures reached by the jets Jet1, Jet2, and Jet3 generated at t = 300 s, t = 250 s, and t = 190 s, respectively (left to right). Temporal evolution is shown for $log{T}_{i,n}(x,y)$ for ions (

**upper**) and neutrals (

**lower**).

**Figure 5.**Maximum heights, ${y}_{\mathrm{max}}$, of Jet1, Jet2, and Jet3 versus the corresponding vertical position of the initial velocity pulse in ${y}_{0}$ for ${A}_{v}=100$ km/s for the cases of the uniform (

**left**) and flux tube (

**right**) magnetic filelds. Here, the open circle represents ion jets with ${\mathbf{S}}_{in}\ne 0$; the asterisks represents neutral jets with ${\mathbf{S}}_{in}\ne 0$; the red plus symbol represents ion jets with ${\mathbf{S}}_{in}=0$; and the green plus symbol represents neutral jets with ${\mathbf{S}}_{in}=0$. See text for details.

**Figure 6.**

**Upper**: the difference between the neutral and ion speeds evaluated along $x=0$, for Jet1 (red), Jet2 (green), and Jet3 (blue) at the corresponding ${y}_{\mathrm{max}}$ values for the uniform (

**left**) and flux tube (

**right**) magnetic fields.

**Lower:**the heat ${Q}_{i}^{i,n}$, generated by the interaction between fluids evaluated along $x=0$ for Jet1 (red), Jet2 (green), and Jet3 (blue) at the corresponding ${t}_{{y}_{\mathrm{max}}}$ values for the uniform (

**left**) and flux tube (

**right**) magnetic fields.

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**MDPI and ACS Style**

Díaz-Figueroa, E.E.; de Parga, G.A.; González-Avilés, J.J.
Influence of the Magnetic Field Topology in the Evolution of Small-Scale Two-Fluid Jets in the Solar Atmosphere. *Physics* **2023**, *5*, 261-275.
https://doi.org/10.3390/physics5010020

**AMA Style**

Díaz-Figueroa EE, de Parga GA, González-Avilés JJ.
Influence of the Magnetic Field Topology in the Evolution of Small-Scale Two-Fluid Jets in the Solar Atmosphere. *Physics*. 2023; 5(1):261-275.
https://doi.org/10.3390/physics5010020

**Chicago/Turabian Style**

Díaz-Figueroa, Elton Everardo, Gonzalo Ares de Parga, and José Juan González-Avilés.
2023. "Influence of the Magnetic Field Topology in the Evolution of Small-Scale Two-Fluid Jets in the Solar Atmosphere" *Physics* 5, no. 1: 261-275.
https://doi.org/10.3390/physics5010020