Solitary Alfvén Waves

TL;DR

This work constructs and analyzes a three-dimensional solitary, open-field-line Alfvén wave packet (Alfvénon) as an exact nonlinear solution to ideal MHD, motivated by Parker Solar Probe observations of switchbacks. A convergent Helmholtz-Hodge–based algorithm is developed to produce divergence-free, near-unit-magnitude magnetic fields with localized perturbations, from which initial conditions for a full MHD simulation are built. Direct MHD simulations demonstrate the Alfvénon’s high stability and Alfvénicity over many Alfvén crossing times, with energy transfer to internal energy via parametric decay and non-Alfvénic modes emerging over time. The work argues for open, three-dimensional topology as essential to the Alfvénon’s existence and coherence and suggests broad implications for solar wind dynamics, with potential relativistic generalizations and links to high-energy phenomena such as FRBs.

Abstract

We present a three-dimensional numerical model of a solitary spherically polarized Alfvén wave packet -- an Alfvénon, characterized by open field-line topology and magnetic field reversals, resembling the switchbacks observed by Parker Solar Probe to be a nearly ubiquitous feature of turbulence in the inner heliosphere. Direct magnetohydrodynamic simulations of the constructed Alfvénon demonstrates remarkable stability, confirming its nature as an exact, nonlinear solution of the ideal MHD equations.

Figures (7)

• Figure 1: Solitary spherically polarized Alfvén wave packets (switchbacks) from PSP Observations. Panels show (a,b) magnetic field magnitude and components, (c) Electron pitch angle distribution (d-f) velocity-magnetic field correlations (darker lines are proton bulk speeds), (g) proton (electron) number density from Quasi-Thermal-Noise, (h) proton plasma $\beta = n_p k_B T_p / (B^2/2\mu_0)$ and (i) radial distance of PSP. Carrington longitude is shown on top.
• Figure 2: Constant $|B|$ restriction for forward propagating SPAWs. Left: forward-pointing $\vec{b}_0$. Right: backward-pointing $\vec{b}_0$.
• Figure 3: Isosurfaces of $|\vec{B}_0 \cdot \nabla \vec{B}|$.
• Figure 4: Spatial profiles and field-line angles at four times ($t=0.00$, $0.05$, $5.00$, $40.00$). Column 1: 1D cuts of $|B|$, $B_x$, $B_y$, $B_z$, $u_x$, $u_y$, $u_z$ along the $x$-axis at $iy=151$, $iz=118$. Columns 2--4: 2D slices of $\theta=\cos^{-1}(B_x/|B|)$ at planes $ix=95$, $iy=151$, and $iz=118$, respectively.
• Figure 5: Time evolution. (a) Standard deviation of $\rho$ versus time. Probability histograms at $t=0.00$, $0.05$, $5.00$, and $40.00$ for (b) density $\rho$ and (c) angle $\theta=\cos^{-1}(B_x/|B|)$. (d) Magnetic, kinetic and Internal energy versus time.