Addendum: Babic, S., et al. Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities. Physics 2020, 2, 352–367

In [...]

Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities

In this paper, we give new formulas for calculating the self-inductance for circular coils of the rectangular cross-sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions, we can obtain the special cases for the self-inductance of the thin-disk pancake and the thin-wall solenoids that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin-wall solenoid is obtained for the first time in the literature. In this paper, we do not use special functions such as the elliptical integrals of the first, second and third kind, nor Struve and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in excellent agreement. We consider this approach novel because of its simplicity in the self-inductance calculation of the previously-mentioned configurations.

The Fast and Accurate Calculation of the Self Inductance for the Circular Coils of the Rectangular Cross Section with the Radial and the Azimuthal Current Densities

In this paper we give the new formulas for calculating the self-inductance for the circular coils of the rectangular cross sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions we can obtain the special cases for the self-inductance of the thin disk pancake and the thin wall solenoid that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin wall solenoid is obtained for the first time in the literature. In this paper we do not use special functions such as the elliptical integrals of the first, second and third kind, Struve, and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in the excellent agreement. This is way we consider this approach as the novelty because of its simplicity in the self -inductance calculation of the previously mentioned configurations.

Saturn’s ring current observed during Cassini’s Grand Finale

<p>The presence of a substantial azimuthal current sheet in Saturn’s magnetosphere was identified in Voyager and Pioneer magnetometer data.  Data from these spacecraft showed depressions in the strength of the field below that expected for the internal field of the planet alone.  This ring current was  modelled  as a simple axisymmetric current system by Connerney et al. [1980, 1983].  In this study we utilise the Connerney ring current model to look at the size, shape, current density and total current of Saturn’s ring current as observed during the Cassini proximal orbits.  We compare the variations in these parameters with the phases of the planetary period oscillations and with the occurrence of magnetospheric storms as determined from propagated solar wind data and LEMMS electron and proton data. Overall, we find that Saturn’s ring current is a dynamical environment which varies in size and magnitude due to  both  planetary period oscillations and solar-driven storms.  </p>

1-D Modeling of the Screw-Pinch Plasma in PROTO-SPHERA

A simple steady-state model for a 3-species mixture (ions, electrons, and neutrals) in a screw-pinch plasma configuration is developed. The model is applied to the central plasma column of the PROTO-SPHERA experiment. Degree of ionization, azimuthal current density, and azimuthal ion velocity are calculated. Full ionization is found at plasma temperatures above 1.5 eV, with neutrals confined in an outer shell where radial plasma flow develops and drives both azimuthal current and azimuthal flow.

A magnetodisc model service for planetary space weather studies

Theoretical models play an important role in the Planetary Space Weather Services (PSWS) of the European Planetary Network (“Europlanet”), due to their ability to predict the physical response of magnetospheric environments to compressions or rarefactions in the upstream solar wind flow. We illustrate this aspect by presenting examples of some calculations done with the UCL Magnetodisc Model in both “Jupiter” and “Saturn” mode. Similar model outputs can now be provided via the PSWS MAGNETODISC service. For each planet’s space environment, we present example model outputs showing the effect of compressions and rarefactions on the global magnetic field, plasma pressure and azimuthal current density. As a simple illustration of the physics underlying these reference models, we quantify solar wind effects by comparing the “compressed” and “expanded” outputs to a nominal “average-state” model, reflecting more typical solar wind dynamic pressures. We also describe the implementation of the corresponding PSWS MAGNETODISC Service, through which similar outputs may be obtained by potential users.