Influence of Solar Sails on Magnetic Field Measurements in Space Plasmas

TL;DR

The study assesses how a solar sail carrying a magnetometer can perturb ambient space-plasma magnetic fields through eddy currents and magnetic pileup. By deriving a quasistatic diffusion framework and explicit expressions for the induced fields, it shows that for a realistic 40×40 m sail the eddy-current perturbation remains well below the 1% level at magnetometer-relevant frequencies, and magnetic pileup is unlikely in the electron-dominated, sub-electron-scale regime. The work yields a practical sail-size threshold $L<\dfrac{8}{\pi\mu_0\sigma h f_{mag}}|\Delta B_i/B_i|$ and provides analytic guidance (Appendix A) for evaluating sail-induced magnetic perturbations. Overall, the results support the feasibility of magnetometer-equipped solar sail missions under current designs, while outlining parametric regimes where sail-plasma interactions could become significant and warrant mitigation or more detailed kinetic modeling.

Abstract

Solar sail technology is ready to be deployed in a satellite mission carrying a science-grade magnetometer. In preparation for such a mission, it is essential to characterize the interactions between the sail and the ambient plasma that could affect the magnetometer readings. The solar wind magnetic field is a key parameter in space weather prediction, because it governs the energy-releasing magnetic reconnection process at Earth's magnetopause. This paper investigates the influence of solar sails on the ambient magnetic field, particularly focusing on two critical electromagnetic effects: eddy currents and magnetic pileup. We find the induced eddy currents in the metallic sail can significantly perturb the local magnetic field at high frequencies. We also suggest that magnetic pileup can influence the spacecraft's environment when the sail size is comparable to the electron kinetic scales of the surrounding plasma. This research provides an initial guide for determining when sail-plasma interactions could impact magnetometer performance.

Figures (6)

• Figure 1: The magnetic frequency power spectrum in the solar wind, modified with author's permission from verscharen19. The plot combines magnetometer data from the ACE and Cluster missions, to display the spectrum over a broad range of frequencies. Note that the assumed magnetometer's Nyquist frequency $f_{mag}/2 = 5~Hz$ lies in the dissipation range. The instrument covers the lower-frequency (injection and inertial) ranges of the turbulent spectrum as well.
• Figure 2: We model the solar sail as a thin circular disk, to estimate the effects on the square sail of similar dimensions (figures from tan14_fermilab_eddy_currents, modified and included with author's permission). a) Diagram of a metal disk with radius $R$ and thickness $h$ suffused by a homogeneous time-varying magnetic field $\mathbf{B}(\mathbf{x}, t) = \mathbf{\hat{z}}B_z(t)$. b) At an arbitrary point P along the axis of symmetry (cylindrical radius $r = 0$), we may calculate the perturbation field $\mathbf{B_z^\prime}(\mathbf{x}, t)|_{r=0} = \mathbf{\hat{z}} B_z^\prime(z, t)$. The field $\mathbf{B^\prime}$ is generated by the induced azimuthal current $dI_\theta(r)$.
• Figure 3: The quantities $B_z(t)$, $B_z^\prime(z=0, t)$, and $B_{tot,z}(z=0, t)$ are assumed to be harmonically varying with angular frequency $\omega=2\pi f$, are shown in the complex plane---see eqs. (\ref{['eddy_current_B_eq_w_phase']}) and (\ref{['Btot_eq']}).
• Figure 4: The plot shows the magnetic error metric $\mathcal{E}_1 = |B^\prime_z(z=0,t)/B_z(t)|$, from equation (\ref{['eddy_current_B_err_eq']}). According to this formula, $\mathcal{E}_1$ depends linearly on both the frequency $f$ of the applied sinusoidal field and the sail dimension $h \cdot R$. The white diagonal line divides the plot, into a blue region that satisfies the worst-case error tolerance requirement $|B^\prime_z/B_z|<0.01$ and a red region that violates this requirement. The shaded region in the lower left corner is relevant to the hypothetical solar sail mission, as it is bounded by horizontal and vertical dashed lines which respectively show the mission's parameters $h \cdot R$ (where $R = L/2$) and Nyquist frequency $f_{mag}/2$ (Table \ref{['params_table']}). The x-axis annotations show the approximate frequency regimes typical for fluxgate ($\lesssim$10 Hz) and search coil ($\sim$Hz--kHz) magnetometers.
• Figure 5: The plot, analogous to Figure \ref{['sail_induced_B_fig']}, shows the dependence of the magnetic error metric $\mathcal{E}_2$ (eq. \ref{['eddy_current_B_err_eq2']}) on the frequency $f$ and sail dimension $h \cdot R$.