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We propose a new method of the automated identification of current sheets (CSs) that represents a formalization of the visual inspection approach employed in case studies. CSs are often identified by eye via the analysis of characteristic changes in the interplanetary magnetic field (IMF) and plasma parameters. Known visual and semi-automated empirical methods of CS identification are exact but do not allow a comprehensive statistical analysis of CS properties. Existing automated methods partially solve this problem. Meanwhile, these methods suggest an analysis of variations of the IMF and its direction only. In our three-parameter empirical method, we employ both the solar wind plasma and IMF parameters to identify CSs of various types. Derivatives of the IMF strength, the plasma beta and the ratio of the Alfvén speed VA to the solar wind speed V taken with the one-second cadence are used. We find that the CS daily rate R correlates with the solar wind temperature T rather than with V and is proportional to the sum of the kinetic and thermal energy density ~ V2(N+5N′)+10T(N+N′), where N′=2cm^-3 is the background level of the solar wind density N. Maxima of R are associated with stream/corotating interaction regions and interplanetary mass ejection sheaths. A multiyear list of CSs identified at 1 AU can be found at https://csdb.izmiran.ru .
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1. Introduction
Current sheets (CSs) in the solar wind are specific discontinuities carrying the electric current that contrib-
utes to the global electric circuit of the heliosphere (Kislov etal.,2015,2019; Maiewski etal.,2020; Suess
etal.,2009; Svalgaard etal.,1974; Wilcox & Ness1965). On the one hand, these structures may be formed as
a result of turbulence and various dynamical processes occurring in the solar wind, and, on the other hand,
some CSs are of solar origin. One of the most important features known about CSs is that, independently
of their origin, their width is approximately the same (several proton gyroradii), while their elongation
varies considerably depending on the way of their formation (Malova etal.,2017). The CSs that represent
elongated neutral lines of the solar magnetic field are the most stable structures that may extend to the outer
heliosphere, and, in turn, the turbulence-born CSs are much shorter, very dynamic and unstable by nature
(Li,2008; Podesta,2017; Zelenyi etal.,2020; Zhdankin etal.,2013).
The last decade brought a lot of discoveries about properties of CSs in space plasmas, mainly owing to
the fast development of the numerical analysis methods such as magnetohydrodynamic (MHD) numerical
simulations of fluids that allow studying CS formation in turbulent plasmas (e.g., www.mhdturbulence.
com; Burkhart et al.,2020), the Test Particle and Particle-In-Cell (PIC) coding on supercomputers (e.g.,
Hesse etal.,2001; Muñoz & Büchner,2018; Pritchett,2003; Xia & Zharkova,2018,2020), also implement-
ing General-Purpose Graphics Processing Units (e.g., https://gyires.inf.unideb.hu/KMITT/a53/ch05.html;
Dokken et al.,2007; Mingalev et al., 2019, 2020; Stantchev etal.,2009). Theoretical studies of processes
associated with CSs, including numerical simulations employing hybrid models, PIC and MHD/Hall-MHD
Abstract We propose a new method of the automated identification of current sheets (CSs) that
represents a formalization of the visual inspection approach employed in case studies. CSs are often
identified by eye via the analysis of characteristic changes in the interplanetary magnetic field (IMF)
and plasma parameters. Known visual and semi-automated empirical methods of CS identification are
exact but do not allow a comprehensive statistical analysis of CS properties. Existing automated methods
partially solve this problem. Meanwhile, these methods suggest an analysis of variations of the IMF and
its direction only. In our three-parameter empirical method, we employ both the solar wind plasma and
IMF parameters to identify CSs of various types. Derivatives of the IMF strength, the plasma beta and
the ratio of the Alfvén speed VA to the solar wind speed V taken with the one-second cadence are used.
We find that the CS daily rate R correlates with the solar wind temperature T rather than with V and is
proportional to the sum of the kinetic and thermal energy density V2(N+5N′)+10T(N+N′), where
N′=2cm−3 is the background level of the solar wind density N. Maxima of R are associated with stream/
corotating interaction regions and interplanetary mass ejection sheaths. A multiyear list of CSs identified
at 1 AU can be found at https://csdb.izmiran.ru.
Plain Language Summary We formalize an experience of observers in identifying current
sheets (CSs) via the analysis of typical changes in the interplanetary magnetic field and solar wind plasma
parameters. A new automated method of CS identification is created, and an open access multi-year
database of CSs observed at 1 AU is compiled (see https://csdb.izmiran.ru). We find that the daily rate of
CSs is determined by variations of the kinetic and thermal energy density of the solar wind.
KHABAROVA ET AL.
© 2021. American Geophysical Union.
All Rights Reserved.
Automated Identification of Current Sheets—A New Tool
to Study Turbulence and Intermittency in the Solar Wind
Olga Khabarova1,2 , Timothy Sagitov3 , Roman Kislov1,2 , and Gang Li4
1Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation of the Russian Academy of
Sciences (IZMIRAN), Troitsk, Moscow, Russia, 2Space Research Institute of the Russian Academy of Sciences (IKI),
Moscow, Russia, 3Higher School of Economics University (HSE), Moscow, Russia, 4Center for Space Plasma and
Aeronomic Research (CSPAR), University of Alabama in Huntsville, Huntsville, AL, USA
Key Points:
A new method of the automated
identification of current sheets (CSs)
is proposed, and the current sheet
database https://csdb.izmiran.ru is
created
The number of CSs per day (R) is
determined by variations of the
kinetic and thermal energy density
of the solar wind
R dramatically increases in stream/
corotating interaction regions and
interplanetary mass ejection sheaths
Correspondence to:
O. Khabarova,
habarova@izmiran.ru
Citation:
Khabarova, O., Sagitov, T., Kislov,
R., & Li, G. (2021). Automated
identification of current sheets—A
new tool to study turbulence and
intermittency in the solar wind. Journal
of Geophysical Research: Space Physics,
126, e2020JA029099. https://doi.
org/10.1029/2020JA029099
Received 30 DEC 2020
Accepted 13 JUL 2021
10.1029/2020JA029099
Special Section:
Solar and Heliospheric Plasma
Structures: Waves, Turbulence,
and Dissipation
RESEARCH ARTICLE
1 of 25
PREPRINT
Published in Journal of Geophysical Research: Space Physics, 126, e2020JA029099.
https://doi. org/10.1029/2020JA029099 (2021)
Journal of Geophysical Research: Space Physics
simulations, show that CSs effectively contribute to the solar wind dynamics and energy transformation
occurring at different scales, from MHD energy-containing scales to kinetic (see Donato et al.,2012; le
Roux etal.,2018,2020; Papini etal.,2019; Pezzi etal.,2021; Servidio etal.,2010; Wan etal.,2015; Zhdankin
etal.,2013 and references therein).
Recent advances in case studies of CSs in the solar wind have also contributed to better understanding of the
CS fine structure and processes associated with CS dynamics. Overall, there were confirmed (a) 3-D stochas-
tic or turbulent nature of CSs, (b) self-organization of CSs, (c) their multi-layered fine structure, (d) a strong
connection between CSs and magnetic islands/plasmoids, and (e) their important role in particle accelera-
tion in space plasmas (e.g., Adhikari etal.,2019; Eriksson etal.,2014; Khabarova & Zank,2017; Khabarova
etal.,2015,2016,2021; Lazarian etal.,2020; Le Roux etal,2019; Malandraki etal.,2019; Tan,2020; Zhark-
ova & Khabarova,2012,2015). Li etal.(2011) and, recently, Borovsky and Burkholder(2020) have shown
from observations that the presence of CSs in the solar wind determines a power spectral index of high-fre-
quency magnetic field variations, presumably, not only because of CS typical scales and frequency of their
detection by a spacecraft but also due to various dynamical processes occurring at CSs. This is consistent
with the results of numerical simulations of Franci etal.(2017) who have found that magnetic reconnec-
tion at ion-scale CSs leads to the development of the turbulent cascade at sub-ion scales, impacting spectra
of magnetic fluctuations. In turn, it is known from numerical testing that turbulence enhances magnetic
reconnection at CSs (see Kowal etal.,2009 and references therein) and it also leads to the formation of new
CSs (e.g., Cerri & Califano,2017). Therefore, since CSs are structures mutually linked with magnetic re-
connection and turbulence, it is very important to know their properties as well as properties of the plasma
containing them.
CSs in the solar wind are associated with two types of turbulence. First, strong and long-lived CSs mainly
of the solar origin represent a source of secondary CSs and 3-D flux ropes/plasmoids (or 2-D magnetic is-
lands) created by instabilities and magnetic reconnection that undergoes especially intensively if such CSs
are disturbed. Dynamical processes occurring at strong CSs lead to the formation of a wide analogue of the
heliospheric plasma sheet around them. This region is usually treated as turbulent or having signatures
of intermittency. On the other hand, turbulent solar wind far from such CSs is never too quiet and always
shows signatures of turbulent cascade leading to the occurrence of small-scale and short-lived CSs and mag-
netic islands observed from the Sun to the outer heliosphere (see Khabarova etal.,2021; Pezzi etal.,2021
and references therein).
In contrast to case studies and simulations, statistical studies of CSs are infrequent in this area (e.g., Bor-
ovsky & Denton,2011; Li,2008; Li etal.,2011; Malova etal.,2017; Podesta,2017; Suess etal.,2009; Zhang
etal.,2008), and, obviously, a lot of information is still missed because of the lack of a comprehensive sta-
tistical analysis. The absence of an easily accessible database of CSs subsequently identified for a prolonged
period lays researches under a necessity to compile their own short CS lists coming from case studies (e.g.,
Borovsky & Burkholder,2020; Burkholder & Otto, 2019; Malova etal., 2017; Suess etal.,2009; https://
lasp.colorado.edu/mms/sdc/public/about/events/#/. The magnetic reconnection exhaust list compiled by J.
Gosling (http://www.srl.caltech.edu/ACE/ASC/DATA/level3/swepam/ACE_ExhaustList.pdf) may also be
considered as a list of manually-picked CSs appropriate for statistical purposes since reconnection exhausts
are located in the nearest vicinity of corresponding reconnecting CSs.
Such lists typically consist of tens-hundreds CSs or reconnection exhaust crossings randomly picked for
months or even years, while the rate of the occurrence of CSs is hundreds CSs per hour (see Li,2008;
Podesta,2017, and results of this study). Therefore, a problem of the insufficient progress in CS studies is
that the manual identification of CSs remains the most frequently used way to analyze CS properties. A
significant loss of information under such an approach is obvious.
To solve the problem, methods of the CS identification that suggest some automatization have been pro-
posed. An automated method of identification of discontinuities of various types can be used first, - for ex-
ample, a Partial Variance of Increments method (Greco etal.,2009,2018) that identifies all discontinuities,
including shocks, or a method of the identification of magnetic holes carrying CSs at their borders (Winter-
halter etal.,1994; Zhang etal.,2008). If the identification of coherent structures is subsequently comple-
mented by a visual inspection, this allows extracting of CSs from the whole body of events (e.g., Malandraki
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etal., 2019; Zhang et al.,2008). An additional automated check for features typical for CSs (for example,
an analysis of the magnetic field shear angle variations) is possible too (e.g., Yordanova etal.,2020). Such
methods are called semi-automated.
There are fully automated methods allowing the CS identification (Azizabadi etal.,2021; Li,2008; Pecora
etal.,2021; Podesta,2017; Zhdankin etal., 2013). The most popular among them are Gang Li's method
(Li,2008) and John Podesta's method (Podesta,2017). Gang Li's method is based on the analysis of the in-
terplanetary magnetic field (IMF) angle variations, supposing that a CS crossing is always accompanied by
a sharp change in the local magnetic field direction (Li,2008; Li etal.,2011; Miao etal.,2011). The method
works well in turbulent plasmas. The current density calculation is the other way to find a CS location
(Podesta,2017). To calculate the necessary derivatives, one should perform a transition from time depend-
ences B(t) to spatial В(ξ). When studying CSs associated with turbulence, Taylor's hypothesis is usually
employed, according to which disturbances propagate together with the plasma flow, that is dB/dtVSW dB/
=0, where VSW is the solar wind speed, B is the magnetic field vector, and ξ is the coordinate along the
solar wind speed direction (see Podesta,2017 for detailed explanations). Using Taylor's hypothesis, one can
identify CSs embedded in specific flows and consisting of particles that move with the structure. Within
this approach, all automated methods cited above can successfully be applied to the turbulent solar wind.
Meanwhile, some CSs are associated with plasma structures which propagate with the speed different from
the surrounding solar wind speed, that is such current-carrying structures are not embedded in the free-
ly expanding solar wind and consist of different particles all the time. This is the case of quasi-station-
ary CSs formed (a) at shocks and strong discontinuities, including the heliospheric current sheet (HCS)
and other CSs of the solar origin, the terrestrial magnetopause, leading edges of interplanetary coronal
mass ejections (ICMEs), and fast flows from coronal holes, and (b) owing to interactions of wave fronts
(Khabarova & Zank,2017; Khabarova etal., 2015,2016; Khabarova, Malandraki, etal., 2017; Khabarova,
Malova, etal.,2017; Khabarova, Zank, etal.,2017; Le Roux etal.,2019; Malandraki etal.,2019; Svalgaard
etal.,1974; Wilcox & Ness,1965). If a spacecraft crosses such a structure, an attempt to calculate the electric
current density according to Taylor's hypothesis may lead to an error, and the obtained electric current may
have an incorrect magnitude and direction. Furthermore, the larger-scale CSs of the non-turbulent origin
may create or be surrounded by other structures, namely, secondary CSs and magnetic islands that cannot
formally be attributed to turbulence either but is treated as intermittent structures in case studies (e.g.,
Adhikari etal.,2019; Khabarova etal.,2015). A notable example is the heliospheric plasma sheet (HPS) sur-
rounding the HCS (Simunac etal.,2012; Winterhalter etal.,1994). Multiple structures observed within the
HPS represent both CSs originated from the extension of coronal streamers and locally-born coherent struc-
tures, namely, CSs and magnetic islands (Khabarova & Zastenker,2011; Khabarova etal.,2015; Khabarova,
Malandraki, etal.,2017; Khabarova, Zank, etal.,2017; Maiewski etal.,2020).
Therefore, it makes sense to enhance a CS identification based on variations of the magnetic field by con-
sidering additional plasma features widely used by specialists to find CSs by eye (Adhikari etal., 2019;
Khabarova & Zank,2017; Khabarova etal.,2015,2016,2020; Khabarova, Malandraki, etal.,2017; Khabaro-
va, Zank, etal.,2017; Malova etal.,2017; Suess etal., 2009). Note that the method proposed in this work
is not based on calculating the current density and is independent of the applicability/inapplicability of
Taylor's hypothesis. Meanwhile, we discuss it in Section4 in connection with validation of our method that
suggests calculation of the electric current density.
In this work, we formalize the experience of observers in visual inspection of typical changes of the IMF
and the solar wind plasma parameters at CS crossings, turning it into a new automated method of CS iden-
tification. A multi-year list of CSs observed at 1 AU is compiled as a result of this study. The creation of an
open-access database allows a new level of statistical analysis to be applied to a large number of CSs since
their properties may sometimes be missed or incorrectly understood from the analysis of small samples of
CSs. The database is also useful for case studies since observers can instantly find a location of CSs within
a time interval under study. Finally, knowing the number of CSs per interval and their properties, one may
study turbulence and intermittency in different samples of the solar wind.
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2. Data and Method
2.1. Data
Our study is mainly based on an analysis of the Advanced Composition Explorer (ACE) measurements.
ACE is one of the key 1 AU spacecraft located between the Earth and the Sun at the 1st Lagrange point (see
http://www.srl.caltech.edu/ACE/, Stone etal.,1998). We have used the following ACE data for 2004–2010:
the IMF vector B measured with the one second resolution, the corresponding <|B|> (the magnetic field
magnitude), and the 64-second-resolution plasma data, namely, the solar wind proton number density N,
the solar wind bulk speed V, and the radial component of the proton temperature T (https://cdaweb.gsfc.
nasa.gov/).
The other dataset employed is from the STEREO Ahead (A) and STEREO Behind (B) spacecraft that move
nearly along the Earth's orbit in the opposite direction with respect to each other (see https://stereo-ssc.nas-
com.nasa.gov/data.shtml and Kaiser etal.,2008). STEREO A is a little closer to the Sun, and STEREO B is a
little further from the Sun than the Earth (Kaiser etal.,2008). The STEREO mission data on B with the one
second resolution https://stereo-dev.epss.ucla.edu/l1_data, and the plasma parameters (N, V and T) with
the 60s resolution are obtained from https://cdaweb.gsfc.nasa.gov/. Currently, only STEREO A remains
operating, but we use the STEREO A and STEREO B data for several-day-long intervals taken in 2007–2010
when both spacecraft functioned normally. The STEREO data are used in validation of our method but not
employed in the current sheet identification for creating the open-access database.
The plasma data have been interpolated and calculated with the one-second span that allows us to compute
the plasma beta β (the ratio of the plasma pressure to the magnetic pressure) and the Alfvén speed VA with
the span corresponding to the IMF resolution (see the parameter derivation technique at https://omniweb.
gsfc.nasa.gov/ftpbrowser/bow_derivation.html). At the next step, the one-second derivatives of B, β, and
VA/V are calculated to identify CSs (see Section2.2).
In order to validate our method, we identify a stream interaction region (SIR) from ACE and STEREO A
data and trace it, following 3-D pictures of the normalized density in the ecliptic plane reconstructed with
the ENLIL modeling that show the solar wind in white-light as if obtained from the Heliospheric Imager
(HI) instruments on board of the STEREO spacecraft (http://helioweather.net). Using HIs is a unique way
to look at the dynamic picture of the behavior of streams/flows in the interplanetary medium (Conlon
etal.,2015). One can find key information about HI observations in white light, the techniques allowing the
solar wind density reconstruction from the observations, and the related studies in the following articles:
Bisi etal.(2008); Eyles etal.(2009); Rouillard etal.(2008); Jackson etal.(2009); Scott etal.(2019); Barnard
etal.(2020). Here, the ENLIL HI density reconstructions are used to check if the SIR identified by us in situ
with two spacecraft is an uninterrupted and freely propagating/rotating structure. The latter is necessary to
validate our method with an alternative technique.
Finally, a CS database for ACE compiled by Gang Li according to his method of automated CS identification
(Li,2008) has been compared with the database resulting from our study (https://csdb.izmiran.ru).
2.2. Method
We suggest a formalization of the long-time experience of observers in the visual identification of CSs based
on the analysis of the IMF and plasma parameters that vary sharply at CSs of different origins in the solar
wind (Adhikari etal.,2019; Behannon etal.,1981; Blanco etal.,2006; Khabarova & Zank,2017; Khabarova
etal.,2015,2016; Malova at al.2017; Simunac etal.,2012; Suess etal.,2009; Zhang etal.,2008; Zharkova &
Khabarova,2012,2015). As an example, a characteristic crossing of a CS detected by the Wind spacecraft at
1 AU on June 25, 2004 is shown in Figure1 (modified from Khabarova etal.,2021). The IMF magnitude B
sharply decreases because of the neutral line crossing. Bx, the IMF component in the Earth-Sun (x) direction
in the GSE coordinate system, and the other in-ecliptic component, By, pass through zero at the CS. Generally,
a CS crossing is characterized by a sign reverse of at least one of the IMF components in a coordinate system
oriented along and across the CS plane. Consequently, the azimuthal IMF angle Bphi sharply varies, indicating
the IMF vector direction changes to the opposite. V and T may slightly increase at CSs, owing to ongoing mag-
netic reconnection (Adhikari etal.,2019; Gosling etal.,2005; Phan etal.,2020). In the particular case, there
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Figure 1. Typical behavior of the interplanetary magnetic field (IMF) and plasma parameters at a current sheet
(CS) crossing observed by the Wind spacecraft on June 25, 2004. From top to bottom: the IMF magnitude, the IMF
components Bx, By, and Bz (GSE), the IMF azimuthal angle Bphi, the solar wind speed Vx (the dominant component) and
Vy component, the solar wind proton density Np, and the plasma beta. CS crossing and the associated changes in the
IMF and plasma parameters are depicted by the pink stripe and arrows. Modified from Khabarova etal.(2021).
Journal of Geophysical Research: Space Physics
are clear signatures of magnetic reconnection at the CS reflected in±spikes in the Vy component encom-
passing the CS and an increase in the temperature at the CS (not shown). The solar wind density increases
at the CS, which, in combination with the decreasing B leads to the plasma beta increase at the CS crossing.
The solar wind speed change itself is usually too weak and cannot be used for the CS identification. A
decrease of the VA/V ratio observed at CSs is usually substantial and may be considered as an important
key to recognize CSs. Figure2 shows statistical results obtained by Suess etal.,2009 for CSs identified in
2004–2006 and early 2007. The solar wind proton density increases in the nearest vicinity of CSs, and the
VA/Vp ratio statistically decreases at CSs.
It should be noted that although CSs are crossed for seconds, their crossings are seen differently under
different time/space resolutions. Crossings of strong CSs (the HCS, for example) statistically analyzed with
the hourly and/or daily resolution are associated with an increase in B. This is a common signature of the
approach of an observational device to any electric current-carrying surface/conductor, as known in all
scientific branches, including geophysics, since it comes from the Biot-Savart law. A bell-like profile of the
total magnetic field is typical for crossings of such structures. In the solar wind, the electric current flows in
CSs in a form of the net of thin wires (see, e.g., Lazarian etal.,2012 and Kowal etal.,2012), which makes
even small-scale profiles of specific CSs a bit complicated and depending on the way they are crossed by a
spacecraft. Magnetic reconnection and formation of plasmoids at CSs also result in a complex behavior of
key solar wind parameters in a wider vicinity of such CSs. However, at the statistical level, the |B| increase
near strong CSs is clearly seen on large scales. For example, a superposed epoch analysis shows that daily
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Figure 2. Statistical (superposed epoch analysis) results for the solar wind proton density (upper panel) and the Alfven
speed to the solar wind proton speed Va/Vp ratio in the vicinity of current sheets (CSs) identified by Suess etal.(2009) in
2004–2006 and early 2007. Advanced Composition Explorer (ACE) data. Adapted from Suess etal.(2009). Permission to
reprint is obtained from the Copyright Clearance Center (License Number 5061650837423).
Journal of Geophysical Research: Space Physics
averaged B peaks on the day of the HCS crossing (Khabarova & Zastenker,2011), while under at least a
minute resolution, the HCS crossing is characterized by the decrease in B.
The IMF strength and density increase observed around the HCS at large scales may also be explained by
the occurrence of dynamical processes at CSs that change properties of plasma surrounding CSs (see Malova
etal.,2017,2018; Zelenyi etal.,2016; Zharkova & Khabarova,2012,2015 and references therein), while the
IMF strength decrease at the midplane of strong CSs observed with a high resolution is simply explained by
the occurrence of the zero B line at which at least one of the magnetic field components crosses zero (Malova
etal.,2017,2018; Zimbardo etal.,2004). Here we are talking about observations of CSs with a high resolution.
The main features seen with a resolution not worse than one minute that may characterize a CS crossing
are following: (a) a decrease in B, (b) a decrease in VA/V, and (c) an increase in β. It is easy to find that all
other peculiarities are linked with the listed ones. We develop a combined method based on that employed
by observers since CS crossings may be reflected differently in changes of the solar wind/IMF parameters,
that is sometimes not all of the signatures mentioned above appear altogether. If one wants not to miss as
many CSs as possible, it is better to consider a combination of different signatures.
Since the automatization of the CS recognition process requires setting the same rules for CSs occurring in
different plasmas under different conditions, normalization should be performed. Hence, after obtaining B,
VA/V, and β, we calculate their one-second derivatives. One can suggest then that spikes of the derivatives
reflect the location of CSs.
Noise cutoff or a threshold choice is the most sensitive point of all methods for identifying CSs. Its intro-
duction is always based on experience and common sense. We have chosen to carefully compare the results
with clear cases of CS crossings discussed in literature and find the optimal parameter levels above which
the peaks correspond to the CS location in the best way. The first threshold of β= 3 for a one second resolu-
tion data has been imposed. The next important point is that the signatures of a CS crossing discussed above
should be considered altogether. In statistical terms, this means finding a maximum correlation between
different datasets to restrict final results by those complying with necessary signatures observed in all key
parameters. Applying the maximum correlation condition, we finally obtain the following thresholds: val-
ues above dB/dt=−0.14, below dβ/dt=0.11, and above d(VA/V)/dt=−0.003 are considered as noise; here
t=1s. Note that the thresholds will be different if one considers a lower resolution or averaged data. We
treat variations in dB/dt as the main feature, therefore only the spikes that appear simultaneously in dB/dt
and any of two other parameters are considered as pointing out the CS location.
Additionally to the list of CSs obtained with the method, we compute the magnetic field shear angle observed
at the identified CSs using the well-known formula (Li,2008; Miao etal.,2011; Yordanova etal.,2020):
 
 
 
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arccos , / ·
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arccos , / ·
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(1)
We modify the formula as
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arccos 16 , 16 / 16 · 16 ,
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arccos 16 , 16 / 16 · 16 ,
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arccos 16 , 16 / 16 · 16 ,arccos 16 , 16 / 16 · 16 ,arccos 16 , 16 / 16 · 16 ,
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arccos 16 , 16 / 16 · 16 ,arccos 16 , 16 / 16 · 16 ,arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,arccos 16 , 16 / 16 · 16 ,
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d t t t t
d t t t t
arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,
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arccos 16 , 16 / 16 · 16 ,
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arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,
arccos 16 , 16 / 16 · 16 ,arccos 16 , 16 / 16 · 16 ,arccos 16 , 16 / 16 · 16 ,
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arccos 16 , 16 / 16 · 16 ,
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arccos 16 , 16 / 16 · 16 ,
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(2)
using the time step dt =16s. These are the key points on which a new method of the automated identi-
fication of CSs is based. Details are illustrated below step by step in the process of identification of CSs
embedded in a SIR.
3. Identification of CSs–Results
3.1. Illustration of Finding CSs From the ACE and STEREO Data
To demonstrate how the method works, we apply the technique to a SIR, the region not freely propagating in the
solar wind but resulting from the interaction of a rotating high-speed flow from a coronal hole with the ambient
slower solar wind. A SIR resembles an ICME sheath by properties since it is equally turbulent and full of numerous
discontinuities, CSs and magnetic islands (e.g., Ho etal.,1996; Jian etal.,2006; Khabarova, Zank, etal.,2017; Tessein
etal.,2011). A description of key features of SIRs and their long-lived counterparts, corotating interaction regions
(CIRs), can be found in a comprehensive review by Ian Richardon (see Richardson,2018 and references therein).
KHABAROVA ET AL.
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Journal of Geophysical Research: Space Physics
SIRs are important drivers of space weather, living in the interplanetary medium much longer than ICMEs
that quickly expand, pass 1 AU in 1–3days and fade with distance. Since SIRs are linked to coronal hole
flows, they rotate for many days, striking planets and spacecraft one by one, which gives us an opportunity
to study these large-scale structures as a whole and in detail. SIRs/CIRs can be traced remotely via HIs de-
signed to observe dynamics of dense solar wind structures in white light (see Section2.1). Such a tracking is
necessary (a) to be sure that two different spacecraft detect the same flow (if one analyzes in situ measure-
ments), (b) to be confident that the flow is not interrupted by an ICME for time enough to observe it in situ,
and, finally, (c) to analyze a longitudinal evolution of SIRs/CIRs.
Figure3 is an example of the analysis of the SIR evolution using both the predicted STEREO HI remote
view of the SIR and in situ measurements. Figures3a and3b show an ecliptic cut of a reconstructed image
of the solar wind density as predicted by ENLIL for STEREO HI. The Earth is the green dot, the Sun is in
the center, seen from the solar North Pole, and two SIRs resemble rotating sleeves. The intensity of gray
corresponds to the normalized density value (darker means denser). The red circle indicates the SIR subse-
quently detected by ACE and STEREO A with a several-day delay. For the corresponding movie see http://
helioweather.net, click Archive–date - anim-sta1dej/anim-stb1dej. We use these reconstructions to be sure
that the particular SIR reached both ACE and STEREO A uninterrupted (see Section 4.1 below). The SIR
arrival is identified via in situ data from both spacecraft.
A SIR represents a transition area between the fast solar wind associated with a coronal hole and the sur-
rounding slow solar wind. The SIR is characterized by compression reflected in the enhanced N and B,
which is typically observed at its outer edge, and V mostly begins to increase after the crossing of the stream
interface (SI), a tangential discontinuity separating slow and fast solar wind within the SIR (e.g., Richard-
son,2018), although some signatures of the V growth can sometimes be seen before the SI crossing. SIRs
may be imagined as dense turbulent shells surrounding high-speed rotating flows from coronal holes.
Figure3c shows that a typical feature characterizing an approach of the high-speed coronal hole flow is a
growth of N in the background of a constant or slightly increasing V. After the passage of the SI at which
N sharply falls but still remains above quiet period values and V sharply increases, the spacecraft occurs in
the part of the SIR affected by the high-speed coronal hole flow in which V typically keeps growing. The SI
located inside the SIR is a very bright and easy-to-identify structure that allows studying the SIR rotation
via in situ observations successfully. In our case, we track the SI to compute the electric current density to
check the location of CSs by an independent method (see Section4).
The leading part of the SIR marked by yellow in Figure3c has been used as a test bench to compute deriva-
tives of B, β, and VA/V (see Section2.2). In this particular case, the beginning of the SIR was detected by ACE
on June 25, 2010 16:00:50, and the SI within the SIR was crossed on June 26, 2010 02:48:18. The same SIR
arrived at STEREO А on June 30, 2010 17:11:49, and the SI was detected on July 1, 2010 03:29:48.
In Figure4 we show a typical example of the CS identification for the period of the ACE encounter with the
SIR. Another example is the identification of CSs in a fragment of the same SIR observed by STEREO A (see
Figure5). Figure5 is analogous to Figure4 but shows CSs identified in another time interval. The threshold
for cutting off the noise is shown by the horizontal red line for each parameter. The spikes occurring out of the
noise level indicate the CS location. The noise level is calculated as described in Section2.2. Only the spikes
simultaneously observed in the B derivative and any of the other parameters are treated as CS indicators.
As a result of the study, we have compiled a list of CSs idenitifed from the ACE data (1 AU) with the one
second cadence for 1998–2012. The CS database representing a set of the three-month-length CS lists is
available at the dedicated IZMIRAN website https://csdb.izmiran.ru. Additionally to indicating a location
of each CS, the list contains the following parameters observed at the CS crossing: B, N, V, T, β, VA, and three
derivatives on the analysis of which the method is based (see Section2.2).
So far, the 1 AU current sheet database consists of the three-month-length “output_ACE_1s_YYYY_MM-
MM.csv” files and the format “IMF_angle_YYYY_MM-MM” indicate files with computed shear angles at
CSs. The plain text files contain information about the current sheet location and the corresponding plasma
and IMF parameters:
KHABAROVA ET AL.
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Journal of Geophysical Research: Space Physics
1. date (location of the current sheet pointed with the one-second resolution),
2. <|B|>, nT (the IMF magnitude) - B in the manuscript,
3. H_DENSITY_#/cc (the solar wind density, 1/cm3) - N in the manuscript,
4. SW_H_SPEED_km/s (the solar wind proton speed, km/s) - V in the manuscript,
5. H_TEMP_RADIAL_Kelvin (the radial component of the solar wind temperature, K) - T in the
manuscript,
6. Beta (the plasma beta β),
7. VA (the Alfvén speed, km/s) - VA,
8. B_der (the derivative of <|B|>) - dB/dt,
9. Beta_der (the β derivative) - dβ/dt,
10. VA/V_der (the derivative of the Alfvén speed to the solar wind speed ratio) - d(VA/V)/dt in the manuscript.
KHABAROVA ET AL.
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Figure 3. Stream interaction region (SIR) subsequently observed by Advanced Composition Explorer (ACE) and
STEREO A on June 25–30, 2010. (a) Normalized plasma density shown in the ecliptic plane is reconstructed by ENLIL
predicting the HI STEREO observations. Earth–the green dot; the Sun is the yellow dot in the center. Red circles
encompass the SIR of interest. SIR passes the Earth. (b) The same but the SIR reaches STEREO A. Corresponding
movie can be seen at http://helioweather.net/archive/2010/06/sta1dej.html. (c) In situ observations of the solar wind
density N and speed V by ACE (black) and STEREO A (red) are used to find the time of arrival of the stream interface to
both spacecraft in order to compute the angular speed of the rotating SIR. The STEREO A profile is shifted to ACE for
24:41:30.
Journal of Geophysical Research: Space Physics
This is an open access database, and the website does not require a registration, but a reference to the web-
site and this article is necessary if one uses the CS database and/or the method.
3.2. What Determines the Current Sheet Occurrence in the Solar Wind?
It is easy to find in Figures4 and5 that the number of CSs may reach hundreds per hour or several thou-
sands per day in the most turbulent regions. Figure6 illustrates this with a CS daily occurrence rate or,
in other words, the number of CSs per day (R) as observed in 1998–2010 (Figure6a). The red solid curve
represents R smoothed using a 27-point Savitzky-Golay filter with the 3rd degree polynomial (Savitzky &
Golay,1964), and the dash line is a one-year smoothed R. Figure6b shows the number of sunspots per day
smoothed in the same way in order to estimate if R depends on solar cycle. If one calculates a Pearson co-
efficient of correlation of R versus the sunspot number based on initial daily data from OMNIweb (https://
omniweb.gsfc.nasa.gov/ow.html), the result will be −0.08, which means no correlation at all. Smoothing
increases it, as shown in Figure6c. A 27-days-window smooth gives the correlation coefficient of −0.44,
which still means no correlation, and a one-year-window gives a negative correlation of −0.67. Note that
the increase of the correlation coefficient upon increasing the window up to the total length of the time
period analyzed is usually considered as an artificial statistical result of smoothing rather than a physical
KHABAROVA ET AL.
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Figure 4. Example of automated identification of current sheets (CSs) via the three-parameter method. Based on the
analysis of the Advanced Composition Explorer (ACE) data, one second cadence. From top to bottom: derivatives of B,
β, and VA/V. Red lines indicate the noise cut off level (see Section2.2). Spikes indicate the CS location. Database of CSs
identified at 1 AU is provided at https://csdb.izmiran.ru.
Journal of Geophysical Research: Space Physics
result. A conclusive solar cycle dependence/independence analysis can be performed with a larger database
only. So far, we can suggest that, upon Figure6, there is no obvious solar cycle dependence although some
connection between R and the sunspot number is possible due to the R dependence on the SIR and ICME
occurrence rates (see a related discussion in Section 5). Further investigations will be made in this area
when we extend the database.
The bright feature that meets the eye is quasi-regular variations seen in R. We find that this is a reflection
of the CS production increase in turbulent and intermittent regions associated with SIRs/CIRs, the ICME
sheaths and the related increase in the solar wind energy flow. A preliminary analysis allows us to conclude
that the highest peaks of R seen in Figure6 correspond to either SIR/CIR or ICME sheath observation pe-
riods. One can compare known ICME/SIR lists (see http://www.srl.caltech.edu/ACE/ASC/DATA/level3/
index.html) with R to see this feature. Using our database, we show this in Figures7 and8.
Figure7 depicts results of a superposed epoch analysis of R versus the day with respect to the ICME sheath/
SIR crossing, as observed in 1998–2010. In the SIR case (the upper panel), R begins to grow before the SIR
arrival, and its peak occurs at the SI. Since the location of SI varies from one SIR to another, there are sev-
eral secondary peaks around the main one. The R profile around ICMEs (the lower panel) is different. The
number of CSs per hour increases exactly at the beginning of the ICME sheath crossing, that is mostly at
the shock, and decreases much faster than observed in the SIR case, which is understandable because SIRs
are generally wider than ICME sheaths.
KHABAROVA ET AL.
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Figure 5. Analogous to Figure3, but for STEREO A data, one second cadence.
Journal of Geophysical Research: Space Physics
One may suggest that the found peaking of R within ICME sheaths/SIRs is related to the turbulence level
observed downstream of ICME-driven interplanetary shocks and within SIRs in which the SI represents the
strongest discontinuity at 1 AU. It is quite probable that the bottom figure will change dramatically at far-
ther heliocentric distances since SIR-associated shocks are usually formed farther than 1 AU, and properties
of turbulent plasma within SIRs should vary with distance.
The R distributions for hours in which SIRs are observed (red bars) and for hours without SIRs (blue bars)
can be found in Figures8a and8b shows histograms of the distribution of R observed within ICME sheaths
(red bars) and outside ICME sheaths (blue bars). One can see that red histograms are shifted to larger values
in both cases, which confirms that the number of CSs increases in ICME sheaths and SIRs.
We also illustrate this point with Figure 9 that shows typical variations in R observed before, during and
after a SIR (Figure9a) and an ICME (Figure9b). The SIR in Figure9a was observed in the period of May
3–5, 2004. This is SIR no. one shown in Figure 3 of Jian etal.(2011). A shock pair did not form at the SIR's
edges at 1 AU. Figure9a shows that R quickly reaches its maximum within the SIR and slowly decreases
afterward within the associated coronal hole flow.
The very strong ICME detected by ACE from May 15, 2005–May 17, 2005 was characterized by a classic
ICME-driven forward interplanetary shock followed by the compressed turbulent sheath (see Figure 1 of
Dasso etal.,2009) with which the R peak is associated (Figure9b). An important feature seen in Figure9b
is a precursor representing a prolonged moderate R increase before the ICME approach. This phenomenon
has been discussed before in terms of the crossing of a magnetic cavity filled with magnetic islands/plas-
moids or flux ropes formed between the HCS and an ICME (Adhikari etal.,2019; Khabarova etal.,2016;
Khabarova, Malandraki, etal.,2017; Khabarova, Zank, etal.,2017). Note that the increase of the number of
magnetic islands and the increase of the CS number are linked since magnetic islands are separated by CSs
(e.g., Malandraki etal.,2019).
R correlates with T in a higher degree than with V and other key plasma/IMF parameters. The correspond-
ing Pearson correlation coefficients CR-X (X=T, V, B, N) calculated for the entire database from 2004 to 2010
are as follows: CR-T=0.66, CR-V=0.46, CR-B=0.43, and CR-N=0.21.
Let us derive a formula that expresses R as a function of physical parameters. CSs are characterized by an in-
creased energy density compared to the surrounding plasma. In particular, CSs can be distinguished by the
extrema of β and B because of that. Therefore, one can expect the number of CSs per day to be proportional
to the average energy density in such regions. We will search for the best correlation between R and key
KHABAROVA ET AL.
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Figure 6. Number of current sheets (CSs) per day (R) observed at 1 AU in 1998–2010 versus the sunspot number. (a) Red curve represents R smoothed with a
27-days (point) Savitzky-Golay filter, and the yellow curve shows a one-year smooth by the same method. The 3rd degree polynomial is used. (b) Analogous to
(a) but for the number of sunspots per day. (c) Correlation coefficient between (a and b) at different window widths.
Journal of Geophysical Research: Space Physics
solar wind parameters, trying to find a function (i.e., the best-fit parameter RE) that depends on the kinetic
energy density (the first term), the thermal energy density (the second term), and the magnetic field energy
density (the third term).
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.
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1 2 3 4 51 2 3 4 5
R m V N a N k T B
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D D DD D DD D D
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R m V N a N k T B
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D D DD D D
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1 2 3 4 51 2 3 4 5
1 2 3 4 5
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D D D
D D D
D D D
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D D D
D D DD D D
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/ 2
2 22 2
1 2 3 4 51 2 3 4 5
E pE p
D
DDDDDD
1 2 3 4 51 2 3 4 51 2 3 4 5
(3)
Here α1,2,3,4,5 are dimensional constant factors, mp the proton mass, and k denotes the Boltzmann constant.
V is measured in km/s, T - in K, N - in cm−3, and B is measured in nT. Parameters α1, α3, and α5 describe
the impact of the corresponding types of energy on the CS rate, while α2 and α4 reflect the presence of the
low-density plasma, in the background of which RE variations caused by SIRs/CIRs and ICMEs occur.
An empirical search for the best-fit parameter shows that observed R highly correlates with a function of
the following form:
KHABAROVA ET AL.
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Figure 7. Results of the superposed epoch analysis of the number of current sheets per hour observed within and near SIRs (the upper panel) and ICME
sheaths (the bottom panel) for 1998–2010. The leading edge of a SIR/ICME sheath is shown by the vertical red line (zero in the bottom panel).
Journal of Geophysical Research: Space Physics
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/ 5000
E
  
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R V N N N N T
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E
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R V N N N N T
R V N N N N T
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 
                         
(4)
Here, all values are reduced to the units of (1), and N′=2cm−3 corresponds to the concentration observed at
1 AU in the background solar wind. The magnetic field energy term is absent in (4) since its inclusion does
not lead to obtaining a better result. The basis of a composite function method of the best correlation finding
is described in Khabarova and Zastenker(2011) and Khabarova and Savin(2015). The normalization factor
of 1/5000 is chosen to make RE|R.
KHABAROVA ET AL.
10.1029/2020JA029099
14 of 25
Figure 8. Distributions of R within and outside SIRs and ICME sheaths for 1998–2010. (a) Histograms of the R occurrence calculated for hours in which SIRs
are observed (red bars) and not observed (blue bars). (b) Analogous to (a) but for ICME sheaths. The occurrence of R is normalized and shown in percentages
from the total number of events. Hours with SIRs are not included in the “no ICMEs” statistics, and hours during which ICME sheaths are observed are not
included in the “no SIR” statistics not to contaminate the blue histograms. Hours analyzed: ICME sheath – 866, SIRs – 15,540, calm – 68,021. Red histograms
are shifted to larger values. This indicates that R statistically increases within ICME sheaths and SIRs.
Figure 9. Typical variations of R associated with SIRs (a) and ICMEs (b). From top to bottom: solar wind speed V, temperature T, and R (from Advanced
Composition Explorer (ACE)).
Journal of Geophysical Research: Space Physics
Figure10 shows examples of the comparison of R versus T and R versus the best-fit parameter in the form
of Equation4 as observed for three months in 2004 (Figure10a) and 2010 (Figure10b). The correlation co-
efficient between R and the best-fit parameter is 0.82 for the whole 2004–2010 database. It may reach 0.9
in some months. In particular, the correlation between R and the best-fit parameter is 0.87 for the period
shown in Figures10a and 0.86 for the period shown in Figure10b. This is far larger than any of the correla-
tion coefficients CR-X (X=T, V, B, N) calculated for the same period.
One can find that (4) has the following general form in the CGS metric system:
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/ 5000
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.
E
R
V N N kT k cm K R
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V N N kT k cm K R
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V N N kT k cm K R
V N N kT k cm K R
(5)
Here ρ=mpN is the solar wind density, and ρ′=mp N′. The denominator in (5) is a constant dimensional
normalization factor. Formula5 is useful for a theoretical analysis. Meanwhile, observers will obtain R di-
rectly from the empirical formula4, taking the parameters from the ACE database, since RE|R.
4. Validation of the Method
4.1. Validation by the Electric Current Density Calculation
In order to check if the method of identifying CSs proposed above reflects reality in terms of revealing spa-
tial variations of the electric current, we will estimate the current density j and compare the location of its
peaks with the location of CSs identified with our method.
To calculate j in a chosen SIR/CIR's region, one should know details of the angular rotation of the SIR/CIR,
which can be found if the SIR/CIR is subsequently detected by one spacecraft after another. First,
P
0
rot ,
B j
P
P
0
B j
rot ,rot ,
P
PPP
0
rot ,
rot ,
(6)
here µ0 = 1.256637062 10−6 H/m in the SI system of units. The electric displacement currents can be ig-
nored in the case of slowly evolving CSs. To have (6) in the form of the dependence of B on coordinates, it
is necessary to understand how a particular CIR/SIR moves. Here, we assume for simplicity that the only
movement is CIR/SIR's rotation around the rotation axis of the Sun in the ecliptic plane with the angular
velocity ω in the chosen reference Radial-Tangential-Normal frame (RTN).
In speculations and calculations below, r denotes the radial coordinate in the RTN reference system, the
normal component is S, and the tangential is W. Then, r=rAU cos(ωt+φ) and W=rAU sin(ωt+φ), where φ
is the initial phase, rAU is the distance from the Sun to the spacecraft, which is different for each spacecraft
involved in calculations.
Considering B(t) as B(t(r, W, S)), where t is time, it is easy to find that
 
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P
Z M Z Z M Z
 
 
 
 
0
P
P
AU
Z M Z Z M Z
Z M Z Z M Z
AU
cos / .
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AU
W r
 
 
sin /
 
   
N
dB
dB
W r
W r
j t r t r
 
 
Z M Z Z M Z
Z M Z Z M Z
 
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  
  
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M ZZ M Z Z M Z
AU
cos / .cos / .
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Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M Z
  
     
AU
W r
sin /
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      
N
dB
W r
W r
dt
j t r t rj t r t r
dt
Z M Z Z M ZZ M Z Z M Z
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M Z
j t r t r
j t r t r
j t r t r
 
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Z M Z Z M ZZ M Z Z M ZZ M Z Z M Z
Z M Z Z M Z
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Z M Z Z M Z
Z M Z Z M ZZ M Z Z M ZZ M Z Z M Z
  
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 
 
  
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M Z
sin /
 
      
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M Z
 
 
  
 
  
 
     
cos / .
 
 
 
 
 
  
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M Z
  
  
 
  
 
     
W r
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M Z
W r
sin /
 
   
 
  
 
     
Z M Z Z M ZZ M Z Z M Z
Z M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M Z
  
     
 
     
 
             
j t r t rj t r t r
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M Z
Z M Z Z M ZZ M Z Z M ZZ M Z Z M ZZ M Z Z M Z
(7)
The initial phase φ can be chosen arbitrarily. However, it determines whether the first and second terms are
of the same order or not, which potentially may lead to the diminishing of the role of one of the magnetic
field components. Therefore, it is reasonable to take the following quantity j0 to estimate the current density:
 
P Z Z
 
 
0 0
P Z Z
P Z Z
/ / / / .
 
 
 
 
 
 
 
 
 
 
 
 
AU
/ / / / .
/ / / / .
j dB dt r dB dt r
   
P Z ZP Z Z
 
 
 
 
P Z Z
P Z Z
P Z Z
P Z Z
/ / / / ./ / / / .
 
 
 
 
P Z ZP Z Z
P Z ZP Z Z
   
 
 
 
   
 
 
 
       
 
 
 
 
 
   
 
     
 
   
 
         
AU
/ / / / .
P Z Z
P Z Z
P Z Z
P Z Z
 
           
 
         
(8)
Here, j0 is the upper limit for the electric current density in the S direction.
The next step is the calculation of the angular velocity. Let us introduce the following notations:
- L is the angular velocity of the spacecraft with respect to the Sun, where L=1, 2 denotes, respectively, the
1st and the second spacecraft that subsequently detect the rotating CIR/SIR front;
- is the angular velocity of the CIR/SIR with respect to the Sun, determined by the difference t of the
moments of arrival of the CIR/SIR front to the 1st (t1) and 2nd spacecraft (t2);
- HCIL,1 is the heliographic longitude of the spacecraft L at t1 in the Heliocentric Inertial (HCI) system of
coordinates, and
- HCIL,2 is the heliographic longitude of the spacecraft L at the point of time t2, in HCI.
KHABAROVA ET AL.
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Figure 10. Finding the function that determines R. Examples are given for the three month-length periods in 2004 (a) and 2010 (b). Upper panels: the
solar wind temperature T versus R. Lower panels: R versus the best-fit parameter [V2(N+5N′)+10T(N+N′)]/5000, where N′=2cm−3 is the level of the
background density of the undisturbed solar wind. Correlation coefficients between R and T (upper panels) are 0.72 (a) and 0.64 (b). Correlation coefficients
between R and the best-fit parameter (lower panels) are 0.87 and 0.86, respectively. Based on the analysis of the data from Advanced Composition Explorer
(ACE).
Journal of Geophysical Research: Space Physics
Then the corresponding angular velocities are: 1 = (HCI1,2 – HCI1,1)/(t2 t1); 2 = (HCI2,2HCI2,1)/(t2t1);
= (HCI2,2 – HCI1,1)/(t2t1). The angular velocities of each spacecraft are different, so the angular velocity
of the CIR/SIR relative to each spacecraft will be different. Therefore, ω=L is the angular velocity of
the CIR/SIR with respect to the spacecraft L=1, 2.
The final step is the derivation of the formula for the electric current density. For the convenience of calcu-
lations, we transform (6) to the following form:
0
 
 
j w dB dt dB dt
  
0
   
 
 
 
 
 
 
 
 
 
 
  
j w dB dt dB dt
j w dB dt dB dt
  
  
   
 
 
  
   
 
 
  
  
  
 
  
 
     
(9)
where
 
 
 
 
1
4
 
 
 
 
 
 
10 / 1.2566 7 215
  
4
w r
 
 
   
 
 
 
 
 
 
  
 
 
 
 
  
 
 
  
¸ ¸ ¸ ¸
 
 
 
 
 
 
  
 
 
 
    
10 / 1.2566 7 215
  
 
 
4
w r
w r
 
   
   
    
 
 
 
 
 
        
 
 
 
 
 
 
     
 
 
 
 
  
 
 
  
 
 
  
 
      
 
   
 
 
     
 
 
 
 
  
     
 
 
 
 
 
  
 
 
           
(10)
and [ω] is the angular velocity of the CIR/SIR with respect to the spacecraft under consideration, multiplied
by 106. [rAU] is the position of the spacecraft with respect to the Sun in astronomical units. If the magnetic
field is measured in nT, then the current density will be in nA/m2.
Note that since only sharp changes in the current density but not the absolute values matter for the analysis
we propose, both [ω] and [rAU] can be considered as constants in SI for simplification. Meanwhile, other
tasks would require detailed calculations of the parameters as described above. This technique can be con-
sidered as an additional and independent method of CS identification.
Figures11a and11b represent a pair of two-panel graphs, the upper of which is for the electric current
density and the lower depict the localization of CSs derived from the three-parameter method. In the upper
panel, we define CSs as peaks with a height exceeding 0.5nA/m2, thus cutting off the background currents.
For easier comparison, a typical “0–1” view of the CS location is modulated by the electric current density
corresponding to each time at which a CS is identified (see the lower panels in Figure11). Figures11a shows
calculations based on the ACE data, and Figures11b shows the same for STEREO A. Fragments are arbitrar-
ily chosen from the “yellow stripe” region indicated in Figure3. When calculating the correlation between
the two rows, we take the current density from the validation method: if it is higher than the background
the value is 1, otherwise it is 0. Comparing the location of spikes of the electric current density with the
location of CSs from our CS database, one can conclude that the correlation between the two is very high,
reaching 0.9.
4.2. Validation by the Comparison With Gang Li's Method of CS Identifying
Gang Li's method (Li, 2008) is based on the analysis of local variations of the IMF direction that become
dramatic at CSs. It is usually applied to identifying CSs in turbulent plasmas (see Section1). On the one
hand, we understand that the three-parameter method is completely different from (Li,2008), but on the
other hand, it would be useful to compare results of both.
We apply both techniques to the ACE data, analyzing the location of CSs observed in 2004. Figures12a
and12b show two fragments of rows of CSs identified by our method (the upper panels) and Li's method
(the lower panels). The obtained results are promising. Despite the differences mentioned above, the corre-
lation between the two rows is 0.8. The fact that two methods give little different pictures of the current
sheet location is understandable. The mismatches seen in Figure12 may be determined (a) by different
targets of two methods (sometimes they identify not overlapping classes of CSs) and/or (b) by different
sensitivity of the methods because of the different cut off levels (see Section1 and Section5). A detailed
comparison of different methods identifying CSs is a future task. Here, it is important to find that the two
methods show similar results.
5. Discussion and Conclusions
A new method of the automated identification of CSs has been created. We use a simple approach popular
among observers to find CSs via a visual analysis of the behavior of both IMF and plasma parameters. The
method suggests identifying CSs of various types, from short and unstable turbulence-born CSs embedded
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Figure 11. Electric current density calculated with an alternative method (top panels, blue bars) and CSs identified via the three-parameter method discussed
above (bottom panels, red bars) for two randomly chosen time intervals of the event shown in Figure2 by yellow stripe. Current density is cut off at 0.5nA/m2
to remove the noise. (a) Example for the ACE spacecraft. (b) Example for the STEREO A spacecraft.
Journal of Geophysical Research: Space Physics
in the streaming solar wind to quasi-stable CSs associated with wave processes and large-scale solar-con-
nected objects. Note that our method is not aimed at identifying all CSs in the solar wind but at creating a
database that might be used for comprehensive statistical studies. A list of CSs identified at 1 AU from the
1998–2012 ACE data can be found at https://csdb.izmiran.ru, and the list will be expanded soon.
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Figure 12. Comparison of results of the new three-parameter method (upper panels, blue bars) and Gang Li's method
of current sheets (CS) identifying (lower panels, red bars). Randomly chosen time intervals on April 2–3, 2004 and April
15, 2004. One second cadence. Based on the analysis of the ACE spacecraft data.
Journal of Geophysical Research: Space Physics
The main statistical results obtained with the CS database are as follows:
1. On average, one-three thousand CSs are detected daily at the Earth's orbit. The number of CSs per day
is determined by the sum of the kinetic and thermal energy densities in a high degree (the correlation
coefficient is 0.8).
The best-fit parameter is (V2 (N+5N′)+10(N +N′)T)/5000 if V is given in km/s, T - in K, N is given in
cm−3, B is measured in nT, and N′=2cm−3. The second, thermal term makes a one order larger input in
the parameter than the kinetic one since the correlation with the temperature is better than with the speed.
Meanwhile, without the first term, it is impossible to follow smaller-scale variations in the CS daily rate.
2. The daily CS occurrence is found to be almost insensitive to the magnetic energy density variations.
Peaks of the number of CSs per day are found to occur in SIRs/CIRs and ICME sheaths. The result is con-
firmed statistically.
3. There is clustering of CSs. This fact is in agreement with the facts that (a) in realistic plasmas, the elec-
tric current is predicted to flow along multiple CSs rather than along one (Kowal et al.,2012; Lazarian
etal.,2020), (b) multiple CSs with the electric current of the same direction tend to merge, and, on the other
hand, (c) strong CSs create an analogue of the plasma sheet consisting of secondary CSs around (e.g., H. V.
Malova etal.,2017).
4. There is no obvious connection between the daily CS rate and the solar cycle. However, this preliminary
conclusion should be reconsidered after the expansion of the CS database to several solar cycles and carry-
ing out an analysis of the nature of long-term variations of the CS rate.
It should be noted that an impact of the solar cycle on the daily CS rate is possible. The presence of a nega-
tive correlation between R and the sunspot number at large temporal scales may indicate that the behavior
of R is slightly impacted by ICMEs and mostly determined by SIRs. Indeed, the occurrence rate of ICMEs
follows the solar cycle very well, correlating positively (Möstl et al.,2020), while the SIR occurrence rate
is more irregular and generally anti-correlates with the sunspot number (Yermolaev etal., 2012; Zhang
etal.,2007). The variable relative impact of the rates may lead to the observed picture of R variations over
the 11-year solar cycle. A further study will be carried out to clarify this point.
Using the created database, it is possible to study properties of both CSs (at small scales) and the solar
wind containing them (at larger scales). Since CSs are associated with turbulent plasmas, their rate may be
considered as one of characteristics of turbulence and intermittency (as shown in Malandraki etal.,2019).
For example, effects of clustering and an increase of the number of CSs in SIRs/CIRs and ICME sheaths
definitely reflect properties of turbulence in the corresponding regions. A turbulent ICME sheath created
downstream of the interplanetary shock is a well-known source of CSs and magnetic islands (see Chian &
Muñoz,2011; Khabarova et al., 2021; Pezzi et al., 2021; Zank etal.,2015 and references therein). Less is
known about the formation of CSs in SIRs (Khabarova etal.,2021) although SIRs are treated as turbulent
regions as well (Richardson,2018).
CSs also represent separators of magnetic islands occurring in turbulent plasma (Khabarova
etal.2015,2016,2021; Le Roux etal.,2019; Malandraki etal.,2019; Zank etal.,2015), therefore it would be
perspective to combine the database of CSs (https://csdb.izmiran.ru) and the database of flux ropes http://
fluxrope.info (Zheng & Hu,2018), studying associated effects, including particle acceleration in the areas
filled with CSs and magnetic islands.
Understanding the physical nature of the obtained dependence between the CS occurrence and the solar
wind energy density is a subject of future studies since it may be interpreted in different ways. On the
one hand, a good correlation between the CS occurrence and the solar wind temperature has been known
for years. It is often explained in terms of the solar wind heating by dissipation at turbulence-born CSs
(e.g., Adhikari etal.,2017; Karimabadi etal.,2013; Wan etal.,2015,2016; Wu etal.,2013). Meanwhile,
the heating effect is supposed to be localized in the nearest vicinity of CSs, which is debated, especially
for strong CSs. For example, Borovsky and Denton(2011) claim no correlation between strong CSs and
local heating.
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One can suggest from our results that CSs are intensively formed in hot plasma flows rather than represent
a direct source of heating. Indeed, in addition to turbulence, CSs can appear at plasma irregularities caused
by thermal fluctuations and asymmetries, which increase in regions with the raised temperature (Landau
& Lifshitz,1980; Lifshitz & Pitaevskii,1981). CSs occur in such regions owing to the development of insta-
bilities in plasma with temperature anisotropies and the increased magnetic reconnection rate (see Gingell
etal.,2015 and references therein). Therefore, CSs may be formed due to local processes caused by large-
scale plasma motions like those associated with SIRs/CIRs and ICMEs.
Substantial heating of particles can also be determined by intermittency, when the impact of turbulence-as-
sociated effects mentioned above is not essential. An intermittency phenomenon takes place if there are al-
ternating regions with ordered laminar and turbulent flows (Landau & Lifshitz,1987; Landau etal.,1984).
Regular quasi-stationary structures separated from chaotic regions by CSs are associated with such flows.
In this case, the CSs can potentially gather in “sandwiches” consisting of several CSs due to the spatial
quasi-periodicity (e.g., Bykov etal.,2008). This is consistent with the observed clustering of CSs. The sand-
wich-like regions may scatter some particles passing through them and accelerate other particles, the phase
of which turns out to be favorable upon entering the layer, for example, in the way suggested by Zelenyi
etal.(2011).
The other aspect is that one may suggest that the good correlation between the CS occurrence rate and T
is just because of the good T-V correlation (Borovsky & Denton,2011). However, (a) the CS daily rate does
not correlate with V well, and (b) the good T-V correlation paradigm cannot be applied to SIRs and ICMEs
in which R reaches its peak values, as seen from observations. Using an ICME as an example, Matthaeus
etal. (2006) have shown that the correlation between V and T is significantly reduced in the presence of
non-spherically-symmetric processes. One can see an illustration of this effect in Figure6. T increases only
for a short period at the leading edges of the fast speed coronal hole flow (Figure6a) and the ICME (Fig-
ure6b), but V remains high many hours after that. More studies are necessary to clarify this point.
Overall, many questions regarding properties of CSs in the solar wind and their impact on plasma heating
and particle acceleration remain open. The CS list compiled as a result of this study opens an opportunity
to answer the questions. The database will grow and include data for the entire period of 1 AU in situ ob-
servations starting with IMP8 and ending with the DSCOVR spacecraft. We also plan to compile CS lists
for the STEREO spacecraft, Ulysses, Parker Solar Probe and Solar Orbiter. The database is open access, and
the community members are welcome to employ the method and the CS list for their statistical and case
studies.
Data Availability Statement
The authors are grateful to the CDAWeb team for providing open access data for the magnetic field from
ACE (N. Ness, Bartol Research Institute) and the ACE/SWEPAM Solar Wind Experiment 64-s level 2 data
(D.J. McComas, SWRI) at the CDAWeb platform https://cdaweb.gsfc.nasa.gov . The STEREO mission data
are obtained from the UCLA STEREO Data Server (https://stereo-dev.epss.ucla.edu/l1_data) and CDAWeb
(https://cdaweb.gsfc.nasa.gov). The authors thank Dusan Odstrcil for providing the solar wind density re-
constructions from STEREO HI on the ENLIL Solar Wind Prediction website http://helioweather.net. The
sunspot number data are obtained from the OMNIWeb website https://omniweb.gsfc.nasa.gov/ow.html,
thanks to Dr. Natalia Papitashvili and Robert Candey. The database resulting from our study is available
at https://csdb.izmiran.ru. The authors thank Andrei Osin for his help in maintaining the website at the
IZMIRAN institutional server.
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Adhikari, L., Zank, G. P., Hunana, P., Shiota, D., Bruno, R., Hu, Q., & Telloni, D. (2017). II. Transport of nearly incompressible magnetohy-
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Acknowledgments
O. Khabarova and R. Kislov are sup-
ported by Russian Science Foundation
grant No. 20-42-04418. G. Li's work on
comparison of CS databases is support-
ed in part by NASA grants K99055CT,
80NSSC19K0831 and 80NSSC19K0079
at UAH. T. Sagitov acknowledges the
HSE's encouragement of student's
scientific activity.
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... Spacecraft routinely observe electric-current-carrying thin plasma layers, or current sheets (CSs), in collisionless space plasmas (e.g., Nakamura et al. 2006;Sundkvist et al. 2007;Greco et al. 2009;Podesta 2017a;Azizabadi et al. 2021;Jain et al. 2021;Khabarova et al. 2021b). In the solar wind, CSs are formed at discontinuities that separate regions with differently directed magnetic fields (Syrovatskiǐ 1971). ...
... These are secondary signatures identifying ion-dominated CSs. An overview of both visual and automated methods of CS identification in the heliosphere can be found in Khabarova et al. (2021b). ...
... Below, we will show an example of crossing of such a CS with MMS in the solar wind. If one knows specific features characterizing the occurrence of strong electron-dominated CSs in the solar wind, then it is possible to apply commonly accepted techniques for CS identification to recognition of electrondominated CSs from the in situ data, using an ordinary spacecraft resolution of 1−3 s (Khabarova et al. 2021b). It also would be interesting and useful to find secondary or indirect signatures of strong electron-carried currents. ...
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Current sheets (CSs) are preferred sites of magnetic reconnection and energy dissipation in astrophysical plasmas. Electric currents in them may be carried by both electrons and ions. In our prior theoretical studies of the CS formation in turbulent plasmas, we utilized fully kinetic and hybrid code simulations with ions considered as particles and electrons—as a massless fluid. We found that electron-dominated CSs in which electrons become the main carriers of the electric current and contributors to energy dissipation may form inside or nearby ion-dominated CSs. These structures represent a distinguished type of CSs and should not be mixed up with so-called electron-scale CSs. Current simulations show that such CSs are characterized by the electron-to-ion bulk speed ratio ( u e / u i ) increases that can be seen at ion scales according to theoretical predictions and high-resolution observations from the Magnetospheric Multiscale mission. Therefore, applying the u e / u i parameter to the solar wind data may allow locating the strongest electron-dominated CSs with an ordinary spacecraft resolution of 1−3 s. This study shows that, indeed, electron-dominated CSs observed during a period of quiet solar wind conditions at 1 au impact the surrounding plasma, which may be reflected in sharp changes of u e / u i . Electron-dominated CSs are found to be localized in the vicinity of ion-dominated CSs identified via changes in the magnetic field and plasma parameters, displaying the same clustering. We conclude that u e / u i may be used as one of the key parameters for statistical studies of CSs in the solar wind and analyzing the role of electrons in them.
... Spacecraft routinely observe electric-current-carrying thin plasma layers, current sheets (CSs), in collisionless space plasmas (e.g., Sundkvist et al. 2007;Greco et al. 2009;Azizabadi et al. 2021;Jain et al. 2021;Khabarova et al. 2021a)). In the solar wind, CSs are formed at discontinuities that separate regions with differently-directed magnetic fields (Syrovatskiǐ 1971). ...
... These are secondary signatures identifying ion-dominated CSs. An overview of both visual and automated methods of CS identification in the heliosphere can be found in (Khabarova et al. 2021a). ...
... Below, we will show an example of crossing of such a CS with MMS in the solar wind. If one knows specific features characterizing the occurrence of strong electron-dominated CSs in the solar wind, then it is possible to apply commonly accepted techniques for CS identifying to recognition of electron-dominated CSs from the in situ data, using an ordinary spacecraft resolution of one-three seconds (Khabarova et al. 2021a). It also would be interesting and useful to find secondary or indirect signatures of strong electron-carried currents. ...
Preprint
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Current sheets (CSs) are preferred sites of magnetic reconnection and energy dissipation in turbulent collisionless astrophysical plasmas. In our prior theoretical studies of processes associated with the CS formation in turbulent plasmas, for which we utilized fully kinetic and hybrid code simulations with ions considered as particles and electrons - as a massless fluid, we found that (i) inside ion-scale CSs thin electron-scale CSs form, (ii) with the CS thinning the electron-to-ion bulk speed ratio $u_e/u_i$ increases, and (iii) the electrons become the main carriers of the electric currents and contributors to energy dissipation. The question arises: is it possible to find electron-dominated-CSs in natural plasmas, using the $u_e/u_i$ signature as a search criterion? We apply this parameter to the solar wind to locate electron CSs there at least approximately. Existing methods of identification of CSs in the solar wind focus on the search for ion-scale structures by considering changes in the magnetic field and plasma parameters. We now found that electron-dominated CSs observed during a period of quiet solar wind conditions at 1 AU can be identified by sharp variations of $u_e/u_i$ often localized in the vicinity of ion-scale CSs, showing the same clustering. We conclude that $u_e/u_i$ may be used as one of key parameters for probing CSs and the role of electrons in them. https://arxiv.org/abs/2112.03639
... The boundaries of CSs are associated with spatial variations or reversals of the local magnetic field. In recent years, a variety of methods, suitable for the detection of sharp gradients in a turbulent field, have been proposed (Bruno et al. 1999;Hada et al. 2003;Khabarova et al. 2021;Pecora, F. et al. 2021). A convenient statistical tool to perform this study, is the Partial Variance of Increments P V I (Greco et al. 2008). ...
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P SP and SolO data are utilized to investigate magnetic field intermittency in the solar wind (SW). Small-scale intermittency (20 − 100d i) is observed to radially strengthen when methods relying on higher-order moments are considered (SF q , SDK), but no clear trend is observed at larger scales. However, lower-order moment-based methods (e.g., PVI) are deemed more appropriate for examining the evolution of the bulk of Coherent Structures (CSs), P V I ≥ 3. Using PVI, we observe a scale-dependent evolution in the fraction of the dataset occupied by CSs, f P V I≥3. Specifically, regardless of the SW speed, a subtle increase is found in f P V I≥3 for = 20d i , in contrast to a more pronounced radial increase in CSs observed at larger scales. Intermittency is investigated in relation to plasma parameters. Though, slower SW speed intervals exhibit higher f P V I≥6 and higher kurtosis maxima, no statistical differences are observed for f P V I≥3. Highly Alfvénic intervals, display lower levels of intermittency. The anisotropy with respect to the angle between the magnetic field and SW flow, Θ V B is investigated. Intermittency is weaker at Θ V B ≈ 0 • and is strengthened at larger angles. Considering the evolution at a constant alignment angle, a weakening of intermittency is observed with increasing advection time of the SW. Our results indicate that the strengthening of intermittency in the inner heliosphere is driven by the increase in comparatively highly intermittent perpendicular 2 intervals sampled by the probes with increasing distance, an effect related directly to the evolution of the Parker spiral.
... On the other hand, this limits their validity to scales much larger than the electron scales. Space observations of collisionless plasma turbulence by multi-spacecraft missions (Cluster and MMS) in the Earth's magnetosphere and the solar wind, however, revealed electron-and ion-scale breaks in the power spectra as well as the formation of current sheet (CS) structures from ion to electron scales [20][21][22] . On the other hand, even hybrid-kinetic simulations with inertia-less electrons have already shown that in evolving turbulent CSs, the electrons become the main current carriers 15 and that these CSs thin down to the grid scale 23 . ...
Preprint
The dissipation mechanism of the magnetic energy in turbulent collisionless space and astrophysical plasmas is still not well understood. Its investigation requires efficient kinetic simulations of the energy transfer in collisionless plasma turbulence. In this respect, hybrid-kinetic simulations, in which ions are treated as particles and electrons as an inertial fluid, have begun to attract a significant interest recently. Hybrid-kinetic models describe both ion- and electron scale processes by ignoring electron kinetic effects so that they are computationally much less demanding compared to fully kinetic plasma models. Hybrid-kinetic codes solve either the Vlasov equation for the ions (Eulerian Vlasov-hybrid codes) or the equations of motion of the ions as macro-particles (Lagrangian Particle-in-Cell (PIC)-hybrid codes). They consider the inertia of the electron fluid using different approximations. We check the validity of these approximations by employing our recently massively parallelized three-dimensional PIC-hybrid code CHIEF which considers the electron inertia without any of the common approximations. In particular we report the results of simulations of two-dimensional collisionless plasma turbulence. We conclude that the simulation results obtained using hybrid-kinetic codes which use approximations to describe the electron inertia need to be interpreted with caution. We also discuss the parallel scalability of CHIEF, to the best of our knowledge, the first PIC-hybrid code which without approximations describes the inertial electron fluid.
... Several algorithms with some similarities and differences in their approaches have been used for the automatic detection of current sheets in simulations of 3D magnetohydrodynamic turbulence, [33][34][35] 2D kinetic turbulence of electron-ion plasmas, [36][37][38] 3D kinetic turbulence of pair plasmas 39 and also in satellite observations of solar wind. 40 Zhdankin et al. 34 suggested an algorithm to identify and characterize current sheets in magnetohydrodynamic (MHD) turbulence. The algorithm requires to choose optimum values of three parameters for a statistically meaningful identification and characterization of current sheets. ...
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Full-text available
Current sheets forming in an ion-kinetic turbulent collisionless plasma are characterized by utilizing the results of two-dimensional hybrid-kinetic numerical simulations (ions treated as kinetic species using particle-in-cell method and electrons treated as mass-less fluid). For this sake, the algorithm, proposed by Zhdankin et al. [Astrophys. J. 771, 124 (2013)] for the identification and characterization of current sheets forming in magnetohydrodynamic plasma turbulence, is extended to current sheets forming in a much noisier kinetic plasma turbulence. Effects of the algorithm parameters on the identification of current sheets in plasma turbulence are analyzed. Based on this analysis, appropriate values of algorithm parameters for the current sheet identification are chosen. Current sheets are statistically characterized in terms of their main properties—the peak current density, the peak current carrier velocity (mainly electrons), the thickness, the length, and also the aspect ratio (length/thickness). Results of the characterization show that the current sheets have a tendency to thin down to below ion inertial length scale until numerical (grid-resolution based) dissipation stops any further thinning. Simulations that include the physics at the electron inertial scales, e.g., hybrid simulations with electron inertia, are required to fully address the current sheet thinning processes and determination of the final thicknesses of current sheets.
... Several algorithms with some similarities and differences in their approaches have been used for the automatic detection of current sheets in simulations of 3D magnetohydrodynamic turbulence, [33][34][35] 2D kinetic turbulence of electron-ion plasmas, [36][37][38] 3D kinetic turbulence of pair plasmas 39 and also in satellite observations of solar wind. 40 Zhdankin et al. 34 suggested an algorithm to identify and characterize current sheets in magnetohydrodynamic (MHD) turbulence. The algorithm requires to choose optimum values of three parameters for a statistically meaningful identification and characterization of current sheets. ...
Preprint
The properties of current sheets forming in a ion-kinetically turbulent collisionless plasma are investigated by utilizing the results of two-dimensional hybrid-kinetic numerical simulations. For this sake the algorithm proposed by Zhdankin et al. (2013) for the analysis of current sheets forming in MHD-turbulent plasmas, was extended to analyse the role and propertes of current sheets formating in a much noisier kinetically turbulent plasma. The applicability of this approach to the analysis of kinetically-turbulent plasmas is verified. Invesigated are, e.g., the effects of the choice of parameters on the current sheet recognition, viz. the threshold current density, the minimum current density and of the local regions around current density peaks. The main current sheet properties are derived, their peak current density, the peak current carrier velocity (mainly electrons), the thickness and length of the current sheets, i.e. also their aspect ratio (length/thickness). By varying the grid resolution of the simulations it is shown that, as long as the electron inertia is not taken into account, the current sheets thin down well below ion inertial length scale until numerical (grid-resolution based) dissipation stops any the further thinning.
... electron/ion density (for electrons from 0.6 cm −3 at current sheet edge to 0.7 cm −3 at the current sheet center, less than 20%) in the field reversal region. Development of automated methods for the detection of current sheets in space observations (Khabarova et al. 2021) and numerical simulations (Azizabadi et al. 2021) of plasma turbulence is required to study the detailed structure of current sheets formed in plasma turbulence. Studies on current sheet equilibria based on such detection would be instrumental to understand the role of plasma instabilities in collisionless dissipation (Zelenyi et al. 2020). ...
Preprint
In collisionless and turbulent space plasmas, e.g., of the solar wind or the magnetosheath of the Earth's magnetosphere, dissipation of macroscopic energy into heat occurs in and around current sheets self-consistently formed in the turbulence. Instabilities in these current sheets driven by free energy sources provided by spatial gradients or non-Maxwellean features of the velocity distribution function can provide collisionless dissipation and influence the properties of the turbulence. In order to determine the free energy sources provided by the spatial gradients of plasma number density and electron/ion bulk velocities in current sheets formed in collisionless turbulent plasmas with an applied external magnetic field, we carried out two-dimensional PIC-hybrid-code simulations. We found that current sheets in a collisionless turbulent plasma are formed primarily by electron shear flows with electron bulk velocity much larger than the ion bulk velocity while the density variations through the current sheets are relatively small ($<$ 10\%). The electron bulk velocities and, thus, the current densities inside the sheets are directed mainly parallel to the external magnetic field. The shear in the perpendicular electron and ion bulk velocities generates electron- and ion-flow vorticities in the direction parallel to the external magnetic field. Inside the current sheets the parallel electron-flow vorticity exceeds the parallel ion-flow vorticity, it changes its sign around the current sheet centers and peaks near the edges of current sheets. An ion temperature anisotropy develops near current sheets during their formation. It correlates well with the parallel ion vorticity as well as with the parallel electron vorticity. Theoretical estimates in the limit of un-magnetized ions support the simulation results.
Article
Full-text available
Current sheets forming in an ion-kinetic turbulent collisionless plasma are characterized by utilizing the results of two-dimensional hybrid-kinetic numerical simulations (ions treated as kinetic species using particle-in-cell method and electrons treated as mass-less fluid). For this sake, the algorithm, proposed by Zhdankin et al. [Astrophys. J. 771, 124 (2013)] for the identification and characterization of current sheets forming in magnetohydrodynamic plasma turbulence, is extended to current sheets forming in a much noisier kinetic plasma turbulence. Effects of the algorithm parameters on the identification of current sheets in plasma turbulence are analyzed. Based on this analysis, appropriate values of algorithm parameters for the current sheet identification are chosen. Current sheets are statistically characterized in terms of their main properties—the peak current density, the peak current carrier velocity (mainly electrons), the thickness, the length, and also the aspect ratio (length/thickness). Results of the characterization show that the current sheets have a tendency to thin down to below ion inertial length scale until numerical (grid-resolution based) dissipation stops any further thinning. Simulations that include the physics at the electron inertial scales, e.g., hybrid simulations with electron inertia, are required to fully address the current sheet thinning processes and determination of the final thicknesses of current sheets.
Article
Full-text available
Our understanding of processes occurring in the heliosphere historically began with reduced dimensionality - one-dimensional (1D) and two-dimensional (2D) sketches and models, which aimed to illustrate views on large-scale structures in the solar wind. However, any reduced dimensionality vision of the heliosphere limits the possible interpretations of in-situ observations. Accounting for non-planar structures, e.g. current sheets, magnetic islands, flux ropes as well as plasma bubbles, is decisive to shed the light on a variety of phenomena, such as particle acceleration and energy dissipation. In part I of this review, we have described in detail the ubiquitous and multi-scale observations of these magnetic structures in the solar wind and their significance for the acceleration of charged particles. Here, in part II, we elucidate existing theoretical paradigms of the structure of the solar wind and the interplanetary magnetic field, with particular attention to the fine structure and stability of current sheets. Differences in 2D and 3D views of processes associated with current sheets, magnetic islands and flux ropes are discussed. We finally review the results of numerical simulations and in-situ observations, pointing out the complex nature of magnetic reconnection and particle acceleration in a strongly turbulent environment.