磁帆的普适标度关系：稀星际介质极限下的动量制动
Universal scaling relation for magnetic sails: momentum braking in the limit of dilute interstellar media
摘要：
激光推进研究的最新进展大大推进了在几十年内实现星际空间飞行的前景。在这里，我们研究被动减速通过电离星际介质的动量制动。由于星际密度低，需要非常大的面积与质量的关系，大约每$\mathrm{cm}^{3}$ 0.1个粒子或更低，这可能通过超导线圈产生的磁帆来实现。积分星际质子击中毕-萨环的运动方程，我们评估的有效反射面积$A(v)$的速度$v$的工艺。我们发现，数值数据拟合超过两个数量级的缩放关系$A(v)\ =\ 0.081A_R\log^3(I/(βI_c))$，其中$A_R=πR^2$是裸帆面积，$I$的电流和$β=v/c$。临界电流$I_c$为$1.55\cdot10^6$安培。由此产生的通用减速剖面可以进行分析评估，并优化任务参数，以达到最小的飞行器质量。对于一个样本高速过境比邻星的情况下，我们发现，磁动量制动将涉及令人生畏的质量要求的顺序$10^3$吨。对Trappist-1系统的低速飞行任务可以在另一边用一个1.5吨重的航天器实现，这将进一步符合目前设想的定向能发射系统的规格。然而，延长的巡航时间为$10^4$年的数量级意味着，对Trappist-1系统的飞行任务只适用于与时间限制无关的飞行任务概念。
英文摘要：
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 $A(v)\ =\ 0.081A_R\log^3(I/(βI_c))$, where $A_R=πR^2$ is the bare sail area, $I$ the current and $β=v/c$. 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.
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