Description
Geodesic acoustic modes (GAMs) are axisymmetric oscillations that develop in toroidal plasmas because of the compression of the poloidal E×B flow [1]. Being part of the complex interplay between drift-wave turbulence and zonal flow dynamics [2], their role in turbulence regulation is actively investigated [3]. By taking the nonlinear modification of the dispersion properties of the plasma due to the GAM itself into account, GAM packets are found to obey a nonlinear Schrödinger equation (NLSE) [4] and to be subject to modulational instability in the anomalous-dispersion regime [5].
In this contribution, the nonlinear dynamics of GAM packets is investigated focusing on the signatures in the wavenumber spectrum of the four wave mixing (FWM) associated with the cubic nonlinearity resulting from the GAM self-interaction [6]. To this goal, numerical solutions of the NLSE are compared to nonlinear simulations of GAM packets performed with the gyrokinetic code ORB5 [7]. The periodic spreading of the spectrum known e.g. from nonlinear-fibre optics [8] is recovered and discussed for different dispersion regimes and packet widths. In gyrokinetic simulations, the spreading is stopped by the onset of small-scale damping, as reported in [4]. In the case of modulated, very broad packets, the behaviour of pump waves and sidebands agrees with analytic predictions obtained from the NLSE. Periodic breathers are observed. For narrower packets, the energy transfer between pump and sidebands is altered by the coupling to further spectral components and the appearance of the modulational instability can be strongly inhibited. Bicoherence diagnostics and a time trace of the nonlinear driving terms are used to identify the interacting spectral components.
[1] N. Winsor et al. Phys. Fluids 11, 2448 (1968).
[2] P. H. Diamond et al., Plasma Phys. Controlled Fusion 47, R35 (2005).
[3] G. Conway et al., Nucl. Fusion 62, 013001 (2022).
[4] E. Poli et al. Phys. Plasmas 28, 112505 (2021).
[5] D. Korger et al. J. Plasma Phys. 91, E17 (2025).
[6] D. Korger et al. in preparation.
[7] E. Lanti et al., Comput. Phys. Commun. 251, 107072 (2020).
[8] G. Agrawal, Nonlinear Fiber Optics, 6th ed. (Academic Press, 2019).