Nonlinear dynamics of small-scale Alfvén waves

Journal Article · Thu Nov 02 00:00:00 EDT 2023 · Physics of Plasmas

DOI:https://doi.org/10.1063/5.0151035· OSTI ID:2281250

Mallet, Alfred ^[1]; Dorfman, Seth ^[2]; Abler, Mel ^[3]; Bowen, Trevor A. ^[4]; Chen, Christopher K. ^[5]

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1. Univ. of California, Berkeley, CA (United States). Space Sciences Lab.; Space Science Institute
2. Space Science Institute, Boulder, CO (United States); Univ. of California, Los Angeles, CA (United States)
3. Space Science Institute, Boulder, CO (United States)
4. Univ. of California, Berkeley, CA (United States). Space Sciences Lab.
5. Queen Mary Univ. of London (United Kingdom)

Herein we study the nonlinear evolution of very oblique small-scale Alfvén waves with k_⊥d_i≳1. At these scales, the waves become significantly compressive, unlike in magnetohydrodynamics, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes are small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when k_⊥d_i~1. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfvén waves, an inherently three-dimensional effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfvén wave also becomes dispersive once one or more of k_⊥ρ_s, k_⊥d_e, or k_∥d_i becomes significant: for oblique waves at low β as studied here, this can be at a much smaller scale than d_i. We show that the timescale for one-dimensional steepening of two-fluid Alfvén waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfvén wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.

• Research Organization: Space Science Institute, Boulder, CO (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Fusion Energy Sciences (FES)
• Grant/Contract Number: SC0021237; SC0021291; SC0023326
• OSTI ID: 2281250
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 11 Vol. 30; ISSN 1070-664X
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Hall effect
non linear dynamics
plasma waves
solar corona
solar wind