Mars lacks a substantial magnetic field; as a result, the solar wind ablates the Martian atmosphere, and cosmic rays from solar flares make the surface uninhabitable. Therefore, any terraforming attempt will require an artificial Martian magnetic shield. The fundamental challenge of building an artificial magnetosphere is to condense planetary-scale currents and magnetic fields down to the smallest mass possible. Superconducting electromagnets offer a way to do this. However, the underlying physics of superconductors and electromagnets limits this concentration. Based upon these fundamental limitations, we show that the amount of superconducting material is proportional to $B_{\rm c}^{-2}a^{-3}$, where Bc is the critical magnetic field for the superconductor and a is the loop radius of a solenoid. Since Bc is set by fundamental physics, the only truly adjustable parameter for the design is the loop radius; a larger loop radius minimizes the amount of superconducting material required. This non-intuitive result means that the ‘intuitive’ strategy of building a compact electromagnet and placing it between Mars and the Sun at the first Lagrange point is unfeasible. Considering reasonable limits on Bc, the smallest possible loop radius is ~10 km, and the magnetic shield would have a mass of ~ 1019 g. Most high-temperature superconductors are constructed of rare elements; given solar system abundances, building a superconductor with ~ 1019 g would require mining a solar system body with several times 1025 g; this is approximately 10% of Mars. We find that the most feasible design is to encircle Mars with a superconducting wire with a loop radius of ~3400 km. The resulting wire diameter can be as small as ~5 cm. With this design, the magnetic shield would have a mass of ~ 1012 g and would require mining ~ 1018 g, or only 0.1% of Olympus Mons.

中文翻译：

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火星磁屏蔽的基本物理和资源要求

火星缺乏强大的磁场；结果，太阳风消融了火星大气，来自太阳耀斑的宇宙射线使火星表面无法居住。因此，任何地球化尝试都需要人造火星磁屏蔽。建造人造磁层的基本挑战是将行星尺度的电流和磁场凝聚到尽可能小的质量。超导电磁体提供了一种方法来做到这一点。然而，超导体和电磁体的基本物理特性限制了这种浓度。基于这些基本限制，我们表明超导材料的数量与$B_{\rm c}^{-2}a^{-3}$， 在哪里乙C是超导体的临界磁场，一种是螺线管的环半径。自从乙C由基础物理设置，设计中唯一真正可调节的参数是环半径；较大的环路半径可最大限度地减少所需超导材料的数量。这种非直观的结果意味着构建紧凑电磁体并将其放置在火星和太阳之间的第一个拉格朗日点的“直观”策略是不可行的。考虑合理的限制乙C，最小可能的环路半径约为 10 公里，磁屏蔽的质量约为 1019G。大多数高温超导体由稀有元素构成。给定太阳系的丰度，建造一个约 1019g 将需要开采一个具有数倍 10 的太阳系天体25G; 这大约是火星的 10%。我们发现最可行的设计是用环半径约为 3400 公里的超导线环绕火星。由此产生的线径可以小至约 5 厘米。采用这种设计，磁屏蔽的质量约为 1012g 并且需要采矿 ~ 1018g，或仅 0.1% 的 Olympus Mons。