arXiv subjects

Sofiane Bourouaine

Publications and source records attributed to Sofiane Bourouaine.

At least 19 recordsLinked to original sources

arXiv2026

Negative and Positive Cascade Rates of Slow Alfvénic Turbulence in Switchback and Non-switchback Intervals: \emph{Wind} Observations

We estimate the turbulent cascade rate in imbalanced Alfvénic turbulence in the slow solar wind using a Politano--Pouquet-based approach that does not require an isotropic assumption. We analyze selected 8-hour intervals provided by \emph{Wind} spacecraft. These intervals are characterized by near-homogeneity, weak velocity shear, and imbalanced Alfvénic fluctuations, and are classified as switchback or non-switchback depending on the angular spread of the magnetic field relative to the mean field. Switchback intervals are identified by large magnetic-field rotations, whereas non-switchback intervals exhibit only small angular deviations. Our results show that non-switchback intervals exhibit a positive total cascade rate and power spectra consistent with a $-3/2$ scaling, indicative of a forward energy cascade. In contrast, switchback intervals are characterized by a negative total cascade rate (inverse cascade), and by steeper power spectra with a spectral index of approximately $-1.6$. This indicates that large magnetic-field rotations can substantially modify the scale-to-scale energy transfer in Alfvénic slow solar wind. The results suggest that switchbacks may be associated with additional physical processes, such as local instabilities, or reconnection-related structures, that alter the direction and magnitude of the turbulent cascade. These findings may help explain previous reports of negative cascade rates in imbalanced Alfvénic solar-wind turbulence.

astro-ph.SR↗

arXiv2026

The integral and correlation scales of solar wind turbulence

Many works have attempted to estimate the correlation and integral timescales associated with turbulent fluctuations in the solar wind, which are interpreted as length scales based on Taylor's~Hypothesis. However, accurate estimates of these timescales from spacecraft observations heavily rely on the accurate estimation of autocorrelation functions (ACF), which have been recently shown to depend strongly on the interval length used to estimate them. In this Letter, we show that this dependence on interval length may be artificial because common ACF estimators do not correctly capture the long-lag behavior of the true ACF of the underlying turbulence. We introduce a new ergodicity-based methodology to unambiguously estimate the integral timescale, and a new ACF estimator with better ergodic convergence than current ones. Due to its ergodic properties, the new ACF estimator properly captures the long-lag behavior, and is independent of the interval length. We use this approach to estimate the integral and correlation scales of magnetic fluctuations in the solar wind near $1~{\rm au}$.

physics.plasm-ph↗

arXiv2025

Energetically-dominant Sunward-Propagating Alfvén Waves Near 1 au and Their Relation to Large-scale Magnetic Switchbacks

In this letter, we investigate the population of energetically-dominant sunward-propagating Alfvén waves (SAWs) using more than 20 years of data provided by the Wind spacecraft near 1 au. We refer to SAWs as energetically-dominant sunward-propagating Alfvén waves within inertial range scales. Key parameters such as normalized cross helicity, plasma incompressibility, and magnetic incompressibility are used to determine the SAWs. Incorporating the polarity of the heliospheric magnetic field, AW modes are identified, which enables the determination of the propagation direction. Occurrence rates of SAWs vary from 1% to 14% depending on the time scale and solar wind stream type considered. Particularly, the relationship between large-scale magnetic field switchbacks (SBs) and SAWs (for a 1-hour long time scale) is investigated. A methodology utilizing pitch angle distributions of suprathermal electron strahl is employed to identify inverted magnetic field topology. The intervals containing SAWs are cross-referenced and examined with intervals identified as SBs. For a sample of 1636 1-hour SAW intervals, 17.5% are associated with magnetic field switchbacks occurring at scales larger than one hour. The analysis lends support to the idea of switchbacks as one of the candidate sources for a portion of the SAW population.

physics.space-ph↗

arXiv2025

Wave Particle Interaction in the Upstream of ICME Shocks

Shocks associated with Interplanetary Coronal Mass Ejections are known to energize charged particles and give rise to Solar Energetic Particles. Many of these energetic particles move ahead of the shock to create a foreshock region. The foreshock region primarily consists of solar wind plasma, exhibiting turbulent velocity and magnetic fields. Such turbulent behavior results from inherent solar wind turbulence modified by energetic particles. We analyze magnetic field data from six such ICME shocks observed by the Wind spacecraft. The analysis of the shock upstream shows that the magnetic power spectral density (PSD) maintains a power-law slope of $-5/3$. We also identify clear intermittent peaks in the PSD. After characterizing these peaks, we investigate various possibilities for their generation. Our analysis indicates that these peaks in the PSD are due to the resonant interaction of Alfvén waves with the bulk solar wind protons and protons with energy up to $10$~keV. However, evidence of Alfvén wave interaction with highly energetic protons is not evident in our analysis, and we anticipate that such evidence is obscured by the prevailing solar wind turbulence in the shock upstream.

astro-ph.SR↗

arXiv2024

On the Heating of the Slow Solar-Wind by Imbalanced Alfvén-Wave Turbulence from 0.06 au to 1 au: Parker Solar Probe and Solar Orbiter observations

In this work we analyze plasma and magnetic field data provided by the Parker Solar Probe (\emph{PSP}) and Solar Orbiter (\emph{SO}) missions to investigate the radial evolution of the heating of Alfvénic slow wind (ASW) by imbalanced Alfvén-Wave (AW) turbulent fluctuations from 0.06 au to 1 au. in our analysis we focus on slow solar-wind intervals with highly imbalanced and incompressible turbulence (i.e., magnetic compressibility $C_B=δB/B\leq 0.25$, plasma compressibility $C_n=δn/n\leq 0.25$ and normalized cross-helicity $σ_c\geq 0.65$). First, we estimate the AW turbulent dissipation rate from the wave energy equation and find that the radial profile trend is similar to the proton heating rate. Second, we find that the scaling of the empirical AW turbulent dissipation rate $Q_W$ obtained from the wave energy equation matches the scaling from the phenomenological AW turbulent dissipation rate $Q_{\rm CH09}$ (with $Q_{\rm CH09}\simeq 1.55 Q_W$) derived by~\cite{chandran09} based on the model of reflection-driven turbulence. Our results suggest that, as in the fast solar wind, AW turbulence plays a major role in the ion heating that occurs in incompressible slow-wind streams.

physics.space-ph↗

arXiv2022

On the Statistics of Elsasser Increments in Solar Wind and Magnetohydrodynamic Turbulence

We investigate the dependency with scale of the empirical probability distribution functions (PDF) of Elsasser increments using large sets of WIND data (collected between 1995 and 2017) near 1 au. The empirical PDF are compared to the ones obtained from high-resolution numerical simulations of steadily driven, homogeneous Reduced MHD turbulence on a $2048^3$ rectangular mesh. A large statistical sample of Alfvénic increments is obtained by using conditional analysis based on the solar wind average properties. The PDF tails obtained from observations and numerical simulations are found to have exponential behavior in the inertial range, with an exponential decrement that satisfies power-laws of the form $α_l\propto l^{-μ}$, where $l$ the scale size, with $μ$ around 0.2 for observations and 0.4 for simulations. PDF tails were extrapolated assuming their exponential behavior extends to arbitrarily large increments in order to determine structure function scaling laws at very high orders. Our results points to potentially universal scaling laws governing the PDF of Elsasser increments and to an alternative methodology to investigate high-order statistics in solar wind observations.

astro-ph.SR↗

arXiv2021

Applicability of Taylor's Hypothesis during Parker Solar Probe perihelia

We investigate the validity of Taylor's Hypothesis (TH) in the analysis of Alfvénic fluctuations of velocity and magnetic fields in solar wind streams measured by Parker Solar Probe (PSP)~during the first four encounters. We use PSP velocity and magnetic field measurements from 24 h intervals selected from each of the first four encounters. The applicability of TH is investigated by measuring the parameter $ε=δu_0/\sqrt{2}V_\perp$, which quantifies the ratio between the typical speed of large-scale fluctuations, $δu_0$, and the local perpendicular PSP speed in the solar wind frame, $V_\perp$. TH is expected to be applicable for $ε\lesssim0.5$ when PSP is moving nearly perpendicular to the local magnetic field in the plasma frame, irrespective of the Alfvén Mach number $M_{\rm A}=V_{\rm SW}/V_{\rm A}$, where $V_{\rm SW}$ and $V_{\rm A}$ are the local solar wind and Alfvén speed, respectively. For the four selected solar wind intervals we find that between 10% to 60% of the time the parameter $ε$ is below 0.2 when the sampling angle (between the spacecraft velocity in the plasma frame and the local magnetic field) is greater than $30^\circ$. For angles above $30^\circ$, the sampling direction is sufficiently oblique to allow one to reconstruct the reduced energy spectrum $E(k_\perp)$ of magnetic fluctuations from its measured frequency spectra. The spectral indices determined from power-law fits of the measured frequency spectrum accurately represent the spectral indices associated with the underlying spatial spectrum of turbulent fluctuations in the plasma frame. Aside from a frequency broadening due to large-scale sweeping that requires careful consideration, the spatial spectrum can be recovered to obtain the distribution of fluctuation's energy among scales in the plasma frame.

astro-ph.SR↗

arXiv2020

Turbulence characteristics of switchbacks and non-switchbacks intervals observed by \emph{Parker Solar Probe}

We use \emph{Parker Solar Probe} (\emph{PSP}) in-situ measurements to analyze the characteristics of solar wind turbulence during the first solar encounter covering radial distances between $35.7R_\odot$ and $41.7R_\odot$. In our analysis we isolate so-called switchback (SB) intervals (folded magnetic field lines) from non-switchback (NSB) intervals, which mainly follow the Parker spiral field. Using a technique based on conditioned correlation functions, we estimate the power spectra of Elsasser, magnetic and bulk velocity fields separately in the SB and NSB intervals. In comparing the turbulent energy spectra of the two types of intervals, we find the following characteristics: 1) The decorrelation length of the backward-propagating Elsasser field $z^-$ is larger in the NSB intervals than the one in the SB intervals; 2) the magnetic power spectrum in SB intervals is steeper, with spectral index close to -5/3, than in NSB intervals, which have a spectral index close to -3/2; 3) both SB and NSB turbulence are imbalanced with NSB having the largest cross-helicity, 4) the residual energy is larger in the SB intervals than in NSB, and 5) the analyzed fluctuations are dominated by Alfvénic fluctuations that are propagating in the \emph{sunward} (\emph{anti-sunward}) direction for the SB (NSB) turbulence. These observed features provide further evidence that the switchbacks observed by \emph{PSP} are associated with folded magnetic field lines giving insight into their turbulence nature.

physics.space-ph↗

arXiv2020

Two-time energy spectrum of weak magnetohydrodynamic turbulence

In this work a weak-turbulence closure is used to determine the structure of the two-time power spectrum of weak magnetohydrodynamic (MHD) turbulence from the nonlinear equations describing the dynamics. The two-time energy spectrum is a fundamental quantity in turbulence theory from which most statistical properties of a homogeneous turbulent system can be derived. A closely related quantity, obtained via a spatial Fourier transform, is the two-point two-time correlation function describing the space-time correlations arising from the underlying dynamics of the turbulent fluctuations. Both quantities are central in fundamental turbulence theories as well as in the analysis of turbulence experiments and simulations. However, a first-principles derivation of these quantities has remained elusive due to the statistical closure problem, in which dynamical equations for correlations at order $n$ depend on correlations of order $n+1$. The recent launch of the Parker Solar Probe (PSP), which will explore the near-Sun region where the solar wind is born, has renewed the interest in the scientific community to understand the structure, and possible universal properties of space-time correlations. The weak MHD turbulence regime that we consider in this work allows for a natural asymptotic closure of the two-time spectrum, which may be applicable to other weak turbulence regimes found in fluids and plasmas. An integro-differential equation for the scale-dependent temporal correlation function is derived for incompressible Alfvénic fluctuations whose nonlinear dynamics is described by the reduced MHD equations.

physics.plasm-ph↗

arXiv2020

The Eulerian space-time correlation of strong Magnetohydrodynamic Turbulence

The Eulerian space-time correlation of strong Magnetohydrodynamic (MHD) turbulence in strongly magnetized plasmas is investigated by means of direct numerical simulations of Reduced MHD turbulence and phenomenological modeling. Two new important results follow from the simulations: 1) counter-propagating Alfvénic fluctuations at a each scale decorrelate in time at the same rate in both balanced and imbalanced turbulence; and 2) the scaling with wavenumber of the decorrelation rate is consistent with pure hydrodynamic sweeping of small-scale structures by the fluctuating velocity of the energy-containing scales. An explanation of the simulation results is proposed in the context of a recent phenomenological MHD model introduced by Bourouaine and Perez 2019 (BP19) when restricted to the strong turbulence regime. The model predicts that the two-time power spectrum exhibits an universal, self-similar behavior that is solely determined by the probability distribution function of random velocities in the energy-containing range. Understanding the scale-dependent temporal evolution of the space-time turbulence correlation as well as its associated universal properties is essential in the analysis and interpretation of spacecraft observations, such as the recently launched Parker Solar Probe (PSP).

astro-ph.SR↗

arXiv2020

Interpreting solar wind turbulent spectra beyond Taylor's Hypothesis

In this paper we apply a methodology, recently proposed by Bourouaine and Perez (2019) (BP19), to interpret solar-wind turbulent power spectra beyond Taylor approximation (TA). The turbulent power spectra were measured using \emph{Helios} spacecraft data near 0.6 au. We use the model proposed in BP19 to reproduce the field-perpendicular power spectrum $E(k_\perp)$ of anti-sunward Alfvénic fluctuations in the plasma frame (where $k_\perp$ is the field-perpendicular wavenumber) from the corresponding measured frequency power spectrum $P_{\rm sc}(ω,θ_b)$ along the sampling angle $θ_b$, which is the angle between the local magnetic field and the sampling direction. Here $ω=2πf$ and $f$ is the frequency of the time signal. Interestingly enough, we found that for all corresponding measured frequency power spectrum $P_{\rm sc}(ω,θ_b)$ the reproduced field-perpendicular power spectrum $E(k_\perp)$ is the same and independent of the considered sampling angle $θ_b$. This finding is consistent with the fact that the analyzed turbulence is strong and highly anisotropic with $k_\| \ll k_\perp$ (where $k_\|$ is the field-parallel wavenumber). Furthermore, for this specific time signal we found that the commonly used TA is still approximately valid with the important difference that a broadening in $k_\perp$ for each angular frequency $ω$ is present. This broadening can be described in the context of the methodology proposed in BP19.

astro-ph.SR↗

arXiv2019

On the interpretation of Parker Solar Probe Turbulent Signals

In this letter we propose a practical methodology to interpret future Parker Solar Probe (PSP) turbulent time signals even when Taylor's hypothesis is not valid. By extending Kraichnan's sweeping model used in hydrodynamics we derive the Eulerian spacetime correlation function in magnetohydrodynamics (MHD) turbulence. It is shown that in MHD, the temporal decorrelation of small-scale fluctuations arises from a combination of hydrodynamic sweeping induced by large-scale fluid velocity $δu_0$ and by the Alfvénic propagation along the local magnetic field. The resulting temporal part of the space-time correlation function is used to determine the wavenumber range $Δk_\perp=[k_{\rm min},k_{\rm max}]$ of the turbulent fluctuations that contribute to the power of a given frequency $ω$ of the time signal measured in the spacecraft frame. Our analysis also shows that the shape of frequency power spectrum $P_{sc}(ω)$ of the time signal will follow the same power-law of the reduced power spectrum $E(k_\perp)\sim k^{-α}_\perp$ in the plasma frame, where $α$ is the spectral index. The proposed framework for the analysis of PSP time signals entirely relies on two simple dimensionless parameters that can be empirically obtained from PSP measurements, namely, $ε=δu_0/\sqrt 2 V_\perp$ (where $V_\perp$ is the perpendicular velocity of PSP seen in the plasma frame) and the spectral index $α$.

astro-ph.SR↗

arXiv2019

Radial evolution of stochastic heating in low-$β$ solar wind

We consider the radial evolution of perpendicular ion heating due to the violation of magnetic moment conservation caused by Alfven and kinetic Alfven wave turbulence. This process, referred to as stochastic heating, can be quantified by the ratio between the average velocity fluctuations at the ion gyroradius and the perpendicular ion thermal speed $ε\equiv δv / v_{t\perp}$. Using 17 years of Helios observations, we constrain how much energy could be dissipated by this mechanism between 0.29 and 0.98 au. We find that stochastic heating likely operates throughout the entire inner heliosphere, but that its radial dependence is steeper than that of empirically derived dissipation rates, being $r^{-2.5}$ compared with $r^{-2.08}$. This difference is significantly increased in fast solar wind streams to $r^{-3.1}$ compared with $r^{-1.8}$.

physics.space-ph↗

arXiv2017

The Development of Magnetic Field Line Wander by Plasma Turbulence

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices, and the fundamental processes of turbulence, magnetic reconnection, and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfven wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

physics.plasm-ph↗

arXiv2015

Deceleration of Alpha Particles in the Solar Wind by Instabilities and the Rotational Force: Implications for Heating, Azimuthal Flow, and the Parker Spiral Magnetic Field

Protons and alpha particles in the fast solar wind are only weakly collisional and exhibit a number of non-equilibrium features, including relative drifts between particle species. Two non-collisional mechanisms have been proposed for limiting differential flow between alpha particles and protons: plasma instabilities and the rotational force. Both mechanisms decelerate the alpha particles. In this paper, we derive an analytic expression for the rate $Q_{\mathrm{flow}}$ at which energy is released by alpha-particle deceleration, accounting for azimuthal flow and conservation of total momentum. We show that instabilities control the deceleration of alpha particles at $r< r_{\mathrm{crit}}$, and the rotational force controls the deceleration of alpha particles at $r> r_{\mathrm{crit}}$, where $r_{\mathrm{crit}} \simeq 2.5 \,\mathrm{AU}$ in the fast solar wind in the ecliptic plane. We find that $Q_{\mathrm{flow}}$ is positive at $r<r_{\mathrm{crit}}$ and $Q_{\mathrm{flow}} = 0$ at $r\geq r_{\mathrm{crit}}$, consistent with the previous finding that the rotational force does not lead to a release of energy. We compare the value of~$Q_{\mathrm{flow}}$ at $r< r_{\mathrm{crit}}$ with empirical heating rates for protons and alpha particles, denoted $Q_{\mathrm{p}}$ and $Q_α$, deduced from in-situ measurements of fast-wind streams from the \emph{Helios} and \emph{Ulysses} spacecraft. We find that $Q_{\mathrm{flow}}$ exceeds $Q_α$ at $r < 1\,\mathrm{AU}$, and that $Q_{\mathrm{flow}}/Q_{\rm p}$ decreases with increasing distance from the Sun from a value of about one at $r=0.29 - 0.42\,\mathrm{AU}$ to about 1/4 at 1 AU. We conclude that the continuous energy input from alpha-particle deceleration at $r< r_{\mathrm{crit}}$ makes an important contribution to the heating of the fast solar wind.

physics.space-ph↗

arXiv2013

Limits on Alpha Particle Temperature Anisotropy and Differential Flow from Kinetic Instabilities: Solar Wind Observations

Previous studies have shown that the observed temperature anisotropies of protons and alpha particles in the solar wind are constrained by theoretical thresholds for pressure-anisotropy-driven instabilities such as the Alfvén/ion-cyclotron (A/IC) and fast-magnetosonic/whistler (FM/W) instabilities. In this letter, we use a long period of in-situ measurements provided by the {\em Wind} spacecraft's Faraday cups to investigate the combined constraint on the alpha-proton differential flow velocity and the alpha-particle temperature anisotropy due to A/IC and FM/W instabilities. We show that the majority of the data are constrained to lie within the region of parameter space in which A/IC and FM/W waves are either stable or have extremely low growth rates. In the minority of observed cases in which the growth rate of the A/IC (FM/W) instability is comparatively large, we find relatively higher values of $T_{\perpα}/T_{\perp p}$ ($T_{\parallelα}/T_{\parallel p}$) when alpha-proton differential flow velocity is small, where $T_{\perpα}$ and $T_{\perp p}$ ($T_{\parallelα}$ and $T_{\parallel p}$) are the perpendicular (parallel) temperatures of alpha particles and protons. We conjecture that this observed feature might arise from preferential alpha-particle heating which can drive the alpha particles beyond the instability thresholds.

astro-ph.SR↗

arXiv2013

Instabilities Driven by the Drift and Temperature Anisotropy of Alpha Particles in the Solar Wind

We investigate the conditions under which parallel-propagating Alfvén/ion-cyclotron (A/IC) waves and fast-magnetosonic/whistler (FM/W) waves are driven unstable by the differential flow and temperature anisotropy of alpha particles in the solar wind. We focus on the limit in which $w_{\parallel α} \gtrsim 0.25 v_{\mathrm A}$, where $w_{\parallel α} $ is the parallel alpha-particle thermal speed and $v_{\mathrm A}$ is the Alfvén speed. We derive analytic expressions for the instability thresholds of these waves, which show, e.g., how the minimum unstable alpha-particle beam speed depends upon $w_{\parallel α}/v_{\mathrm A}$, the degree of alpha-particle temperature anisotropy, and the alpha-to-proton temperature ratio. We validate our analytical results using numerical solutions to the full hot-plasma dispersion relation. Consistent with previous work, we find that temperature anisotropy allows A/IC waves and FM/W waves to become unstable at significantly lower values of the alpha-particle beam speed $U_α$ than in the isotropic-temperature case. Likewise, differential flow lowers the minimum temperature anisotropy needed to excite A/IC or FM/W waves relative to the case in which $U_α=0$. We discuss the relevance of our results to alpha particles in the solar wind near 1 AU.

physics.space-ph↗

arXiv2013

A Parallel-Propagating Alfvénic Ion-Beam Instability in the High-Beta Solar Wind

We investigate the conditions under which parallel-propagating Alfvén/ion-cyclotron waves are driven unstable by an isotropic ($T_{\perp α} = T_{\parallelα}$) population of alpha particles drifting parallel to the magnetic field at an average speed $U_α$ with respect to the protons. We derive an approximate analytic condition for the minimum value of $U_α$ needed to excite this instability and refine this result using numerical solutions to the hot-plasma dispersion relation. When the alpha-particle number density is $\simeq 5%$ of the proton number density and the two species have similar thermal speeds, the instability requires that $β_{\rm p} \gtrsim 1$, where $β_{\rm p}$ is the ratio of the proton pressure to the magnetic pressure. For $1\lesssim β_{\mathrm p}\lesssim 12$, the minimum $U_α$ needed to excite this instability ranges from $0.7v_{\mathrm A}$ to $0.9v_{\mathrm A}$, where $v_{\mathrm A}$ is the Alfvén speed. This threshold is smaller than the threshold of $\simeq 1.2v_{\mathrm A}$ for the parallel magnetosonic instability, which was previously thought to have the lowest threshold of the alpha-particle beam instabilities at $β_{\mathrm p}\gtrsim 0.5$. We discuss the role of the parallel Alfvénic drift instability for the evolution of the alpha-particle drift speed in the solar wind. We also analyze measurements from the \emph{Wind} spacecraft's Faraday cups and show that the $U_α$ values measured in solar-wind streams with $T_{\perp α}\approx T_{\parallelα}$ are approximately bounded from above by the threshold of the parallel Alfvénic instability.

physics.space-ph↗