Equilibrium states of confined ions in two dimensions

Ions that are trapped in two dimensions and are subject to a harmonic confining potential have widely varying stationary states that exhibit various asymptotic forms and bifurcations. We present a ‘birds-eye’ view of these structures for N = 2 to 5 ions, and the full range of anisotropy. These results may be interrogated in detail using the software provided here. Energy variations at bifurcation points and limits are also identified; for N = 5 these include blue-sky (or saddle-node) bifurcations. A limited attempt is also made to explore such features for a larger system of ions, i.e. N = 10.被束缚于二维空间且受简谐约束势（harmonic confining potential）作用的离子，存在多种迥异的定态（stationary states）结构，这些结构展现出多样的渐近形式（asymptotic forms）与分岔（bifurcations）现象。我们针对离子数N=2至5以及全范围各向异性（anisotropy）的情况，给出了这类结构的鸟瞰式概览。借助本文所提供的配套软件，可对上述结果展开细致的探究分析。本研究还确定了分岔点与分岔极限处的能量变化；当离子数N=5时，此类分岔包含蓝天分岔（blue-sky bifurcation，亦称鞍结点分岔（saddle-node bifurcation））。此外，本研究还针对更大规模的离子体系（即N=10）开展了此类特性的初步探索尝试。