Petri Toivanen

Invited Article: Electric solar wind sail: Toward test missions

The electric solar wind sail (E-sail) is a space propulsion concept that uses the natural solar wind dynamic pressure for producing spacecraft thrust. In its baseline form, the E-sail consists of a number of long, thin, conducting, and centrifugally stretched tethers, which are kept in a high positive potential by an onboard electron gun. The concept gains its efficiency from the fact that the effective sail area, i.e., the potential structure of the tethers, can be millions of times larger than the physical area of the thin tethers wires, which offsets the fact that the dynamic pressure of the solar wind is very weak. Indeed, according to the most recent published estimates, an E-sail of 1 N thrust and 100 kg mass could be built in the rather near future, providing a revolutionary level of propulsive performance (specific acceleration) for travel in the solar system. Here we give a review of the ongoing technical development work of the E-sail, covering tether construction, overall mechanical design alternatives, guidance and navigation strategies, and dynamical and orbital simulations.

Magnetospheric field and current distributions during the substorm recovery phase

We have studied 11 substorm recovery phase events in which magnetic field and energetic particle data were available near the midnight sector from the GEOS 2 satellite. Comparison with the Tsyganenko magnetic field model shows that, after the expansion phase, BZ is large and decreases gradually toward the model value during the recovery phase, whereas deviations of BX and BY relative to the model values are small after the effects of the substorm current wedge have disappeared. We have modeled this sequence by using temporally evolving current systems implemented as additions to the Tsyganenko model. The tail current sheet thickness and the cross-tail current intensity at different radial distances were varied using six free parameters in the model. The parameters were evaluated using a least squares fit for each of the 11 events separately. The results suggest that at the beginning of the recovery phase the current sheet was relatively thick close to the inner edge of the plasma sheet. Model fittings produced two different field configurations. In seven events the cross-tail current was weak, and the field configuration was highly dipolar. In four events the near-Earth current was weak, but stronger currents remained in the midtail region. In these latter events the field configuration at the beginning of the recovery phase included a region where BZ was negative. This negative BZ and the associated near-Earth neutral line disappeared later as the current system developed toward the quiet time configuration. The magnetic field configuration, current distributions, and particle drift paths during the substorm recovery phase are examined and compared with those prevailing during the substorm growth phase.

Spin Plane Control and Thrust Vectoring of Electric Solar Wind Sail

The electric solar wind sail is a propulsion system that uses long centrifugally spanned and electrically charged tethers to extract the solar wind momentum for spacecraft thrust. The sail angle with respect to the sun direction can be controlled by modulating the voltage of each tether separately to produce net torque for attitude control and thrust vectoring. A solution for the voltage modulation that maintains any realistic sail angle under constant solar wind is obtained. Together with the adiabatic invariance of the angular momentum, the tether spin rate and coning angle are solved as functions of temporal changes in the solar wind dynamic pressure, the tether length, or the sail angle. The obtained modulation also gives an estimate for the fraction of sail performance (electron gun power) to be reserved for sail control. We also show that orbiting around the sun with a fixed sail angle leads to a gradual increase (decrease) in the sail spin rate when spiraling outward (inward). This effect arises fr...

Mapping between the ionospheric and the tail electric fields in a time-dependent Earth's magnetosphere

In this paper we use the concept of the Faraday loop to connect the ionosphere and the tail along the geomagnetic field lines to study the coupling between ionospheric and magnetospheric electric fields. The formulation using the Faraday loop shows that the coupling consists of three contributions: One is the familiar mapping of the ionospheric field to the tail along equipotential magnetic field lines. The other two are parallel potential differences between the tail and the ionosphere distributed across the magnetic field lines and magnetic flux transport across the Faraday loop due to time evolution of the magnetic field, which gives rise to an inductive electric field perpendicular to the magnetic field. Application of this method requires a model for the ionospheric electric field, a model distribution of the parallel potential differences, and a time-evolving magnetic field model. In the present study the ionospheric electric field pattern is described using a statistical model. The parallel potential differences are modeled by Gaussian distributions in latitude as narrow longitudinally elongated ridges. The magnetic field model describes the time evolution of the geomagnetic field during the substorm growth phase. We show that the effects of parallel potential differences and the inductive fields are of the same order as the mapped ionospheric field, and hence they must be taken into account when the large-scale coupling is studied.

Effects of the large‐scale electric field on particle drifts in the near‐Earth tail

Large-scale electric field contributes to the charged particle drift motion directly through the E × B drift and indirectly through energization caused by magnetic drifts parallel to the electric field and through pitch angle changes due to magnetic field gradients perpendicular to the electric field. In this paper, we describe these effects on particle drifts in the near-Earth tail, where the electric field pattern can be expected to be complex, especially near the inner edge of the plasma sheet. We use the Tsyganenko 1989 model to describe the near-Earth tail magnetic field. The ionospheric Heppner-Maynard model is mapped to the magnetosphere to model various electric field structures that are not included in a simple model that combines the corotation electric field with a constant cross-tail convection electric field. The simple model is used as a reference when the results deduced from the Heppner-Maynard model are discussed. Because these field models are numerically tedious, the bounce-averaged drift equations are used. They also provide a practical way to include complex electric field models. In addition, we study the electric field mapping in a stretched magnetic field configuration typical for substorm growth phases. Furthermore, it is shown that the inductive electric field associated with temporal stretching during substorm growth phases can be comparable to the typical values of the convective electric field due to earthward plasma convection.

Thrust vectoring of an electric solar wind sail with a realistic sail shape

Abstract The shape of a rotating electric solar wind sail under the centrifugal force and solar wind dynamic pressure is modeled to address the sail attitude maintenance and thrust vectoring. The sail rig assumes centrifugally stretched main tethers that extend radially outward from the spacecraft in the sail spin plane. Furthermore, the tips of the main tethers host remote units that are connected by auxiliary tethers at the sail rim. Here, we derive the equation of main tether shape and present both a numerical solution and an analytical approximation for the shape as parametrized both by the ratio of the electric sail force to the centrifugal force and the sail orientation with respect to the solar wind direction. The resulting shape is such that near the spacecraft, the roots of the main tethers form a cone, whereas towards the rim, this coning is flattened by the centrifugal force, and the sail is coplanar with the sail spin plane. Our approximation for the sail shape is parametrized only by the tether root coning angle and the main tether length. Using the approximate shape, we obtain the torque and thrust of the electric sail force applied to the sail. As a result, the amplitude of the tether voltage modulation required for the maintenance of the sail attitude is given as a torque-free solution. The amplitude is smaller than that previously obtained for a rigid single tether resembling a spherical pendulum. This implies that less thrusting margin is required for the maintenance of the sail attitude. For a given voltage modulation, the thrust vectoring is then considered in terms of the radial and transverse thrust components.

ESTCube-1 in-orbit experience and lessons learned

In this article, we report on the in-orbit experience - an overview of ESTCube-1 operations from the launch until the experiment, as well as on lessons learned from five years of development and almost two years of operations. Lessons are identified from the point of view of system engineering, electrical engineering, mechanical engineering, software engineering, testing and measurements, payload, and management. Detailed flight results of ESTCube-1 will be provided in dedicated articles. We hope that other teams can benefit from our experience.

Time‐dependent modeling of particles and electromagnetic fields during the substorm growth phase: Anisotropy of energetic electrons

We use a bounce averaged drift model with realistic electromagnetic fields together with magnetic field and electron data obtained by CRRES to study energetic electron distributions during the growth phase of an isolated substorm on December 12, 1990. The magnetic field model includes the actual time evolution of the geomagnetic field as measured by CRRES. The inductive electric field caused by the time evolution of the magnetic field configuration is included in the drift model to consider fully electromagnetic fields. The drift motion is computed for all pitch angles and for the entire energy range covered by the medium-energy spectrometer on CRRES. By using the Liouville theorem we are able to map electron distributions from orbit to orbit to model their time evolution in the model fields. To test the model predictions, we examine the substorm growth phase on December 12, 1990: A quiet period of about 20 hours preceded the growth phase that led to the expansion phase of a 500-nT substorm. The outer belt energetic electron distributions showed a clear development of magnetic field-aligned pitch angle anisotropy. This period was covered by two CRRES orbits, 339 and 340. During orbit 339, CRRES measured a quiet time distribution of energetic electrons. During orbit 340 the substorm onset was seen as a rapid dipolarization of the magnetic field and by a dispersionless electron injection. The quiet time fluxes were used as initial conditions for the model for fluxes during the growth phase. We conclude that pitch angle dependent energization of the drifting electrons caused by the inductive electric field plays an essential role in development of the outer belt electron distributions during the substorm growth phase.

Electric Solar Wind Sail: Deployment, Long-Term Dynamics, and Control Hardware Requirements

The deployment, dynamics, and control of the electric solar wind sail is addressed in terms of the single tether motion. Based on a simple model of a rotating rigid tether as a spherical pendulum, estimates for the goodness of the control system are shown for strictly planar tether tip orbits. It is concluded that the control system is rather inefficient for a slowly rotating sail with a large tether coning angle. The results are conservative as they do not take into account the actual shape of the tether. The long and short-term effects on the sail rotation rate arising from the single tether dynamics are addressed. We also present preliminary results on a new control scheme assuming non-planar tether tip orbits. It is argued that the scheme will improve the electric sail control system efficiency.