Contributions of the high‐degree multipoles of Neptune's magnetic field: An Euler potentials approach

Abstract

Abstract. A new technique of calculating the Euler potentials a and/3 based on the geometrical relations between the magnetic field structure and Euler potentials [Huang and Yu, 1995] was used to determine the a and/3 coordinates of Neptune's magnetic field. The result is a mathematical definable coordinate system for a field of which the nondipole terms are nonnegligible. A framework is thus established for future studying of plasma dynamics such as particle drifts and plasma convection. The magnetic field model used is the Goddard Space Flight Center/Bartol Research Institute's I8E1 model. The full I8E1 model was used to investigate the significance of the higher-degree multipoles beyond the octupole (up to the eighth degree in the spherical harmonic expansions), particularly near the planet's surface. The results were compared to those of the 08 model, which is a simplified version of the I8E1. We found that the higher-degree terms do not change significantly the overall results of the 08. However, on the planet's surface, footprints of inner drift shells fall into a few concentrated areas, opening more regions into which no particle from these drift shells can precipitate. Close examination of these "open" regions indicates that they are isolated magnetic field systems that may trap particles locally. Our results entail new interpretation of the Voyager 2 UV spectrometer measurements on the planet's nightside surface emissions. Particle precipitation emissions are found to be concentrated on the areas into which the drift shells collapse. These areas of high concentration of drift shell footprints and emissions indicate that the strong emissions are due to high particle downflux into these regions of high magnetic field intensity. Our results suggest that magnetic moments higher than the octupole may constitute nonnegligible components of the magnetic field of planets that have high nondipole terms, such as Neptune and Uranus. For Neptune the high-degree terms should be included for studying plasma processes within two planetary radii.

A numerical method to compute Euler potentials for non dipolar magnetic fields

“…This particular choice is made in reference to BoÈ strom (1975), Peymirat and Fontaine (1994b) and Stern (1994b) who showed that the derivation of the magnetospheric plasma transport equations is simpli®ed if a 1 is function of 5 only. Ho et al (1997) with h pa2 and hence dh = 0. Along a curve of constant value of a 1 on ,…”

“…Equation (16) would be equivalent to the relationship used by Ho et al (1997) if the unit area were the elementary area in the (r, h, u) space. a 1 (5) is de®ned similarly to the dipole approximation as…”

“…Our purpose is to compute the Euler potentials for non-dipolar magnetic con®gurations. Following Ho et al (1997), we propose a simple numerical method which applies to regions of closed magnetic ®eld lines. Section 2 brie¯y recalls some mathematical properties of the Euler potentials and Sect.…”

“…Tsyganenko and Stern (1996) and Khurana (1997) modelled the Euler potentials as theoretical functions ®tted to databases, to reproduce respectively the distribution of the ®eld aligned currents and the jovian magnetic ®eld. More recently, Ho et al (1997) developed a general numerical method to compute the Euler potentials associated with the Neptune's magnetic ®eld. This method uses the relationship between Euler potentials and the magnetic¯ux per unit area.…”

Euler potentials for two current sheets of nonzero thickness along ambient uniform magnetic field

“…To find Euler potentials for more complex fields, e.g., magnetospheric models, various numerical methods have been developed [Ho et al, 1997;Peymirat and Fontaine, 1999, and references therein]. They could be tested using our analytic results which enable to calculate Euler potentials and to trace magnetic field lines with high accuracy.…”