What are Switchbacks?

TL;DR

The paper tackles the puzzle of Parker Solar Probe switchbacks—magnetic reversals with near-constant magnitude—by formulating a solitary Alfvén-wave framework under the constraints $|\vec{B}|=\text{const}$, $\rho=\text{const}$, and $p=\text{const}$. It shows that solitary Alfvénic perturbations satisfy $\vec{u}_1 = \pm \vec{b}_1$ and obey wave dynamics $\partial_t^2 \vec{u}_1 = (\vec{b}_0 \cdot \nabla)^2 \vec{u}_1$, then constructs a three-dimensional switchback field $\vec{G}_A$ via a convergent Helmholtz–Hodge projection from a localized perturbation. The 1D cuts of $\vec{B}$ reveal sharp reversals with constant $|\vec{B}|$, while the curvature indicator $\Phi_B = |(\vec{B}_0 \cdot \nabla)\vec{B}|$ isolates regions that deflect field lines; a critical amplitude around $A \approx 20$ triggers rotational discontinuities, producing prominent switchbacks and linking the phenomenon to twist-to-writhe–like elastic behavior of open field lines. These results provide a geometric, topological interpretation of PSP switchbacks and offer a pathway to explore relaxing the constant-$|\vec{B}|$ constraint and the role of plasma $\beta$ in shaping switchback properties.

Abstract

We present a solitary Alfvén wave model that exhibits nontrivial three-dimensional twisting of open magnetic field lines while preserving constant $|B|$. Embedded rotational discontinuities sharply deflect the otherwise uniform field lines, producing localized, large-amplitude field reversals in one-dimensional profiles that closely resemble the ``switchbacks'' observed by the Parker Solar Probe in the inner heliosphere. This indicates that switchbacks, as seen in one-dimensional spacecraft time series, arise from traversals through strongly curved segments of open magnetic field lines.

Figures (4)

• Figure 1: Contour of $\theta(x,y,z)$ of the switchback model.
• Figure 2: Field-line structure of a switchback. (a) 1D profile at iy=151 and iz=118. (b-d) x-y/x-z/y-z projection of the field-lines passing (91,151,118) and (95,151,118). Contours show equivalue lines of $Phi_B=100,200$.
• Figure 3: Contour surfaces of $\Phi_B(x,y,z)$ at values 100 (purple) and 200 (yellow), with magnetic field lines overlaid. The red line indicates the x-direction profile through $(95,151,118)$. Magenta and cyan curves show representative field lines passing through $(91,151,118)$ (red) and $(95,151,118)$ (blue), respectively. Small black dots mark the 26 neighboring grid points around each location, with their field lines shown in light red and light blue respectively.
• Figure 4: Distribution of (a) $\Phi_B$, (b) $\theta$, and (c) $|B|$ for different initial amplitudes $A$ in $\vec{F}_0$.