Construction of Solar-Wind-Like Magnetic Fields

Fluctuations in the solar wind fields tend to not only have velocities and magnetic fields correlated in the sense consistent with Alfvén waves traveling from the Sun, but they also have the magnitude of the magnetic field remarkably constant despite their being broadband. This Letter provides, for the first time, a method for constructing fields with nearly constant magnetic field, zero divergence, and with any specified power spectrum for the fluctuations of the components of the field. Every wave vector, $\mathbf{k}$, is associated with two polarizations; the relative phases of these can be chosen to minimize the variance of the field magnitude while retaining the “random” character of the fields. The method is applied to a case with one spatial coordinate that demonstrates good agreement with observed time series and power spectra of the magnetic field in the solar wind, as well as with the distribution of the angles of rapid changes (“discontinuities”), thus showing a deep connection between two seemingly unrelated issues. It is suggested that using this construction will lead to more realistic simulations of solar wind turbulence and of the propagation of energetic particles.

Figure 1

Time series of artificially generated magnetic fields for random phases that depend on one dimension. The top trace is the field magnitude, and the other two traces are the components of the transverse fields.

Figure 2

Time series of artificially generated magnetic fields after the phase optimization. Note that the magnitude of the field is now quite constant.

Figure 3

Spectrum of artificially generated magnetic fields. The upper line is the total power in the transverse components, the dashed line is the power in the magnitude of the field for random phases, and the lowest line is the power in the magnitude after the optimization of the phases.

Figure 4

Time series of measured magnetic fields. Data are 1-sec ACE magnetometer data starting at 1 October 2007, $15:36$ UTC. The top trace is $|\mathbf{B}|$, and the other traces are for the components: radial (solid), tangential (dot-dashed), and normal (dashed).

Figure 5

Spectrum of measured magnetic fields (solid; sum of component spectra above, and power in the magnitude below) and of the constructed fields (dot-dashed). Units for the measured spectrum are $n{T}^2/Hz$.

Figure 6

Distribution of angles between 3920 vectors measured 15 points apart. The solid line is for the randomly phased construction, the dashed line for the optimized phase case, and dot-dashed line is the ACE result.