Universal scaling relation for magnetic sails: momentum braking in the limit of dilute interstellar media

TL;DR

This paper derives a universal scaling law for magnetic sails used in interstellar deceleration, showing how their effective reflection area depends on velocity and current, and evaluates mission feasibility for different targets.

Contribution

It introduces a universal scaling relation for magnetic sail momentum braking and analyzes its implications for interstellar mission design and mass requirements.

Findings

Scaling relation for reflection area: A(v) = 0.081A_R log^3(I/(eta I_c))

High-speed transit to Proxima Centauri requires massive spacecraft (~1000 tons)

Low-speed mission to Trappist-1 feasible with a 1.5-ton spacecraft

Abstract

The recent progress in laser propulsion research has advanced substantially the prospects to realize interstellar spaceflight within a few decades. Here we examine passive deceleration via momentum braking from ionized interstellar media. The very large area to mass relations needed as a consequence of the low interstellar densities, of the order of 0.1 particles per $\mathrm{cm}^{3}$, or lower, are potentially realizable with magnetic sails generated by superconducting coils. Integrating the equations of motion for interstellar protons hitting a Biot Savart loop we evaluate the effective reflection area $A(v)$ in terms of the velocity $v$ of the craft. We find that the numerical data is fitted over two orders of magnitude by the scaling relation $A(v)\ =\ 0.081A_R\log^3(I/(\beta I_c))$, where $A_R=\pi R^2$ is the bare sail area, $I$ the current and $\beta=v/c$. The critical current $I_c$ is $1.55\cdot10^6$ Ampere. The resulting universal deceleration profile can be evaluated analytically and mission parameters optimized for a minimal craft mass. For the case of a sample high speed transit to Proxima Centauri we find that magnetic momentum braking would involve daunting mass requirements of the order of $10^3$ tons. A low speed mission to the Trappist-1 system could be realized on the other side already with a 1.5 ton spacecraft, which would be furthermore compatible with the specifications of currently envisioned directed energy launch systems. The extended cruising times of the order of $10^4$ years imply however that a mission to the Trappist-1 system would be viable only for mission concepts for which time constrains are not relevant.