Overdamped Alfvén waves due to ion-neutral collisions in the solar chromosphere

Abstract

Alfvénic waves are ubiquitous in the solar atmosphere and their dissipation may play an important role in atmospheric heating. In the partially ionized solar chromosphere, collisions between ions and neutrals are an efficient dissipative mechanism for Alfvén waves with frequencies near the ion-neutral collision frequency. The collision frequency is proportional to the ion-neutral collision cross section for momentum transfer. Here, we investigate Alfvén wave damping as a function of height in a simplified chromospheric model and compare the results for two sets of collision cross sections, namely those of the classic hard-sphere model and those based on recent quantum-mechanical computations. We find important differences between the results for the two sets of cross sections. There is a critical interval of wavelengths for which impulsively excited Alfvén waves are overdamped as a result of the strong ion-neutral dissipation. The critical wavelengths are in the range from 1 km to 50 km for the hard-sphere cross sections, and from 1 m to 1 km for the quantum-mechanical cross sections. Equivalently, for periodically driven Alfvén waves there is an optimal frequency for which the damping is most effective. The optimal frequency varies from 1 Hz to 102 Hz for the hard-sphere cross sections, and from 102 Hz to 104 Hz for the quantum-mechanical cross sections. Future observations at sufficiently high spatial or temporal resolution may show the importance of high-frequency Alfvén waves for chromospheric heating. For instance, the Atacama Large Millimeter/submillimeter Array (ALMA) may be able to detect the critical wavelengths and optimal frequencies and so to test the effective collision cross section in the chromospheric plasma.