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Abstract We study anisotropic magnetohydrodynamic (MHD) turbulence in the slow solar wind measured by Parker Solar Probe (PSP) and Solar Orbiter (SolO) during its first orbit from the perspective of variance anisotropy and correlation anisotropy. We use the Belcher & Davis approach (M1) and a new method (M2) that decomposes a fluctuating vector into parallel and perpendicular fluctuating vectors. M1 and M2 calculate the transverse and parallel turbulence components relative to the mean magnetic field direction. The parallel turbulence component is regarded as compressible turbulence, and the transverse turbulence component as incompressible turbulence, which can be either Alfvénic or 2D. The transverse turbulence energy is calculated from M1 and M2, and the transverse correlation length from M2. We obtain the 2D and slab turbulence energy and the corresponding correlation lengths from those transverse turbulence components that satisfy an angle between the mean solar wind flow speed and mean magnetic field θ UB of either (i) 65° < θ UB < 115° or (ii) 0° < θ UB < 25° (155° < θ UB < 180°), respectively. We find that the 2D turbulence component is not typically observed by PSP near perihelion, but the 2D component dominates turbulence in the innermore »Free, publiclyaccessible full text available July 1, 2023

Abstract During its 10th orbit around the Sun, the Parker Solar Probe sampled two intervals where the local Alfvén speed exceeded the solar wind speed, lasting more than 10 hours in total. In this paper, we analyze the turbulence and wave properties during these periods. The turbulence is observed to be Alfvénic and unbalanced, dominated by outwardpropagating modes. The power spectrum of the outwardpropagating Elsässer z + mode steepens at high frequencies while that of the inwardpropagating z − mode flattens. The observed Elsässer spectra can be explained by the nearly incompressible (NI) MHD turbulence model with both 2D and Alfvénic components. The modeling results show that the z + spectra are dominated by the NI/slab component, and the 2D component mainly affects the z − spectra at low frequencies. An MHD wave decomposition based on an isothermal closure suggests that outwardpropagating Alfvén and fast magnetosonic wave modes are prevalent in the two subAlfvénic intervals, while the slow magnetosonic modes dominate the superAlfvénic interval in between. The slow modes occur where the wavevector is nearly perpendicular to the local mean magnetic field, corresponding to nonpropagating pressurebalanced structures. The alternating forward and backward slow modes may also be features of magneticmore »Free, publiclyaccessible full text available August 1, 2023

Abstract The structure of shocks and turbulence are strongly modified during the acceleration of cosmic rays (CRs) at a shock wave. The pressure and the collisionless viscous stress decelerate the incoming thermal gas and thus modify the shock structure. A CR streaming instability ahead of the shock generates the turbulence on which CRs scatter. The turbulent magnetic field in turn determines the CR diffusion coefficient and further affects the CR energy spectrum and pressure distribution. The dissipation of turbulence contributes to heating the thermal gas. Within a multicomponent fluid framework, CRs and thermal gas are treated as fluids and are closely coupled to the turbulence. The system equations comprise the gas dynamic equations, the CR pressure evolution equation, and the turbulence transport equations, and we adopt typical parameters for the hot ionized interstellar medium. It is shown that the shock has no discontinuity but possesses a narrow but smooth transition. The selfgenerated turbulent magnetic field is much stronger than both the largescale magnetic field and the preexisting turbulent magnetic field. The resulting CR diffusion coefficient is substantially suppressed and is more than three orders smaller near the shock than it is far upstream. The results are qualitatively consistent with certainmore »Free, publiclyaccessible full text available June 1, 2023

Abstract Zank et al. developed models describing the transport of lowfrequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Elsässar variables and then taking “moments” subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large, of order unity, or small. Here, we show explicitly that the three sets of turbulence transport models admit a conservation representation that resembles the wellknown WKB transport equation for Alfvén wave energy density after introducing appropriate definitions of the “pressure” associated with the turbulent fluctuations. This includes introducing a distinct turbulent pressure tensor for 3D incompressible turbulence (the large plasma beta limit) and pressure tensors for quasi2D and slab turbulence (the plasma beta orderunity or small regimes) that generalize the form of the WKB pressure tensor. Various limits of the different turbulent pressure tensors are discussed. However, the analogy between the conservation form of the turbulence transport models and the WKB model is not close for multiple reasons, including that the turbulence models express fully nonlinear physical processes unlike the strictly linear WKB description. The analysis presented here both serves as amore »Free, publiclyaccessible full text available April 1, 2023

Abstract We investigate the interaction of turbulence with shock waves by performing 2D hybrid kinetic simulations. We inject forcefree magnetic fields upstream that are unstable to the tearingmode instability. The magnetic fields evolve into turbulence and interact with a shock wave whose sonic Mach number is 2.4. Turbulence properties, the total and normalized residual energy and the normalized cross helicity, change across the shock wave. While the energy of velocity and magnetic fluctuations is mostly distributed equally upstream, the velocity fluctuations are amplified dominantly downstream of the shock wave. The amplitude of turbulence spectra for magnetic, velocity, and density fluctuations are also increased at the shock wave while their spectral index remains unchanged. We compare our results with the Zank et al. model of turbulence transmission across a shock, and find that it provides a reasonable explanation for the spectral change across the shock wave. We find that particles are efficiently accelerated at the shock front, and a powerlaw spectrum forms downstream. This can be explained by diffusive shock acceleration, in which particles gain energy by being scattered upstream and downstream of a shock wave. The trajectory of an accelerated particle suggests that upstream turbulence plays a role scattering ofmore »Free, publiclyaccessible full text available February 1, 2023

Abstract Particle acceleration behind a shock wave due to interactions between magnetic islands in the heliosphere has attracted attention in recent years. The downstream acceleration may yield a continuous increase of particle flux downstream of the shock wave. Although it is not obvious how the downstream magnetic islands are produced, it has been suggested that current sheets are involved in the generation of magnetic islands due to their interaction with a shock wave. We perform 2D hybrid kinetic simulations to investigate the interaction between multiple current sheets and a shock wave. In the simulation, current sheets are compressed by the shock wave and a tearing instability develops at the compressed current sheets downstream of the shock. As the result of this instability, the electromagnetic fields become turbulent and magnetic islands form well downstream of the shock wave. We find a “postcursor” region in which the downstream flow speed normal to the shock wave in the downstream rest frame is decelerated to ∼ 1 V A immediately behind the shock wave, where V A is the upstream Alfvén speed. The flow speed then gradually decelerates to 0 accompanied by the development of the tearing instability. We also observe an efficient productionmore »Free, publiclyaccessible full text available December 1, 2022

Abstract The Parker Solar Probe (PSP) entered a region of subAlfvénic solar wind during encounter 8, and we present the first detailed analysis of lowfrequency 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, crosshelicity, and residual energy, we find that PSP observed primarily Alfvénic fluctuations, a consequence of the highly fieldaligned flow that renders quasi2D fluctuations unobservable to PSP. We extend Taylor’s hypothesis to sub and superAlfvénic flows. Spectra for the fluctuating forward and backward Elsässer variables (
^{±}, respectively) are presented, showing thatz ^{+}modes dominatez ^{−}by an order of magnitude or more, and thez ^{+}spectrum is a power law in frequency (parallel wavenumber)z f ^{−3/2}( ) compared to the convex ${k}_{\parallel}^{3/2}$ ^{−}spectrum withz f ^{−3/2}( ) at low frequencies, flattening around a transition frequency (at which the nonlinear and Alfvén timescales are balanced) to ${k}_{\parallel}^{3/2}$f ^{−1.25}at higher frequencies. The observed spectra are well fitted using a spectral theory for nearly incompressible magnetohydrodynamics assuming a wavenumber anisotropy , that the ${k}_{\perp}\sim {k}_{\parallel}^{3/4}$ ^{+}fluctuations experience primarily nonlinear interactions, and that the minorityz ^{−}fluctuations experience both nonlinear and Alfvénic interactions withz ^{+}fluctuations. The density spectrum is a powermore »z 
Aims. Solar Orbiter (SolO) was launched on February 9, 2020, allowing us to study the nature of turbulence in the inner heliopshere. We investigate the evolution of anisotropic turbulence in the fast and slow solar wind in the inner heliosphere using the nearly incompressible magnetohydrodynamic (NI MHD) turbulence model and SolO measurements. Methods. We calculated the two dimensional (2D) and the slab variances of the energy in forward and backward propagating modes, the fluctuating magnetic energy, the fluctuating kinetic energy, the normalized residual energy, and the normalized crosshelicity as a function of the angle between the mean solar wind speed and the mean magnetic field ( θ UB ), and as a function of the heliocentric distance using SolO measurements. We compared the observed results and the theoretical results of the NI MHD turbulence model as a function of the heliocentric distance. Results. The results show that the ratio of 2D energy and slab energy of forward and backward propagating modes, magnetic field fluctuations, and kinetic energy fluctuations increases as the angle between the mean solar wind flow and the mean magnetic field increases from θ UB = 0° to approximately θ UB = 90° and then decreases as θ UB → 180°.more »Free, publiclyaccessible full text available December 1, 2022

Aims. An interplanetary coronal mass ejection (ICME) event was observed by the Solar Orbiter at 0.8 AU on 2020 April 19 and by Wind at 1 AU on 2020 April 20. Futhermore, an interplanetary shock wave was driven in front of the ICME. Here, we focus on the transmission of the magnetic fluctuations across the shock and we analyze the characteristic wave modes of solar wind turbulence in the vicinity of the shock observed by both spacecraft. Methods. The observed ICME event is characterized by a magnetic helicitybased technique. The ICMEdriven shock normal was determined by magnetic coplanarity method for the Solar Orbiter and using a mixed plasma and field approach for Wind. The power spectra of magnetic field fluctuations were generated by applying both a fast Fourier transform and Morlet wavelet analysis. To understand the nature of waves observed near the shock, we used the normalized magnetic helicity as a diagnostic parameter. The waveletreconstructed magnetic field fluctuation hodograms were used to further study the polarization properties of waves. Results. We find that the ICMEdriven shock observed by Solar Orbiter and Wind is a fast, forward oblique shock with a more perpendicular shock angle at the Wind position. After themore »Free, publiclyaccessible full text available December 1, 2022

Context. Flux ropes in the solar wind are a key element of heliospheric dynamics and particle acceleration. When associated with current sheets, the primary formation mechanism is magnetic reconnection and flux ropes in current sheets are commonly used as tracers of the reconnection process. Aims. Whilst flux ropes associated with reconnecting current sheets in the solar wind have been reported, their occurrence, size distribution, and lifetime are not well understood. Methods. Here we present and analyse new Solar Orbiter magnetic field data reporting novel observations of a flux rope confined to a bifurcated current sheet in the solar wind. Comparative data and largescale context is provided by Wind. Results. The Solar Orbiter observations reveal that the flux rope, which does not span the current sheet, is of ion scale, and in a reconnection formation scenario, existed for a prolonged period of time as it was carried out in the reconnection exhaust. Wind is also found to have observed clear signatures of reconnection at what may be the same current sheet, thus demonstrating that reconnection signatures can be found separated by as much as ∼2000 Earth radii, or 0.08 au. Conclusions. The Solar Orbiter observations provide new insight into the hierarchymore »Free, publiclyaccessible full text available December 1, 2022