Solar sail with superconducting circular current-carrying wire

Abstract

Background: A solar sail presents a large sheet of low areal density membrane and is the most elegant propellant-less propulsion system for the future exploration of the Solar System and beyond. By today the study on sail membrane deployment strategies has attracted considerable attention. Goal: In this work we present an idea of the deployment and stretching of the circular solar sail. We consider the superconducting current loop attached to the thin membrane %to develop a new (method) approach of deployment of a solar sail and and predict that a superconducting current loop can deploy and stretch the circular solar sail membrane. Method: In the framework of a strict mathematical approach based on the classical electrodynamics and theory of elasticity the magnetic field induced by the superconducting current loop and elastic properties of a circular solar sail membrane and wire loop are analyzed. The formulas for the wire and sail membrane stresses and strains caused by the current in the superconducting wire are derived. Results: The obtained analytical expressions can be applied to a wide range of solar sail sizes. Numerical calculations for the sail of radius of 5 m to 150 m made of CP1 membrane of the thickness of 3.5 $\mu m$ attached to Bi$-$2212 superconducting wire with the cross-section radius of 0.5 mm to 10 mm are presented. Calculations are performed for the engineering current densities of 100 A/mm$^{2}$ to 1000 A/mm$^{2}$. Conclusion: Our calculations demonstrate the feasibility of the proposed idea for the solar sail deployment for the future exploration of the deep space by means of the light pressure propellant.