1,355,247 research outputs found
Analytic studies of dispersive properties of shear Alfvén and acoustic wave spectra in tokamaks
No full textThe properties of the low frequency shear Alfvén and acoustic wave spectra in toroidal geometry are examined analytically and numerically considering wave particle interactions with magnetically trapped and circulating particles, using the theoretical model described in [I. Chavdarovski and F. Zonca, Plasma Phys. Controlled Fusion 51, 115001 (2009)] and following the framework of the generalized fishbone-like dispersion relation. Effects of trapped particles as well as diamagnetic effects on the frequencies and damping rates of the beta-induced Alfvén eigenmodes, kinetic ballooning modes and beta-induced Alfvén-acoustic eigenmodes are discussed and shown to be crucial to give a proper assessment of mode structure and stability conditions. Present results also demonstrate the mutual coupling of these various branches and suggest that frequency as well as mode polarization are crucial for their identification on the basis of experimental evidence. © 2014 AIP Publishing LLC
Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation
No full textA unified theoretical framework is presented for analyzing various branches of drift Alfvén waves and describing their linear and nonlinear behaviors, covering a wide range of spatial and temporal scales. Nonlinear gyrokinetic quasineutrality condition and vorticity equation, derived for drift Alfvén waves excited by energetic particles in fusion plasmas, are cast in integral form, which is generally variational in the linear limit; and the corresponding gyrokinetic energy principle is obtained. Well known forms of the kinetic energy principle are readily recovered from this general formulation. Furthermore, it is possible to demonstrate that the general fishbone like dispersion relation, obtained within the present theoretical framework, provides a unified description of drift Alfvén waves excited by energetic particles as either Alfvén eigenmodes or energetic particle modes. The advantage of the present approach stands in its capability of extracting underlying linear and nonlinear physics as well as spatial and temporal scales of the considered fluctuation spectrum. For these reasons, this unified theoretical framework can help understanding experimental observations as well as numerical simulation and analytic results with different levels of approximation. Examples and applications are given in Paper II [F. Zonca and L. Chen, "Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation," Phys. Plasmas 21, 072121 (2014)]. © 2014 EURATOM
[Primo Zonca (1895), funerary sculpture]
No full textFrom Berresford: Primo Zonca (1895), Giulio Monteverde, Cimitero de Verano, Rome.Angel.Title from Berresford
Nonlinear dynamics of nonadiabatic chirping-frequency Alfvén modes in tokamak plasmas
No full textFrequency chirping of Alfvén modes, a phenomenon observed in tokamak fusion plasmas driven by energetic particles (EPs), can result in significant losses of EPs. In this study, we use the global gyrokinetic code ORB5 (Lanti et al 2020 Comput. Phys. Commun. 251 107072) to investigate the nonlinear dynamics of non-adiabatic frequency chirping EP modes (EPMs). Our results illuminate non-perturbative features of EPMs caused by the presence of EPs. Additionally, we find that, with a fixed safety factor profile and a single toroidal mode number, the frequency chirping rate is linearly proportional to the mode saturation amplitude, as predicted by the theory (Chen and Zonca 2016 Rev. Mod. Phys. 88 015008)
Transport theory of phase space zonal structures
No full textWe adopt gyrokinetic theory to extract the phase space zonal structure from the flux surface averaged particle response, that is, the nonlinear response that is undamped by collisionless processes. We argue that phase space zonal structures are a proper definition for the nonlinear distortion of the plasma reference state and, thus, of the generally non-Maxwellian neighboring nonlinear equilibria consistent with toroidal symmetry breaking fluctuations. Evolution equations for phase space zonal structures are derived and discussed, along with the corresponding density and energy transport equations. It is shown that this approach is consistent with the usual evolution of macroscopic plasma profiles under the action of fluctuation induced fluxes, when the deviation of the reference state from local Maxwellian response is small. In particular, the present results recover those of a previous article [M. V. Falessi and F. Zonca, Phys. Plasmas 25, 032306 (2018)], where transport equations holding on the reference state length scale have been derived using the moment approach introduced in the classical review work by Hinton and Hazeltine
Exit versus escape for stochastic dynamical systems and application to the computation of the bursting time duration in neuronal networks
No full text<p>We study the exit time of two-dimensional dynamical systems perturbed by a small noise that exhibits two peculiar behaviors:<br>
1) the maximum of the probability density function of trajectories is not located at the point attractor (fig. 1). The distance between the maximum and the attractor increases with the noise amplitude and can be computed using WKB approximation and numerical simulations [1].<br>
2) For such systems, exiting from the basin of attraction is not sufficient to guarantee a full escape, due to trajectories that can return several times inside the basin of attraction after crossing the boundary, before eventually escaping far away (fig. 2). We decompose the escape time into the time to reach the boundary of the basin of attraction for the first time plus the time spent oscillating in and out of the basin of attraction. This allows us to show that the mean escape time is increased by a factor between 2 and 3 compared to the mean first passage time [1,2].<br>
We apply these results to study neuronal networks that can generate bursting events. The interburst corresponds to an escape with multiple re-entries inside the basin of attraction.<br>
To conclude, escaping far away from a basin of attraction is not equivalent to reaching the boundary, thus providing an explanation for non-Poissonian long-interburst durations present in neuronal dynamics.<br>
</p>
<p><strong>The Matlab source code associated to [1] is organized in four sub folders: </strong></p>
<p><strong>01_SimData</strong> contains the result of the model simulations presented in [1].</p>
<p><strong>02_Functions</strong> contains the models (3D facilitation-depression model, 2D reduction of the facilitation-depression model, generic 2D model), the function used to count the round-trips around the separatrix and functions to plot the different phase spaces of the models.</p>
<p><strong>03_Scripts</strong> contains scripts which can be used to run the stochastic simulations of the models and to generate the simulation data.</p>
<p><strong>04_Figures </strong>contains one script for each figure of [1].</p>
<p> </p>
<p><strong>The Matlab source code associated to [2] is organized in four sub folders</strong></p>
<p><strong>Figures </strong>contains one script for each figure of [2].</p>
<p><strong>Functions</strong> contains the models (2D reduction of the facilitation-depression model, generic 2D model - which are the same ones as used in [1]), the function used to count the round-trips around the separatrix and functions to plot the different phase spaces of the models.</p>
<p><strong>DimensionOne</strong> contains scripts that can be used to study the escape phenomenon in dimension one.</p>
<p><strong>SimData</strong> contains the result of the model simulations presented in [1].</p>
<p><em><strong>Please quote the zenodo or doi reference when using the source code.</strong></em></p>
<p> </p>
<p><strong>References</strong><br>
[1] L. Zonca & D. Holcman, <em>Exit versus escape for stochastic dynamical systems and application to the computation of the bursting time duration in neuronal networks</em>, Journal of nonlinear science, 2022.<br>
[2] L. Zonca & D. Holcman, <em>Escape from an attractor generated by recurrent exit, </em>Physical Review Research, 2021.</p>
The mixed WKB-full-wave approach and its application to lower hybrid wave propagation and absorption
No full textThe mixed WKB-full-wave approach for calculating the 2D mode structure in tokamak plasmas is further developed based on our previous work [A. Cardinali et al., Phys. Plasmas 10, 4199 (2003) and Z. X. Lu et al., Phys. Plasmas, 19, 042104 (2012)]. A new scheme for theoretical analysis and numerical implementation of the mixed WKB-full-wave approach is formulated, based on scale separation and asymptotic analysis, to investigate lower hybrid wave (LHW) propagation and absorption. As a novel method, its comparison with other approaches is discussed. Its application to LHW propagation in concentric circular tokamak plasmas using typical FTU discharge parameters, is also demonstrated. © 2014 AIP Publishing LLC
- …
