反磁剪切托卡马克等离子体中低频剪切阿尔芬波的理论研究

Theoretical studies of low-frequency shear Alfvén waves in reversed shear tokamak plasmas

位于动理学热离子带隙附近的低频阿尔芬扰动因可以与高能量粒子或背景热粒子发生相互作用而引起了广泛的关注.本文在一般鱼骨模色散关系的理论框架下,针对反磁剪切托卡马克等离子体中观测到的由高能量粒子或者背景热粒子激发的低频剪切阿尔芬波的线性特性进行了一系列的理论研究.由于这些低频剪切阿尔芬波与2019年DⅢ-D开展的专门研究高能量离子驱动低频不稳定的实验密切相关,因此本文通过采用DⅢ-D具有代表性实验的平衡参数,证明了实验上观测的低频模和比压阿尔芬本征模分别是以阿尔芬极化为主的反应型和耗散型不稳定模,因此,将前者称为低频阿尔芬模更准确.由于受逆磁和捕获粒子动理学效应的影响,低频阿尔芬模既可以在低频区(频率小于热离子的渡越或反弹频率)与比压阿尔芬声模耦合,又可以在高频区(频率大于或近似等于热离子的渡越频率)与比压阿尔芬本征模耦合,此外,由于受到不同激发机制的影响,与局域在安全因子最小值有理面附近的低频阿尔芬模相比,驱动比压阿尔芬本征模的高能量离子的压强梯度在偏离安全因子最小值的有理面时达到最大值,相应的比压阿尔芬本征模的本征函数在高能量离子驱动最大的径向位置处出现峰值.通过改变安全因子最小值理论上重现了实验上观测的比压阿尔芬本征模和低频阿尔芬模的上升频谱特征.研究还表明,比压阿尔芬声模由于受到强烈的朗道阻尼,因而很难被高能量粒子激发,这与基于第一性原理的理论预测和模拟结果一致.本文证明了一般鱼骨模色散关系在解释和预测实验和数值模拟结果方面的强大能力.

The low-frequency Alfvénic fluctuations in the kinetic thermal-ion gap frequency range have aroused the interest of researchers since they can interact with background thermal particles and/or energetic particles.In the theoretical framework of the general fishbone-like dispersion relation(GFLDR),we theoretically investigate and delineate the linear wave properties of the low-frequency shear Alfvén wave excited by energetic and/or thermal particles observed in tokamak experiments with reversed magnetic shear.These low-frequency shear Alfvén waves are closely related to the dedicated experiment on energetic ion-driven low-frequency instabilities conducted on DIII-D in 2019.Therefore,adopting the representative experimental equilibrium parameters of DIII-D,in this work we demonstrate that the experimentally observed low-frequency modes and beta-induced Alfvén eigenmodes(BAEs)are,respectively,the reactive-type unstable mode and dissipative-type unstable mode,each with dominant Alfvénic polarization,thus the former being more precisely called low-frequency Alfvén modes(LFAMs).More specifically,due to diamagnetic and trapped particle effects,the LFAM can be coupled with the beta-induced Alfvén-acoustic mode(BAAE)in the low-frequency range(frequency much less than the thermal-ion transit frequency and/or bounce frequency),or with the BAE in the high frequency range(frequency higher than or comparable to the thermal-ion transit frequency),resulting in reactive-type instabilities.Moreover,due to different instability mechanisms,the maximal drive of BAEs occurs in comparison with LFAMs,when the minimum of the safety factor(qmin)from a rational number.Meanwhile,the BAE eigenfunction peaks at the radial position of the maximum energetic particle pressure gradient,resulting in a large deviation from the qmin The ascending frequency spectrum patterns of the experimentally observed BAEs and LFAMs can be theoretically reproduced by varying qmin,and they can also be well explained based on the GFLDR.In particular,it is confirmed that the stability of the BAAE is not affected by energetic ions,which is consistent with the first-principle-based theory predictions and simulation results.The present analysis illustrates the solid predictive capability of the GFLDR and its practical applications in enhancing the ability to explain experimental and numerical simulation results.