1 Department of Physics, Visva-Bharati University, Santiniketan, Bolpur
731235, India
2 Department of Physics, Ramakrishna Mission Residential College, Narendrapur,
Kolkata 700103, India
3 Department of Physics, Indian Institute of Technology Madras, Chennai,
600036, India
4 Department of Physics, Government General Degree College at Kushmandi,
Dakshin Dinajpur 733121, India
5Institute of Natural Sciences and Applied Technology, Kolkata 700032, India

# Two-stream Plasma Instability as a Potential Mechanism for Particle
Escape from the Venusian Ionosphere

S. Dey1 S. Ghosh2 D. Maity1 A. De3 S. Chandra4,5*

###### Abstract

In this work we investigate the possibility of two-stream instability in the
Venusian atmosphere to lead to momentum transfer to subsequent escape of
Hydrogen and Oxygen ions from the ionosphere. We employ the hydrodynamic model
and obtain the linear dispersion relation from which the two-stream
instability is studied. Further the interaction of solar wind with the ions of
Venus ionosphere from which the instability sets in, has been studied with the
data from ASPERA-4 of Venus Express (VEX). The data supports the fact that the
two-stream instability can provide sufficient energy to accelerate ions to
escape velocity of the planet and thus leave the Venusian ionosphere.

###### keywords:

Two Stream Instability, Linear Dispersion, Solar Wind (SW), Hydrodynamic
Model, Venus Express (VEX), ASPERA-4

###### pacs:

96.30.Ea; 94.20.wh; 52.35.Qz; 11.55.Fv; 52.25.Jm

<EMAIL_ADDRESS>
19 August 20212 June 20225 July 2022

00.XXXX/XXXXXX-XXX-XXX-X #### 000 2022 01-08 8

##  1 Introduction

Planets that have strong magnetic fields in their interior region, like Earth,
Jupiter, Saturn, and Mercury, are enclosed by invisible magnetosphere [1]. The
charged particles of the solar wind radiation (electrons and protons) are
deflected by their magnetic fields as they stream far away from the Sun. This
deflection by the magnetic field creates a magnetic sphere that acts as a
protective ”bubble” covering the planet [2]. Venus has no intrinsic magnetic
field to act as a protection against the incoming stream of charged particles.
However, the solar wind and UV radiation from sun, pulls out electrons from
the atoms and molecules within the higher atmosphere, making a section of
electrically charged gas referred to as the ionosphere. The planet is
protected partially by the induced magnetic force field due to this
ionosphere. But this induced magnetic field is very small in magnitude and not
sufficient to deflect the solar wind unlike other planets. Thus, the electrons
in the solar wind end up directly interacting with the higher atmosphere. We
have suggested a likely ion escape route resulting from the instability under
some physical conditions. We have used analytical and simulation tools and
their outcomes, which depend on the occurrences of the ionization processes,
as well as solar wind conditions. Newborn ions are at rest relative to the
Venus frame. From previous studies [3], [4] we can observe that ion
acceleration on Venus can occur through three mechanisms: (a) ion uptake
(through acceleration in a convective electric field), (b) through induced
instabilities in the ionosphere, and lastly (c) through polarization
electrical fields at low altitude on the night side of the Venusian
ionosphere. We are going to explore the second mechanism of ion acceleration
in this paper.

This paper explores the possibility of two-stream instability to cause ions to
escape from the atmosphere of Venus. It has been observed that the critical
condition under which the instability can occur for the classical regime plays
a major role in particle energization. The following is the outline of the
paper. We discuss the fluid model of Venusian plasma in section 2, the
dispersion relation has been obtained in section 3, section 4 finally
describes the possible ion escape mechanisms via two-stream instability by
analyzing the Venus Express data.

##  2 Fluid model of the Venusian ionosphere

In 1937 Jeffreys [5] first built the model of Venus from Bullens’ model [6] of
the Earth. In 1983, Zharkov [7] provided a complete model of Venus. Venus has
an extremely low magnetic field. So planetary magnetosphere is less important
in this case. A magnetospheric plasma shell which exists around some planets
have been investigated by many authors [8, 9, 10, 11, 12, 13, 14] but not with
respect to Venus. We have considered a homogeneous plasma [15, 16] comprised
of electrons and ions. The basic governing equations for the fluid model [17,
18, 19, 20, 21, 22, 23, 24, 25, 26, 27] are as follows [28, 29, 30, 31, 32]:

$\frac{\partial n_{j}}{\partial
t}+\mathbf{\nabla}\cdot\left(n_{j}\mathbf{v_{j}}\right)=0$ (1)

$\left(\frac{\partial\mathbf{v_{j}}}{\partial
t}+\mathbf{v_{j}\cdot\nabla}\mathbf{v_{j}}\right)=-\frac{Q_{j}}{m_{j}}\left(\mathbf{\nabla}\phi-\mathbf{v_{j}}\times\mathbf{B}\right)-\frac{1}{m_{j}n_{j}}\mathbf{\nabla}P_{j}$
(2)

$\mathbf{\nabla}\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}$ (3)

The terms are on the right side of equation (2) specified as Lorentz force,
stress term [33]. Let us assume the equation of state [28] is given by:

$P_{j0}=n_{j0}k_{B}T$ (4)

where $n_{j}$ signifies the number density, $v_{j}$ represents the fluid
velocity, $p_{j}$ indicates the pressure, $m_{j}$ represents the mass,
$\mathbf{E}$ and $\mathbf{B}$ represents the electric and magnetic field
respectively, and $k_{B}$ is the Boltzmann constant.

##  3 Dispersion Relation

As the solar wind flows freely into the Venusian atmosphere, it excites the
neutral particles to form ions. This constitutes the plasma of the ionsphere.
The resulting magnetic field has a very low value unlike the intrinsic
magnetic fields of planets like, Earth, Jupiter, etc. The electrons in the
solar winds streams into the stationary ions of the ionsphere. This relative
motion between the ions and fast moving electrons causes the so called two-
stream instability. Two-stream instability can be discussed based on the
consideration of electron-ion streams having densities $n_{e},n_{i}$ and
temperatures $T_{e}$, $T_{i}$ with the velocities $v_{e},v_{i}$. The electron
and ion thermal velocities are $v_{T,e},v_{T,i}$. We further investigate
whether the aforesaid situation is relevant with Venusian ionosphere or not.
Here $\omega_{pi}$ and $\omega_{pe}$ represents the plasma frequency with
which ions and electrons oscillate, respectively. We get the dispersion as
follows:

$1-\frac{\omega_{pe}^{2}/4}{\left(\omega-
kv_{e}\right)^{2}-k^{2}v_{T,e}^{2}/2}-\frac{\omega_{pi}^{2}/4}{(\omega-
kv_{i})^{2}-k^{2}v_{T,i}^{2}/2}=0$ (5)

$v_{T,e}=\sqrt{2T_{e}/m_{e}}$ and $v_{T,i}=\sqrt{2T_{i}/m_{i}}$ are the
thermal speed of electrons and ions respectively [28]. The equation is quite
same to the results in [28],[34] and Hsia [35] discarding the thermal terms.
We can simplify by normalizing the time and relative velocity (or drift
velocity) as $1/\omega_{pe}$ and $\omega_{pe}/k$ respectively. Relative
velocity, $v\equiv v_{e}-v_{i}$ can be obtain by a simple analysis where,
$v_{e}$ and $v_{i}$ are oppositely directed. For electron-positron pair plasma
it can be shown that purely oscillating two stream instability can be possible
for $m_{e}/m_{p}=1$ ,where the relative velocity needs to be periodic
$sin(\omega_{0}t)$. From Qin et al.[36] we can clearly see that the growth
rate has a dependence on $\omega_{p}/\omega_{0}$ and $kv/\omega_{pe}$ in a
very complex way with $\omega_{p}=\sqrt{2}\omega_{pe}$. If the driving
frequency is slightly higher or lower than the plasma frequency, the
oscillations become unstable.

###  3.1 Conditions for onset of instability:

We simplify the equation (5) in the rest frame of ions:

$\mathcal{F}(\omega)=\frac{\omega_{pe}^{2}/4}{\left(\omega-
kv_{e}\right)^{2}-k^{2}v_{T,e}^{2}/2}+\frac{\omega_{pi}^{2}/4}{\omega^{2}-k^{2}v_{T,i}^{2}/2}$
(6)

For extremum point we have,

$\begin{split}\xi=&\left[q+\left\\{q^{2}+\left(r-p^{2}\right)^{3}\right\\}^{1/2}\right]^{1/3}+\\\
&\left[q-\left\\{q^{2}+\left(r-p^{2}\right)^{3}\right\\}^{1/2}\right]^{1/3}+p\end{split}$
(7)

Where,
$\alpha=\frac{\omega_{pi}^{2}}{\omega_{pe}^{2}},\xi=\frac{\omega}{kv_{e}},p=\frac{2\alpha^{2}}{3(1+\alpha^{2})},\\\
q=\frac{p^{3}+\left[(-2\alpha^{2})\left\\{\alpha^{2}-1-\left(1+\alpha^{2}\right)\frac{v_{0}^{2}}{2v_{e}^{2}}\right\\}-3\left(1+\alpha^{2}\right)\frac{v_{0}^{2}}{2v_{e}^{2}}\right]}{6\left(1+\alpha^{2}\right)^{2}},\\\
r=\frac{\alpha^{2}-1-\left(1+\alpha^{2}\right)\frac{v_{0}^{2}}{2v_{e}^{2}}}{3\left(1+\alpha^{2}\right)}$
and $v_{0}$ is the speed at thermal equilibrium. Now at that point,

$\begin{split}\omega\equiv\omega_{s}=&kv_{e}\left[q+\left\\{q^{2}+\left(r-p^{2}\right)^{3}\right\\}^{1/2}\right]^{1/3}+\\\
&kv_{e}\left[q-\left\\{q^{2}+\left(r-p^{2}\right)^{3}\right\\}^{1/2}\right]^{1/3}+pkv_{e}\end{split}$
(8)

The condition for instability, $\mathcal{F}(\omega_{s})>1$

If the above obtained value for $\omega_{s}$ is substituted in the expression
for $\mathcal{F}(\omega)$ and is equated to 1, then by little algebraic
manipulation, $v_{e}$ will be determined. We define this electron velocity
satisfying the instability condition to be the threshold velocity($v_{th}$).

$v_{th}\equiv
v=\frac{\omega_{pe}}{k}\left[1+\left(\frac{m_{e}}{m_{p}}^{1/3}\right)\right]^{3/2}$
(9)

Any relative electron velocity greater than this threshold velocity will make
the system unstable and the resultant instability might accelerate the ions to
escape velocity. Detailed discussion on this is done in the subsequent
sections.

##  4 Discussion

The particles have a speed near to the phase speed with which plasma waves can
supply the energy necessary for escape. A probable process for coupling of
collisionless momentum between the plasmas which are interpenetrating with
each other at the blocking layer might result in a stream of electrons causing
the streaming instability.

Figure 1: Phase space particle-in-cell simulation of streaming instability
occurring in (a) and (b) when the velocity of threshold ($v\equiv v_{th}$) is
much lower than relative velocity. Captured for specific time values as
indicated, (a) 20 s, (b) 30 s. Figure 2: Phase space particle-in-cell
simulation of streaming instability occurring in (c) and (d) when the
threshold velocity is large enough than the relative velocity. Captured for
specific time values as indicated, (c) 20 s, (d) 30 s

###  4.1 Analysis with PIC simulation

In this system, electrons got accelerated by the electric field in the
vicinity of particle following the Poisson equation,

$\frac{d^{2}\phi(x_{j})}{dx^{2}}\approx\frac{\phi_{j+1}+\phi_{j-1}-2\phi_{j}}{(\Delta
x)^{2}}$

Using the above equation, we looked for the potential at each point in the
mesh. We assumed a periodic sinusoidal boundary condition and interpolated
from adjacent grid-points $j$ and $j+1$. Using the leap-frog integration
method, we calculated the velocity and position at each time step.

####  4.1.1 Simulation Parameters:

The parameter values for our configurations are as follows: the PIC algorithm
were simulated with 40000 number of particles $(N)$ and 400 number of mesh
cells. The growing of instability were measured with a time step $(dt)$ of 1
sec from $t=1$ to $50$. To construct the matrix for the gradient operator for
computing the first derivative we used the minimum separation $\Delta
x=0.125$. To calculate the initial gravitational accelerations of electrons we
have used those values. Next we constructed two oppositely moving streams
adding the periodic perturbation with amplitude of sinusoidal function around
0.1. Initial relative velocity is taken as 4.5 km/s.

####  4.1.2 Initial Conditions:

In our code, we implemented two uniform counter-propagating streams travel
initially (t=0). The orientations of the particles are chosen randomly with a
uniform distribution. The velocities are measured using a Gaussian centered
distribution about the rate of streams. A tiny perturbation in periodic form
(sinusoidal function) is applied to the velocity distribution. We simulated
with a large number of particles (around 40000 particles) in phase space.

####  4.1.3 Emergent Phase-space:

Let now discuss how the ions get energize by interpenetrating flow of
particles. A prevalent electric field, which is not stable, links the two
streams. The energy from the strongly interacting streams is transferred to
the driven electric field. The streams mix as the destabilizing electric field
increases and continue to act, ultimately destroying the streams or dispersing
the particles in phase space. As the acceleration of the streams grows, the
instability tends to increase, potentially causing the streams to become more
turbulent. Several electrons have been ascertained moving at a faster rate
than their initial velocity due to a boost in energy from the wave, continuing
to increase their velocity at the outlay of the wave energy, leading to a
reduction in wave velocity. The energy due to the electric field increases as
the stream velocity increases. The energy of the particles increased as the
density of the streaming particles increased, however, at different rates.
Indicating that the streaming particles become thermalized across the
simulation, causing the plasma to become much more intense.

In order to analyze the distribution of the variables like density,
temperature, velocity, data should be organized according to the occurrence of
different results in each category. We have carried out a particle-in-cell
(PIC) simulation which is depicted in figure (1) and figure (2) and the
procedure has been discussed in the appendix section. Plasma waves are formed
by the free energy imparted to the system by the inward streaming solar wind
electrons, and due to this particles starts disappearing from the simulation
box. Thereafter, a particle starved region in phase-space emerge. The
relatively moving particles pile over each other. Both components exist side
by side to the right, form a distribution of particles that is unstable for
the aforesaid instability under the condition that threshold velocity is much
lower than relative velocity. The instability due to relative propagating
particles in the inhomogeneous plasma becomes saturated, generating phase
space starved pockets as particles are trapped by an increasingly unstable
mode [37]. In the phase space simulation, the process takes place spatially
and temporally as well. We investigated the efficiency of emerging two-stream
instability of interacting solar wind ions with Venusian ionospheric plasma.
The conservation of streaming energy for this case using the Poisson equation
is obeyed. For time scale t=0 to 50 sec, the growing of two-stream instability
has been checked for different initial conditions such as relative velocities
and densities to study the regions where the energy conservation is obeyed. We
have checked the energy conservation with relative velocity, 4.5 $km/s$ and
density around 4 $cm^{-3}$. We have checked the ratio of energy of electrons
to the initial energy with time scale (t). Initially the energy is zero. Then
the instability sets in and the energy increases. Eventually the system comes
to a dynamic equilibrium at a time scale, $t\approx 30s$, and the energy
becomes constant at around 2.14 eV. When the accelerated stream of particles
interacts with the stationary component of the electrons which were reflected
further, a phase space trench forms toward the left of the box. It has been
found that an electron-depleted region drifts away from the center of the
phase space with increasing time.

Data Table 1: Parameters for the Instability and the ion energization Parameter | Notation | Value
---|---|---
Density of SW | $n_{sw}$ | $5~{}cm^{-3}$
Velocity of SW | $v_{sw}$ | $350~{}km/s$
Temperature of SW electrons | $T_{e}$ | $27~{}eV$
Thermal velocity of electrons | $v_{the}$ | $2500~{}km/s$
Planetary ion temperature | $T_{ion}$ | $0.3-0.4~{}eV$
Electron plasma frequency | $f_{e}$ | $9~{}kHz$
Surface gravity of Venus | $g_{v}$ | $8.88~{}m/s^{2}$

We have considered two situations here; one is when the velocity of threshold
is lower than the relative velocity, and another is when the velocity of
threshold is higher than the relative velocity. At first, all particles are
able to flow smoothly. Figure (1) shows the growth of the charges in phase
space at different time. When the threshold velocity is much lower than
relative velocity, all electrons become kinetic. Electrons subject to strong
acceleration become kinetic. On other hand Figure (2) shows that the threshold
velocity is large enough than the relative velocity then no instability
arises. Now, we have already discussed that the threshold for instability,
$\mathcal{F}(\omega_{s})>1$. We have used the data of the ionosphere of Venus.
As we have seen two-stream instability is not seen everywhere in the
ionosphere. there are some specific regions where the particles are able to
get energy from such instability. In the next part of our study we have
focused on that regions where ion-loss occurs. Our study lies in that velocity
regime on which two-stream instability leads to a strong acceleration of
planetary ions which are very energetic in the range of suprathermal energies
[38]. Some newer simulation studies based on homotopy [39, 40, 41, 42, 43]
could provide some additional information.

###  4.2 A Morphology of Ion Escape Process

In different regions of the ionosphere, the average energies of the ions are
different that corresponds to different fluxes of particle escape.

Figure 3: A schematic diagram of energy-momentum transfer within deep magneto-
tail region. Colored arrows indicate the flow of the SW, flow of planetary
plasma.

The maps of the measured fluxes are shown in the following Figure (4) for the
ions $H^{+}$, $O^{+}$ at the tail of the Venus plasma sheet [44, 45]. A
schematic section is given in Figure (3).

Figure 4: Measured flux map of (a) $O^{+}$, (b) $H^{+}$ fluxes within the
magneto tail area of Venus (obtained by Barabash et al.)[54] in
”Venus–solar–electrical coordinate”[50]. Colour map indicates the energy (eV)
and dots are flux $\left(cm^{-2}s^{-1}\right)$

This section focuses on possible regions of ion escape from the observations
of VEX, specifically from the instrument ASPERA-4. We represented the ion
escape over the aforesaid velocity regime for two-stream instability. New
patch retrieved from PDS-PPI IGPP UCLA [46, 47] extending upon ion densities
and magnetic field have been used here.

It has been seen that ions that escape slowly carry the higher mass loss.
Like, if we consider for a while, that $O^{+}$ ions flow with velocity ’v’
comprise that streaming instability, then it is the cause for supplying the
velocity for escape. Thermal velocity is very near to the velocity of escape.
The $\Phi_{max}$ (maximum flux) will be large than solar wind (SW) flux by the
factor of that velocity v [48]. We assumed that planetary ions are escaping
across the plasma sheet, therefore the area where the exchange of momenta
starts is given by,

$\centering S_{V}=\pi(R_{B}^{2}-R_{I}^{2})\@add@centering$ (10)

$R_{B}$ and $R_{I}$ are the radii of the boundaries where exchange of momenta
starts and Venusian ionosphere respectively. Estimated flux,
$\Phi_{V}\sim\frac{m_{SW}v_{SW}}{m_{i}v}\Phi_{SW}$ where, the flux of the
solar wind is $\Phi_{SW}$ and $\Phi_{v}$ is the flux due to ions [3].

###  4.3 A Possible Way of the Particle Escape Process

A simple estimation of the flux escaping from Venus caused by the solar wind
stands on momentum conservation. It has been found that ions like $O^{+}$
which are comparatively heavier than $H^{+}$ ions remain uninfluenced by the
magnetic field. This causes an electric field to appear that extracts and also
accelerate the planetary ions like $H^{+},O^{+}$ to reach quasi-neutrality
condition[49]. A cross-sectional view of flux measurement of ions like oxygen
and hydrogen in the Venusian magnetotail region in ”Venus-Solar-Electric
coordinate system” [50] is shown in Figure (4). The vertical red arrow defines
the electric field.

Density over magnetic field distribution was shown in Figure (5). Higher
density regions are slightly experienced by induced magnetic field. The
thermal leakage of lighter ions, mostly $H^{+}$ ions, is quite dominant in
Venus [51]. On other hand, heavier atoms like that of Oxygen ($O^{+}$) follow
the mechanism,

$O_{2}^{+}+e^{-}\rightarrow O^{*}(normal)+O^{*}(energetic)$

and energy is supplied by two-stream instability for escape. Our investigation
therefore can only explain ion-loss within the energy range 10 to 100 eV.

Hartle and Grabowsky [52, 53] have shown that the lighter ion streams in the
Venus ionospheric zone are caused by the magnetic and the electrical pressure
gradients given by:

$~{}qn_{e}\mathbf{E}=-\nabla P_{e}-\nabla\frac{B_{z}^{2}}{2\mu_{0}}$ (11)

Figure 5: Density of Oxygen like heavy ions over z-component of magnetic field
plot and heatmap for Venus plasma ionosphere

We see that planetary protons or lighter ions $(H^{+})$ move quite faster than
the comparably heavier ions $(O^{+})$ which are still much slower than ions in
the solar wind flow. Bulk speeds of oxygen and hydrogen ions are grouped
around, $V_{O^{+}}=V_{H^{+}}\times\sqrt{\frac{m_{H^{+}}}{m_{O^{+}}}}$ implying
that the relation between the possible velocities of escape for particles with
approximately same energy. In an effect, it may be concluded though subject to
different electric fields, the ion’s energy gain of similar order is obtained
through the exchange of momentum [55]. The relative velocity regime associated
with our simulation strictly relates to the flux map in figure (4). This shows
a correspondence between simulation and particle escape scenarios.

The flux map showing the sky blue bubbles in figure (4)
($10^{1}-10^{2}~{}eV$), are the regions where the instability is dominating.
In this regions our PIC code is forming the instability. The particles can be
out of the ionosphere of the planet if the ion velocity is greater than the
escape velocity. Using the condition $\mathcal{F}(\omega_{s})>1$ we had got
the threshold velocity to be :

$v_{th}\equiv
v=\frac{\omega_{pe}}{k}\left[1+\left(\frac{m_{e}}{m_{p}}^{1/3}\right)\right]^{3/2}$
(12)

From this the Threshold Energy ($E_{th}$) comes out to be about 5.0661 $eV$
and using the fact that the extra energy is due to instability is about 2.138
$eV$. The escape energy of oxygen ions is nearly 8.7 eV. From the cross-
sectional view, the energies of oxygen ions ranges from 10-100 eV, and the
excess energy can be estimated using the threshold. We got extra energy of
about 2 to 4 eV, which is enough to escape from the ionosphere.

So, the fundamental problem of depletion of the Hydrogen and Oxygen ions from
the atmosphere can be directly related to the energization of ions through
two-stream instability induced by the solar wind. The streaming instability
energizes the ions, pushing them to velocities higher than the escape
velocity, causing the loss of planetary ions.

Interestingly the rate of escape of the ions in the Venusian ionosphere,
estimated by the various authors [56, 57, 58] based on the observations by
ASPERA-4 and in distinct energy spectra are quite similar in their form and is
in tune with this present investigation. It may be also possible that some
shock like nonlinear resonant mechanisms can accelerate the process [30, 59,
60, 61, 62]. In this respect some recent works can provide some insight [63,
64].

##  5 Appendix

We have designed a Particle-in-cell (PIC) simulation Figure (1) to demonstrate
the phase space mechanism and two-stream instability. We have framed a python
code to simulate the instability. At the beginning we calculate the
acceleration on each particle due to the field then compute the electron
number density on the mesh by placing the particles into the 2 nearest bins (j
and j+1, with proper weights) and then normalized them. Next we applied a
periodic boundary condition on them following which we solved the Poisson
Equation and applied derivative to get the electric field and interpolated the
grid value onto the locations of particle. Afterward, we run our defined
functions in the main PIC simulation function with appropriate parameter
values. They are constructed by two matrices to computer Gradient and
Laplacian for $1^{st}$ and $2^{nd}$ derivatives. Finally, simulating in main
loop with drift (and applied some periodic boundary conditions) we obtain the
two-stream instability in phase space. Such instabilities can be explained
elaborately in the light of studies carried out by some authors [65, 66, 67,
68, 69] using dynamical systems [70, 71, 72, 73, 74]. In Figure (4) Flux map
has been shown in ”Venus solar electrical coordinate” using python this has
been motivated by Barabash et al.[54] Density map Figure (5) of Hydrogen and
Oxygen is plotted first and then smoothen using the sigmas in python
numerically.

##  6 ORCID iDs

Suman Dey  https://orcid.org/0000-0003-1029-3807
Saptarshi Ghosh  https://orcid.org/0000-0001-8585-9743
Debjit Maity  https://orcid.org/0000-0001-8366-1872
Ayanabha De  https://orcid.org/0000-0001-8845-184X
Swarniv Chandra  https://orcid.org/0000-0001-9410-1619

## Acknowledgement

This work based on the data of the Venus Solar Wind Interactions, administered
by Brecht, S. H.; Ledvina, S. A., with the identifier urn:nasa:pds:venus-
solar-wind-interactions::1.0 which is archived at The NASA Planetary Data
System (PDS), doi.org/10.17189/
1520598\. This work makes use of data which are licensed under the terms of CC
Attribution 4.0. These data were retrieved from PDS-PPI IGPP UCLA[46, 47]
provided by European Space Agency (ESA). We also acknowledge the support
received from the Institute of Natural Sciences and Applied Technology,
Kolkata. The authors thank the reviewers whose comments and suggestions have
helped to improve this manuscript.

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