Field-aligned Flow Research Articles

Resonant Absorption of Standing Magnetohydrodynamic Waves in Coronal Loops in the Absence of Directional Symmetry: The Effect of Plasma Flow

The oscillation properties of standing magnetohydrodynamic (MHD) waves in coronal loops have been investigated. The coronal loop is modeled as a straight cylinder with a purely longitudinal magnetic field and a field-aligned plasma flow. The loop model includes an inhomogeneous transitional layer that causes the wave to be resonantly damped. Our aim is to determine the damping rate of the standing MHD waves in flowing loops, in which the directional symmetry of the loop has been broken due to the presence of plasma flow. To do this, the standing wave has been considered as the superposition of two propagating waves with opposite directions of propagation but the same oscillation frequency and damping rate. Due to the absence of directional symmetry in the loop, it seems that the propagating components of the standing wave cannot have the same oscillation frequency and damping rate. To overcome this problem, in the perturbation method employed, we let both the oscillation frequency and damping rate be perturbed. As the flow speed increases the oscillation frequency of the standing wave decreases but its damping rate increases. As a result, the ratio of the oscillation frequency to the damping rate of the standing wave becomes a more decreasing function of the flow speed. The flow is an important quantity in determining the effectiveness of resonant absorption. In flowing loops even in the case of a thin transitional layer, resonant absorption can result in a damping rate on the order of the period time, which is in agreement with observations.

Response of ion velocities of daytime ionospheric wavenumber-4 to solar activity observed by ROCSAT-1 and DEMETER

The electron/ion density/temperature and ion velocities observed by the ROCSAT-1 and DEMETER satellites are used to examine the daytime wavenumber-4 (WN4) feature in the equatorial/low latitude ionosphere during various months and solar activity levels of 1999–2010. A moving median process has been employed to isolate WN4 features and calculate their amplitudes, while the upward ion drift is used to estimate electric fields. The ROCSAT-1 and DEMETER ion density, ion temperature, and ion velocity generally yield prominent WN4 features over the center of Pacific Ocean, the west side of South America, the center of the Atlantic Ocean, and Southern India. The correlation coefficient between the deviation of ion density and upward ion drift is significant during high solar activity of 1999–2004, while it approaches to zero during low solar activity of 2004–2010. This confirms that the longitudinal variation of the upward ion drift is essential during high solar activity, and the associated amplitude of dynamo eastward electric field is in the range of 0.10–0.14 mV/m, which is 15–19% of daily dynamo electric field. By contrast, the deviation of the ion density and the northward field-aligned ion flow show a clear anti-correlation which yields a maximum coefficient in August during low solar activity but no correlation during high solar activity. These indicate that the longitudinal variation of the meridional field-aligned ion flow could play an important role during low solar activity, and its amplitude is in the range of 10.44–13.91 m/s, which is 10–13% of the ambient ion flows.

Coupled nonlinear drift and IAWs in streaming O–H plasma of upper ionosphere

Nonlinear structures formed by the coupled drift wave (DW) and ion acoustic waves (IAWs) are studied in a magnetized inhomogeneous collisionless bi-ion plasma with ions shear flow along the ambient magnetic field B=B0ẑ. The electrons are assumed to follow double spectral index (r, q) distribution in which r shows the flat top nature, while q is responsible for the shape of the distribution at the tail. A nonlinear differential equation is derived, and its solutions in the form of double layers (DLs) and solitons are obtained in different limits. It is pointed out that the presence of (0.4%) protons in the oxygen plasma of ionosphere should not be ignored because acoustic speeds corresponding to oxygen and hydrogen ions have small ratio of about four and drift wave frequency may lie in the same range. It is found that only the rarefactive solitons can be formed by the nonlinear DW and IAWs in the inhomogeneous oxygen hydrogen (O–H) plasma. However, the theoretical model predicts that both compressive and rarefactive DLs may be formed. The linear instabilities of low-frequency electrostatic waves due to field-aligned shear flow of ions have also been investigated.

Large Photospheric Doppler Shift in Solar Active Region 12673. I. Field-aligned Flows

Delta (δ) sunspots sometimes host fast photospheric flows along the central magnetic polarity inversion line (PIL). Here we study the strong Doppler shift signature in the central penumbral light bridge of solar active region NOAA 12673. Observations from the Helioseismic and Magnetic Imager (HMI) indicate highly sheared and strong magnetic fields. Large Doppler shifts up to 3.2 km s−1 appeared during the formation of the light bridge and persisted for about 16 hr. A new velocity estimator, called DAVE4VMwDV, reveals fast converging and shearing motion along the PIL from HMI vector magnetograms, and recovers the observed Doppler signal much better than an old version of the algorithm. The inferred velocity vectors are largely (anti-)parallel to the inclined magnetic fields, suggesting that the observed Doppler shift contains a significant contribution from the projected field-aligned flows. High-resolution observations from the Hinode/Spectro-Polarimeter further exhibit a clear correlation between the Doppler velocity and the cosine of the magnetic inclination, which is in agreement with HMI results and consistent with a field-aligned flow of about 9.6 km s−1. The complex Stokes profiles suggest significant gradients of physical variables along the line of sight. We discuss the implications on the δ-spot magnetic structure and the flow-driving mechanism.

Field-aligned and Magnetic Reconnection Flows in a Magnetohydrodynamic Simulation of Prominence-cavity System

Nested ring-shaped line-of-sight (LOS) oriented flows in coronal cavities have been observed in recent years but rarely explained. Using a magnetohydrodynamic simulation of a prominence-cavity system, we investigate the relationship between the simulated field-aligned flows, magnetic reconnection flows, and the LOS-oriented flows observed by the Coronal Multi-Channel Polarimeter. The field-aligned flows are along magnetic field lines toward the dips and driven by the hydrodynamic forces exerted by the prominence condensation. The reconnection flows are driven by the overlying reconnection and tether-cutting reconnection. The velocity of the reconnection flows increases from the quasi-static phase to the fast-rise phase, reaching several kilometers per second, which is similar to the speed of the field-aligned flows. We calculate the synthetic Doppler images by forward modeling and compare them with the observed LOS-oriented flows. The synthetic images show that the LOS-oriented flows of one ring with opposite internal flow driven by the field-aligned flows are identified in the simulation. And the synthetic images integrated along three different LOSs can resemble the observed direction reversal of the LOS-oriented flow in about 20 hr, when the included angle of two adjacent LOSs is about 10°. These results suggest that the observed LOS-oriented flows of one ring with an opposite internal flow may be explained by the LOS integration effect of field-aligned flows along different loops.

Nonlinear Damping and Field-aligned Flows of Propagating Shear Alfvén Waves with Braginskii Viscosity

Braginskii magnetohydrodynamics (MHD) provides a more accurate description of many plasma environments than classical MHD since it actively treats the stress tensor using a closure derived from physical principles. Stress tensor effects nonetheless remain relatively unexplored for solar MHD phenomena, especially in nonlinear regimes. This paper analytically examines nonlinear damping and longitudinal flows of propagating shear Alfvén waves. Most previous studies of MHD waves in Braginskii MHD have considered the strict linear limit of vanishing wave perturbations. We show that those former linear results only apply to Alfvén wave amplitudes in the corona that are so small as to be of little interest, typically a wave energy less than 10−11 times the energy of the background magnetic field. For observed wave amplitudes, the Braginskii viscous dissipation of coronal Alfvén waves is nonlinear and a factor around 109 stronger than predicted by the linear theory. Furthermore, the dominant damping occurs through the parallel viscosity coefficient η 0, rather than the perpendicular viscosity coefficient η 2 in the linearized solution. This paper develops the nonlinear theory, showing that the wave energy density decays with an envelope . The damping length L d exhibits an optimal damping solution, beyond which greater viscosity leads to lower dissipation as the viscous forces self-organize the longitudinal flow to suppress damping. Although the nonlinear damping greatly exceeds the linear damping, it remains negligible for many coronal applications.

Creation of solitons and density cavities by lower hybrid waves

Formation of Korteweg-de Vries (KdV) solitons by nonlinear lower hybrid waves (LHWs) is not possible in usual electron ion plasma because a dispersive term does not have a suitable form. It is pointed out that the dispersion characteristics of electrostatic LHWs are modified in the presence of field-aligned shear flow to produce KdV solitons with negative electrostatic potential as it has been observed by satellites in the upper ionosphere. Plasma density decreases within the solitary structures. The parallel electron velocity shear ve0=ve0(x)ẑ also gives rise to unstable waves in the intermediate frequency range in linear limit whereas the ambient magnetic field B0=B0ẑ is assumed to be constant. The instability and structure size depend upon the electron parallel velocity shear parameter Se=1Ωedve0(x)dx (where Ωe is the electron gyrofrequency) and the propagation direction with respect to the ambient magnetic field B0. The theoretical model is applied to the upper ionosphere, and the estimated width of the structures turns out to be of the order of 70 m, which is closer to the observations.

Electron-acoustic solitons and double layers in a non-uniform plasma with field-aligned shear flow

Electron-acoustic solitary waves (EASWs) are investigated in a non-uniform electron plasma with field-aligned shear flow and two electron populations: hot and cold. Hot electrons are assumed to follow kappa distribution and temperature of cold electrons is considered to be less than those of hot electrons , whereas ions provide a stationary background of positive charge. Intermediate frequency drift wave couples with electron-acoustic wave (EAW) due to plasma density inhomogeneity. It is pointed out that the linear phase speed of the waves weakly depend upon the superthermality and temperature ratio of hot to cold electrons. Set of two fluid partial differential equations is reduced to an ordinary differential equation in a co-moving frame which has soliton solution in one limit. This ordinary differential equation can also be expressed in the form of an energy integral equation which admits double layer (DL) solution in another limit under appropriate boundary conditions. The results are applied to broadband electrostatic noise (BEN) in the dayside auroral zone of ionosphere.

Modeling of Joint Parker Solar Probe–Metis/Solar Orbiter Observations

We present the first theoretical modeling of joint Parker Solar Probe (PSP)–Metis/Solar Orbiter (SolO) quadrature observations. The combined observations describe the evolution of a slow solar wind plasma parcel from the extended solar corona (3.5–6.3 R ⊙) to the very inner heliosphere (23.2 R ⊙). The Metis/SolO instrument remotely measures the solar wind speed finding a range from 96 to 201 km s−1, and PSP measures the solar wind plasma in situ, observing a radial speed of 219.34 km s−1. We find theoretically and observationally that the solar wind speed accelerates rapidly within 3.3–4 R ⊙ and then increases more gradually with distance. Similarly, we find that the theoretical solar wind density is consistent with the remotely and in-situ observed solar wind density. The normalized cross helicity and normalized residual energy observed by PSP are 0.96 and −0.07, respectively, indicating that the slow solar wind is very Alfvénic. The theoretical NI/slab results are very similar to PSP measurements, which is a consequence of the highly magnetic field-aligned radial flow ensuring that PSP can measure slab fluctuations and not 2D ones. Finally, we calculate the theoretical 2D and slab turbulence pressure, finding that the theoretical slab pressure is very similar to that observed by PSP.

Study of space plasma waves with flow

A fundamental reality throughout the space is the existence of magnetic field-aligned flows. Ion beams parallel to the magnetic field are a hallmark of the upward current region. Large electric fields found in the Earth’s auroral zone produce shears in the ion flow both parallel and perpendicular to the magnetic field. These shears are observed simultaneously and result from the localized nature of the large, high-altitude, perpendicular electric fields and their equipotential closure at altitudes above the ionosphere. In regions where auroral ion beams form (3000–6000 km), the magnitude of the shear in the ion flow along the magnetic field is typically an order of magnitude larger than its magnitude in the perpendicular flow. At higher altitudes, shears in the parallel flow decrease with the magnetic field; while shears in the perpendicular flow are relatively constant with altitude. We study these interesting space plasma using a project which is meant mainly for students.

Turbulence in the Sub-Alfvénic Solar Wind

Abstract The Parker Solar Probe (PSP) entered a region of sub-Alfvénic solar wind during encounter 8, and we present the first detailed analysis of low-frequency turbulence properties in this novel region. The magnetic field and flow velocity vectors were highly aligned during this interval. By constructing spectrograms of the normalized magnetic helicity, cross-helicity, and residual energy, we find that PSP observed primarily Alfvénic fluctuations, a consequence of the highly field-aligned flow that renders quasi-2D fluctuations unobservable to PSP. We extend Taylor’s hypothesis to sub- and super-Alfvénic flows. Spectra for the fluctuating forward and backward Elsässer variables ( z ±, respectively) are presented, showing that z + modes dominate z − by an order of magnitude or more, and the z + spectrum is a power law in frequency (parallel wavenumber) f −3/2 ( k ∥ − 3 / 2 ) compared to the convex z − spectrum with f −3/2 ( k ∥ − 3 / 2 ) at low frequencies, flattening around a transition frequency (at which the nonlinear and Alfvén timescales are balanced) to f −1.25 at higher frequencies. The observed spectra are well fitted using a spectral theory for nearly incompressible magnetohydrodynamics assuming a wavenumber anisotropy k ⊥ ∼ k ∥ 3 / 4 , that the z + fluctuations experience primarily nonlinear interactions, and that the minority z − fluctuations experience both nonlinear and Alfvénic interactions with z + fluctuations. The density spectrum is a power law that resembles neither the z ± spectra nor the compressible magnetic field spectrum, suggesting that these are advected entropic rather than magnetosonic modes and not due to the parametric decay instability. Spectra in the neighboring modestly super-Alfvénic intervals are similar.

Small-scale Magnetic Flux Ropes and Their Properties Based on In Situ Measurements from the Parker Solar Probe

Abstract We report small-scale magnetic flux ropes via the in situ measurements from the Parker Solar Probe during the first six encounters, and present additional analyses to supplement our prior work in Chen et al. These flux ropes are detected by the Grad–Shafranov-based algorithm, with their durations and scale sizes ranging from 10 s to ≲1 hr and from a few hundred kilometers to 10−3 au, respectively. They include both static structures and those with significant field-aligned plasma flows. Most structures tend to possess large cross helicity, while the residual energy is distributed over wide ranges. We find that these dynamic flux ropes mostly propagate in the antisunward direction relative to the background solar wind, with no preferential signs of magnetic helicity. The magnetic flux function follows a power law and is proportional to scale size. We also present case studies showing reconstructed two-dimensional (2D) configurations, which confirm that both the static and dynamic flux ropes have a common configuration of spiral magnetic field lines (also streamlines). Moreover, the existence of such events hints at interchange reconnection as a possible mechanism for generating flux rope-like structures near the Sun. Lastly, we summarize the major findings, and discuss the possible correlation between these flux rope-like structures and turbulence due to the process of local Alfvénic alignment.

MHD and Ion Kinetic Waves in Field-aligned Flows Observed by Parker Solar Probe

Abstract Parker Solar Probe (PSP) observed predominately Alfvénic fluctuations in the solar wind near the Sun where the magnetic field tends to be radially aligned. In this paper, two magnetic-field-aligned solar wind flow intervals during PSP’s first two orbits are analyzed. Observations of these intervals indicate strong signatures of parallel/antiparallel-propagating waves. We utilize multiple analysis techniques to extract the properties of the observed waves in both magnetohydrodynamic (MHD) and kinetic scales. At the MHD scale, outward-propagating Alfvén waves dominate both intervals, and outward-propagating fast magnetosonic waves present the second-largest contribution in the spectral energy density. At kinetic scales, we identify the circularly polarized plasma waves propagating near the proton gyrofrequency in both intervals. However, the sense of magnetic polarization in the spacecraft frame is observed to be opposite in the two intervals, although they both possess a sunward background magnetic field. The ion-scale plasma wave observed in the first interval can be either an inward-propagating ion cyclotron wave (ICW) or an outward-propagating fast-mode/whistler wave in the plasma frame, while in the second interval it can be explained as an outward ICW or inward fast-mode/whistler wave. The identification of the exact kinetic wave mode is more difficult to confirm owing to the limited plasma data resolution. The presence of ion-scale waves near the Sun suggests that ion cyclotron resonance may be one of the ubiquitous kinetic physical processes associated with small-scale magnetic fluctuations and kinetic instabilities in the inner heliosphere.

Generation of Short-scale Electrostatic Fields in the Solar Atmosphere and the Role of Helium Ions

Abstract Theoretical models are presented to show that expansion of plasma in the radial direction from a denser solar surface to a rarefied upper atmosphere with short-scale inhomogeneous field-aligned flows and currents in the form of thin threads itself is an important source of electrostatic instabilities. Multifluid theory shows that the shear flow–driven purely growing electric fields appear in the transition region. On the other hand, plasma kinetic theory predicts that the short-scale current sheets (or filaments) produce current-driven electrostatic ion acoustic (CDEIA) waves in the hydrogen plasma of the transition region that damp out in the system through wave–particle interactions and increase the temperature. Similar processes take place in the solar corona and act positively for increasing the temperature further and maintaining it. The shear flow–driven instabilities and CDEIA waves have short perpendicular wavelengths of the order of 1 m and low frequencies of the order of 1 or several Hz when the ions’ shear flow scale length is considered to be of the order of 1 km. It is pointed out that the purely growing fluid instabilities turn into oscillatory instabilities and the growth rates of kinetic CDEIA wave instabilities are reduced when the dynamics of 10% helium ions is taken into account along with 90% hydrogen ions. Therefore, the role of helium ions should not be ignored in the study of wave dynamics in solar plasma.

On the propagation of electrostatic wave modes in the inhomogeneous ionospheric plasma of Venus

The influence of gradients of number density, magnetic field, and flow velocity in a plasma on the propagation of low-frequency electrostatic waves is investigated in plasma conditions relevant for the Venusian ionosphere (vicinity of Venus terminator). For this purpose, we assume a collisionless inhomogeneous plasma model consisting of two positive ion species, hydrogen H+ and oxygen O+, as well as neutralizing electrons. Linear dispersion relations predict two types of plasma modes, namely, ion-acoustic mode and drift mode. It is found that these modes have relatively long wavelengths, extending to 10 km and frequencies on the order of ∼10−3−10−2 Hz. The characteristics of these modes show a strong dependence on the gradients of plasma parameters, and numerical analysis reveals that the coupling of these modes may lead to nonlinear instabilities. However, unstable modes occur only when the field-aligned shear flows are introduced. These results help explain the presence of low-frequency electrostatic modes and their basic features in the Venusian ionosphere, and will allow future studies to extend modeling to other planetary or even cometary conditions.

Small-scale Magnetic Flux Ropes with Field-aligned Flows via the PSP In Situ Observations

Abstract Magnetic flux rope, formed by the helical magnetic field lines, can sometimes maintain its shape while carrying significant plasma flow that is aligned with the local magnetic field. We report the existence of such structures and static flux ropes by applying the Grad-Shafranov-based algorithm to the Parker Solar Probe in situ measurements in the first five encounters. These structures are detected at heliocentric distances, ranging from 0.13 to 0.66 au, in a 4-month time period. We find that flux ropes with field-aligned flows, although they occur more frequently, have certain properties similar to those of static flux ropes, such as the decaying relations of the magnetic fields within structures with respect to heliocentric distances. Moreover, these events are more likely with magnetic pressure dominating over the thermal pressure. About one-third of events are detected in the relatively fast solar wind. Taking into account the high Alfvénicity, we also compare with switchback spikes identified during three encounters and interpret their interrelations. We find that some switchbacks can be detected when the spacecraft traverses flux-rope-like structures. The cross-section maps for selected events are presented via the new Grad-Shafranov-type reconstruction. Finally, the possible evolution of the magnetic flux rope structures in the inner heliosphere is discussed.

Testing of the new JOREK stellarator-capable model in the tokamak limit

In preparation for extending the JOREK nonlinear magnetohydrodynamics (MHD) code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (Nikulsin et al., Phys. Plasmas, vol. 26, 2019, 102109) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.

Kink instability of triangular jets in the solar atmosphere

Context. It is known that hydrodynamic triangular jets (i.e. the jet with maximal velocity at its axis, which linearly decreases at both sides) are unstable to anti-symmetric kink perturbations. The inclusion of the magnetic field may lead to the stabilisation of the jets. Jets and complex magnetic fields are ubiquitous in the solar atmosphere, which suggests the possibility of the kink instability in certain cases. Aims. The aim of the paper is to study the kink instability of triangular jets sandwiched between magnetic tubes (or slabs) and its possible connection to observed properties of the jets in the solar atmosphere. Methods. A dispersion equation governing the kink perturbations is obtained through matching of analytical solutions at the jet boundaries. The equation is solved analytically and numerically for different parameters of jets and surrounding plasma. The analytical solution is accompanied by a numerical simulation of fully non-linear magnetohydrodynamic (MHD) equations for a particular situation of solar type II spicules. Results. Magnetohydrodynamic triangular jets are unstable to the dynamic kink instability depending on the Alfvén Mach number (the ratio of flow to Alfvén speeds) and the ratio of internal and external densities. When the jet has the same density as the surrounding plasma, only super-Alfvénic flows are unstable. However, denser jets are also unstable in a sub-Alfvénic regime. Jets with an angle to the ambient magnetic field have much lower thresholds of instability than field-aligned flows. Growth times of the kink instability are estimated to be 6−15 min for type I spicules and 5−60 s for type II spicules matching with their observed lifetimes. The numerical simulation of full non-linear equations shows that the transverse kink pulse locally destroys the jet in less than a minute in type II spicule conditions. Conclusions. Dynamic kink instability may lead to the full breakdown of MHD flows and consequently to an observed disappearance of spicules.

Switchbacks Explained: Super-Parker Fields—The Other Side of the Sub-Parker Spiral

Abstract We provide a simple geometric explanation for the source of switchbacks and associated large and one-sided transverse flows in the solar wind observed by the Parker Solar Probe (PSP). The more radial, sub-Parker spiral structure of the heliospheric magnetic field observed previously by Ulysses, ACE, and STEREO is created within rarefaction regions where footpoint motion from the source of fast into slow wind at the Sun creates a magnetic fieldline connection across solar wind speed shear. Conversely, when footpoints move from the source of slow wind into faster wind, a super-Parker spiral field structure is formed: below the Alfvén critical point, one-sided transverse field-aligned flows develop; above the Alfvén critical point, the field structure contracts between adjacent solar wind flows, and the radial field component decreases in magnitude with distance from the Sun, eventually reversing into a switchback. The sub-Parker and super-Parker spirals behave functionally as opposites. Observations from PSP confirm the paucity of switchbacks within rarefaction regions and immediately outside these rarefaction regions, we observe numerous switchbacks in the magnetic field that are directly associated with abrupt transients in solar wind speed. The magnetic field strength, the radial component of the magnetic field, the speed gradients, radial Alfvén speed, and the ratio of the sound speed to the radial Alfvén speed all conform to predictions based on the sub-Parker and super-Parker spirals within rarefaction regions and solar wind speed enhancements (spikes or jets), respectively. Critically, the predictions associated with the super-Parker spiral naturally explain the observations of switchbacks being associated with unexpectedly large and one-sided tangential flows.

Signatures of Cross-sectional Width Modulation in Solar Spicules due to Field-aligned Flows

Abstract We report the first observational detection of frequency modulation in the cross-sectional width of spicule structures due to field-aligned plasma flows. Cross-sectional width variations were estimated for the least superimposed off-limb spicules observed in high-resolution Hα imaging spectroscopy data. Analysis of estimated cross-sectional widths suggest periodic oscillations, concurrent with 2D numerical modeling for a jet structure in a stratified solar atmosphere. Spectral analysis for both observed and simulated cross-sectional widths indicate frequency modulation as noticeable shifts in estimated periodicities during rise and fall phases of field-aligned plasma flows in the jet structure. Furthermore, the presence of the first overtone in a dynamic/spicular waveguide is also evident in both the observed and the simulated jet structures. These harmonics can be an important tool for future chromospheric magnetoseismology investigations and applications to dynamic waveguides (like spicules).