存在阻力和散射时边缘不稳定波的解析准定常演变
Analytic quasi-steady evolution of a marginally unstable wave in the presence of drag and scattering
摘要：
研究了一维尾部碰撞问题，以确定当有效碰撞远大于不稳定增长率（$ν\gg γ$）时，阻力对接近边缘稳定性（$1-γ_d/γ_L\ll 1$）的准定常解的影响。在这个共同的托卡马克制度，它严格表明，范式的Berk-Breizman三次方程的非线性模式演化减少到一个更简单的微分方程，被称为时间局部三次方程，可以直接求解。据发现，除了增加饱和振幅，阻力引入了一个移动的表观振荡频率调制的饱和波包络。模式演化的解析解与数值积分的Berk-Breizman三次方程和完全非线性的一维Vlasov模拟之间存在很好的一致性。为了验证的目的，实验隔离阻力对饱和模式振幅的贡献进行了探索，但复杂的现实是，在现实的情况下，阻力的量不能独立于其他关键参数而变化。虽然阻力的影响是温和的，当阻力与散射$α/ν$的比率非常小时，当$α/ν\gtrsim 0.5$时，它可以变得很大，这表明在聚变等离子体中的快离子驱动的不稳定性的定量模型中，阻力应占。
英文摘要：
The 1D bump-on-tail problem is studied in order to determine the influence of drag on quasi-steady solutions near marginal stability ($1-γ_d/γ_L\ll 1$) when effective collisions are much larger than the instability growth rate ($ν\gg γ$). In this common tokamak regime, it is rigorously shown that the paradigmatic Berk-Breizman cubic equation for the nonlinear mode evolution reduces to a much simpler differential equation, dubbed the time-local cubic equation, which can be solved directly. It is found that in addition to increasing the saturation amplitude, drag introduces a shift in the apparent oscillation frequency by modulating the saturated wave envelope. Excellent agreement is found between the analytic solution for the mode evolution and both the numerically integrated Berk-Breizman cubic equation and fully nonlinear 1D Vlasov simulations. Experimentally isolating the contribution of drag to the saturated mode amplitude for verification purposes is explored but complicated by the reality that the amount of drag can not be varied independently of other key parameters in realistic scenarios. While the effect of drag is modest when the ratio of drag to scattering $α/ν$ is very small, it can become substantial when $α/ν\gtrsim 0.5$, suggesting that drag should be accounted for in quantitative models of fast-ion-driven instabilities in fusion plasmas.
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