We investigate mechanisms of wave particle heating of ionospheric O⁺ ions resulting from broadband extremely low frequency (BBELF) waves using numerical test particle simulations that take into account ion‐neutral collisions, in order to explain observations from the Enhanced Polar Outflow Probe (e‐POP) satellite at low altitudes (∼400 km) (Shen et al., 2018, https://doi.org/10.1002/2017JA024955). We argue that in order to reproduce ion temperatures observed at e‐POP altitudes, the most effective ion heating mechanism is through cyclotron acceleration by short‐scale electrostatic ion cyclotron (EIC) waves with perpendicular wavelengths λ _⊥ ≤ 200 m. The interplay between finite perpendicular wavelengths, wave amplitudes, and ion‐neutral collision frequencies collectively determine the ionospheric ion heating limit, which begins to decrease sharply with decreasing altitude below approximately 500 km, where the ratio becomes larger than 10⁻³, ν _c and f _{c i} denoting the O⁺‐O collision frequency and ion cyclotron frequency. We derive, both numerically and analytically, the ion gyroradius limit from heating by an EIC wave at half the cyclotron frequency. The limit is 0.28λ _⊥. The ion gyroradius limit from an EIC wave can be surpassed either through adding waves with different λ _⊥ or through stochastic “breakout,” meaning ions diffuse in energy beyond the gyroradius limit due to stochastic heating from large‐amplitude waves. Our two‐dimensional simulations indicate that small‐scale (<1 km) Alfvén waves cannot account for the observed ion heating through trapping or stochastic heating.

中文翻译：

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低空BBELF波对O +离子加热的影响：测试粒子模拟

我们使用考虑离子中性碰撞的数值测试粒子模拟研究了宽带超低频（BBELF）波产生的电离层O ⁺离子的波粒加热机制，目的是解释增强型极性流出探针（e- POP）在低海拔高度（卫星〜 400公里）（Shen等人，2018，https://doi.org/10.1002/2017JA024955）。我们认为，为了在电子POP高度观察到再生离子温度，最有效的离子加热机构是通过短尺度静电离子回旋加速器（EIC）波回旋加速器加速度与垂直波长λ _⊥  ≤200 米 有限垂直波长之间的相互作用，波振幅，和离子中性碰撞频率共同确定电离层的离子加热限制，这开始与下降低于约500公里，这里的比例高度急剧下降变得大于10 ^-3，ν _Ç和˚F _ç我表示将O ⁺ -O碰撞频率和离子回旋频率。从数值和分析上，我们都通过回旋加速器频率的一半的EIC波加热产生的离子陀螺半径极限。该限制是0.28 λ _⊥。EIC波的离子陀螺半径极限可以通过添加不同的波来超越λ _⊥或通过随机“突破”，这意味着在离子超出限制回转半径能量扩散由于从大振幅波随机加热。我们的二维模拟表明，小规模（<1 km）的Alfvén波无法解释通过俘获或随机加热观察到的离子加热。