arXiv subjects

Jiansen He

Publications and source records attributed to Jiansen He.

At least 37 records · Page 2Linked to original sources

arXiv2022

On the scaling and anisotropy of two subranges in the inertial range of solar wind turbulence

Intermittency and anisotropy are two important aspects of plasma turbulence, which the solar wind provides a natural laboratory to investigate. However, their forms and nature are still under debate, making it difficult to achieve a consensus in the theoretical interpretation. Here, we perform higher-order statistics for the observations in the fast solar wind at 1.48 au obtained by Ulysses and in the slow solar wind at 0.17 au obtained by Parker Solar Probe (PSP). We find that two subranges clearly exist in the inertial range and they present distinct features with regard to the intermittency and anisotropy. The subrange 1 with smaller scale has a multifractal scaling with the second index $ξ(2) \sim 2/3$ and the subrange 2 with larger scale is also multifractal but with $ξ(2) \sim 1/2$. The break between two subranges locates at the same spatial scale for both Ulysses and PSP observations. Subrange 1 is multifractal in the direction perpendicular to the local magnetic field with $ξ_{\perp}(2) \sim 2/3$ and seems to be monoscaling in the parallel direction with $ξ_{\parallel}(2) \sim 1$. Subrange 2 is multifractal in both parallel and perpendicular directions with $ξ_{\perp}(2) \sim 1/2$ and $ξ_{\parallel}(2) \sim 2/3$. Both subrange 1 and subrange 2 present power and wavevector anisotropies. The distinct features of two subranges suggest that a transition from weak to strong turbulence may occur and the spatial scale of the break may not evolve with the solar wind expansion. These new results update our knowledge of the inertial range and provide strong observational constraints on the understanding of intermittency and anisotropy in solar wind turbulence.

astro-ph.SR↗

arXiv2022

Coherence of ion cyclotron resonance for damping ion cyclotron waves in space plasmas

Ion cyclotron resonance is one of the fundamental energy conversion processes through field-particle interaction in collisionless plasmas. However, the key evidence for ion cyclotron resonance (i.e., the coherence between electromagnetic fields and the ion phase space density) and the resulting damping of ion cyclotron waves (ICWs) has not yet been directly observed. Investigating the high-quality measurements of space plasmas by the Magnetospheric Multiscale (MMS) satellites, we find that both the wave electromagnetic field vectors and the bulk velocity of the disturbed ion velocity distribution rotate around the background magnetic field. Moreover, we find that the absolute gyro-phase angle difference between the center of the fluctuations in the ion velocity distribution functions and the wave electric field vectors falls in the range of (0, 90) degrees, consistent with the ongoing energy conversion from wave-fields to particles. By invoking plasma kinetic theory, we demonstrate that the field-particle correlation for the damping ion cyclotron waves in our theoretical model matches well with our observations. Furthermore, the wave electric field vectors ($δ\mathbf{E'}_{\mathrm {wave,\perp}}$), the ion current density ($δ\mathbf{J}_\mathrm {i,\perp}$) and the energy transfer rate ($δ\mathbf{J}_\mathrm {i,\perp}\cdot δ\mathbf{E'}_{\mathrm {wave,\perp}}$) exhibit quasi-periodic oscillations, and the integrated work done by the electromagnetic field on the ions are positive, indicates that ions are mainly energized by the perpendicular component of the electric field via cyclotron resonance. Therefore, our combined analysis of MMS observations and kinetic theory provides direct, thorough, and comprehensive evidence for ICW damping in space plasmas.

physics.plasm-ph↗

arXiv2021

Observations of rapidly growing whistler waves in front of space plasma shock

Whistler mode wave is a fundamental perturbation of electromagnetic fields and plasmas in various environments including planetary space, laboratory and astrophysics. The origin and evolution of the waves are a long-standing question due to the limited instrumental capability in resolving highly variable plasma and electromagnetic fields. Here, we analyse data with the high time resolution from the multi-scale magnetospheric spacecraft in the weak magnetic environment (i.e., foreshock) enabling a relatively long gyro-period of whistler mode wave. Moreover, we develop a novel approach to separate the three-dimensional fluctuating electron velocity distributions from their background, and have successfully captured the coherent resonance between electrons and electromagnetic fields at high frequency, providing the resultant growth rate of unstable whistler waves. Regarding the energy origin for the waves, the ion distributions are found to also play crucial roles in determining the eigenmode disturbances of fields and electrons. The quantification of wave growth rate can significantly advance the understandings of the wave evolution and the energy conversion with particles.

physics.space-ph↗

arXiv2021

Growth of Outward Propagating Fast-Magnetosonic/Whistler Waves in the Inner Heliosphere Observed by Parker Solar Probe

The solar wind in the inner heliosphere has been observed by Parker Solar Probe (PSP) to exhibit abundant wave activities. The cyclotron wave modes in the sense of ions or electrons are among the most crucial wave components. However, their origin and evolution in the inner heliosphere close to the Sun remain mysteries. Specifically, it remains unknown whether it is an emitted signal from the solar atmosphere or an eigenmode growing locally in the heliosphere due to plasma instability. To address and resolve this controversy, we must investigate the key quantity of the energy change rate of the wave mode. We develop a new technique to measure the energy change rate of plasma waves, and apply this technique to the wave electromagnetic fields measured by PSP. We provide the wave Poynting flux in the solar wind frame, identify the wave nature to be the outward propagating fast-magnetosonic/whistler wave mode instead of the sunward propagating waves. We provide the first evidence for growth of the fast-magnetosonic/whistler wave mode in the inner heliosphere based on the derived spectra of the real and imaginary parts of the wave frequencies. The energy change rate rises and stays at a positive level in the same wavenumber range as the bumps of the electromagnetic field power spectral densities, clearly manifesting that the observed fast-magnetosonic/whistler waves are locally growing to a large amplitude.

astro-ph.SR↗

arXiv2021

Coronal microjets in quiet-Sun regions observed with the Extreme Ultraviolet Imager onboard Solar Orbiter

We report the smallest coronal jets ever observed in the quiet Sun with recent high resolution observations from the High Resolution Telescopes (HRI-EUV and HRI-Lyα) of the Extreme Ultraviolet Imager (EUI) onboard Solar Orbiter. In the HRI-EUV (174 Å) images, these microjets usually appear as nearly collimated structures with brightenings at their footpoints. Their average lifetime, projected speed, width, and maximum length are 4.6 min, 62 km s^(-1), 1.0 Mm, and 7.7 Mm, respectively. Inverted-Y shaped structures and moving blobs can be identified in some events. A subset of these events also reveal signatures in the HRI-Lyα (H I Lyα at 1216 Å) images and the extreme ultraviolet images taken by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory. Our differential emission measure analysis suggests a multi-thermal nature and an average density of ~1.4x10^9 cm^(-3) for these microjets. Their thermal and kinetic energies were estimated to be ~3.9x10^24 erg and ~2.9x10^23 erg, respectively, which are of the same order of the released energy predicted by the nanoflare theory. Most events appear to be located at the edges of network lanes and magnetic flux concentrations, suggesting that these coronal microjets are likely generated by magnetic reconnection between small-scale magnetic loops and the adjacent network field.

astro-ph.SR↗

arXiv2021

Power Anisotropy, Dispersion Signature and Turbulence Diffusion Region in the 3D Wavenumber Domain of Space Plasma Turbulence

We explore the multi-faceted important features of turbulence (e.g., anisotropy, dispersion, diffusion) in the three-dimensional (3D) wavenumber domain ($k_\parallel$, $k_{\perp,1}$, $k_{\perp,2}$), by employing the k-filtering technique to the high-quality measurements of fields and particles from the MMS multi-spacecraft constellation. We compute the 3D power spectral densities (PSDs) of magnetic and electric fluctuations (marked as $\rm{PSD}(δ\mathbf{B}(\mathbf{k}))$ and $\rm{PSD}(δ\mathbf{E}'_{\langle\mathbf{v}_\mathrm{i}\rangle}(\mathbf{k}))$), both of which show a prominent spectral anisotropy in the sub-ion range. We give the first 3D image of the bifurcation between power spectra of the electric and magnetic fluctuations, by calculating the ratio between $\rm{PSD}(δ\mathbf{E}'_{ \langle\mathbf{v}_\mathrm{i}\rangle}(\mathbf{k}))$ and $\rm{PSD}(δ\mathbf{B}(\mathbf{k}))$, the distribution of which is related to the non-linear dispersion relation. We also compute the ratio between electric spectra in different reference frames defined by the ion bulk velocity, that is $\mathrm{PSD}(δ{\mathbf{E}'_{\mathrm{local}\ \mathbf{v}_\mathrm{i}}})/\mathrm{PSD}(δ{\mathbf{E}'_{ \langle\mathbf{v}_\mathrm{i}\rangle}})$, to visualize the turbulence ion diffusion region (T-IDR) in wavenumber space. The T-IDR has an anisotropy and a preferential direction of wavevectors, which is generally consistent with the plasma wave theory prediction based on the dominance of kinetic Alfvén waves (KAW). This work manifests the worth of the k-filtering technique in diagnosing turbulence comprehensively, especially when the electric field is involved.

physics.plasm-ph↗

arXiv2021

Possible Generation Mechanism for Compressional Alfvénic Spikes as Observed by Parker Solar Probe

The solar wind is found by Parker Solar Probe (PSP) to be abundant with Alfvénic velocity spikes and magnetic field kinks. Temperature enhancement is another remarkable feature associated with the Alfvénic spikes. How the prototype of these coincident phenomena is generated intermittently in the source region becomes a hot topic of wide concerns. Here we propose a new model introducing guide-field discontinuity into the interchange magnetic reconnection between open funnels and closed loops with different magnetic helicities. The modified interchange reconnection model not only can accelerate jet flows from the newly opening closed loop but also excite and launch Alfvénic wave pulses along the newly-reconnected and post-reconnected open flux tubes. We find that the modeling results can reproduce the following observational features: (1) Alfvén disturbance is pulsive in time and asymmetric in space; (2) Alfvénic pulse is compressible with temperature enhancement and density variation inside the pulse. We point out that three physical processes co-happening with Alfvén wave propagation can be responsible for the temperature enhancement: (a) convection of heated jet flow plasmas (decrease in density), (b) propagation of compressed slow-mode waves (increase in density), and (c) conduction of heat flux (weak change in density). We also suggest that the radial nonlinear evolution of the Alfvénic pulses should be taken into account to explain the formation of magnetic switchback geometry.

astro-ph.SR↗

arXiv2021

Anisotropy of Solar-Wind Turbulence in the Inner Heliosphere at Kinetic Scales: PSP Observations

The anisotropy of solar wind turbulence is a critical issue in understanding the physics of energy transfer between scales and energy conversion between fields and particles in the heliosphere. Using the measurement of \emph{Parker Solar Probe} (\emph{PSP}), we present an observation of the anisotropy at kinetic scales in the slow, Alfvénic, solar wind in the inner heliosphere. \textbf{The magnetic compressibility behaves as expected for kinetic Alfvénic turbulence below the ion scale.} A steepened transition range is found between the inertial and kinetic ranges in all directions with respect to the local background magnetic field direction. The anisotropy of $k_\perp \gg k_\parallel$ is found evident in both transition and kinetic ranges, with the power anisotropy $P_\perp/P_\parallel > 10$ in the kinetic range leading over that in the transition range and being stronger than that at 1 au. The spectral index varies from $α_{t\parallel}=-5.7\pm 1.0$ to $α_{t\perp}=-3.7\pm 0.3$ in the transition range and $α_{k\parallel}=-3.12\pm 0.22$ to $α_{k\perp}=-2.57\pm 0.09$ in the kinetic range. The corresponding wavevector anisotropy has the scaling of $k_\parallel \sim k_\perp^{0.71\pm 0.17}$ in the transition range, and changes to $k_\parallel \sim k_\perp^{0.38\pm 0.09}$ in the kinetic range, consistent with the kinetic Alfvénic turbulence at sub-ion scales.

physics.space-ph↗

arXiv2021

Formation of solar quiescent coronal loops through magnetic reconnection in an emerging active region

Coronal loops are building blocks of solar active regions. However, their formation mechanism is still not well understood. Here we present direct observational evidence for the formation of coronal loops through magnetic reconnection as new magnetic fluxes emerge into the solar atmosphere. Extreme-ultraviolet observations of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) clearly show the newly formed loops following magnetic reconnection within a plasma sheet. Formation of the loops is also seen in the hα line-core images taken by the New Vacuum Solar Telescope. Observations from the Helioseismic and Magnetic Imager onboard SDO show that a positive-polarity flux concentration moves towards a negative-polarity one with a speed of ~0.4 km/s, before the formation of coronal loops. During the loop formation process, we found signatures of flux cancellation and subsequent enhancement of the transverse field between the two polarities. The three-dimensional magnetic field structure reconstructed through a magnetohydrostatic model shows field lines consistent with the loops in AIA images. Numerous bright blobs with an average width of 1.37 Mm appear intermittently in the plasma sheet and move upward with a projected velocity of ~114 km/s. The temperature, emission measure and density of these blobs are about 3 MK, 2.0x10^(28) cm^(-5) and 1.2x10^(10) cm^(-3), respectively. A power spectral analysis of these blobs indicates that the observed reconnection is likely not dominated by a turbulent process. We have also identified flows with a velocity of 20 to 50 km/s towards the footpoints of the newly formed coronal loops.

astro-ph.SR↗

arXiv2020

Encounter of Parker Solar Probe and a Comet-like Object During Their Perihelia: Model Predictions and Measurements

Parker Solar Probe (PSP) aims at exploring the nascent solar wind close to the Sun. Meanwhile, PSP is also expected to encounter small objects like comets and asteroids. In this work, we survey the ephemerides to find a chance of recent encounter, and then model the interaction between released dusty plasmas and solar wind plasmas. On 2019 September 2, a comet-like object 322P/SOHO just passed its perihelion flying to a heliocentric distance of 0.12 au, and swept by PSP at a relative distance as close as 0.025 au. We present the dynamics of dust particles released from 322P, forming a curved dust tail. Along the PSP path in the simulated inner heliosphere, the states of plasma and magnetic field are sampled and illustrated, with the magnetic field sequences from simulation results being compared directly with the in-situ measurements from PSP. Through comparison, we suggest that 322P might be at a deficient activity level releasing limited dusty plasmas during its way to becoming a "rock comet". We also present images of solar wind streamers as recorded by WISPR, showing an indication of dust bombardment for the images superposed with messy trails. We observe from LASCO coronagraph that 322P was transiting from a dimming region to a relatively bright streamer during its perihelion passage, and simulate to confirm that 322P was flying from relatively faster to slower solar wind streams, modifying local plasma states of the streams.

astro-ph.EP↗

arXiv2020

Isotropic Scaling Features Measured Locally in the Solar Wind Turbulence with Stationary Background Field

The scaling anisotropy is crucial to interpret the nonlinear interactions in solar wind turbulence. Previous observations provide diverse results and the structure function analyses are also reported to be an approach to investigate the scaling anisotropy based on a local magnetic field. However, the determination of the sampling angle with respect to the local background magnetic field requires that the observed time series for the average are time stationary. Whether or not this required time stationarity is compatible with the measurements has not been investigated. Here we utilize the second-order structure function method to study the scaling anisotropy with a time-stationary background field.We analyze 88 fast solar wind intervals each with time durations larger than 2 days measured by WIND spacecraft in the period 2005-2018. We calculate the local magnetic field as the average of the time series B whose time stationarity is fulfilled by our criterion phi smaller than 10 deg (phi is the angle between the two averaged magnetic fields after cutting B into two halves). We find for the first time the isotropic scaling feature of the magnetic-trace structure functions with scaling indices -0.63 pm 0.08 and -0.70 pm 0.04, respectively, with the local magnetic field parallel and perpendicular to the solar wind velocity directions. The scaling for the velocity-trace structure functions is also isotropic and the indices are -0.47 pm 0.10 and -0.51 pm 0.09. We also find that with increasing phi threshold to 90 deg, the scaling index of the magnetic-trace structure function in the parallel direction decreases to -0.81, while the rms of the instantaneous angle between magnetic field and solar wind velocity increases up to 45deg at the timescale 150 s, indicating a mix of perpendicular measurements into parallel ones at large scales.

physics.space-ph↗

arXiv2020

Energy Supply for Heating the Slow Solar Wind Observed by Parker Solar Probe between 0.17 and 0.7 au

Energy supply sources for the heating process in the slow solar wind remain unknown. The Parker Solar Probe (PSP) mission provides a good opportunity to study this issue. Recently, PSP observations have found that the slow solar wind experiences stronger heating inside 0.24 au. Here for the first time we measure in the slow solar wind the radial gradient of the low-frequency breaks on the magnetic trace power spectra and evaluate the associated energy supply rate. We find that the energy supply rate is consistent with the observed perpendicular heating rate calculated based on the gradient of the magnetic moment. Based on this finding, one could explain why the slow solar wind is strongly heated inside 0.25 au but expands nearly adiabatically outside 0.25 au. This finding supports the concept that the energy added from the energy-containing range is transferred by an energy cascade process to the dissipation range, and then dissipates to heat the slow solar wind. The related issues for further study are discussed.

physics.space-ph↗

arXiv2020

Contribution of Magnetic Reconnection Events to Energy Dissipation in Magnetosheath Turbulence

By analyzing the magnetosheath measurements from MMS, we obtain the statistical results for the contribution of magnetic reconnection (MR) events at electron scales to the energy dissipation of coherent structures. The Partial Variance of Increments (PVI) method is employed to find coherent structures in the magnetic field data. The current sheet structures with reversal of magnetic field components are further selected. We consider the following criteria to identify the MR events, such as current sheet with magnetic field reversal, significant energy dissipation, and evident electron outflow velocity. Statistically, for most MR events, their PVI values are larger than that of other types of coherent structures, and their energy dissipations are also stronger than that of others. However, due to the relatively small proportion of MR events, their contribution to coherent structures' energy dissipation is relatively trivial. If taken into account the dissipation of non-coherent structures, the MR's contribution to energy dissipation would be less. Hence, we suggest that MR events, though have strong dissipation locally, are not the major contributor to the energy dissipation in the magnetosheath. After analyzing the features of non-MR current sheets, we propose that non-MR current sheets are mainly coherent structures inherent to kinetic Alfvén fluctuations.

physics.plasm-ph↗

arXiv2020

Wave Composition, Propagation, and Polarization of MHD Turbulence within 0.3AU as Observed by PSP

Turbulence, a ubiquitous phenomenon in interplanetary space, is crucial for the energy conversion of space plasma at multiple scales. This work focuses on the propagation, polarization and wave composition properties of the solar wind turbulence within 0.3AU, and its variation with heliocentric distances at MHD scales (from 10s to 1000s in the spacecraft frame). We present the probability density function of propagation wavevectors (${\rm{PDF}}(k_\parallel,k_\perp)$) for solar wind turbulence winthin 0.3 AU for the first time: (1) wavevectors cluster quasi-(anti-)parallel to the local background magnetic field for $kd_{\rm i}<0.02$, where $d_{\rm i}$ is the ion inertial length; (2) wavevectors shift to quasi-perpendicular directions for $kd_{\rm i}>0.02$. Based on our wave composition diagnosis, we find that: the outward/anti-sunward Alfvén mode dominates over the whole range of scales and distances, the spectral energy density fraction of the inward/sunward fast mode decreases with distance, and the fractional energy densities of the inward and outward slow mode increase with distance. The outward fast mode and inward Alfvén mode represent minority populations throughout the explored range of distances and scales. On average, the degree of anisotropy of the magnetic fluctuations defined with respect to the minimum variation direction decreases with increasing scale, with no trend in distance at all scales. Our results provide comprehensive insight into the scenario of transport and transfer of the solar wind fluctuations/turbulence in the inner heliosphere.

physics.space-ph↗

arXiv2020

Global maps of the magnetic field in the solar corona

Understanding many physical processes in the solar atmosphere requires determination of the magnetic field in each atmospheric layer. However, direct measurements of the magnetic field in the Sun's corona are difficult to obtain. Using observations with the Coronal Multi-channel Polarimeter, we have determined the spatial distribution of the plasma density in the corona, and the phase speed of the prevailing transverse magnetohydrodynamic waves within the plasma. We combine these measurements to map the plane-of-sky component of the global coronal magnetic field. The derived field strengths in the corona from 1.05 to 1.35 solar radii are mostly 1-4 Gauss. These results demonstrate the capability of imaging spectroscopy in coronal magnetic field diagnostics.

astro-ph.SR↗

arXiv2020

Observational quantification of three-dimensional anisotropies and scalings of space plasma turbulence at kinetic scales

A statistical survey of spectral anisotropy of space plasma turbulence is performed using five years measurements from MMS in the magnetosheath. By measuring the five-point second-order structure functions of the magnetic field, we have for the first time quantified the three-dimensional anisotropies and scalings at sub-ion-scales ($<$ 100 km). In the local reference frame $(\hat L_{\perp}, \hat l_{\perp}, \hat l_{\parallel})$ defined with respect to local mean magnetic field $\boldsymbol {B}_0$ (Chen et al. 2012), the "statistical eddies" are found to be mostly elongated along $\boldsymbol {B}_0$ and shortened in the direction perpendicular to both $\boldsymbol {B}_0$ and local field fluctuations. From several $d_i$ (ion inertial length) toward $\sim$ 0.05 $d_i$, the ratio between eddies' parallel and perpendicular lengths features a trend of rise then fall, whereas the anisotropy in the perpendicular plane appears scale-invariant. Specifically, the anisotropy relations for the total magnetic field at 0.1-1.0 $d_i$ are obtained as $l_{\parallel} \simeq 2.44 \cdot l_{\perp}^{0.71}$, and $L_{\perp} \simeq 1.58 \cdot l_{\perp}^{1.08}$, respectively. Our results provide new observational evidence to compare with phenomenological models and numerical simulations, which may help to better understand the nature of kinetic scale turbulence.

physics.space-ph↗

arXiv2020

Magnetic Energy Transfer and Distribution between Protons and Electrons for Alfvénic Waves at Kinetic Scales in Wavenumber Space

Turbulent dissipation is considered a main source of heating and acceleration in cosmological plasmas. The alternating current Joule-like term, $\langleδj \cdot δE\rangle$, is used to measure the energy transfer between electromagnetic (EM) fields and particles. Because the electric field depends on the reference frame, in which frame to calculate $\langleδj\cdot δE\rangle$ is an important issue. We compute the scale-dependent energy transfer rate spectrum in wavevector space, and investigate the electric-field fluctuations in two reference frames: $δE$ in the mean bulk flow frame and $δE'$ in the local bulk flow frame (non-inertial reference frame). Considering Alfvénic waves, we find that $\langleδj\cdotδE^\prime\rangle$, which neglects the contribution of work done by the ion inertial force, is not consistent with the magnetic field energy damping rate ($2γδB^2$) according to linear Maxwell-Vlasov theory, while $\langleδj\cdot δE\rangle$ is exactly the same as $2γδB^2$ in wavenumber space $(k_\parallel, k_\perp)$, where $γ$ is the linear damping rate. Under typical conditions of solar wind at 1 au, we find in our theoretical calculation that the field energy is mainly converted into proton kinetic energy leaving the residual minor portion for electrons. Although the electrons gain energy in the direction perpendicular to the mean magnetic field, they return a significant fraction of their kinetic energy in the parallel direction. Magnetic-field fluctuations can transfer particle energy between the parallel and perpendicular degrees of freedom. Therefore, $\langleδj_\parallel\cdot δE_\parallel\rangle$ and $\langleδj_\perp\cdot δE_\perp\rangle$ cannot solely describe the energy transfer in parallel direction and perpendicular direction, respectively.

physics.space-ph↗

arXiv2020

The Radial Dependence of Proton-scale Magnetic Spectral Break in Slow Solar Wind during PSP Encounter 2

Magnetic field fluctuations in the solar wind are commonly observed to follow a power law spectrum. Near proton-kinetic scales, a spectral break occurs which is commonly interpreted as a transition to kinetic turbulence. However, this transition is not yet entirely understood. By studying the scaling of the break with various plasma properties, it may be possible to constrain the processes leading to the onset of kinetic turbulence. Using data from Parker Solar Probe (\textit{PSP}), we measure the proton scale break over a range of heliocentric distances, enabling a measurement of the transition from inertial to kinetic scale turbulence under various plasma conditions. We find that the break frequency $f_b$ increases as the heliocentric distance $r$ decreases in the slow solar wind following a power law $f_b\sim r^{-1.11}$. We also compare this to the characteristic plasma ion scales to relate the break to the possible physical mechanisms occurring at this scale. The ratio between $f_b$ and $f_c$, the Doppler shifted ion cyclotron resonance scale, is approximately unity for all plasma $β_p$. At high $β_p$ the ratio between $f_b$ and $f_ρ$, the Doppler shifted gyroscale, is approximately unity; while at low $β_p$ the ratio between $f_b$ and $f_d$, the Doppler shifted proton-inertial length is unity. Due to the large comparable Alfvén and solar wind speeds, we analyze these results using both the standard and modified Taylor hypothesis, demonstrating robust statistical results.

physics.space-ph↗