A method for analyzing fundamental kinetic plasma parameters, such as linear drive and external damping rate, based on experimental observations of chirping Alfvén eigenmodes, is presented. The method, which relies on new semiempirical laws for nonlinear chirping characteristics, consists of fitting procedures between the so-called Berk-Breizman model and the experiment in a quasiperiodic chirping regime. This approach is applied to the toroidicity induced Alfvén eigenmode ͑TAE͒ on JT-60 Upgrade ͑JT-60U͒ ͓N. Oyama et al., Nucl. Fusion 49, 104007 ͑2009͔͒, which yields an estimation of the kinetic parameters and suggests the existence of TAEs far from marginal stability. Two collision models are considered, and it is shown that dynamical friction and velocity-space diffusion are essential to reproduce nonlinear features observed in experiments. The results are validated by recovering measured growth and decay of perturbation amplitude and by estimating collision frequencies from experimental equilibrium data.

The so-called Berk-Breizman model is applied to a cold bulk, weak warm beam, one-dimensional plasma, to investigate the kinetic instability arising from the resonance of a single electrostatic wave with an energetic particle beam. A Vlasov code is developed to solve the initial value problem for the full-f distribution, and the nonlinear evolution is categorized in the whole parameter space as damped, steady-state, periodic, chaotic, or chirping. The saturation level of steady-state solutions and the bifurcation between steady-state and periodic solutions near marginal stability match analytic predictions. The limit of a perturbative numerical approach when the resonant region extends into the bulk is shown. Frequency sweeping is observed, with time-evolution approaching theoretical results. A new method to extract the dissipation rate from frequency diagnostics is proposed. For small collision rates, instabilities are observed in the linearly barely stable region.

The variety of scalar and vector fields in laboratory and nature plasmas is formed by plasma turbulence. Drift-wave fluctuations, driven by density gradients in magnetized plasmas, are known to relax the density gradient while they can generate flows. On the other hand, the sheared flow in the direction of magnetic fields causes Kelvin-Helmholtz type instabilities, which mix particle and momentum. These different types of fluctuations coexist in laboratory and nature, so that the multiple mechanisms for structural formation exist in extremely non-equilibrium plasmas. Here we report the discovery of a new order in plasma turbulence, in which chained structure formation is realized by cross-interaction between inhomogeneities of scalar and vector fields. The concept of cross-ferroic turbulence is developed, and the causal relation in the multiple mechanisms behind structural formation is identified, by measuring the relaxation rate and dissipation power caused by the complex turbulence-driven flux.

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Eigenmode analysis of geodesic acoustic modes (GAMs) driven by fast ions is performed, based on a set of gyrokinetic equations. Resonance to the magnetic drift of the fast ions can destabilize GAMs. A new branch is found in the family of GAMs, whose frequency is close to the magnetic drift frequency of the fast ions. The poloidal eigenfunction of this branch has bump structures in the poloidal direction where the resonance of the magnetic drift with the mode is strong. The ion heating rate by the GAMs is evaluated in the framework of quasi-linear theory. The heating is localized poloidally around the resonance locations. Owing to the bumps in the eigenfunction, the magnitude of the heating is much larger than that estimated without the magnetic drift resonance.

The Berk-Breizman (BB) extension of the bump-on-tail instability includes a finite, fixed wave damping (γ d), and a collision operator with drag (ν f) and diffusion (ν d). The BB model is applied to a one-dimensional plasma, to investigate the kinetic nonlinearities, which arise from the resonance of a single electrostatic wave with an energeticparticle beam. For a fixed value of the linear drive normalized to the linear frequency, γ L0 /ω 0 = 0.1, the long-time nonlinear evolution is systematically categorized as damped, steady-state, periodic, chaotic and chirping. The chirping regime is subcategorized as periodic, chaotic, bursty and intermittent. Up-down asymmetry and hooked chirping branches are also categorized. For large drag, holes with quasi-constant velocity are observed, in which case the solution is categorized into steady, wavering and oscillating holes. Two complementary parameter spaces are considered: (1) the (γ d , ν d) space for fixed ν d /ν f ratios; (2) the (ν f , ν d) space for fixed γ d /γ L0 ratios, close to and far from marginal stability. The presence of drag and diffusion (instead of a Krook model) qualitatively modifies the nonlinear bifurcations. The bifurcations between steady-state, periodic and steady-hole solutions agree with analytic theory. Moreover, the boundary between steady and periodic solutions agrees with analytic theory. Nonlinear instabilities are found in both subcritical and barely unstable regimes. Quasi-periodic chirping is shown to be a special case of bursty chirping, limited to a region relatively far from marginal stability.

The nonlinear stability of current-driven ion-acoustic waves in collisionless electron-ion plasmas is analyzed. Seminal simulations from the 1980s are revisited. Accurate numerical treatment shows that subcritical instabilities do not grow from an ensemble of waves, except very close to marginal stability and for large initial amplitudes. Further from marginal stability, one isolated phase-space structure can drive subcritical instabilities by stirring the phase-space in its wake. Phase-space turbulence, which includes many structures, is much more efficient than an ensemble of waves or an isolated hole for driving subcritically particle redistribution, turbulent heating and anomalous resistivity. Phase-space jets are observed in subcritical simulations.

In a collisionless plasma, it is known that linearly stable modes can be destabilized (subcritically) by the presence of structures in phase space. However, nonlinear growth requires the presence of a seed structure with a relatively large threshold in amplitude. We demonstrate that, in the presence of another, linearly unstable (supercritical) mode, wave-wave coupling can provide a seed, which is significantly below the threshold, but can still grow by (and only by) the collaboration of fluid and kinetic nonlinearities. By modeling the subcritical mode kinetically, and the impact of the supercritical mode by simple wave-wave coupling equations, it is shown that this new kind of subcritical instability can be triggered, even when the frequency of the supercritical mode is rapidly sweeping. The model is applied to the bursty onset of geodesic acoustic modes in a LHD experiment. The model recovers several key features such as relative amplitude, time scales, and phase relations. It suggests that the strongest bursts are subcritical instabilities, driven by this mechanism of combined fluid and kinetic nonlinearities.