arXiv subjects

Benjamin D. G. Chandran

Publications and source records attributed to Benjamin D. G. Chandran.

At least 37 records · Page 2Linked to original sources

arXiv2021

An approximate analytic solution to the coupled problems of coronal heating and solar-wind acceleration

Between the base of the solar corona and the Alfven critical point, the solar-wind density decreases by approximately five orders of magnitude, but the temperature varies by a factor of only a few. In this paper, I show that such quasi-isothermal evolution out to the Alfven critical point is a generic property of outflows powered by reflection-driven Alfven-wave (AW) turbulence, in which outward-propagating AWs partially reflect, and counter-propagating AWs interact to produce a cascade of fluctuation energy to small scales, which leads to turbulent heating. Approximating the sub-Alfvenic region as isothermal, I first present a simplified calculation of the mass outflow rate, asymptotic wind speed, and coronal temperature that neglects conductive losses and the wave pressure force. I then develop a more detailed model of the transition region, corona, and solar wind that accounts for the heat flux from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for this heat flux by balancing, within the transition region, conductive heating against internal-energy losses from radiation, pdV work, and advection. The density at the coronal base is determined by locally balancing turbulent heating and radiative cooling. I solve the equations of the model analytically in two different parameter regimes. Analytic and numerical solutions to the model equations agree with a number of observations.

astro-ph.SR↗

arXiv2021

Evolution of large-amplitude Alfvén waves and generation of switchbacks in the expanding solar wind

Motivated by recent Parker Solar Probe (PSP) observations of "switchbacks" (abrupt, large-amplitude reversals in the radial magnetic field, which exhibit Alfvénic correlations) we examine the dynamics of large-amplitude Alfvén waves in the expanding solar wind. We develop an analytic model which makes several predictions: switchbacks should preferentially occur in regions where the solar wind plasma has undergone a greater expansion, the switchback fraction at radii comparable to PSP should be an increasing function of radius, and switchbacks should have their gradients preferentially perpendicular to the mean magnetic field direction. The expansion of the plasma generates small compressive components as part of the wave's nonlinear evolution: these are maximized when the normalized fluctuation amplitude is comparable to $\sinθ$, where $θ$ is the angle between the propagation direction and the mean magnetic field. These compressive components steepen the primary Alfvénic waveform, keeping the solution in a state of nearly constant magnetic field strength as its normalized amplitude $δB/B$ grows due to expansion. The small fluctuations in the magnetic-field-strength are minimized at a particular $θ$-dependent value of $β$, usually of order unity, and the density and magnetic-field-strength fluctuations can be correlated or anticorrelated depending on $β$ and $θ$. Example solutions of our dynamical equation are presented; some do indeed form magnetic-field reversals. Our predictions appear to match some previously unexplained phenomena in observations and numerical simulations, providing evidence that the observed switchbacks result from the nonlinear evolution of the initially small-amplitude Alfvén waves already known to be present at the coronal base.

physics.space-ph↗

arXiv2021

How Alfvén waves energize the solar wind: heat vs work

A growing body of evidence suggests that the solar wind is powered to a large extent by an Alfvén-wave (AW) energy flux. AWs energize the solar wind via two mechanisms: heating and work. We use high-resolution direct numerical simulations of reflection-driven AW turbulence (RDAWT) in a fast-solar-wind stream emanating from a coronal hole to investigate both mechanisms. In particular, we compute the fraction of the AW power at the coronal base ($P_{\rm AWb}$) that is transferred to solar-wind particles via heating between the coronal base and heliocentric distance $r$, which we denote $χ_{\rm H}(r)$, and the fraction that is transferred via work, which we denote $χ_{\rm W}(r)$. We find that $χ_{\rm W}(r_{\rm A})$ ranges from 0.15 to 0.3, where $r_{\rm A}$ is the Alfvén critical point. This value is small compared to~one because the Alfvén speed $v_{\rm A} $ exceeds the outflow velocity $U$ at $r r_{\rm A}$, where $v_{\rm A} < U$, the AWs are in an approximate sense "stuck to the plasma", which helps them do pressure work as the plasma expands. However, much of the AW power has dissipated by the time the AWs reach $r=r_{\rm A}$, so the total rate at which AWs do work on the plasma at $r>r_{\rm A}$ is a modest fraction of $P_{\rm AWb}$. We find that heating is more effective than work at $r<r_{\rm A}$, with $χ_{\rm H}(r_{\rm A})$ ranging from 0.5 to 0.7. The reason that $χ_{\rm H} \geq 0.5$ in our simulations is that an appreciable fraction of the local AW power dissipates within each Alfvén-speed scale height in RDAWT, and there are a few Alfvén-speed scale heights between the coronal base and $r_{\rm A}$.

astro-ph.SR↗

arXiv2021

Multiscale Solar Wind Turbulence Properties inside and near Switchbacks measured by Parker Solar Probe

Parker Solar Probe (PSP) routinely observes magnetic field deflections in the solar wind at distances less than 0.3 au from the Sun. These deflections are related to structures commonly called 'switchbacks' (SBs), whose origins and characteristic properties are currently debated. Here, we use a database of visually selected SB intervals - and regions of solar wind plasma measured just before and after each SB - to examine plasma parameters, turbulent spectra from inertial to dissipation scales, and intermittency effects in these intervals. We find that many features, such as perpendicular stochastic heating rates and turbulence spectral slopes are fairly similar inside and outside of SBs. However, important kinetic properties, such as the characteristic break scale between the inertial to dissipation ranges differ inside and outside these intervals, as does the level of intermittency, which is notably enhanced inside SBs and in their close proximity, most likely due to magnetic field and velocity shears observed at the edges. We conclude that the plasma inside and outside of a SB, in most of the observed cases, belongs to the same stream, and that the evolution of these structures is most likely regulated by kinetic processes, which dominate small scale structures at the SB edges.

astro-ph.SR↗

arXiv2020

In-situ switchback formation in the expanding solar wind

Recent near-sun solar-wind observations from Parker Solar Probe have found a highly dynamic magnetic environment, permeated by abrupt radial-field reversals, or "switchbacks." We show that many features of the observed turbulence are reproduced by a spectrum of Alfvénic fluctuations advected by a radially expanding flow. Starting from simple superpositions of low-amplitude outward-propagating waves, our expanding-box compressible MHD simulations naturally develop switchbacks because (i) the normalized amplitude of waves grows due to expansion and (ii) fluctuations evolve towards spherical polarization (i.e., nearly constant field strength). These results suggest that switchbacks form in-situ in the expanding solar wind and are not indicative of impulsive processes in the chromosphere or corona.

physics.space-ph↗

arXiv2020

Inner-Heliosphere Signatures of Ion-Scale Dissipation and Nonlinear Interaction

We perform a statistical study of the turbulent power spectrum at inertial and kinetic scales observed during the first perihelion encounter of Parker Solar Probe. We find that often there is an extremely steep scaling range of the power spectrum just above the ion-kinetic scales, similar to prior observations at 1 AU, with a power-law index of around $-4$. Based on our measurements, we demonstrate that either a significant ($>50\%$) fraction of the total turbulent energy flux is dissipated in this range of scales, or the characteristic nonlinear interaction time of the turbulence decreases dramatically from the expectation based solely on the dispersive nature of nonlinearly interacting kinetic Alfvén waves.

astro-ph.SR↗

arXiv2019

Cross Helicity Reversals In Magnetic Switchbacks

We consider 2D joint distributions of normalised residual energy $σ_r(s,t)$ and cross helicity $σ_c(s,t)$ during one day of Parker Solar Probe's (PSP's) first encounter as a function of wavelet scale $s$. The broad features of the distributions are similar to previous observations made by HELIOS in slow solar wind, namely well correlated and fairly Alfvénic, except for a population with negative cross helicity which is seen at shorter wavelet scales. We show that this population is due to the presence of magnetic switchbacks, brief periods where the magnetic field polarity reverses. Such switchbacks have been observed before, both in HELIOS data and in Ulysses data in the polar solar wind. Their abundance and short timescales as seen by PSP in its first encounter is a new observation, and their precise origin is still unknown. By analysing these MHD invariants as a function of wavelet scale we show that MHD waves do indeed follow the local mean magnetic field through switchbacks, with net Elsasser flux propagating inward during the field reversal, and that they therefore must be local kinks in the magnetic field and not due to small regions of opposite polarity on the surface of the Sun. Such observations are important to keep in mind as computing cross helicity without taking into account the effect of switchbacks may result in spurious underestimation of $σ_c$ as PSP gets closer to the Sun in later orbits.

physics.space-ph↗

arXiv2019

The Enhancement of Proton Stochastic Heating in the near-Sun Solar Wind

Stochastic heating is a non-linear heating mechanism driven by the violation of magnetic moment invariance due to large-amplitude turbulent fluctuations producing diffusion of ions towards higher kinetic energies in the direction perpendicular to the magnetic field. It is frequently invoked as a mechanism responsible for the heating of ions in the solar wind. Here, we quantify for the first time the proton stochastic heating rate $Q_\perp$ at radial distances from the Sun as close as $0.16$ au, using measurements from the first two Parker Solar Probe encounters. Our results for both the amplitude and radial trend of the heating rate, $Q_\perp \propto r^{-2.5}$, agree with previous results based on the Helios data set at heliocentric distances from 0.3 to 0.9 au. Also in agreement with previous results, $Q_\perp$ is significantly larger in the fast solar wind than in the slow solar wind. We identify the tendency in fast solar wind for cuts of the core proton velocity distribution transverse to the magnetic field to exhibit a flat-top shape. The observed distribution agrees with previous theoretical predictions for fast solar wind where stochastic heating is the dominant heating mechanism.

astro-ph.SR↗

arXiv2019

Self-induced Scattering of Strahl Electrons in the Solar Wind

We investigate the scattering of strahl electrons by microinstabilities as a mechanism for creating the electron halo in the solar wind. We develop a mathematical framework for the description of electron-driven microinstabilities and discuss the associated physical mechanisms. We find that an instability of the oblique fast-magnetosonic/whistler (FM/W) mode is the best candidate for a microinstability that scatters strahl electrons into the halo. We derive approximate analytic expressions for the FM/W instability threshold in two different $β_{\mathrm c}$ regimes, where $β_{\mathrm c}$ is the ratio of the core electrons' thermal pressure to the magnetic pressure, and confirm the accuracy of these thresholds through comparison with numerical solutions to the hot-plasma dispersion relation. We find that the strahl-driven oblique FM/W instability creates copious FM/W waves under low-$β_{\mathrm c}$ conditions when $U_{0\mathrm s}\gtrsim 3w_{\mathrm c}$, where $U_{0\mathrm s}$ is the strahl speed and $w_{\mathrm c}$ is the thermal speed of the core electrons. These waves have a frequency of about half the local electron gyrofrequency. We also derive an analytic expression for the oblique FM/W instability for $β_{\mathrm c}\sim 1$. The comparison of our theoretical results with data from the \emph{Wind} spacecraft confirms the relevance of the oblique FM/W instability for the solar wind. The whistler heat-flux, ion-acoustic heat-flux, kinetic-Alfvén-wave heat-flux, and electrostatic electron-beam instabilities cannot fulfill the requirements for self-induced scattering of strahl electrons into the halo. We make predictions for the electron strahl close to the Sun, which will be tested by measurements from \emph{Parker Solar Probe} and \emph{Solar Orbiter}.

physics.space-ph↗

arXiv2019

Reflection-driven MHD turbulence in the solar atmosphere and solar wind

We present 3D numerical simulations and an analytic model of reflection-driven MHD turbulence in the solar wind. Our simulations describe transverse, non-compressive MHD fluctuations within a narrow magnetic flux tube that extends from the photosphere out to a heliocentric distance $r$ of 21 solar radii $(R_s)$. We launch outward-propagating "$z^+$ fluctuations" into the simulation domain by imposing a randomly evolving photospheric velocity field. As these fluctuations propagate away from the Sun, they undergo partial reflection, producing inward-propagating "$z^-$ fluctuations." Counter-propagating fluctuations subsequently interact, causing fluctuation energy to cascade to small scales and dissipate. Our analytic model incorporates alignment, allows for strongly or weakly turbulent nonlinear interactions, and divides the $z^+$ fluctuations into two populations with different characteristic radial correlation lengths. The inertial-range power spectra in our simulations evolve toward a $k_\perp^{-3/2}$ scaling at $r>10 R_s$, where $k_\perp$ is the wave-vector component perpendicular to the background magnetic field. In two of our simulations, the $z^+$ power spectra are much flatter between the coronal base and $r \simeq 4 R_s$. We argue that these spectral scalings are caused by: (1) high-pass filtering in the upper chromosphere; (2) the anomalous coherence of inertial-range $z^-$ fluctuations in a reference frame propagating outwards with the $z^+$ fluctuations; and (3) the change in the sign of the radial derivative of the Alfvén speed at $r=r_m \simeq 1.7 R_s$, which disrupts this anomalous coherence between $r=r_m$ and $r\simeq 2r_m$. At $r>1.3 R_s$, the turbulent heating rate in our simulations is comparable to the heating rate in a previously developed solar-wind model that agreed with a number of observational constraints.

physics.space-ph↗

arXiv2019

Hybrid-Kinetic Simulations of Ion Heating in Alfvénic Turbulence

We present three-dimensional, hybrid-kinetic numerical simulations of driven Alfvén-wave turbulence of relevance to the collisionless near-Earth solar wind. Special attention is paid to the spectral transition that occurs near the ion-Larmor scale and to the origins of preferential perpendicular ion heating and of non-thermal wings in the parallel distribution function. Several novel diagnostics are used to show that the ion heating rate increases as the kinetic-Alfvén-wave fluctuations, which comprise the majority of the sub-ion-Larmor turbulent cascade, attain near-ion-cyclotron frequencies. We find that ${\approx}75$-$80\%$ of the cascade energy goes into heating the ions, broadly consistent with the near-Earth solar wind. This heating is accompanied by clear velocity-space signatures in the particle energization rates and the distribution functions, including a flattened core in the perpendicular-velocity distribution and non-Maxwellian wings in the parallel-velocity distribution. The latter are attributed to transit-time damping and the pitch-angle scattering of perpendicularly heated particles into the parallel direction. Accompanying these features is a steepening of the spectral index of sub-ion-Larmor magnetic-field fluctuations beyond the canonical $-2.8$, as field energy is transferred to thermal energy. These predictions may be tested by measurements in the near-Earth solar wind.

astro-ph.HE↗

arXiv2019

Interplay between intermittency and dissipation in collisionless plasma turbulence

We study the damping of collisionless Alfvénic turbulence by two mechanisms: stochastic heating (whose efficiency depends on the local turbulence amplitude $δz_λ$) and linear Landau damping (whose efficiency is independent of $δz_λ$), describing in detail how they affect and are affected by intermittency. The overall efficiency of linear Landau damping is not affected by intermittency in critically balanced turbulence, while stochastic heating is much more efficient in the presence of intermittent turbulence. Moreover, stochastic heating leads to a drop in the scale-dependent kurtosis over a narrow range of scales around the ion gyroscale.

physics.plasm-ph↗

arXiv2018

Stochastic proton heating by kinetic-Alfvén-wave turbulence in moderately high-$β$ plasmas

Stochastic heating refers to an increase in the average magnetic moment of charged particles interacting with electromagnetic fluctuations whose frequencies are smaller than the particles' cyclotron frequencies. This type of heating arises when the amplitude of the gyroscale fluctuations exceeds a certain threshold, causing particle orbits in the plane perpendicular to the magnetic field to become stochastic rather than nearly periodic. We consider the stochastic heating of protons by Alfvén-wave (AW) and kinetic-Alfvén-wave (KAW) turbulence, which may make an important contribution to the heating of the solar wind. Using phenomenological arguments, we derive the stochastic-proton-heating rate in plasmas in which $β_{\rm p} \sim 1-30$, where $β_{\rm p}$ is the ratio of the proton pressure to the magnetic pressure. (We do not consider the $β_{\rm p} \gtrsim 30$ regime, in which KAWs at the proton gyroscale become non-propagating.) We test our formula for the stochastic-heating rate by numerically tracking test-particle protons interacting with a spectrum of randomly phased AWs and KAWs. Previous studies have demonstrated that at $β_{\rm p} \lesssim 1$, particles are energized primarily by time variations in the electrostatic potential and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the electrostatic potential. In contrast, at $β_{\rm p} \gtrsim 1$, particles are energized primarily by the solenoidal component of the electric field and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the magnetic field.

physics.plasm-ph↗

arXiv2018

NHDS: The New Hampshire Dispersion Relation Solver

NHDS is the New Hampshire Dispersion Relation Solver. This article describes the numerics of the solver and its capabilities. The code is available for download on https://github.com/danielver02/NHDS.

physics.space-ph↗

arXiv2018

Heating of Accretion-Disk Coronae and Jets by General Relativistic MHD Turbulence

Turbulence in an accretion disk launches Alfvén waves (AWs) that propagate away from the disk along magnetic field lines. Because the Alfvén speed varies with distance from the disk, the AWs undergo partial non-WKB reflection, and counter-propagating AWs subsequently interact, causing AW energy to cascade to small scales and dissipate. To investigate this process, we introduce an Elsasser-like formulation of general relativistic MHD (GRMHD) and develop the theory of general relativistic reduced MHD in an inhomogeneous medium. We then derive a set of equations for the mean-square AW amplitude $M_+$ and turbulent heating rate $Q$ under the assumption that, in the plasma rest frame, AWs propagating away from the disk are much more energetic than AWs propagating toward the disk. For the case in which the background flow is axisymmetric and time-independent, we solve these equations analytically to determine $M_+$ and $Q$ as functions of position. We find that, for an idealized thin disk threaded by a large-scale poloidal magnetic field, the AW energy flux is $\sim (ρ_{\rm b}/ρ_{\rm d})^{1/2} β_{\rm net,d}^{-1/2}$ times the disk's radiative flux, where $ρ_{\rm b}$ and $ρ_{\rm d}$ are the mass densities at the coronal base and disk midplane, respectively, and $β_{\rm net,d}$ is the ratio (evaluated at the disk midplane) of plasma-plus-radiation pressure to the pressure of the average vertical magnetic field. This energy flux could have a significant impact on disk coronae and outflows. To lay the groundwork for future global simulations of turbulent disk coronae and jets, we derive a set of averaged GRMHD equations that account for reflection-driven AW turbulence using a sub-grid model.

astro-ph.HE↗

arXiv2018

ALPS: The Arbitrary Linear Plasma Solver

The Arbitrary Linear Plasma Solver (ALPS) is a parallelised numerical code that solves the dispersion relation in a hot (even relativistic) magnetised plasma with an arbitrary number of particle species with arbitrary gyrotropic equilibrium distribution functions for any direction of wave propagation with respect to the background field. ALPS reads the background momentum distributions as tables of values on a $(p_{\perp},p_{\parallel})$ grid, where $p_{\perp}$ and $p_{\parallel }$ are the momentum coordinates in the directions perpendicular and parallel to the background magnetic field, respectively. We present the mathematical and numerical approach used by ALPS and introduce our algorithms for the handling of poles and the analytic continuation for the Landau contour integral. We then show test calculations of dispersion relations for a selection of stable and unstable configurations in Maxwellian, bi-Maxwellian, $κ$-distributed, and Jüttner-distributed plasmas. These tests demonstrate that ALPS derives reliable plasma dispersion relations. ALPS will make it possible to determine the properties of waves and instabilities in the non-equilibrium plasmas that are frequently found in space, laboratory experiments, and numerical simulations.

physics.space-ph↗

arXiv2017

Parametric Instability, Inverse Cascade, and the $1/f$ Range of Solar-Wind Turbulence

In this paper, weak turbulence theory is used to investigate the nonlinear evolution of the parametric instability in 3D low-$β$ plasmas at wavelengths much greater than the ion inertial length under the assumption that slow magnetosonic waves are strongly damped. It is shown analytically that the parametric instability leads to an inverse cascade of Alfvén wave quanta, and several exact solutions to the wave kinetic equations are presented. The main results of the paper concern the parametric decay of Alfvén waves that initially satisfy $e^+ \gg e^-$, where $e^+$ and $e^-$ are the frequency ($\,f$) spectra of Alfvén waves propagating in opposite directions along the magnetic field lines. If $e^+$ initially has a peak frequency $f_0$ (at which $f e^+$ is maximized) and an "infrared" scaling $f^p$ at smaller $f$ with $-1 < p < 1$, then $e^+$ acquires an $f^{-1}$ scaling throughout a range of frequencies that spreads out in both directions from $f_0$. At the same time, $e^-$ acquires an $f^{-2}$ scaling within this same frequency range. If the plasma parameters and infrared $e^+$ spectrum are chosen to match conditions in the fast solar wind at a heliocentric distance of 0.3 astronomical units (AU), then the nonlinear evolution of the parametric instability leads to an $e^+$ spectrum that matches fast-wind measurements from the Helios spacecraft at 0.3 AU, including the observed $f^{-1}$ scaling at $f \gtrsim 3 \times 10^{-4} \mbox{ Hz}$. The results of this paper suggest that the $f^{-1}$ spectrum seen by Helios in the fast solar wind at $f \gtrsim 3\times 10^{-4} \mbox{ Hz}$ is produced in situ by parametric decay and that the $f^{-1}$ range of $e^+$ extends over an increasingly narrow range of frequencies as $r$ decreases below 0.3 AU. This prediction will be tested by measurements from the Parker Solar Probe.

physics.space-ph↗

arXiv2016

Collisionless Isotropization of the Solar-Wind Protons by Compressive Fluctuations and Plasma Instabilities

Compressive fluctuations are a minor yet significant component of astrophysical plasma turbulence. In the solar wind, long-wavelength compressive slow-mode fluctuations lead to changes in $β_{\parallel \mathrm p}\equiv 8πn_{\mathrm p}k_{\mathrm B}T_{\parallel \mathrm p}/B^2$ and in $R_{\mathrm p}\equiv T_{\perp \mathrm p}/T_{\parallel \mathrm p}$, where $T_{\perp \mathrm p}$ and $T_{\parallel \mathrm p}$ are the perpendicular and parallel temperatures of the protons, $B$ is the magnetic field strength, and $n_{\mathrm p}$ is the proton density. If the amplitude of the compressive fluctuations is large enough, $R_{\mathrm p}$ crosses one or more instability thresholds for anisotropy-driven microinstabilities. The enhanced field fluctuations from these microinstabilities scatter the protons so as to reduce the anisotropy of the pressure tensor. We propose that this scattering drives the average value of $R_{\mathrm p}$ away from the marginal stability boundary until the fluctuating value of $R_{\mathrm p}$ stops crossing the boundary. We model this "fluctuating-anisotropy effect" using linear Vlasov--Maxwell theory to describe the large-scale compressive fluctuations. We argue that this effect can explain why, in the nearly collisionless solar wind, the average value of $R_{\mathrm p}$ is close to unity.

physics.space-ph↗