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Turbulent rotations of the magnetic field vector are observed in the Alfvénic streams of the solar wind where the magnetic field strength remains close to a constant. They can lead to reversals of the radial magnetic field component or switchbacks. It is not ruled out from the data that the rotations are divisible into the sum of small random angular deflections. In this work, we develop tools aimed at the analysis of the one-point statistical properties of the directional fluctuations of the magnetic field vector in the solar wind. The angular fluctuations are modeled by a drift-diffusion process which admits the exponential distribution as steady-state solution. Realizations of the stochastic process are obtained by solving the corresponding Langevin equation. It is shown that the cumulative effects of consecutive small-angle deflections can yield frequent reversals of the magnetic field vector even when the concentration parameter of the directional data is large. The majority of the rotations are associated with nearly transverse magnetic field fluctuations in this case.

 

 We present a stochastic field line mapping model where the interplanetary magnetic field lines are described by a density distribution function satisfying a Fokker–Planck equation that is solved numerically. Due to the spiral geometry of the nominal Parker field and to the evolving nature of solar wind turbulence, the heliospheric diffusion of the magnetic field lines is both heterogeneous and anisotropic, including a radial component. The longitudinal distributions of the magnetic field lines are shown to be close to circular Gaussian distributions, although they develop a noticeable skewness. The magnetic field lines emanating from the Sun are found to differ, on average, from the spirals predicted by Parker. Although the spirals remain close to Archimedean, they are here underwound, on average. Our model predicts a spiral angle that is smaller by ∼5° than the Parker spiral angle at Earth’s orbit for the same solar wind speed ofV_sw= 400 km s⁻¹. It also predicts an angular position on the solar disk of the best magnetically connected footpoint to an observer at 1 au that is shifted westward by ∼10° with respect to the Parker’s field model. This significantly changes the angle of the most probable magnetic connection between possible sources on the Sun and observers in the inner heliosphere. The results have direct implications for the heliospheric transport of “scatter-free” electrons accelerated in the aftermath of solar eruptions.

 

We used the stream-aligned magnetohydrodynamics (SA-MHD) model to simulate Carrington rotation 2210, which contains Parker Solar Probe’s (PSP) first perihelion at 36.5R_⊙on 2018 November 6, to provide context to the in situ PSP observations by FIELDS and SWEAP. The SA-MHD model aligns the magnetic field with the velocity vector at each point, thereby allowing for clear connectivity between the spacecraft and the source regions on the Sun, without unphysical magnetic field structures. During this Carrington rotation, two stream interaction regions (SIRs) form, due to the deep solar minimum. We include the energy partitioning of the parallel and perpendicular ions and the isotropic electrons to investigate the temperature anisotropy through the compression regions to better understand the wave energy amplification and proton thermal energy partitioning in a global context. Overall, we found good agreement in all in situ plasma parameters between the SA-MHD results and the observations at PSP, STEREO-A, and Earth, including at PSP’s perihelion and through the compression region of the SIRs. In the typical solar wind, the parallel proton temperature is preferentially heated, except in the SIR, where there is an enhancement in the perpendicular proton temperature. This is further showcased in the ion cyclotron relaxation time, which shows a distinct decrease through the SIR compression regions. This work demonstrates the success of the Alfvén wave turbulence theory for predicting interplanetary magnetic turbulence levels, while self-consistently reproducing solar wind speeds, densities, and overall temperatures, including at small heliocentric distances and through SIR compression regions.

 

We provide exact analytical solutions for the magnetic field produced by prescribed current distributions located inside a toroidal filament of finite thickness. The solutions are expressed in terms of toroidal functions, which are modifications of the Legendre functions. In application to the MHD equilibrium of a twisted toroidal current loop in the solar corona, the Grad–Shafranov equation is decomposed into an analytic solution describing an equilibrium configuration against the pinch-effect from its own current and an approximate solution for an external strapping field to balance the hoop force. Our solutions can be employed in numerical simulations of coronal mass ejections (CMEs). When superimposed on the background solar coronal magnetic field, the excess magnetic energy of the twisted current loop configuration can be made unstable by applying flux cancellation to reduce the strapping field. Such loss of stability accompanied by the formation of an expanding flux rope is typical for the Titov & Démoulin eruptive event generator. The main new features of the proposed model are as follows: the filament is filled with finiteβplasma with finite mass and energy, the model describes an equilibrium solution that will spontaneously erupt due to magnetic reconnection of the strapping magnetic field arcade, and there are analytic expressions connecting the model parameters to the asymptotic velocity and total mass of the resulting CME, providing a way to connect the simulated CME properties to multipoint coronograph observations.

 

In this work, we extend Leighton’s diffusion model describing the turbulent mixing of magnetic footpoints on the solar wind source surface. The present Lagrangian stochastic model is based on the spherical Ornstein–Uhlenbeck process with drift that is controlled by the rotation frequency Ω of the Sun, the Lagrangian integral timescaleτ_L, and the root-mean-square footpoint velocityV_rms. The Lagrangian velocity and the positions of magnetic footpoints on the solar wind source surface are obtained from the solutions of a set of stochastic differential equations, which are solved numerically. The spherical diffusion model of Leighton is recovered in the singular Markov limit when the Lagrangian integral timescale tends to zero while keeping the footpoint diffusivity finite. In contrast to the magnetic field lines driven by standard Brownian processes on the solar wind source surface, the interplanetary magnetic field lines are smooth differentiable functions with finite path lengths in our model. The path lengths of the boundary-driven interplanetary magnetic field lines and their probability distributions at 1 au are computed numerically, and their dependency with respect to the controlling parameters is investigated. The path-length distributions are shown to develop a significant skewness as the width of the distributions increases.

 

Abstract We present a Langevin model describing the local structure of the interplanetary magnetic field lines. It is established on the basis of the analysis of the Lagrangian properties of strong Alfvénic turbulence, which provides a new perspective on the critical balance condition. The model is consistent with the k ∥ − 2 spectrum of magnetic fluctuations derived from in situ measurements. We show that the magnetic field line diffusivity at the spacecraft position can be inferred from the wavelet analysis of one-point measurements of the fluctuating magnetic fields in the solar wind independently of the three-dimensional nature of the anisotropy.