We consider ion heating by turbulent Alfvén waves (AWs) and kinetic Alfvén waves (KAWs) with wavelengths (measured perpendicular to the magnetic field) that are comparable to the ion gyroradius and frequencies ω smaller than the ion cyclotron frequency Ω. We focus on plasmas in which β 1, where β is the ratio of plasma pressure to magnetic pressure. As in previous studies, we find that when the turbulence amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion then interacts stochastically with the time-varying electrostatic potential, and the ion's energy undergoes a random walk. Using phenomenological arguments, we derive an analytic expression for the rates at which different ion species are heated, which we test by simulating test particles interacting with a spectrum of randomly phased AWs and KAWs. We find that the stochastic heating rate depends sensitively on the quantity ε = δv ρ/v ⊥, where v ⊥ (v ∥) is the component of the ion velocity perpendicular (parallel) to the background magnetic field B 0, and δv ρ (δB ρ) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case of thermal protons, when ε εcrit, where εcrit is a constant, a proton's magnetic moment is nearly conserved and stochastic heating is extremely weak. However, when εεcrit, the proton heating rate exceeds half the cascade power that would be present in strong balanced KAW turbulence with the same value of δv ρ, and magnetic-moment conservation is violated even when ω Ω. For the random-phase waves in our test-particle simulations, εcrit = 0.19. For protons in low-β plasmas, ε β–1/2δB ρ/B 0, and ε can exceed εcrit even when δB ρ/B 0 εcrit. The heating is anisotropic, increasing v 2 ⊥ much more than v 2 ∥ when β 1. (In contrast, at β 1 Landau damping and transit-time damping of KAWs lead to strong parallel heating of protons.) At comparable temperatures, alpha particles and minor ions have larger values of ε than protons and are heated more efficiently as a result. We discuss the implications of our results for ion heating in coronal holes and the solar wind.
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机译：我们考虑通过湍流Alfvén波（AWs）和动力学Alfvén波（KAWs）加热离子，这些波长的波长（垂直于磁场测量）与离子陀螺半径相当，且频率ω小于离子回旋加速器频率Ω。我们关注于其中β1的等离子体，其中β是等离子体压力与电磁压力之比。与以前的研究一样，我们发现当湍流幅度超过某个阈值时，离子的轨道将变得混乱。然后，离子与随时间变化的静电势随机相互作用，并且离子的能量经历随机游动。使用现象学的论据，我们得出了不同离子物质加热速率的解析表达式，我们通过模拟与随机相变AW和KAW光谱相互作用的测试粒子来进行测试。我们发现随机加热速率敏感地取决于量ε=δvρ/ v⊥，其中v⊥（v∥）是与背景磁场B 0垂直（平行）的离子速度的分量，而δvρ（ δBρ）是陀螺半径范围内速度（磁场）波动的均方根值。在热质子的情况下，当εcrit为εcrit时，质子的磁矩几乎守恒，随机加热极弱。但是，当ε>εcrit时，质子加热速率超过具有相同δvρ值的强平衡KAW湍流中存在的级联功率的一半，并且即使在ωΩ时也违反了磁矩守恒。对于我们的测试粒子模拟中的随机相位波，εcrit= 0.19。对于低β等离子体中的质子，即使δBρ/ B 0εcrit，εβ–1 /2δBρ/ B 0和ε也会超过εcrit。加热是各向异性的，当β1时，v 2 increasing的增加要比v 2 more大得多。（相反，在β1 Landau阻尼和KAW的过渡时间阻尼会导致质子强烈平行加热。）在相当的温度下，α粒子次离子和质子的ε值均比质子大，因此加热效率更高。我们讨论了结果对日冕孔中离子加热和太阳风的影响。
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