Resonance overlap and nonlinear features of the beam–plasma system

Carlevaro, Nakia; Montani, Giovanni; Falessi, Matteo Valerio

doi:10.1017/s0022377820000744

Cited by 9 publications

(15 citation statements)

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“…(1995) and also Carlevaro et al. (2018)) while for the EGAM we have , with in this regime (see § 3), and depending on the EP density (Biancalani et al. 2017).…”

Section: Dynamics Of the Energetic Particles: Analogy With The Beam-psupporting

confidence: 56%

“…where α 3.3 (see well-known literature results in Chen & Zonca (2016), Wu et al (1995) and also Carlevaro et al (2018)) while for the EGAM we have β = β 0 √ ω L,EGAM /ω GAM , with β 0 = 2.66 in this regime (see § 3), and ω L,EGAM depending on the EP density (Biancalani et al 2017). For the four selected EGAM simulations, we get β(0.07, 0.10, 0.176, 0.30) [2.21, 2.17, 2.07, 1.98].…”

Section: Nonlinear Egam Evolutionmentioning

confidence: 95%

“…A measure of the clumps width for a generic initial half-Gaussian velocity distribution, which can be directly extrapolated to the analysis of the present work, has been evaluated in Carlevaro et al. (2018) for several cases outlining the following scaling rule as function of the linear drive: In order to include the dynamic role also of passing but nearly resonant particles (Escande & Elskens 2002), i.e. the region involved in the effective wave–particle power exchange, in the following analysis we consider as the proper nonlinear particle velocity spread the scaled quantity with .…”

Section: Nonlinear Ep Redistribution Of the Egam And Comparison Withmentioning

confidence: 99%

“…This estimate is derived (Carlevaro et al. 2018) characterizing the active overlap of different nonlinear fluctuations (Escande & Doveil 1981; Lichtenberg & Lieberman 2010) and corresponds to the finite distortion of the distribution function, including effects at the edges of the plateau (defined as the flattened region of the distribution function, mainly coinciding with the clump size). We finally obtain the desired formula for the prediction of the nonlinear velocity spread due to the EGAM: and by substituting the value of we obtain: Equation (6.3) has been derived for the EGAM system, using the scaling derived in (5.7) and the normalized mapping of (5.4).…”

Section: Nonlinear Ep Redistribution Of the Egam And Comparison Withmentioning

confidence: 99%

“…Moreover, the scaling of the saturated electric field of EGAMs with the linear growth rate, for saturation due to wave-particle nonlinearity, has been studied with ORB5 (Biancalani et al 2017). The BPS is studied here with a 1-D code treating the thermal plasma as a cold dielectric medium and describing the dynamics of the fast electrons as an N-body problem solved with a Hamiltonian formulation (Carlevaro et al 2015(Carlevaro et al , 2016Carlevaro, Montani & Zonca 2018). A mapping of the velocity space for the EGAM system and for the bump-on-tail (BoT) paradigm for the BPS is also formulated, allowing us to find a one-to-one correspondence between EP redistribution studied in the two problems.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system

et al. 2018

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The nonlinear dynamics of energetic particle (EP) driven geodesic acoustic modes (EGAM) in tokamaks is investigated, and compared with the beam-plasma system (BPS). The EGAM is studied with the global gyrokinetic (GK) particle-in-cell code ORB5, treating the thermal ions and EP (in this case, fast ions) as GK and neglecting the kinetic effects of the electrons. The wave-particle nonlinearity only is considered in the EGAM nonlinear dynamics. The BPS is studied with a 1D code where the thermal plasma is treated as a linear dielectric, and the EP (in this case, fast electrons) with an n-body hamiltonian formulation. A one-to-one mapping between the EGAM and the BPS is described. The focus is on understanding and predicting the EP redistribution in phase space. We identify here two distint regimes for the mapping: in the low-drive regime, the BPS mapping with the EGAM is found to be complete, and in the high-drive regime, the EGAM dynamics and the BPS dynamics are found to differ. The transition is described with the presence of a non-negligible frequency chirping, which affects the EGAM but not the BPS, above the identified drive threshold. The difference can be resolved by adding an ad-hoc frequency modification to the BPS model. As a main result, the formula for the prediction of the nonlinear width of the velocity redistribution around the resonance velocity is provided.

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“…(1995) and also Carlevaro et al. (2018)) while for the EGAM we have , with in this regime (see § 3), and depending on the EP density (Biancalani et al. 2017).…”

Section: Dynamics Of the Energetic Particles: Analogy With The Beam-psupporting

confidence: 56%

Section: Nonlinear Egam Evolutionmentioning

confidence: 95%

Section: Nonlinear Ep Redistribution Of the Egam And Comparison Withmentioning

confidence: 99%

Section: Nonlinear Ep Redistribution Of the Egam And Comparison Withmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system

et al. 2018

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Analysis of the nonlinear dynamics of a chirping-frequency Alfvén mode in a tokamak equilibrium

et al. 2022

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Chirping Alfvén modes are considered as potentially harmful for the confinement of energetic particles in burning tokamak plasmas. In fact, by changing their frequency, they are able to extract as much power as possible from these particles, possibly increasing their transport. In this paper, the nonlinear evolution of a single-toroidal-number chirping mode is analyzed by numerical particle simulation. The relevant resonant structures are identified by numerical techniques based on the use of a coordinate system including two constants of motion: the magnetic moment and a suitable function of the initial particle coordinates. The analysis is focused on the dynamics of two different resonant structures in the particle phase space: those yielding the largest drive during the linear and the nonlinear phase, respectively. It is shown that, for each resonant structure, a density-flattening region is formed around the respective resonance radius, with a radial width that increases as the mode amplitude grows. It is delimited by two steepened negative density gradients, drifting inwards and outward. If the mode frequency were constant, phase-space density flattening would quench the resonant-structure drive as the steepened gradients leave the original resonance region. The frequency chirping, however, causes the resonance radius and the resonance region to drift inwards. This drift, along with a relevant increase in the resonance width, delays the moment in which the inner density gradient reaches the inner boundary of the resonance region, leaving it. On the other hand, the island evolves consistently with the resonance radius; as a consequence, the steepened density gradient further moves inward. This process continues as long as it allows to keep the steepened gradient within the resonance region. When this is no longer possible, the resonant structure ceases to be effective in driving the mode. To further extract energy from the particles, the mode has to tap a different resonant structure, possibly making use of additional frequency variations.

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Prediction of temperature barriers in weakly collisional plasmas by a Lagrangian coherent structures computational tool

et al. 2021

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Analysis of Lagrangian Coherent Structures (LCSs) has been shown to be a valid mathematical approach to explain the formation of transport barriers in magnetized plasmas. Such LCSs, borrowed from fluid dynamics theory, can be considered as the hidden skeleton of the system and can be used for studying a wide spectrum of transport mechanisms, even in plasmas. An LCS can be considered as a generalization for a finite time interval and for a general dynamical system of what manifolds are for Hamiltonian systems. In this paper, we demonstrate that such structures can be particularly useful for underlying the hidden paths governing the motion of magnetic field lines in chaotic magnetic fields.To perform such an analysis, we developed a numerical tool able to detect LCSs for a general dynamical system. The tool is able to deal with general coordinate systems and it is shown to match with other techniques already used to analyse chaotic magnetic fields, e.g. connection length. After the description of the computational tool, we focus on the heat transport equation and the comparison between temperature profile and topology of the LCSs. We provide evidence that numerical simulations are able to reproduce the temperature profiles similar to those observed in reversed field pinch experiments and that our tool successfully predicts the location of temperature gradients. The results suggest that, inside the chaotic region, the field-lines motion is far from stochastic and that the presence of hidden patterns allows the development of high temperature gradients.

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Resonance overlap and nonlinear features of the beam–plasma system

Cited by 9 publications

References 50 publications

Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system

Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system

Analysis of the nonlinear dynamics of a chirping-frequency Alfvén mode in a tokamak equilibrium

Prediction of temperature barriers in weakly collisional plasmas by a Lagrangian coherent structures computational tool

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